Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

Postal Subscription Code 80-965

2018 Impact Factor: 2.483

Front. Phys.    2016, Vol. 11 Issue (4) : 110308-110308    https://doi.org/10.1007/s11467-016-0540-2
REVIEW ARTICLE
Non-canonical distribution and non-equilibrium transport beyond weak system-bath coupling regime: A polaron transformation approach
Dazhi Xu,Jianshu Cao()
Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
 Download: PDF(611 KB)  
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

The concept of polaron, emerged from condense matter physics, describes the dynamical interaction of moving particle with its surrounding bosonic modes. This concept has been developed into a useful method to treat open quantum systems with a complete range of system-bath coupling strength. Especially, the polaron transformation approach shows its validity in the intermediate coupling regime, in which the Redfield equation or Fermi’s golden rule will fail. In the polaron frame, the equilibrium distribution carried out by perturbative expansion presents a deviation from the canonical distribution, which is beyond the usual weak coupling assumption in thermodynamics. A polaron transformed Redfield equation (PTRE) not only reproduces the dissipative quantum dynamics but also provides an accurate and efficient way to calculate the non-equilibrium steady states. Applications of the PTRE approach to problems such as exciton diffusion, heat transport and light-harvesting energy transfer are presented.

Keywords polaron transformation      strong coupling      quantum transport      non-equilibrium steady state     
Corresponding Author(s): Jianshu Cao   
Issue Date: 04 May 2016
 Cite this article:   
Dazhi Xu,Jianshu Cao. Non-canonical distribution and non-equilibrium transport beyond weak system-bath coupling regime: A polaron transformation approach[J]. Front. Phys. , 2016, 11(4): 110308-110308.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-016-0540-2
https://academic.hep.com.cn/fop/EN/Y2016/V11/I4/110308
1 A. G. Redfield, The theory of relaxation processes, Adv. Magn. Reson. 1, 1 (1965)
https://doi.org/10.1016/B978-1-4832-3114-3.50007-6
2 G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48(2), 119 (1976)
https://doi.org/10.1007/BF01608499
3 H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, New York: Oxford University Press, 2002
4 J. Cao, A phase-space study of Bloch–Redfield theory, J. Chem. Phys. 107(8), 3204 (1997)
https://doi.org/10.1063/1.474670
5 S. A. Crooker, J. A. Hollingsworth, S. Tretiak, and V. I. Klimov, Spectrally resolved dynamics of energy transfer in quantum-dot assemblies: Towards engineered energy flows in artificial materials, Phys. Rev. Lett. 89(18), 186802 (2002)
https://doi.org/10.1103/PhysRevLett.89.186802
6 D. Kim, S. Okahara, M. Nakayama, and Y. Shim, Experimental verification of Förster energy transfer between semiconductor quantum dots, Phys. Rev. B 78(15), 153301 (2008)
https://doi.org/10.1103/PhysRevB.78.153301
7 S. I. E. Vulto, M. A. de Baat, R. J. W. Louwe, H. P. Permentier, T. Neef, M. Miller, H. van Amerongen, and T. J. Aartsma, Exciton simulations of optical spectra of the FMO complex from the green sulfur bacterium Chlorobium tepidum at 6 K, J. Phys. Chem. B 102(47), 9577 (1998)
https://doi.org/10.1021/jp982095l
8 T. Brixner, J. Stenger, H. M. Vaswani, M. Cho, R. E. Blankenship, and G. R. Fleming, Two-dimensional spectroscopy of electronic couplings in photosynthesis, Nature 434(7033), 625 (2005)
https://doi.org/10.1038/nature03429
