Optimal block-tridiagonalization of matrices for coherent charge transport
Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning t...
Saved in:
| Published in | Journal of computational physics Vol. 228; no. 23; pp. 8548 - 8565 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Kidlington
Elsevier Inc
10.12.2009
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0021-9991 1090-2716 |
| DOI | 10.1016/j.jcp.2009.08.001 |
Cover
| Abstract | Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport. The reordered Hamiltonian can lead to significant performance gains in transport calculations, and allows to apply conventional two-terminal algorithms to arbitrarily complex geometries, including multi-terminal structures. The block-tridiagonalization algorithm can thus be the foundation for a generic quantum transport code, applicable to arbitrary tight-binding systems. We demonstrate the power of this approach by applying the block-tridiagonalization algorithm together with the recursive Green’s function algorithm to various examples of mesoscopic transport in two-dimensional electron gases in semiconductors and graphene. |
|---|---|
| AbstractList | Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport. The reordered Hamiltonian can lead to significant performance gains in transport calculations, and allows to apply conventional two-terminal algorithms to arbitrarily complex geometries, including multi-terminal structures. The block-tridiagonalization algorithm can thus be the foundation for a generic quantum transport code, applicable to arbitrary tight-binding systems. We demonstrate the power of this approach by applying the block-tridiagonalization algorithm together with the recursive Green's function algorithm to various examples of mesoscopic transport in two-dimensional electron gases in semiconductors and graphene. |
| Author | Richter, Klaus Wimmer, Michael |
| Author_xml | – sequence: 1 givenname: Michael surname: Wimmer fullname: Wimmer, Michael email: Michael.Wimmer@physik.uni-regensburg.de – sequence: 2 givenname: Klaus surname: Richter fullname: Richter, Klaus |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22109204$$DView record in Pascal Francis https://www.osti.gov/biblio/21333893$$D View this record in Osti.gov |
| BookMark | eNp9kUtvFDEQhC0UJDYhP4DbSAiJywztx7zECUUhAUXKhZwtT08762XWHmwnEvx6vNlw4ZCTJfurdlfVKTvxwRNj7zg0HHj3adfscG0EwNjA0ADwV2zDYYRa9Lw7YRsAwetxHPkbdprSDgCGVg0b9v12zW5vlmpaAv6sc3SzM_fBm8X9MdkFXwVb7U25R0qVDbHCsKVIPle4NfGeqhyNT2uI-S17bc2S6Pz5PGN3Xy9_XFzXN7dX3y6-3NSoWpVr5GIeAe0EZYGeOpKCZipPYhpboXoFOLQWpnYaul7acbK2t0YOVgjV8onkGXt_nBtSdjqhy4RbDN4TZi24lHIYZaE-Hqk1hl8PlLLeu4S0LMZTeEiai67rlZKqK-iHZ9QkNIsthtAlvcYSTPythShBClCF648cxpBSJKvL308hlQzcojnoQxd6p0sX-tCFhkGXLoqS_6f8N_wlzeejhkqWj47iwSp5pNnFg9M5uBfUfwGyOqNL |
| CODEN | JCTPAH |
| CitedBy_id | crossref_primary_10_1103_PhysRevB_88_195406 crossref_primary_10_1103_PhysRevB_81_155422 crossref_primary_10_1103_PhysRevB_91_241406 crossref_primary_10_1103_PhysRevLett_106_146801 crossref_primary_10_1088_2053_1583_2_2_024005 crossref_primary_10_1103_PhysRevB_96_134507 crossref_primary_10_1103_PhysRevB_84_075468 crossref_primary_10_1103_PhysRevB_90_115306 crossref_primary_10_1016_j_chemphys_2010_05_001 crossref_primary_10_1103_PhysRevB_81_085303 crossref_primary_10_1103_PhysRevLett_105_246807 crossref_primary_10_1103_PhysRevB_86_081306 crossref_primary_10_1016_j_jcp_2013_12_054 crossref_primary_10_1103_PhysRevB_84_115136 crossref_primary_10_1103_PhysRevLett_108_236601 crossref_primary_10_1103_PhysRevB_97_165405 crossref_primary_10_1038_ncomms3526 crossref_primary_10_1103_PhysRevB_90_205424 crossref_primary_10_1103_PhysRevApplied_16_054053 crossref_primary_10_12693_APhysPolA_118_238 crossref_primary_10_1103_PhysRevB_84_155401 crossref_primary_10_1007_s10825_013_0441_3 crossref_primary_10_1126_science_1221350 crossref_primary_10_1088_0268_1242_30_8_085003 crossref_primary_10_1038_nnano_2014_128 crossref_primary_10_1088_1674_1056_20_9_097201 crossref_primary_10_1016_j_jcp_2017_01_024 crossref_primary_10_1103_PhysRevB_86_165407 crossref_primary_10_1103_PhysRevB_81_155450 crossref_primary_10_1103_PhysRevB_85_155414 crossref_primary_10_1103_PhysRevB_91_125408 crossref_primary_10_1145_2331130_2331138 crossref_primary_10_1103_PhysRevB_85_195432 crossref_primary_10_1103_PhysRevB_89_115421 crossref_primary_10_1088_1367_2630_16_6_063065 crossref_primary_10_1103_PhysRevB_97_085149 crossref_primary_10_1103_PhysRevB_84_205421 crossref_primary_10_1103_PhysRevLett_106_057001 crossref_primary_10_1063_5_0026039 crossref_primary_10_1103_PhysRevB_103_094412 crossref_primary_10_1103_PhysRevB_85_245418 crossref_primary_10_1088_1367_2630_16_11_113058 crossref_primary_10_1088_1367_2630_13_5_053016 crossref_primary_10_1103_PhysRevLett_117_176602 crossref_primary_10_1088_1367_2630_14_12_123006 crossref_primary_10_1016_j_cpc_2020_107676 crossref_primary_10_1016_j_jcp_2019_05_034 crossref_primary_10_1103_PhysRevB_98_094518 crossref_primary_10_1103_PhysRevB_83_085413 |
| Cites_doi | 10.1088/0957-4484/18/43/435402 10.1137/0911048 10.1147/rd.13.0223 10.1103/PhysRevB.71.245321 10.1103/PhysRevB.73.085414 10.1155/2000/19436 10.1103/PhysRevB.65.165401 10.1103/PhysRevLett.45.494 10.1103/PhysRevB.50.7615 10.1103/PhysRevB.59.11936 10.1109/71.780863 10.1002/j.1538-7305.1970.tb01770.x 10.1137/S1064827502401953 10.1088/0305-4608/14/5/016 10.1103/PhysRev.45.815 10.1016/j.jcp.2005.11.010 10.1103/PhysRevB.77.115119 10.1088/0305-4608/15/4/009 10.1007/978-0-387-30440-3_514 10.1103/PhysRevB.40.8169 10.1016/S0167-8191(00)00087-9 10.1103/PhysRevLett.47.882 10.1103/PhysRevB.68.165302 10.1063/1.364151 10.1103/PhysRevB.62.1950 10.1016/S0098-1354(99)00271-9 10.1103/PhysRevB.52.8244 10.1145/800195.805928 10.1145/800153.804930 10.1103/PhysRevB.66.205319 10.1103/PhysRevB.75.045346 10.1103/PhysRevB.74.205323 10.1088/1742-6596/99/1/012010 10.1103/RevModPhys.81.109 10.1137/S1064827598341475 10.1088/0022-3719/14/3/007 10.1016/0098-1354(94)00081-6 10.1007/BFb0030098 10.1002/spe.626 10.1103/PhysRevLett.100.177207 10.1038/nature04233 10.1103/PhysRevB.44.10637 10.1137/S1064827593255135 10.1103/PhysRevB.23.6851 10.1103/PhysRevB.69.155327 10.1063/1.365394 10.1147/rd.323.0384 10.1002/(SICI)1521-3889(199811)7:5/6<498::AID-ANDP498>3.0.CO;2-6 10.1137/0713020 10.1137/S1064827596300656 10.1103/PhysRevB.31.6207 10.1137/0713023 10.1109/DAC.1982.1585498 10.1147/rd.411.0171 10.1007/BFb0018541 10.1103/PhysRevB.69.115325 10.1002/pssb.2221010218 10.1007/BF01328846 |
