Steady-state thermal transport in anharmonic systems: Application to molecular junctions

Physical Review B - Condensed Matter and Materials Physics

Volumn 85, Issue 19, 2012, Pages

  Thingna, Juzar ^a   Garcia Palacios J L ^a,b   Wang, Jian Sheng ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b National University of Singapore   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84861707383     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.85.195452     Document Type: Article

References (62)

1. R. Peierls, Ann. Phys. ANPYA2 0003-3804 10.1002/andp.19293950803 3, 1055 (1929).
2. J. M. Ziman, Electrons and Phonons (Oxford University Press, Oxford, 1963).
3. A. J. H. McGaughey and M. Kaviany, Adv. Heat Trasfer 9780-1202 10.1016/S0065-2717(06)39002-8 39, 169 (2006).
4. N. Mingo and L. Yang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68. 245406 68, 245406 (2003).
5. A. Dhar and D. Sen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73. 085119 73, 085119 (2006); (Pubitemid 43320418)
6. A. Dhar, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730802538522 57, 457 (2008).
7. J.-S. Wang, J. Wang, and J. T. Lü, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2008-00195-8 62, 381 (2008). (Pubitemid 351761911)
8. M. Terraneo, M. Peyrard, and G. Casati, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.094302 88, 094302 (2002).
9. B. Li, L. Wang, and G. Casati, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.184301 93, 184301 (2004).
10. B. Hu, L. Yang, and Y. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.124302 97, 124302 (2006). (Pubitemid 44414328)
11. B. Li, L. Wang, and G. Casati, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2191730 88, 143501 (2006).
12. W. C. Lo, L. Wang, and B. Li, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.77.054402 77, 054402 (2008).
13. D. Segal and A. Nitzan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.034301 94, 034301 (2005). (Pubitemid 40607293)
14. F. Bonetto, J. L. Lebowitz, and L. Rey-Bellet, Mathematical Physics 2000 (Imperial College Press, London, 2000).
15. J. Bricmont and A. Kupiainen, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-007-0284-5 274, 555 (2007).
16. C. Liverani and S. Olla, J. Am. Math. Soc. 0894-0347 10.1090/S0894-0347- 2011-00724-8 25, 555 (2011).
17. S. Lepri, R. Livi, and A. Politi, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(02)00558-6 377, 1 (2003) and references therein. (Pubitemid 36288864)
18. D. Segal, A. Nitzan, and P. Hänggi, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1603211 119, 6840 (2003).
19. Santhosh G. and D. Kumar, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.021105 76, 021105 (2007). (Pubitemid 47210343)
20. A. Dhar, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730802538522 57, 457 (2008).
21. K. Saito and A. Dhar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.040601 104, 040601 (2010).
22. J.-S. Wang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99. 160601 99, 160601 (2007). (Pubitemid 47587577)
23. D. Segal, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73.205415 73, 205415 (2006). (Pubitemid 43752604)
24. L.-A. Wu, C. X. Yu, and D. Segal, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.041103 80, 041103 (2009).
25. K. Saito, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00241-3 61, 34 (2003). (Pubitemid 36185129)
26. J. Wu and M. Berciu, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83. 214416 83, 214416 (2011).
27. K. A. Velizhanin, M. Thoss, and H. Wang, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3483127 133, 084503 (2010).
28. N. Mingo, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.125402 74, 125402 (2006). (Pubitemid 44316377)
29. J.-S. Wang, J. Wang, and N. Zeng, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.033408 74, 033408 (2006); (Pubitemid 44087226)
30. J.-S. Wang, N. Zeng, J. Wang, and C. K. Gan, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.061128 75, 061128 (2007). (Pubitemid 47143707)
31. A. G. Redfield, IBM J. Res. Dev. IBMJAE 0018-8646 10.1147/rd.11.0019 1, 19 (1957).
32. G. Lindblad, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01608499 48, 119 (1976).
33. W. Pauli, in Festschrift zum 60. Geburtstage A. Sommerfeld (Hirzel, Leipzig, 1928).
34. M. Esposito and P. Gaspard, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.68.066112 68, 066112 (2003).
35. H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
36. A. O. Caldeira and A. J. Leggett, Ann. Phys. APNYA6 0003-4916 10.1016/0003-4916(83)90202-6 149, 374 (1983).
37. D. Zueco, Ph.D. thesis, Universidad de Zaragoza, Spain, 2007.
38. R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University Press, Oxford, 2001).
39. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 2008).
40. V. Romero-Rochin and I. Oppenheim, Physica (Utrecht) 0378-4371 10.1016/0378-4371(89)90051-4 155, 52 (1989).
41. R. K. Wangsness and F. Bloch, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.89.728 89, 728 (1953).
42. B. B. Laird, J. Budimir, and J. L. Skinner, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.460626 94, 4391 (1991).
43. W. T. Pollard and R. A. Friesner, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.467222 100, 5054 (1994).
44. D. Kohen and D. J. Tannor, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.470429 103, 6013 (1995).
45. C. H. Fleming and N. I. Cummings, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.031117 83, 031117 (2011).
46. Although we deal with a specific problem of two heat baths, the problem can be easily generalized to multiple heat baths. In case of multiple heat baths, the only change occurs in the evaluation of the reduced density matrix.
47. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Non-equilibrium Statistical Mechanics (Springer-Verlag, Berlin 1985).
48. Since we expand only up to first order in ε, the second-order term H RN α = γ (0) S α 2 plays no role.
49. In general, if the reduced density matrix is correct up to order " 2 n, " where 2 n is the power of ε at which the series is truncated, then we need to have the heat current operator accurate up to order " 2 n + 2 " so that the final expression is accurate up to order " 2 n. "
50. Y. Tanimura and R. Kubo, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.58.101 58, 101 (1989).
51. C. Meier and D. J. Tannor, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.479669 111, 3365 (1999).
52. B. Q. Ai, W. R. Zhong, and B. Hu, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.052102 83, 052102 (2011).
53. N. Li, J. Ren, L. Wang, G. Zhang, P. Hänggi, and B. Li, e-print arXiv: 1108.6120v2 (Rev. Mod. Phys., in press).
54. C. Z. Wang, C. T. Chan, and K. M. Ho, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.42.11276 42, 11276 (1990).
55. Y. H. Lee, R. Biswas, C. M. Soukoulis, C. Z. Wang, C. T. Chan, and K. M. Ho, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.43.6573 43, 6573 (1991).
56. J. Li, L. Porter, and S. Yip, J. Nucl. Mater. JNUMAM 0022-3115 10.1016/S0022-3115(98)00034-8 255, 139 (1998).
57. J.-S. Wang, X. Ni, and J.-W. Jiang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.224302 80, 224302 (2009).
58. M. Schwarz Jr., J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01012880 15, 255 (1976).
59. A. Tari, The Specific Heat of Matter at Low Temperatures (Imperial College Press, London, 2003).
60. T. Nakanishi and S. Yamamoto, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.214418 65, 214418 (2002).
61. Y. Meir and N. S. Wingreen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.2512 68, 2512 (1992).
62. K. Saito and A. Dhar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.180601 99, 180601 (2007). (Pubitemid 350074470)