9 G. S. Engel, T. R. Calhoun, E. L. Read, T. Ahn, T. Mancal, Y. C. Cheng, R. E. Blankenship, and G. R. Fleming, Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems, Nature 446(7137), 782 (2007)
https://doi.org/10.1038/nature05678
10 J. Wu, F. Liu, Y. Shen, J. Cao, and R. J. Silbey, Efficient energy transfer in light-harvesting systems (I): optimal temperature, reorganization energy and spatial–temporal correlations, New J. Phys. 12(10), 105012 (2010)
https://doi.org/10.1088/1367-2630/12/10/105012
11 Y. Tanimura, Stochastic Liouville, Langevin, Fokker–Planck, and master equation approaches to quantum dissipative systems, J. Phys. Soc. Jpn. 75(8), 082001 (2006)
https://doi.org/10.1143/JPSJ.75.082001
12 R. X. Xu and Y. J. Yan, Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach, Phys. Rev. E 75(3), 031107 (2007)
https://doi.org/10.1103/PhysRevE.75.031107
13 N. Makri and D. E. Makarov, Tensor propagator for iterative quantum time evolution of reduced density matrices (I): Theory, J. Chem. Phys. 102(11), 4600 (1995)
https://doi.org/10.1063/1.469508
14 J. Prior, A. W. Chin, S. F. Huelga, and M. B. Plenio, Efficient simulation of strong system-environment interactions, Phys. Rev. Lett. 105(5), 050404 (2010)
https://doi.org/10.1103/PhysRevLett.105.050404
15 S. Tornow, R. Bulla, F. B. Anders, and A. Nitzan, Dissipative two-electron transfer: A numerical renormalization group study, Phys. Rev. B 78(3), 035434 (2008)
https://doi.org/10.1103/PhysRevB.78.035434
16 H. D. Meyer, U. Manthe, and L. Cederbaum, The multi-configurational time-dependent Hartree approach, Chem. Phys. Lett. 165(1), 73 (1990)
https://doi.org/10.1016/0009-2614(90)87014-I
17 M. Thoss, H. Wang, and W. H. Miller, Self-consistent hybrid approach for complex systems: Application to the spin-boson model with Debye spectral density, J. Chem. Phys. 115(7), 2991 (2001)
https://doi.org/10.1063/1.1385562
18 M. Moix, Y. Zhao, and J. Cao, Equilibrium-reduced density matrix formulation: Influence of noise, disorder, and temperature on localization in excitonic systems, Phys. Rev. B 85(11), 115412 (2012)
https://doi.org/10.1103/PhysRevB.85.115412
19 J. Moix, J. Ma, and J. Cao, Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems (III): Exact stochastic path integral evaluation, J. Chem. Phys. 142(9), 094108 (2015)
https://doi.org/10.1063/1.4908601
20 H. Fröhlich, Electrons in lattice fields, Adv. Phys. 3, 325 (1954)
https://doi.org/10.1080/00018735400101213
21 T. Holstein, Studies of polaron motion, Ann. Phys. 8(3), 325 (1959)
https://doi.org/10.1016/0003-4916(59)90002-8
22 R. Silbey and R. A. Harris, Variational calculation of the dynamics of a two level system interacting with a bath, J. Chem. Phys. 80(6), 2615 (1984)
https://doi.org/10.1063/1.447055
23 R. A. Harris and R. Silbey, Variational calculation of the tunneling system interacting with a heat bath (II): Dynamics of an asymmetric tunneling system, J. Chem. Phys. 83(3), 1069 (1985)
https://doi.org/10.1063/1.449469
24 M. Grover and R. Silbey, Exciton migration in molecular crystals, J. Chem. Phys. 54(11), 4843 (1971)
https://doi.org/10.1063/1.1674761
25 S. Jang, Y. C. Cheng, D. R. Reichman, and J. D. Eaves, Theory of coherent resonance energy transfer, J. Chem. Phys. 129(10), 101104 (2008)
https://doi.org/10.1063/1.2977974
26 A. Nazir, Correlation-dependent coherent to incoherent transitions in resonant energy transfer dynamics, Phys. Rev. Lett. 103(14), 146404 (2009)
https://doi.org/10.1103/PhysRevLett.103.146404
27 D. P. S. McCutcheon and A. Nazir, Quantum dot Rabi rotations beyond the weak exciton–phonon coupling regime, New J. Phys. 12(11), 113042 (2010)
https://doi.org/10.1088/1367-2630/12/11/113042