| ContentType | Journal Article |
| Copyright | 2009 Elsevier Inc. 2009 INIST-CNRS |
| Copyright_xml | – notice: 2009 Elsevier Inc. – notice: 2009 INIST-CNRS |
| DBID | AAYXX CITATION IQODW 7SC 7SP 7U5 8FD JQ2 L7M L~C L~D OTOTI |
| DOI | 10.1016/j.jcp.2009.08.001 |
| DatabaseName | CrossRef Pascal-Francis Computer and Information Systems Abstracts Electronics & Communications Abstracts Solid State and Superconductivity Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional OSTI.GOV |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Solid State and Superconductivity Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Physics |
| EISSN | 1090-2716 |
| EndPage | 8565 |
| ExternalDocumentID | 21333893 22109204 10_1016_j_jcp_2009_08_001 S0021999109004367 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 29K 4.4 457 4G. 5GY 5VS 6OB 6TJ 7-5 71M 8P~ 8WZ 9JN A6W AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABBOA ABFNM ABFRF ABJNI ABMAC ABNEU ABTAH ABXDB ABYKQ ACBEA ACDAQ ACFVG ACGFO ACGFS ACNCT ACNNM ACRLP ACZNC ADBBV ADEZE ADFGL ADIYS ADJOM ADMUD AEBSH AEFWE AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AIVDX AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ASPBG AVWKF AXJTR AZFZN BBWZM BKOJK BLXMC CAG COF CS3 D-I DM4 DU5 EBS EFBJH EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA GBOLZ HLZ HME HMV HVGLF HZ~ IHE J1W K-O KOM LG5 LX9 LZ4 M37 M41 MO0 N9A NDZJH O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SBC SDF SDG SDP SES SEW SHN SPC SPCBC SPD SPG SSQ SSV SSZ T5K T9H TN5 UPT UQL WUQ XFK YQT ZMT ZU3 ZY4 ~02 ~G- AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 7SC 7SP 7U5 8FD JQ2 L7M L~C L~D AALMO ABPIF ABPTK ABQIS EFJIC OTOTI |
| ID | FETCH-LOGICAL-c454t-c12d90cfb05487e6e32ede4542b9524740c85f0b5b8673f9bff7fa38f22451be3 |
| IEDL.DBID | AIKHN |
| ISSN | 0021-9991 |
| IngestDate | Thu May 18 22:38:05 EDT 2023 Sat Sep 27 20:05:11 EDT 2025 Mon Jul 21 09:17:02 EDT 2025 Wed Oct 01 05:12:28 EDT 2025 Thu Apr 24 23:08:31 EDT 2025 Fri Feb 23 02:29:12 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 23 |
| Keywords | 72.10.Bg 05C78 05C50 Recursive Green’s function algorithm 02.70.−c Coherent quantum transport Block-tridiagonal matrices Matrix reordering Graph theory 02.10.Ox Semiconductor materials Green function Calculation methods Algorithms 02.70.-c Hamiltonians Recursive Green's function algorithm Calculation Tridiagonal matrix Performance Mesoscopic systems Quantum transport Electron gas |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c454t-c12d90cfb05487e6e32ede4542b9524740c85f0b5b8673f9bff7fa38f22451be3 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 1266744346 |
| PQPubID | 23500 |
| PageCount | 18 |
| ParticipantIDs | osti_scitechconnect_21333893 proquest_miscellaneous_1266744346 pascalfrancis_primary_22109204 crossref_citationtrail_10_1016_j_jcp_2009_08_001 crossref_primary_10_1016_j_jcp_2009_08_001 elsevier_sciencedirect_doi_10_1016_j_jcp_2009_08_001 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2009-12-10 |
| PublicationDateYYYYMMDD | 2009-12-10 |
| PublicationDate_xml | – month: 12 year: 2009 text: 2009-12-10 day: 10 |
| PublicationDecade | 2000 |
| PublicationPlace | Kidlington |
| PublicationPlace_xml | – name: Kidlington – name: United States |
| PublicationTitle | Journal of computational physics |
| PublicationYear | 2009 |
| Publisher | Elsevier Inc Elsevier |
| Publisher_xml | – name: Elsevier Inc – name: Elsevier |
| References | Thouless, Kirkpatrick (bib27) 1981; 14 Hendrickson, Kolda (bib52) 2000; 21 Usuki, Saito, Takatsu, Kiehl, Yokoyama (bib23) 1995; 52 Baranger, DiVincenzo, Jalabert, Stone (bib30) 1991; 44 Camarda, Stadtherr (bib50) 1999; 23 Whaley, Petitet (bib58) 2005; 35 Bowen, Klimeck, Lake, Frensley, Moise (bib11) 1997; 81 Simon, Teng (bib56) 1997; 18 Drouvelis, Schmelcher, Bastian (bib33) 2006; 215 Çatalyürek, Aykanat (bib37) 1996; 1117 Whaley, Petitet, Dongarra (bib59) 2001; 27 D.G. Schweikert, B.W. Kernighan, A proper model for the partitioning of electrical circuits, in: DAC’72: Proceedings of the 9th Workshop on Design Automation, ACM, New York, NY, USA, 1972, pp. 57–62. Mamaluy, Vasileska, Sabathil, Zibold, Vogl (bib26) 2005; 71 Qiao, Wang (bib64) 2007; 18 B. Hendrickson, Graph partitioning and parallel solvers: has the emperor no clothes? in: Workshop on Parallel Algorithms for Irregularly Structured Problems, 1998, pp. 218–225. Kazymyrenko, Waintal (bib63) 2008; 77 O’Neil, Szyld (bib48) 1990; 11 Coon, Stadtherr (bib49) 1995; 19 Lee, Fisher (bib28) 1981; 47 Gibbs, William, Poole, Stockmeyer (bib39) 1976; 13 Hendrickson, Rothberg (bib47) 1998; 20 Sedgewick (bib54) 1992 Çatalyürek, Aykanat (bib38) 1999; 10 Rocha, Garcı´a-Suárez, Bailey, Lambert, Ferrer, Sanvito (bib16) 2006; 73 Lopez Sancho, Lopez Sancho, Rubio (bib19) 1984; 14 Kimball, Shortley (bib7) 1934; 45 A. George, Computer implementation of the finite element method, Tech. Rep. STAN-CS-71-208, Computer Sci. Dept., Stanford Univ., Stanford, CA, 1971. Baranger, Stone (bib5) 1989; 40 Brandbyge, Mozos, Ordejón, Taylor, Stokbro (bib14) 2002; 65 Pauling, Wilson (bib8) 1935 Usuki, Takatsu, Kiehl, Yokoyama (bib22) 1994; 50 Kernighan, Lin (bib43) 1970; 49 Datta (bib17) 2002 Ferry, Goodnick (bib18) 2001 Fisher, Lee (bib4) 1981; 23 Leadbeater, Lambert (bib25) 1998; 7 Wimmer, Adagideli, Berber, Tománek, Richter (bib61) 2008; 100 Frustaglia, Hentschel, Richter (bib9) 2004; 69 Castro Neto, Guinea, Peres, Novoselov, Geim (bib62) 2009; 81 Krstić, Zhang, Butler (bib21) 2002; 66 MacKinnon (bib29) 1985; 59 Lake, Klimeck, Bowen, Jovanovic (bib31) 1997; 81 Kramer, Heller, Parrott (bib34) 2008; 99 E. Cuthill, J. McKee, Reducing the bandwidth of sparse symmetric matrices, in: Proceedings of the 24th National Conference, ACM, New York, 1969, pp. 157–172. Havu, Havu, Puska, Nieminen (bib10) 2004; 69 Aykanat, Pinar, Çatalyürek (bib53) 2004; 25 M. Wimmer, M. Scheid, K. Richter, Spin-polarized quantum transport in mesoscopic conductors: computational concepts and physical phenomena, in: Encyclopedia of Complexity and System Science, Springer, New York, 2009, p. 8597. Büttiker, Imry, Landauer, Pinhas (bib2) 1985; 31 C.M. Fiduccia, R.M. Mattheyses, A linear-time heuristic for improving network partitions, in: DAC’82: Proceedings of the 19th Conference on Design Automation, IEEE Press, Piscataway, NJ, USA, 1982, pp. 175–181. Gupta (bib55) 1997; 41 Garey, Johnson (bib57) 1990 Luisier, Schenk, Fichtner, Klimeck (bib13) 2006; 74 Lassl, Schlagheck, Richter (bib32) 2007; 75 Stone, Szafer (bib3) 1988; 32 Haug, Jauho (bib6) 1998 Rotter, Weingartner, Rohringer, Burgdörfer (bib36) 2003; 68 Karypis, Kumar (bib46) 2000; 11 Klitzing, Dorda, Pepper (bib65) 1980; 45 Lopez Sancho, Lopez Sancho, Rubio (bib20) 1985; 15 Landauer (bib1) 1957; 1 Di Carlo, Pecchia, Latessa, Frauenheim, Seifert (bib15) 2006 Novoselov, Geim, Morozov, Jiang, Katsnelson, Grigorieva, Dubonos, Firsov (bib66) 2005; 438 Lambert, Weaire (bib24) 1980; 101 Rotter, Tang, Wirtz, Trost, Burgdörfer (bib35) 2000; 62 Sanvito, Lambert, Jefferson, Bratkovsky (bib12) 1999; 59 Liu, Sherman (bib42) 1976; 13 Hendrickson (10.1016/j.jcp.2009.08.001_bib52) 2000; 21 Klitzing (10.1016/j.jcp.2009.08.001_bib65) 1980; 45 Usuki (10.1016/j.jcp.2009.08.001_bib22) 1994; 50 Brandbyge (10.1016/j.jcp.2009.08.001_bib14) 2002; 65 10.1016/j.jcp.2009.08.001_bib60 Havu (10.1016/j.jcp.2009.08.001_bib10) 2004; 69 Simon (10.1016/j.jcp.2009.08.001_bib56) 1997; 18 Garey (10.1016/j.jcp.2009.08.001_bib57) 1990 Lake (10.1016/j.jcp.2009.08.001_bib31) 1997; 81 O’Neil (10.1016/j.jcp.2009.08.001_bib48) 1990; 11 Baranger (10.1016/j.jcp.2009.08.001_bib5) 1989; 40 MacKinnon (10.1016/j.jcp.2009.08.001_bib29) 1985; 59 Drouvelis (10.1016/j.jcp.2009.08.001_bib33) 2006; 215 Sanvito (10.1016/j.jcp.2009.08.001_bib12) 1999; 59 Whaley (10.1016/j.jcp.2009.08.001_bib58) 2005; 35 Kernighan (10.1016/j.jcp.2009.08.001_bib43) 1970; 49 Büttiker (10.1016/j.jcp.2009.08.001_bib2) 1985; 31 Aykanat (10.1016/j.jcp.2009.08.001_bib53) 2004; 25 Lopez Sancho (10.1016/j.jcp.2009.08.001_bib20) 1985; 15 Lassl (10.1016/j.jcp.2009.08.001_bib32) 2007; 75 Gibbs (10.1016/j.jcp.2009.08.001_bib39) 1976; 13 Ferry (10.1016/j.jcp.2009.08.001_bib18) 2001 Thouless (10.1016/j.jcp.2009.08.001_bib27) 1981; 14 Rocha (10.1016/j.jcp.2009.08.001_bib16) 2006; 73 Castro Neto (10.1016/j.jcp.2009.08.001_bib62) 2009; 81 Karypis (10.1016/j.jcp.2009.08.001_bib46) 2000; 11 Camarda (10.1016/j.jcp.2009.08.001_bib50) 1999; 23 Leadbeater (10.1016/j.jcp.2009.08.001_bib25) 1998; 7 Qiao (10.1016/j.jcp.2009.08.001_bib64) 2007; 18 Haug (10.1016/j.jcp.2009.08.001_bib6) 1998 Sedgewick (10.1016/j.jcp.2009.08.001_bib54) 1992 Gupta (10.1016/j.jcp.2009.08.001_bib55) 1997; 41 Kazymyrenko (10.1016/j.jcp.2009.08.001_bib63) 2008; 77 Usuki (10.1016/j.jcp.2009.08.001_bib23) 1995; 52 10.1016/j.jcp.2009.08.001_bib40 Wimmer (10.1016/j.jcp.2009.08.001_bib61) 2008; 100 10.1016/j.jcp.2009.08.001_bib41 Bowen (10.1016/j.jcp.2009.08.001_bib11) 1997; 81 Novoselov (10.1016/j.jcp.2009.08.001_bib66) 2005; 438 Mamaluy (10.1016/j.jcp.2009.08.001_bib26) 2005; 71 10.1016/j.jcp.2009.08.001_bib44 Di Carlo (10.1016/j.jcp.2009.08.001_bib15) 2006 10.1016/j.jcp.2009.08.001_bib45 Frustaglia (10.1016/j.jcp.2009.08.001_bib9) 2004; 69 Rotter (10.1016/j.jcp.2009.08.001_bib35) 2000; 62 Stone (10.1016/j.jcp.2009.08.001_bib3) 1988; 32 Kramer (10.1016/j.jcp.2009.08.001_bib34) 2008; 99 Kimball (10.1016/j.jcp.2009.08.001_bib7) 1934; 45 Pauling (10.1016/j.jcp.2009.08.001_bib8) 1935 Çatalyürek (10.1016/j.jcp.2009.08.001_bib38) 1999; 10 Liu (10.1016/j.jcp.2009.08.001_bib42) 1976; 13 Luisier (10.1016/j.jcp.2009.08.001_bib13) 2006; 74 Lambert (10.1016/j.jcp.2009.08.001_bib24) 1980; 101 Çatalyürek (10.1016/j.jcp.2009.08.001_bib37) 1996; 1117 Landauer (10.1016/j.jcp.2009.08.001_bib1) 1957; 1 10.1016/j.jcp.2009.08.001_bib51 Fisher (10.1016/j.jcp.2009.08.001_bib4) 1981; 23 Baranger (10.1016/j.jcp.2009.08.001_bib30) 1991; 44 Whaley (10.1016/j.jcp.2009.08.001_bib59) 2001; 27 Rotter (10.1016/j.jcp.2009.08.001_bib36) 2003; 68 Lopez Sancho (10.1016/j.jcp.2009.08.001_bib19) 1984; 14 Hendrickson (10.1016/j.jcp.2009.08.001_bib47) 1998; 20 Lee (10.1016/j.jcp.2009.08.001_bib28) 1981; 47 Krstić (10.1016/j.jcp.2009.08.001_bib21) 2002; 66 Coon (10.1016/j.jcp.2009.08.001_bib49) 1995; 19 Datta (10.1016/j.jcp.2009.08.001_bib17) 2002 |
