| Comparison among Various Expressions of Complex Admittance for Quantum System in Contact with Heat Reservoir (2009) | |||||||||
Abstract | |||||||||
| Relation among various expressions of the complex admittance for quantum systems in contact with heat reservoir is studied. Exact expressions of the complex admittance are derived in various types of formulations of equations of motion under contact with heat reservoir. Namely, the complex admittance is studied in the so-called relaxation method and also the external-field method. In the former method, the admittance is calculated using the Kubo formula for quantum systems in contact with heat reservoir in no external driving fields, while in the latter method the admittance is directly calculated from equations of motion with external driving terms. In each method, the cases of two types of equation of motions are considered, i.e., the time-convolution (TC) equation and time-convolutionless (TCL) equation. That is, the full of the four cases are studied. It is shown that the expression of the complex admittance obtained using the relaxation method with the TC equation coincides exactly with that obtained using the external-field method with the TC equation. It is also shown that all the expressions of the complex admittance coincide with each other in the lowest Born approximation for the system-reservoir interaction. The formulae necessary for the higher order expansions in powers of the system-reservoir interaction are derived, and also the expressions of the admittance in the $n$-th order approximation are given. By transforming inverse-temperature-integrals into time-integrals, the admittances are also given in the formulae with time-integrals alone.. Comment: 29pages, no figure | |||||||||
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