28 C. K. Lee, J. M. Moix, and J. Cao, Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport, J. Chem. Phys. 142(16), 164103 (2015)
https://doi.org/10.1063/1.4918736
29 C. K. Lee, J. Moix, and J. Cao, Accuracy of second order perturbation theory in the polaron and variational polaron frames, J. Chem. Phys. 136(20), 204120 (2012)
https://doi.org/10.1063/1.4722336
30 C. K. Lee, J. Cao, and J. Gong, Noncanonical statistics of a spin-boson model: Theory and exact Monte Carlo simulations, Phys. Rev. E 86(2), 021109 (2012)
https://doi.org/10.1103/PhysRevE.86.021109
31 H. Dong, S. Yang, X. F. Liu, and C. P. Sun, Quantum thermalization with couplings, Phys. Rev. A 76(4), 044104 (2007)
https://doi.org/10.1103/PhysRevA.76.044104
32 D. Z. Xu, S. W. Li, X. F. Liu, and C. P. Sun, Noncanonical statistics of a finite quantum system with non-negligible system-bath coupling, Phys. Rev. E 90(6), 062125 (2014)
https://doi.org/10.1103/PhysRevE.90.062125
33 C. Wang, J. Ren and J. Cao, Nonequilibrium energy transfer at nanoscale: A unified theory from weak to strong coupling, Scientific Reports 5, 11787 (2015)
https://doi.org/10.1038/srep11787
34 D. Z. Xu, C. Wang, Y. Zhao, and J. Cao, Polaron effects on the performance of light-harvesting systems: A quantum heat engine perspective, New J. Phys. 18(2), 023003 (2016)
https://doi.org/10.1088/1367-2630/18/2/023003
35 A. Ishizaki and G. R. Fleming, On the adequacy of the Redfield equation and related approaches to the study of quantum dynamics in electronic energy transfer, J. Chem. Phys. 130(23), 234110 (2009)
https://doi.org/10.1063/1.3155214
36 L. A. Pachón and P. Brumer, Computational methodologies and physical insights into electronic energy transfer in photosynthetic light-harvesting complexes, J. Phys. Chem. Lett. 2, 2728 (2011), arXiv: 1203.3978
https://doi.org/10.1021/jz201189p
37 H. J. Carmichael, Statistical Methods in Quantum Optics, Springer, 1999
https://doi.org/10.1007/978-3-662-03875-8
38 A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Dynamics of the dissipative two-state system, Rev. Mod. Phys. 59(1), 1 (1987)
https://doi.org/10.1103/RevModPhys.59.1
39 U. Weiss, Quantum Dissipative Systems, Singapore: World Scientific, 2008
40 J. Cao, Effects of bath relaxation on dissipative two-state dynamics, J. Chem. Phys. 112(15), 6719 (2000)
https://doi.org/10.1063/1.481247
41 A. W. Chin, J. Prior, S. F. Huelga, and M. B. Plenio, Generalized polaron ansatz for the ground state of the sub-ohmic spin-boson model: An analytic theory of the localization transition, Phys. Rev. Lett. 107(16), 160601 (2011)
https://doi.org/10.1103/PhysRevLett.107.160601
42 Q. J. Tong, J. H. An, H. G. Luo, and C. H. Oh, Quantum phase transition in the delocalized regime of the spin-boson model, Phys. Rev. B 84(17), 174301 (2011)
https://doi.org/10.1103/PhysRevB.84.174301
43 D. P. S. McCutcheon, N. S. Dattani, E. M. Gauger, B. W. Lovett, and A. Nazir, A general approach to quantum dynamics using a variational master equation: Application to phonon-damped Rabi rotations in quantum dots, Phys. Rev. B 84(8), 081305 (2011)
https://doi.org/10.1103/PhysRevB.84.081305
44 D. Ruelle, Statistical Mechanics: Rigorous Results, New York: Benjamin, 1969
45 R. P. Feynman, Statistical Mechanics. A set of lectures, Longman: Addison Wesley, 1998
46 M. D. Girardeau and R. M. Mazo, Advances in Chemical Physics, Vol. 24, New York: Wiley, 1973
https://doi.org/10.1002/9780470143766.ch4
47 R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics (II): Nonequilibrium Statistical Mechanics, Berlin: Springer-Verlag, 1983