| References_xml | – volume: 32 start-page: 384 year: 1988 end-page: 413 ident: bib3 article-title: What is measured when you measure a resistance? – the Landauer formula revisited publication-title: IBM J. Res. Dev. – volume: 31 start-page: 6207 year: 1985 end-page: 6215 ident: bib2 article-title: Generalized many-channel conductance formula with application to small rings publication-title: Phys. Rev. B – reference: M. Wimmer, M. Scheid, K. Richter, Spin-polarized quantum transport in mesoscopic conductors: computational concepts and physical phenomena, in: Encyclopedia of Complexity and System Science, Springer, New York, 2009, p. 8597. – volume: 23 start-page: 6851 year: 1981 end-page: 6854 ident: bib4 article-title: Relation between conductivity and transmission matrix publication-title: Phys. Rev. B – year: 1992 ident: bib54 article-title: Algorithms in C++ – volume: 69 start-page: 115325 year: 2004 ident: bib10 article-title: Nonequilibrium electron transport in two-dimensional nanostructures modeled using green’s functions and the finite-element method publication-title: Phys. Rev. B – volume: 215 start-page: 741 year: 2006 end-page: 756 ident: bib33 article-title: Parallel implementation of the recursive Green’s function method publication-title: J. Comput. Phys. – volume: 68 start-page: 165302 year: 2003 ident: bib36 article-title: Ballistic quantum transport at high energies and high magnetic fields publication-title: Phys. Rev. B – volume: 74 start-page: 205323 year: 2006 ident: bib13 article-title: Atomistic simulation of nanowires in the publication-title: Phys. Rev. B – volume: 20 start-page: 468 year: 1998 end-page: 489 ident: bib47 article-title: Improving the run time and quality of nested dissection ordering publication-title: SIAM J. Sci. Comput. – year: 1990 ident: bib57 article-title: Computers and Intractability: A Guide to the Theory of NP-Completeness – volume: 45 start-page: 815 year: 1934 end-page: 820 ident: bib7 article-title: The numerical solution of Schrödinger’s equation publication-title: Phys. Rev. – volume: 1 start-page: 223 year: 1957 ident: bib1 article-title: Spatial variation of currents and fields due to localized scatterers in metallic conduction publication-title: IBM J. Res. Dev. – volume: 14 start-page: 1205 year: 1984 end-page: 1215 ident: bib19 article-title: Quick iterative scheme for the calculation of transfer matrices: application to Mo(1 publication-title: J. Phys. F: Met. Phys. – volume: 99 start-page: 012010 year: 2008 ident: bib34 article-title: An efficient and accurate method to obtain the energy-dependent green function for general potentials publication-title: J. Phys.: Conf. Ser. – volume: 59 start-page: 385 year: 1985 end-page: 390 ident: bib29 article-title: The calculation of transport properties and density of states of disordered solids publication-title: Z. Phys. B – volume: 10 start-page: 673 year: 1999 end-page: 693 ident: bib38 article-title: Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication publication-title: IEEE Trans. Parallel Distr. Syst. – volume: 13 start-page: 236 year: 1976 end-page: 250 ident: bib39 article-title: An algorithm for reducing the bandwidth and profile of a sparse matrix publication-title: SIAM J. Numer. Anal. – volume: 81 start-page: 3207 year: 1997 end-page: 3213 ident: bib11 article-title: Quantitative simulation of a resonant tunneling diode publication-title: J. Appl. Phys. – volume: 23 start-page: 1063 year: 1999 end-page: 1073 ident: bib50 article-title: Matrix ordering strategies for process engineering: graph partitioning algorithms for parallel computation publication-title: Comput. Chem. Eng. – reference: E. Cuthill, J. McKee, Reducing the bandwidth of sparse symmetric matrices, in: Proceedings of the 24th National Conference, ACM, New York, 1969, pp. 157–172. – volume: 49 start-page: 291 year: 1970 end-page: 308 ident: bib43 article-title: An efficient heuristic procedure for partitioning graphs publication-title: Bell Syst. Technol. J. – reference: B. Hendrickson, Graph partitioning and parallel solvers: has the emperor no clothes? in: Workshop on Parallel Algorithms for Irregularly Structured Problems, 1998, pp. 218–225. – year: 1998 ident: bib6 article-title: Quantum Kinetics in Transport and Optics of Semiconductors – year: 1935 ident: bib8 article-title: Introduction to Quantum Mechanics – volume: 11 start-page: 285 year: 2000 end-page: 300 ident: bib46 article-title: Multilevel publication-title: VLSI Des. – volume: 45 start-page: 494 year: 1980 end-page: 497 ident: bib65 article-title: New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance publication-title: Phys. Rev. Lett. – volume: 14 start-page: 235 year: 1981 end-page: 245 ident: bib27 article-title: Conductivity of the disordered linear chain publication-title: J. Phys. C: Solid State Phys. – year: 2001 ident: bib18 article-title: Transport in Nanostructures – volume: 52 start-page: 8244 year: 1995 end-page: 8255 ident: bib23 article-title: Numerical analysis of ballistic-electron transport in magnetic fields by using a quantum point contact and a quantum wire publication-title: Phys. Rev. B – volume: 77 start-page: 115119 year: 2008 ident: bib63 article-title: Knitting algorithm for calculating green functions in quantum systems publication-title: Phys. Rev. B – year: 2002 ident: bib17 article-title: Electronic Transport in Mesoscopic Transport – volume: 100 start-page: 177207 year: 2008 ident: bib61 article-title: Spin currents in rough graphene nanoribbons: universal fluctuations and spin injection publication-title: Phys. Rev. Lett. – volume: 81 start-page: 109 year: 2009 ident: bib62 article-title: The electronic properties of graphene publication-title: Rev. Mod. Phys. – volume: 65 start-page: 165401 year: 2002 ident: bib14 article-title: Density-functional method for nonequilibrium electron transport publication-title: Phys. Rev. B – volume: 13 start-page: 198 year: 1976 end-page: 213 ident: bib42 article-title: Comparative analysis of the Cuthill–McKee and the reverse Cuthill–McKee ordering algorithms for sparse matrices publication-title: SIAM J. Numer. Anal. – volume: 25 start-page: 1860 year: 2004 end-page: 1879 ident: bib53 article-title: Permuting sparse rectangular matrices into block-diagonal form publication-title: SIAM J. Sci. Comput. – volume: 73 start-page: 085414 year: 2006 ident: bib16 article-title: Spin and