Abstract.
We consider chains consisting of several identical subsystems weakly coupled by various types of next neighbor interactions. At both ends the chain is coupled to a respective heat bath with different temperature modeled by a Lindblad formalism. The temperature gradient introduced by this environment is then treated as an external perturbation. We propose a method to evaluate the heat current and the local temperature profile of the resulting stationary state as well as the heat conductivity in such systems. This method is similar to Kubo techniques used e.g. for electrical transport but extended here to the Liouville space.
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References
R. Kubo, M. Toda, N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics, Number 31 in Solid-State Sciences, 2nd edn. (Springer, Berlin, Heidelberg, New-York, 1991)
H. Mori, Phys. Rev. 115, 298 (1956)
G.D. Mahan, Many-Particle Physics, 3rd edn. (Plenum Press, New York, London, 2000)
D.N. Zubarev, Nonequilibrium Statistical Thermodynamics, Studies in Soviet Sciences. Consultants Bureau, New York, London, 1974. transl. by P.J. Shepherd
R. Kubo, J. Phys. Soc. Jpn 12, 570 (1957)
J.M. Luttinger, Phys. Rev. 135(6A), A1505 (1964)
X. Zotos, F. Naef, P. Prelovsek, Phys. Rev. B 55(17), 11029 (1997)
F. Heidrich-Meisner, A. Honecker, D.C. Cabra, W. Brenig, Zero-Frequency transport properties of one dimensional spin-1/2 systems, cond-math/0304595, 2003
A. Klümper, K. Sakai, J. Phys. A: Math. Gen. 35, 2173 (2002)
K. Saito, Europhys. Lett. 61, 34 (2003)
K. Saito, S. Takesue, S. Miyashita, Phys. Rev. E 54, 2404 (1996)
G. Lindblad, Commun. Math. Phys. 48, 119 (1976)
K. Saito, S. Miyashita, J. Phys. Soc. Jpn 71, 2485 (2002)
M. Michel, M. Hartmann, J. Gemmer, G. Mahler, Eur. Phys. J. B 34, 325 (2003)
R. Schack, M.C. Caves, J. Mod. Opt. 47(2/3), 387 (2000)
V.E. Tarasov, Phys. Rev. E 66, 056116 (2002)
S. Mukamel, Phys. Rev. E 68(2), 021111 (2003)
S. Nakajima, Prog. Theor. Phys. 20, 948 (1958)
R. Zwanzig, J. Chem. Phys. 33, 1338 (1960)
S. Miyashita, K. Saito, Physica B 329–333, 1142 (2003)
J. Gemmer, M. Michel, G. Mahler, Quantum Thermodynamics, LNP657 (Springer, Heidelberg, Berlin, 2005)
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Michel, M., Gemmer, J. & Mahler, G. Heat conductivity in small quantum systems: Kubo formula in Liouville space. Eur. Phys. J. B 42, 555–559 (2004). https://doi.org/10.1140/epjb/e2005-00014-x
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DOI: https://doi.org/10.1140/epjb/e2005-00014-x