48 A. Nitzan, Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems, Oxford: Oxford University Press, 2006
49 R. P. Feynman and F. L. Jr Vernon, The theory of a general quantum system interacting with a linear dissipative system, Ann. Phys. 24, 118 (1963)
https://doi.org/10.1016/0003-4916(63)90068-X
50 W. H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75(3), 715 (2003)
https://doi.org/10.1103/RevModPhys.75.715
51 J. P. Paz and W. H. Zurek, Quantum limit of decoherence: Environment induced superselection of energy eigenstates, Phys. Rev. Lett. 82(26), 5181 (1999)
https://doi.org/10.1103/PhysRevLett.82.5181
52 D. Braun, F. Haake, and W. T. Strunz, Universality of decoherence, Phys. Rev. Lett. 86(14), 2913 (2001)
https://doi.org/10.1103/PhysRevLett.86.2913
53 W. G. Wang, J. B. Gong, G. Casati, and B. Li, Entanglement-induced decoherence and energy eigenstates, Phys. Rev. A 77(1), 012108 (2008)
https://doi.org/10.1103/PhysRevA.77.012108
54 C. Gogolin, Environment-induced super selection without pointer states, Phys. Rev. E 81(5), 051127 (2010)
https://doi.org/10.1103/PhysRevE.81.051127
55 E. N. Zimanyi and R. J. Silbey, Theoretical description of quantum effects in multi-chromophoric aggregates, Philos. Trans. R. Soc. A 370(1972), 3620 (2012)
56 A. Troisi and G. Orlandi, Charge-transport regime of crystalline organic semiconductors: Diffusion limited by thermal off-diagonal electronic disorder, Phys. Rev. Lett. 96(8), 086601 (2006)
https://doi.org/10.1103/PhysRevLett.96.086601
57 T. Sakanoue and H. Sirringhaus, Band-like temperature dependence of mobility in a solution-processed organic semiconductor, Nat. Mater. 9(9), 736 (2010)
https://doi.org/10.1038/nmat2825
58 J. Singh, E. R. Bittner, D. Beljonne, and G. D. Scholes, Fluorescence depolarization in poly[2-methoxy-5-((2-ethylhexyl)oxy)-1,4-phenylenevinylene]: Sites versus eigenstates hopping, J. Chem. Phys. 131(19), 194905 (2009)
https://doi.org/10.1063/1.3259549
59 M. Bednarz, V. A. Malyshev, and J. Knoester, Temperature dependent fluorescence in disordered Frenkel chains: Interplay of equilibration and local band-edge level structure, Phys. Rev. Lett. 91(21), 217401 (2003)
https://doi.org/10.1103/PhysRevLett.91.217401
60 J. Moix, J. Wu, P. Huo, D. Coker, and J. Cao, Efficient energy transfer in light-harvesting systems (III): The influence of the eighth bacteriochlorophyll on the dynamics and efficiency in FMO, J. Phys. Chem. Lett. 2(24), 3045 (2011)
https://doi.org/10.1021/jz201259v
61 G. T. de Laissardière, J. P. Julien, and D. Mayou, Quantum transport of slow charge carriers in quasicrystals and correlated systems, Phys. Rev. Lett. 97, 026601 (2006)
https://doi.org/10.1103/PhysRevLett.97.026601
62 V. Coropceanu, J. Cornil, D. A. da Silva Filho, Y. Olivier, R. Silbey, and J. L. Bredas, Charge transport in organic semiconductors, Chem. Rev. 107(4), 926 (2007)
https://doi.org/10.1021/cr050140x
63 F. Ortmann, F. Bechstedt, and K. Hannewald, Theory of charge transport in organic crystals: Beyond Holstein’s small-polaron model, Phys. Rev. B 79(23), 235206 (2009)
https://doi.org/10.1103/PhysRevB.79.235206
64 S. Ciuchi, S. Fratini, and D. Mayou, Transient localization in crystalline organic semiconductors, Phys. Rev. B 83(8), 081202 (2011)
https://doi.org/10.1103/PhysRevB.83.081202
65 Y. Cheng and R. J. Silbey, A unified theory for charge-carrier transport in organic crystals, J. Chem. Phys. 128(11), 114713 (2008)
https://doi.org/10.1063/1.2894840
66 J. M. Moix, M. Khasin, and J. Cao, Coherent quantum transport in disordered systems (I): The influence of dephasing on the transport properties and absorption spectra on one-dimensional systems, New J. Phys. 15(8), 085010 (2013)