molecular electronics in atomically generated orbital landscapes publication-title: Phys. Rev. B – volume: 41 start-page: 171 year: 1997 end-page: 184 ident: bib55 article-title: Fast and effective algorithms for graph partitioning and sparse-matrix ordering publication-title: IBM J. Res. Dev. – volume: 47 start-page: 882 year: 1981 end-page: 885 ident: bib28 article-title: Anderson localization in two dimensions publication-title: Phys. Rev. Lett. – volume: 18 start-page: 435402 year: 2007 ident: bib64 article-title: A variant transfer matrix method suitable for transport through multi-probe systems publication-title: Nanotechnology – volume: 66 start-page: 205319 year: 2002 ident: bib21 article-title: Generalized conductance formula for the multiband tight-binding model publication-title: Phys. Rev. B – volume: 19 start-page: 787 year: 1995 end-page: 805 ident: bib49 article-title: Generalized block-tridiagonal matrix orderings for parallel computation in process flowsheeting publication-title: Comput. Chem. Eng. – volume: 438 start-page: 197 year: 2005 end-page: 200 ident: bib66 article-title: Two-dimensional gas of massless dirac fermions in graphene publication-title: Nature – volume: 15 start-page: 851 year: 1985 end-page: 858 ident: bib20 article-title: Highly convergent schemes for the calculation of bulk and surface Green functions publication-title: J. Phys. F: Met. Phys. – volume: 81 start-page: 7845 year: 1997 end-page: 7869 ident: bib31 article-title: Single and multiband modeling of quantum electron transport through layered semiconductor devices publication-title: J. Appl. Phys. – volume: 21 start-page: 2048 year: 2000 end-page: 2072 ident: bib52 article-title: Partitioning rectangular and structurally unsymmetric sparse matrices for parallel processing publication-title: SIAM J. Sci. Comput. – reference: D.G. Schweikert, B.W. Kernighan, A proper model for the partitioning of electrical circuits, in: DAC’72: Proceedings of the 9th Workshop on Design Automation, ACM, New York, NY, USA, 1972, pp. 57–62. – volume: 69 start-page: 155327 year: 2004 ident: bib9 article-title: Aharonov–Bohm physics with spin. II. Spin-flip effects in two-dimensional ballistic systems publication-title: Phys. Rev. B – volume: 11 start-page: 811 year: 1990 end-page: 823 ident: bib48 article-title: A block ordering method for sparse matrices publication-title: SIAM J. Sci. Stat. Comput. – volume: 62 start-page: 1950 year: 2000 end-page: 1960 ident: bib35 article-title: Modular recursive Green’s function method for ballistic quantum transport publication-title: Phys. Rev. B – reference: A. George, Computer implementation of the finite element method, Tech. Rep. STAN-CS-71-208, Computer Sci. Dept., Stanford Univ., Stanford, CA, 1971. – volume: 44 start-page: 10637 year: 1991 end-page: 10675 ident: bib30 article-title: Classical and quantum ballistic-transport anomalies in microjunctions publication-title: Phys. Rev. B – volume: 1117 start-page: 75 year: 1996 end-page: 86 ident: bib37 article-title: Decomposing irregularly sparse matrices for parallel matrix-vector multiplication publication-title: Lect. Notes Comput. Sci. – volume: 71 start-page: 245321 year: 2005 ident: bib26 article-title: Contact block reduction method for ballistic transport and carrier densities of open nanostructures publication-title: Phys. Rev. B – start-page: 153 year: 2006 end-page: 184 ident: bib15 article-title: Tight-binding DFT for molecular electronics (gDFTB) publication-title: Introducing Molecular Electronics – volume: 7 start-page: 498 year: 1998 end-page: 502 ident: bib25 article-title: A decimation method for studying transport properties of disordered systems publication-title: Ann. Phys. – volume: 59 start-page: 11936 year: 1999 end-page: 11948 ident: bib12 article-title: General Green’s-function formalism for transport calculations with publication-title: Phys. Rev. B – volume: 50 start-page: 7615 year: 1994 end-page: 7625 ident: bib22 article-title: Numerical analysis of electron-wave detection by a wedge-shaped point contact publication-title: Phys. Rev. B – volume: 27 start-page: 3 year: 2001 end-page: 35 ident: bib59 article-title: Automated empirical optimization of software and the ATLAS project publication-title: Parallel Comput. – volume: 75 start-page: 045346 year: 2007 ident: bib32 article-title: Effects of short-range interactions on transport through quantum point contacts: a numerical approach publication-title: Phys. Rev. B – volume: 35 start-page: 101 year: 2005 end-page: 121 ident: bib58 article-title: Minimizing development and maintenance costs in supporting persistently optimized BLAS publication-title: Software Pract. Exp. – reference: C.M. Fiduccia, R.M. Mattheyses, A linear-time heuristic for improving network partitions, in: DAC’82: Proceedings of the 19th Conference on Design Automation, IEEE Press, Piscataway, NJ, USA, 1982, pp. 175–181. – volume: 40 start-page: 8169 year: 1989 end-page: 8193 ident: bib5 article-title: Electrical linear-response theory in an arbitrary magnetic field: a new Fermi-surface formation publication-title: Phys. Rev. B – volume: 18 start-page: 1436 year: 1997 end-page: 1445 ident: bib56 article-title: How good is recursive bisection? publication-title: SIAM J. Sci. Comput. – volume: 101 start-page: 591 year: 1980 end-page: 595 ident: bib24 article-title: Decimation and Anderson localization publication-title: Phys. Stat. Solidi (b) – volume: 18 start-page: 435402 year: 2007 ident: 10.1016/j.jcp.2009.08.001_bib64 article-title: A variant transfer matrix method suitable for transport through multi-probe systems publication-title: Nanotechnology doi: 10.1088/0957-4484/18/43/435402 – volume: 11 start-page: 811 issue: 5 year: 1990 ident: 10.1016/j.jcp.2009.08.001_bib48 article-title: A block ordering method for sparse matrices publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0911048 – volume: 1 start-page: 223 issue: 3 year: 1957 ident: 10.1016/j.jcp.2009.08.001_bib1 article-title: Spatial variation of currents and fields due to localized scatterers in metallic conduction publication-title: IBM J. Res. Dev. doi: 10.1147/rd.13.0223 – year: 1990 ident: 10.1016/j.jcp.2009.08.001_bib57 – volume: 71 start-page: 245321 issue: 24 year: 2005 ident: 10.1016/j.jcp.2009.08.001_bib26 article-title: Contact block reduction method for ballistic transport and carrier densities of open nanostructures publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.71.245321 – year: 1992 ident: 10.1016/j.jcp.2009.08.001_bib54 – volume: 73 start-page: 085414 issue: 8 year: 2006 ident: 10.1016/j.jcp.2009.08.001_bib16 article-title: Spin and molecular electronics in atomically generated orbital landscapes publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.73.085414 – year: 2001 ident: 10.1016/j.jcp.2009.08.001_bib18 – volume: 11 start-page: 285 issue: 3 year: 2000 ident: 10.1016/j.jcp.2009.08.001_bib46 article-title: Multilevel k-way hypergraph partitioning publication-title: VLSI Des. doi: 10.1155/2000/19436 – volume: 65 start-page: 165401 issue: 16 year: 2002 ident: 10.1016/j.jcp.2009.08.001_bib14 article-title: Density-functional method for nonequilibrium electron transport publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.65.165401 – volume: 45 start-page: 494 issue: 6 year: 1980 ident: 10.1016/j.jcp.2009.08.001_bib65 article-title: New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.45.494 – volume: 50 start-page: 7615 issue: 11 year: 1994 ident: 10.1016/j.jcp.2009.08.001_bib22 article-title: Numerical analysis of electron-wave detection by a wedge-shaped point contact publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.50.7615 – year: 1998 ident: 10.1016/j.jcp.2009.08.001_bib6 – volume: 59 start-page: 11936 issue: 18 year: 1999 ident: 10.1016/j.jcp.2009.08.001_bib12 article-title: General Green’s-function formalism for transport calculations with spd Hamiltonians and giant magnetoresistance in Co- and Ni-based magnetic multilayers publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.59.11936 – volume: 10 start-page: 673 issue: 7 year: 1999 ident: 10.1016/j.jcp.2009.08.001_bib38 article-title: Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication publication-title: IEEE Trans. Parallel Distr. Syst. doi: 10.1109/71.780863 – volume: 49 start-page: 291 issue: 2 year: 1970 ident: 10.1016/j.jcp.2009.08.001_bib43 article-title: An efficient heuristic procedure for partitioning graphs publication-title: Bell Syst. Technol. J. doi: 10.1002/j.1538-7305.1970.tb01770.x – volume: 25 start-page: 1860 issue: 6 year: 2004 ident: 10.1016/j.jcp.2009.08.001_bib53 article-title: Permuting sparse rectangular matrices into block-diagonal form publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827502401953 – volume: 14 start-page: 1205 issue: 5 year: 1984 ident: 10.1016/j.jcp.2009.08.001_bib19 article-title: Quick iterative scheme for the calculation of transfer matrices: application to Mo(100) publication-title: J. Phys. F: Met. Phys. doi: 10.1088/0305-4608/14/5/016 – volume: 45 start-page: 815 issue: 11 year: 1934 ident: 10.1016/j.jcp.2009.08.001_bib7 article-title: The numerical solution of Schrödinger’s equation publication-title: Phys. Rev. doi: 10.1103/PhysRev.45.815 – volume: 215 start-page: 741 issue: 2 year: 2006 ident: 10.1016/j.jcp.2009.08.001_bib33 article-title: Parallel implementation of the recursive Green’s function method publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2005.11.010 – volume: 77 start-page: 115119 issue: 11 year: 2008 ident: 10.1016/j.jcp.2009.08.001_bib63 article-title: Knitting algorithm for calculating green functions in quantum systems publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.77.115119 – volume: 15 start-page: 851 issue: 4 year: 1985 ident: 10.1016/j.jcp.2009.08.001_bib20 article-title: Highly convergent schemes for the calculation of bulk and surface Green functions publication-title: J. Phys. F: Met. Phys. doi: 10.1088/0305-4608/15/4/009 – ident: 10.1016/j.jcp.2009.08.001_bib60 doi: 10.1007/978-0-387-30440-3_514 – volume: 40 start-page: 8169 issue: 12 year: 1989 ident: 10.1016/j.jcp.2009.08.001_bib5 article-title: Electrical linear-response theory in an arbitrary magnetic field: a new Fermi-surface formation publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.40.8169 – volume: 27 start-page: 3 issue: 1–2 year: 2001 ident: 10.1016/j.jcp.2009.08.001_bib59 article-title: Automated empirical optimization of software and the ATLAS project publication-title: Parallel Comput. doi: 10.1016/S0167-8191(00)00087-9 – volume: 47 start-page: 882 issue: 12 year: 1981 ident: 10.1016/j.jcp.2009.08.001_bib28 article-title: Anderson localization in two dimensions publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.47.882 – volume: 68 start-page: 165302 issue: 16 year: 2003 ident: 10.1016/j.jcp.2009.08.001_bib36 article-title: Ballistic quantum transport at high energies and high magnetic fields publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.68.165302 – volume: 81 start-page: 3207 issue: 7 year: 1997 ident: 10.1016/j.jcp.2009.08.001_bib11 article-title: Quantitative simulation of a resonant tunneling diode publication-title: J. Appl. Phys. doi: 10.1063/1.364151 – volume: 62 start-page: 1950 issue: 3 year: 2000 ident: 10.1016/j.jcp.2009.08.001_bib35 article-title: Modular recursive Green’s function method for ballistic quantum transport publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.62.1950 – volume: 23 start-page: 1063 issue: 8 year: 1999 ident: 10.1016/j.jcp.2009.08.001_bib50 article-title: Matrix ordering strategies for process engineering: graph partitioning algorithms for parallel computation publication-title: Comput. Chem. Eng. doi: 10.1016/S0098-1354(99)00271-9 – volume: 52 start-page: 8244 issue: 11 year: 1995 ident: 10.1016/j.jcp.2009.08.001_bib23 article-title: Numerical analysis of ballistic-electron transport in magnetic fields by using a quantum point contact and a quantum wire publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.52.8244 – ident: 10.1016/j.jcp.2009.08.001_bib40 doi: 10.1145/800195.805928 – ident: 10.1016/j.jcp.2009.08.001_bib44 doi: 10.1145/800153.804930 – volume: 66 start-page: 205319 issue: 20 year: 2002 ident: 10.1016/j.jcp.2009.08.001_bib21 article-title: Generalized conductance formula for the multiband tight-binding model publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.66.205319 – volume: 75 start-page: 045346 issue: 4 year: 2007 ident: 10.1016/j.jcp.2009.08.001_bib32 article-title: Effects of short-range interactions on transport through quantum point contacts: a numerical approach publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.75.045346 – year: 2002 ident: 10.1016/j.jcp.2009.08.001_bib17 – volume: 74 start-page: 205323 issue: 20 year: 2006 ident: 10.1016/j.jcp.2009.08.001_bib13 article-title: Atomistic simulation of nanowires in the sp3d5s∗ tight-binding formalism: from boundary conditions to strain calculations publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.74.205323 – volume: 99 start-page: 012010 year: 2008 ident: 10.1016/j.jcp.2009.08.001_bib34 article-title: An efficient and accurate method to obtain the energy-dependent green function for general potentials publication-title: J. Phys.: Conf. Ser. doi: 10.1088/1742-6596/99/1/012010 – volume: 81 start-page: 109 issue: 1 year: 2009 ident: 10.1016/j.jcp.2009.08.001_bib62 article-title: The electronic properties of graphene publication-title: Rev. Mod. Phys. doi: 10.1103/RevModPhys.81.109 – volume: 21 start-page: 2048 issue: 6 year: 2000 ident: 10.1016/j.jcp.2009.08.001_bib52 article-title: Partitioning rectangular and structurally unsymmetric sparse matrices for parallel processing publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827598341475 – start-page: 153 year: 2006 ident: 10.1016/j.jcp.2009.08.001_bib15 article-title: Tight-binding DFT for molecular electronics (gDFTB) – volume: 14 start-page: 235 issue: 3 year: 1981 ident: 10.1016/j.jcp.2009.08.001_bib27 article-title: Conductivity of the disordered linear chain publication-title: J. Phys. C: Solid State Phys. doi: 10.1088/0022-3719/14/3/007 – volume: 19 start-page: 787 year: 1995 ident: 10.1016/j.jcp.2009.08.001_bib49 article-title: Generalized block-tridiagonal matrix orderings for parallel computation in process flowsheeting publication-title: Comput. Chem. Eng. doi: 10.1016/0098-1354(94)00081-6 – volume: 1117 start-page: 75 year: 1996 ident: 10.1016/j.jcp.2009.08.001_bib37 article-title: Decomposing irregularly sparse matrices for parallel matrix-vector multiplication publication-title: Lect. Notes Comput. Sci. doi: 10.1007/BFb0030098 – volume: 35 start-page: 101 issue: 2 year: 2005 ident: 10.1016/j.jcp.2009.08.001_bib58 article-title: Minimizing development and maintenance costs in supporting persistently optimized BLAS publication-title: Software Pract. Exp. doi: 10.1002/spe.626 – volume: 100 start-page: 177207 issue: 17 year: 2008 ident: 10.1016/j.jcp.2009.08.001_bib61 article-title: Spin currents in rough graphene nanoribbons: universal fluctuations and spin injection publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.100.177207 – year: 1935 ident: 10.1016/j.jcp.2009.08.001_bib8 – volume: 438 start-page: 197 issue: 7065 year: 2005 ident: 10.1016/j.jcp.2009.08.001_bib66 article-title: Two-dimensional gas of massless dirac fermions in graphene publication-title: Nature doi: 10.1038/nature04233 – volume: 44 start-page: 10637 issue: 19 year: 1991 ident: 10.1016/j.jcp.2009.08.001_bib30 article-title: Classical and quantum ballistic-transport anomalies in microjunctions publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.44.10637 – volume: 18 start-page: 1436 issue: 5 year: 1997 ident: 10.1016/j.jcp.2009.08.001_bib56 article-title: How good is recursive bisection? publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827593255135 – volume: 23 start-page: 6851 issue: 12 year: 1981 ident: 10.1016/j.jcp.2009.08.001_bib4 article-title: Relation between conductivity and transmission matrix publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.23.6851 – volume: 69 start-page: 155327 issue: 15 year: 2004 ident: 10.1016/j.jcp.2009.08.001_bib9 article-title: Aharonov–Bohm physics with spin. II. Spin-flip effects in two-dimensional ballistic systems publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.69.155327 – volume: 81 start-page: 7845 issue: 12 year: 1997 ident: 10.1016/j.jcp.2009.08.001_bib31 article-title: Single and multiband modeling of quantum electron transport through layered semiconductor devices publication-title: J. Appl. Phys. doi: 10.1063/1.365394 – volume: 32 start-page: 384 issue: 3 year: 1988 ident: 10.1016/j.jcp.2009.08.001_bib3 article-title: What is measured when you measure a resistance? – the Landauer formula revisited publication-title: IBM J. Res. Dev. doi: 10.1147/rd.323.0384 – volume: 7 start-page: 498 issue: 5-6 year: 1998 ident: 10.1016/j.jcp.2009.08.001_bib25 article-title: A decimation method for studying transport properties of disordered systems publication-title: Ann. Phys. doi: 10.1002/(SICI)1521-3889(199811)7:5/6<498::AID-ANDP498>3.0.CO;2-6 – volume: 13 start-page: 198 issue: 2 year: 1976 ident: 10.1016/j.jcp.2009.08.001_bib42 article-title: Comparative analysis of the Cuthill–McKee and the reverse Cuthill–McKee ordering algorithms for sparse