Terms Of Thermo-field Dynamics Research Articles

Relaxation method and TCLE method of linear response in terms of thermo-field dynamics

The general formulae of the dynamic susceptibility are derived using the relaxation method and the TCLE method for the linear response by introducing the renormalized hat-operator in terms of thermo-field dynamics (TFD). In the former method, the Kubo formula is calculated for systems with no external driving fields, while in the latter method the admittance is directly calculated from time-convolutionless equations with external driving terms. The relation between the two methods is analytically investigated, and also the fluctuation–dissipation theorem is examined for the two methods in terms of TFD. The TCLE method is applied to an interacting spin system, and a formula of the transverse magnetic susceptibility is derived for such a system. The transverse magnetic susceptibility of an interacting spin system with S=1/2 spins is obtained up to the first order in powers of the spin–spin interaction.

Linear Response in an Interacting Boson System

The TCLE method (a method in which the admittance of a system is directly calculated from time-convolutionless equations with external driving terms) formulated in terms of thermo-field dynamics, is applied to a boson system interacting with its surroundings, referred to as the “heat reservoir”, and with an external driving field. For a boson system interacting with its heat reservoir, the fluctuation-dissipation theorem, a dispersion relation, and sum rules are studied through application of the TCLE method. The effects of the interference between the external driving field and the heat reservoir, which give the effects of the initial correlation and memory, as well as the effects of the boson-boson interaction, are numerically investigated for a non-degenerate boson system interacting with its heat reservoir, up to first order in powers of the boson-boson interaction.

A Quantum Field Theoretical Approach to the TCLE Method

In the context of non-equilibrium statistical mechanics, the TCLE method (a method in which the admittance of a system is directly calculated from time-convolutionless equations with external driving terms) for the linear response, is formulated in terms of thermo-field dynamics and in this way, thermo-field dynamics is generalized to the case of a quantal system interacting with its surroundings and with an external driving field. It is applied to interacting boson systems, and an admittance formula for such systems is derived using the TCLE method.

A derivation of the laser master equation in terms of thermo field dynamics

A laser master equation is derived by introducing an appropriate relaxation operator which takes into account correctly the semi-classical part of laser evolution. The introduction of the relaxation operator is done systematically by making use of the general procedure of non-equilibrium thermo field dynamics (NETFD). Elimination of the atom system is performed up to second order with respect to the quantum fluctuation of the electric field (i.e., spontaneous emission of photons).

Spin relaxation in terms of thermo field dynamics

An axiomatic formulation of the thermo field dynamics (TFD) for spin systems is performed, and is applied to the relaxation process of single spin-12. The spin relaxation accompanied with a change of symmetry of the system is also investigated. The time evolution of an order parameter is obtained within the semi-free approximation.