https://doi.org/10.1088/1367-2630/15/8/085010
67 C. Chuang, C. K. Lee, J. M. Moix, J. Knoester, and J. Cao, Quantum diffusion on molecular tubes: Universal scaling of the 1D to 2D transition, arXiv: 1511.01198 (2015)
68 A. O. Niskanen, Y. Nakamura, and J. P. Pekola, Information entropic superconducting microcooler, Phys. Rev. B 76(17), 174523 (2007)
https://doi.org/10.1103/PhysRevB.76.174523
69 K. Le Hur, Kondo resonance of a microwave photon, Phys. Rev. B 85(14), 140506 (2012)
https://doi.org/10.1103/PhysRevB.85.140506
70 M. Galperin, M. A. Ratner, and A. Nitzan, Molecular transport junctions: Vibrational effects, J. Phys.: Condens. Matter 19(10), 103201 (2007)
https://doi.org/10.1088/0953-8984/19/10/103201
71 J. C. Cuevas and E. Scheer, Molecular Electronics: An Introduction to Theory and Experiment, Singapore: World Scientific, 2010
https://doi.org/10.1142/7434
72 D. Segal and A. Nitzan, Spin-boson thermal rectifier, Phys. Rev. Lett. 94(3), 034301 (2005)
https://doi.org/10.1103/PhysRevLett.94.034301
73 D. Segal, Stochastic pumping of heat: Approaching the Carnot efficiency, Phys. Rev. Lett. 101(26), 260601 (2008)
https://doi.org/10.1103/PhysRevLett.101.260601
74 J. Ren, P. Hänggi, and B. Li, Berry-phase-induced heat pumping and its impact on the fluctuation theorem, Phys. Rev. Lett. 104(17), 170601 (2010)
https://doi.org/10.1103/PhysRevLett.104.170601
75 A. Caldeira and A. J. Leggett, Influence of dissipation on quantum tunneling in macroscopic systems, Phys. Rev. Lett. 46(4), 211 (1981)
https://doi.org/10.1103/PhysRevLett.46.211
76 N. B. Li, J. Ren, L. Wang, G. Zhang, P. Hänggi, and B. Li, Phononics: Manipulating heat flow with electronic analogs and beyond, Rev. Mod. Phys. 84(3), 1045 (2012)
https://doi.org/10.1103/RevModPhys.84.1045
77 L. Zhu, S. Kirchner, Q. M. Si, and A. Georges, Quantum critical properties of the Bose–Fermi Kondo model in a large-N limit, Phys. Rev. Lett. 93(26), 267201 (2004)
https://doi.org/10.1103/PhysRevLett.93.267201
78 K. Saito and T. Kato, Kondo signature in heat transfer via a local two-state system, Phys. Rev. Lett. 111(21), 214301 (2013)
https://doi.org/10.1103/PhysRevLett.111.214301
79 A. Ishizaki and G. R. Fleming, Quantum coherence in photosynthetic light harvesting, Annu. Rev. Condens. Matter Phys. 3(1), 333 (2012)
https://doi.org/10.1146/annurev-conmatphys-020911-125126
80 J. L. Wu, R. J. Silbey, and J. Cao, Generic mechanism of optimal energy transfer efficiency: A scaling theory of the mean first-passage time in exciton systems, Phys. Rev. Lett. 110(20), 200402 (2013)
https://doi.org/10.1103/PhysRevLett.110.200402
81 S. F. Huelga and M. B. Plenio, Vibrations, quanta and biology, Contemp. Phys. 54(4), 181 (2013)
https://doi.org/10.1080/00405000.2013.829687
82 M. Esposito, U. Harbola, and S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Rev. Mod. Phys. 81(4), 1665 (2009)
https://doi.org/10.1103/RevModPhys.81.1665
83 T. V. Tscherbul and P. Brumer, Long-lived quasistationary coherences in a V-type system driven by incoherent light, Phys. Rev. Lett. 113(11), 113601 (2014)
https://doi.org/10.1103/PhysRevLett.113.113601
84 J. Olšina, A. G. Dijkstra, C. Wang, and J. Cao, Can natural sunlight induce coherent exciton dynamics? arXiv: 1408.5385 (2014)
85 H. T. Quan, Y. X. Liu, C. P. Sun, and F. Nori, Quantum thermodynamic cycles and quantum heat engines, Phys. Rev. E 76(3), 031105 (2007)
https://doi.org/10.1103/PhysRevE.76.031105
86 M. O. Scully, K. R. Chapin, K. E. Dorfman, M. B. Kim, and A. Svidzinsky, Quantum heat engine power can be increased by noise-induced coherence, Proc. Natl. Acad. Sci. USA 108(37), 15097 (2011)