matrices publication-title: SIAM J. Numer. Anal. doi: 10.1137/0713020 – volume: 20 start-page: 468 issue: 2 year: 1998 ident: 10.1016/j.jcp.2009.08.001_bib47 article-title: Improving the run time and quality of nested dissection ordering publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827596300656 – ident: 10.1016/j.jcp.2009.08.001_bib41 – volume: 31 start-page: 6207 issue: 10 year: 1985 ident: 10.1016/j.jcp.2009.08.001_bib2 article-title: Generalized many-channel conductance formula with application to small rings publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.31.6207 – volume: 13 start-page: 236 issue: 2 year: 1976 ident: 10.1016/j.jcp.2009.08.001_bib39 article-title: An algorithm for reducing the bandwidth and profile of a sparse matrix publication-title: SIAM J. Numer. Anal. doi: 10.1137/0713023 – ident: 10.1016/j.jcp.2009.08.001_bib45 doi: 10.1109/DAC.1982.1585498 – volume: 41 start-page: 171 issue: 1/2 year: 1997 ident: 10.1016/j.jcp.2009.08.001_bib55 article-title: Fast and effective algorithms for graph partitioning and sparse-matrix ordering publication-title: IBM J. Res. Dev. doi: 10.1147/rd.411.0171 – ident: 10.1016/j.jcp.2009.08.001_bib51 doi: 10.1007/BFb0018541 – volume: 69 start-page: 115325 issue: 11 year: 2004 ident: 10.1016/j.jcp.2009.08.001_bib10 article-title: Nonequilibrium electron transport in two-dimensional nanostructures modeled using green’s functions and the finite-element method publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.69.115325 – volume: 101 start-page: 591 issue: 2 year: 1980 ident: 10.1016/j.jcp.2009.08.001_bib24 article-title: Decimation and Anderson localization publication-title: Phys. Stat. Solidi (b) doi: 10.1002/pssb.2221010218 – volume: 59 start-page: 385 issue: 4 year: 1985 ident: 10.1016/j.jcp.2009.08.001_bib29 article-title: The calculation of transport properties and density of states of disordered solids publication-title: Z. Phys. B doi: 10.1007/BF01328846 |
| SSID | ssj0008548 |
| Score | 2.2174869 |
| Snippet | Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the... |
| SourceID | osti proquest pascalfrancis crossref elsevier |
| SourceType | Open Access Repository Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 8548 |
| SubjectTerms | ALGORITHMS Block-tridiagonal matrices Blocking CHARGE TRANSPORT CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Coherent quantum transport Computational techniques ELECTRON GAS Exact sciences and technology GRAPH THEORY Graphene GREEN FUNCTION HAMILTONIANS Mathematical analysis Mathematical methods in physics MATRICES Matrix reordering Optimization Partitioning Physics QUANTUM DECOHERENCE Recursive Green’s function algorithm SEMICONDUCTOR MATERIALS Semiconductors Transport TRANSPORT THEORY |
| Title | Optimal block-tridiagonalization of matrices for coherent charge transport |
| URI | https://dx.doi.org/10.1016/j.jcp.2009.08.001 https://www.proquest.com/docview/1266744346 https://www.osti.gov/biblio/21333893 |
| Volume | 228 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Complete Freedom Collection customDbUrl: eissn: 1090-2716 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: ACRLP dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection customDbUrl: eissn: 1090-2716 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: .~1 dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals [SCFCJ] customDbUrl: eissn: 1090-2716 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: AIKHN dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVLSH databaseName: Elsevier Journals customDbUrl: mediaType: online eissn: 1090-2716 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: AKRWK dateStart: 19660801 isFulltext: true providerName: Library Specific Holdings |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1NT9wwEB3BcumlFErVpXRlpJ6QUmzH-ToiVLSAoBeQuEWxM24X2A1iw5XfzkzirIRQOfSaeCRrbL95lt_MAPxArTFG4yI0eRyZ1NrIuqyI0qpKFSpT25gThS8u0-m1ObtJbtbgeMiFYVllwP4e0zu0Dl8OgzcPH2YzzvHVnEPPykKuo56twwbFnzwfwcbR6fn0cgXIeWJ6QGY1AhkMj5udzOvWDVUrWVSp_hWeRg2dOBZOVkvyne-bXrzB7y4onXyCj4FNiqN-wluwhott2AzMUoRzu_wMZ78JGeY00lLsuovaxxltiz8dCe_TMEXjxbyr1o9LQTxWuOYvJwK2oiulhKIdiqDvwPXJr6vjaRS6KETOJKaNnNJ1IZ23ki8nmGKssUb6pW2RaJMZ6fLES5vYPM1iX1jvM1_FuafgniiL8RcYLZoFfgVhvckK5Y0m3mGQX1jR65o4hyxqogo4Bjk4r3ShxDh3urgvBy3ZbUn-5taXRcndL6Uaw8HK5KGvr_HeYDOsSPlqk5SE_--Z7fHqsQkXxnWsICIbTddzpmtjmLxa1dU8NF2HCy3NGPaHZS7p8PGLSrXA5mlZKqI35IrYpLv_N7Vv8EGHhhRK7sGofXzC78RyWjuB9Z_PahL28guRovsa |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NTxUxEJ_A4yAXFJX4ELEknkxW2m7362iI5MmXF0i4NdvuFB_KW8Jbrv7tzux2McTIwetuJ2lm2pnfpL-ZAfiAWmOKxidoyjQxuXOJ80WV5HWdK1SmcSkXCp-e5bMLc3SZXa7AwVgLw7TK6PsHn9576_hlP2pz_3Y-5xpfzTX0zCzkPurFKqyZTBecgX369YfnUWZmcMfMRaDl49NmT_K69mPPSqZUqn8Fp0lL941pk_WSNBeGkRd_ee8-JB2-gI2IJcXnYbubsIKLl_A84koRb-3yFRx9I79wQysdRa4fSXc3p0Nx1UPwoQhTtEHc9L36cSkIxQrffucywE70jZRQdGML9Ndwcfjl_GCWxBkKiTeZ6RKvdFNJH5zk1ARzTDU2SL-0qzJtCiN9mQXpMlfmRRoqF0IR6rQMFNoz5TDdgsmiXeAbEC6YolLBaEIdBvl9FYNuCHHIqiGggFOQo_Ksjw3Gec7FTzsyya4t6ZsHX1aWZ19KNYWPDyK3Q3eNpxab0SL20RGx5P2fEtth67EIt8X1zB8iGU3JOYO1Kew-surDPjQlw5WWZgp7o5ktXT1-T6kX2N4vrSJwQ6pITb79f1t7D89m56cn9uTr2fFbWNdxNIWSOzDp7u7xHeGdzu325_k3pxz74g |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Optimal+block-tridiagonalization+of+matrices+for+coherent+charge+transport&rft.jtitle=Journal+of+computational+physics&rft.au=Wimmer%2C+Michael&rft.au=Richter%2C+Klaus&rft.date=2009-12-10&rft.pub=Elsevier+Inc&rft.issn=0021-9991&rft.eissn=1090-2716&rft.volume=228&rft.issue=23&rft.spage=8548&rft.epage=8565&rft_id=info:doi/10.1016%2Fj.jcp.2009.08.001&rft.externalDocID=S0021999109004367 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0021-9991&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0021-9991&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0021-9991&client=summon |