Abstract
We give a rigorous (Hamiltonian) treatment of a quantum system weakly coupled to an infinite free reservoir and subject to an external time-dependent driving potential varying on the scale of dissipation. The linear response of the system initially in thermal equilibrium is determined and compared with the usual expressions of linear response theory.
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References
R. Kubo,J. Phys. Soc. Japan 12:570 (1957).
R. Kubo, inLectures in Theoretical Physics (Boulder Summer Institute for Theoretical Physics, 1958) (Interscience, New York, 1959), Vol. 1, p. 120.
R. Balescu,Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1975).
J. L. Lebowitz, inStatistical Mechanics. New Concepts, New Problems, New Applications, S. A. Rice, K. F. Freed, and J. C. Light, eds. (The University of Chicago Press, 1972).
J. Naudt, A. Verbeure, and R. Weder,Comm. Math. Phys. 44:87 (1975).
A. Verbeure and R. Weder,Comm. Math. Phys. 44:101 (1975).
J. L. Lebowitz and A. Shimony,Phys. Rev. 128:1945 (1962).
E. B. Davies,Comm. Math. Phys. 39:91 (1974).
E. B. Davies,Math. Ann. 291:147 (1976).
H. Spohn and J. L. Lebowitz, inAdvances in Chemical Physics (Wiley, New York, to appear).
R. S. Phillips,Trans. Am. Math. Soc. 74:199 (1954).
K. Yosida,Functional Analysis (Springer, Berlin, 1965).
M. Born and V. Fock,Z. Physik 51:165 (1928).
T. Kato,J. Phys. Soc. Japan 5:435 (1950).
T. Kato,Perturbation Theory of Linear Operators (Springer, Berlin, 1966).
H. Spohn,Lett. Math. Phys. 2:33 (1977).
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Work partly supported by NSF grant no. MPS 75-11864-A04.
On leave of absence from Fachbereich Physik der Universität München. Work supported by a DFG fellowship.
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Davies, E.B., Spohn, H. Open quantum systems with time-dependent Hamiltonians and their linear response. J Stat Phys 19, 511–523 (1978). https://doi.org/10.1007/BF01011696
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DOI: https://doi.org/10.1007/BF01011696