Comparison among various expressions of complex admittance for quantum systems in contact with a heat reservoir.
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 relaxation method and 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, 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 turned out that the expression of the complex admittance obtained by using the relaxation method with the TC equation exactly coincides with that obtained by using the external-field method with the TC equation, while other two methods give different forms. It is also explicitly demonstrated that all the expressions of the complex admittance coincide with each other in the lowest Born approximation for the system-reservoir interaction. The formulas necessary for the higher-order expansions in powers of the system-reservoir interaction are derived, and also the expressions of the admittance in the nth order approximation are given. By transforming inverse-temperature integrals into time integrals, the admittances are also given in the formulas with time-integrals alone. To characterize the TC and TCL methods, we study the expressions of the admittances of two exactly solvable models. Each exact form of admittance is compared with the results of the two methods in the lowest Born approximation. It is found that depending on the model, either of TC and TCL would be the better method.
Saeki
Mizuhiko
M
Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyoku, Tokyo 113-0033, Japan.
Uchiyama
Chikako
C
Mori
Takashi
T
Miyashita
Seiji
S
D003198:Computer Simulation; D004735:Energy Transfer; D006358:Hot Temperature; D008956:Models, Chemical; D011789:Quantum Theory