https://doi.org/10.1073/pnas.1110234108
87 K. E. Dorfman, D. V. Voronine, S. Mukamel, and M. O. Scully, Photosynthetic reaction center as a quantum heat engine, Proc. Natl. Acad. Sci. USA 110(8), 2746 (2013)
https://doi.org/10.1073/pnas.1212666110
88 H. E. D. Scovil and E. O. Schulz-DuBois, Three-level masers as heat engines, Phys. Rev. Lett. 2(6), 262 (1959)
https://doi.org/10.1103/PhysRevLett.2.262
89 J. E. Geusic, E. O. Schulz-DuBios, and H. E. D. Scovil, Quantum equivalent of the carnot cycle, Phys. Rev. 156(2), 343 (1967)
https://doi.org/10.1103/PhysRev.156.343
90 E. Geva and R. Kosloff, The quantum heat engine and heat pump: An irreversible thermodynamic analysis of the three-level amplifier, J. Chem. Phys. 104(19), 7681 (1996)
https://doi.org/10.1063/1.471453
91 E. Boukobza and D. J. Tannor, Three-level systems as amplifiers and attenuators: A thermodynamic analysis, Phys. Rev. Lett. 98(24), 240601 (2007)
https://doi.org/10.1103/PhysRevLett.98.240601
92 D. Gelbwaser-Klimovsky and A. Aspuru-Guzik, Strongly coupled quantum heat machines, J. Phys. Chem. Lett. 6(17), 3477 (2015)
https://doi.org/10.1021/acs.jpclett.5b01404
93 J. Cao and R. J. Silbey, Optimization of exciton trapping in energy transfer processes, J. Phys. Chem. A 113(50), 13825 (2009)
https://doi.org/10.1021/jp9032589
94 C. Wang, J. Ren, and J. Cao, Optimal tunneling enhances the quantum photovoltaic effect in double quantum dots, New J. Phys. 16(4), 045019 (2014)
https://doi.org/10.1088/1367-2630/16/4/045019
95 A. G. Dijkstra, C. Wang, J. Cao, and G. R. Fleming, Coherent exciton dynamics in the presence of underdamped vibrations, J. Phys. Chem. Lett. 6(4), 627 (2015)
https://doi.org/10.1021/jz502701u
[1] Qiang Wang, Jian-Wei Li, Bin Wang, Yi-Hang Nie. First-principles investigation of quantum transport in GeP3 nanoribbon-based tunneling junctions[J]. Front. Phys. , 2018, 13(3): 138501-.
[2] Xue-Rong Hu, Ji-Ming Zheng, Zhao-Yu Ren. Strong interlayer coupling in phosphorene/graphene van der Waals heterostructure: A first-principles investigation[J]. Front. Phys. , 2018, 13(2): 137302-.
[3] Shmuel Gurvitz. Wave-function approach to Master equations for quantum transport and measurement[J]. Front. Phys. , 2017, 12(4): 120303-.
[4] Pei-Yun Yang,Wei-Min Zhang. Master equation approach to transient quantum transport in nanostructures[J]. Front. Phys. , 2017, 12(4): 127204-.
[5] Xin-Qi Li. Number-resolved master equation approach to quantum measurement and quantum transport[J]. Front. Phys. , 2016, 11(4): 110307-.
[6] YiJing Yan,Jinshuang Jin,Rui-Xue Xu,Xiao Zheng. Dissipation equation of motion approach to open quantum systems[J]. Front. Phys. , 2016, 11(4): 110306-.
[7] Xiao-Fei Li, Yi Luo. Conductivity of carbon-based molecular junctions from ab-initio methods[J]. Front. Phys. , 2014, 9(6): 748-759.
[8] Yanho Kwok, Yu Zhang, GuanHua Chen. Time-dependent density functional theory for quantum transport[J]. Front. Phys. , 2014, 9(6): 698-710.
[9] Ning Zhan-Yu(宁展宇), Qiao Jing-Si(乔婧思), Ji Wei(季威), Guo Hong(郭鸿). Correlation of interfacial bonding mechanism and equilibrium conductance of molecular junctions[J]. Front. Phys. , 2014, 9(6): 780-788.
[10] Wen-Zhi Zheng(郑文智), Yuan Liang(梁源), Ji-Ping Huang(黄吉平). Equilibrium state and non-equilibrium steady state in an isolated human system[J]. Front. Phys. , 2014, 9(1): 128-135.
[11] Wei-qiang CHEN(陈伟强), Kai-yu YANG(杨开宇), Yi ZHOU(周毅), Fu-chun ZHANG(张富春). Theory for superconductivity in iron pnictides at large coulomb U limit[J]. Front. Phys. , 2009, 4(4): 447-454.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed