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Progress of Theoretical Physics

Relation between Method of TCL Equation with External Terms and Relaxation Method : Quantal Bath Model : Condensed Matter and Statistical Physics

Mizuhiko Saeki

Published Mar 25, 1993• 0 citations
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Relation between Method of TCL Equation with External Terms and Relaxation Method: Quantal Bath Model

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The relation between the method of TCL equation with external driving terms and the relaxation method is discussed analytically in the quantal bath model. It is shown that the interference term in the former method gives the part of second order in powers of the system-bath interaction in the Kubo formula, and that the former method is simpler than the latter method. It is also shown that the relaxation method neglects the low temperature effects which are given by the first part of interference term, and that the relaxation method in the narrowing limit neglects the effects of the interference term completely. The general form of admittance for the case of decoupled initial condition is given by the method of TCL equation with external driving terms, and can be equal to that for the case of thermal equilibrium initial condition. The above facts are verified by applying to a quantal oscillator. Validity of the second-order perturbation calculations is discussed.

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Relation between TCLE Method and Relaxation Method. II

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A general form of admittance is derived using the relaxation method under thermal equilibrium initial conditions from a second-order TCL equation with no external driving terms. Its admittance is shown to include the two interference terms in the TCLE method (method of TCL equations with external driving terms). Effects of the first and second interference terms in the TCLE method are numerically discussed for a quantal spin (magnitude 1/2) interacting with a spin-like bath and with a boson-like bath, respectively. It is shown that the first interference term which represents effects of the initial correlation and which is neglected in the relaxation method under decoupled initial conditions of the spin and bath, produces the effects which enhance the peaks of line shapes slightly and which abase the line shapes at the small frequency region, and becomes larger as the characteristic frequency of the heat bath becomes smaller.

Journal of the Physical Society of Japan•Dec 15, 1999•7 citations
The relation between the method of TCL equation with external driving terms and the relaxation method is discussed analytically in the quantal bath model. It is shown that the interference term in the former method gives the part of second order in powers of the system-bath interaction in the Kubo formula, and that the former method is simpler than the latter method. It is also shown that the relaxation method neglects the low temperature effects which are given by the first part of interference term, and that the relaxation method in the narrowing limit neglects the effects of the interference term completely. The general form of admittance for the case of decoupled initial condition is given by the method of TCL equation with external driving terms, and can be equal to that for the case of thermal equilibrium initial condition. The above facts are verified by applying to a quantal oscillator. Validity of the second-order perturbation calculations is discussed.
The relation between the method of TCL equation with external driving terms and the relaxation method is discussed analytically in the quantal bath model. It is shown that the interference term in the former method gives the part of second order in powers of the system-bath interaction in the Kubo formula, and that the former method is simpler than the latter method. It is also shown that the relaxation method neglects the low temperature effects which are given by the first part of interference term, and that the relaxation method in the narrowing limit neglects the effects of the interference term completely. The general form of admittance for the case of decoupled initial condition is given by the method of TCL equation with external driving terms, and can be equal to that for the case of thermal equilibrium initial condition. The above facts are verified by applying to a quantal oscillator. Validity of the second-order perturbation calculations is discussed.
A general form of admittance is derived using the relaxation method under thermal equilibrium initial conditions from a second-order TCL equation with no external driving terms. Its admittance is shown to include the two interference terms in the TCLE method (method of TCL equations with external driving terms). Effects of the first and second interference terms in the TCLE method are numerically discussed for a quantal spin (magnitude 1/2) interacting with a spin-like bath and with a boson-like bath, respectively. It is shown that the first interference term which represents effects of the initial correlation and which is neglected in the relaxation method under decoupled initial conditions of the spin and bath, produces the effects which enhance the peaks of line shapes slightly and which abase the line shapes at the small frequency region, and becomes larger as the characteristic frequency of the heat bath becomes smaller.