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Thermo Field Dynamics and Kinetic Coefficients of a Charged Boson Gas ∗

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Thermo Field Dynamics for inhomogeneous systems is generalized to quantum fields with a continuous single-particle mass spectrum. The modification of the hamiltonian in states with a local thermal Bogoliubov symmetry is used to calculate thermal conductivity and diffusion coefficient of pions interacting with hot, compressed nuclear matter. ∗ Work supported by GSI

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Cambridge University Press eBooks•Feb 19, 2009•0 citations
Thermo Field Dynamics for inhomogeneous systems is generalized to quantum fields with a continuous single-particle mass spectrum. The modification of the hamiltonian in states with a local thermal Bogoliubov symmetry is used to calculate thermal conductivity and diffusion coefficient of pions interacting with hot, compressed nuclear matter. ∗ Work supported by GSI
Basic equations of nonequilibrium thermo field dynamics of dense quantum systems are presented.A formulation of nonequilibrium thermo field dynamics has been performed using the nonequilibrium statistical operator method by D.N.Zubarev.Hydrodynamic equations have been obtained in thermo field representation.Two levels of the description of kinetics and hydrodynamics of a dense nuclear matter are considered.The first one is a quantum system with strongly coupled states, the second one is a quarkgluon plasma.Generalized transfer equations of a consistent description of kinetics and hydrodynamics have been obtained, as well as limiting cases are considered.
We present basic equations of nonequilibrium thermo field dynamics of dense quantum systems. A formulation of nonequilibrium thermo field dynamics has been performed using the nonequilibrium statistical operator method by D.N.Zubarev. Generalized transfer and hydrodynamic equations of a consistent description of kinetics and hydrodynamics have been obtained in thermo field representation. To demonstrate how obtained results do work at the description of kinetics and hydrodynamics of a dense nuclear matter we consider quantum system with strongly coupled states.
Thermal Bogoliubov transformation is an essential ingredient of the thermo field dynamics—the real time formalism in quantum field and many-body theories at finite temperatures developed by H. Umezawa and coworkers. The approach to study properties of hot nuclei which is based on the extension of the well-known Quasiparticle-Phonon Model to finite temperatures employing the TFD formalism is presented. A distinctive feature of the QPM-TFD combination is a possibility to go beyond the standard approximations like the thermal Hartree-Fock or the thermal RPA ones.
The thermal Bogoliubov transformation in thermo field dynamics is generalized in two respects. First, a generalization of the alpha\\alphaalpha--degree of freedom to tilde non--conserving representations is considered. Secondly, the usual 2times22\\times22times2 Bogoliubov matrix is extended to a 4times44\\times44times4 matrix including mixing of modes with non--trivial multiparticle correlations. The analysis is carried out for both bosons and fermions.
Making use of the thermo field dynamics (TFD) we formulate a calculable method for time-dependent nonequilibrium systems in a time representation (t-representation) rather than in the k0-Fourier representation. The corrected one-body propagator in the t-representation has the form of B−1 (diagonal matrix) B (B being a thermal Bogoliubov matrix). The number parameter in B here is the observed number (the Heisenberg number) with a fluctuation. With the usual definition of the on-shell self-energy a self-consistent renormalization condition leads to a kinetic equation for the number parameter. This equation turns out to be the Boltzmann equation, from which the entropy law follows.
In Chapter 6, we derived a generalized Gross–Pitaevskii condensate equation which is coupled to a kinetic equation for the distribution function for the thermal atoms. However, the kinetic equation in Chapter 6 is only valid in the semiclassical limit. It involves the assumption that the thermal energy k B T is much greater than the spacing between the harmonic trap energy levels ( k B T ≫ω 0 where ω 0 is the trap frequency) and also much greater than the average interaction energy ( k B T ≫ gn ). The ZNG model, based on HF excitations, is still expected to be adequate down to quite low temperatures in trapped Bose gases, as will be shown by the results in Chapter 12. However, the ZNG model will break down at very low temperatures, where the Hartree–Fock excitations must be replaced by the Bogoliubov spectrum. To deal with this, one has to derive a kinetic equation for the Bogoliubov quasiparticle excitations. This is the goal of the present chapter. In this chapter, we use the second-order Beliaev approximation to discuss the nonequilibrium dynamics of a trapped Bose-condensed gas at finite temperatures. In doing to, we combine the second-order Beliaev self-energies with the lower-order Bogoliubov excitation spectrum, including off-diagonal single-particle propagators but still omitting the anomalous correlation functions. This last condition defines the Bogoliubov–Popov approximation. In this chapter, we consider only the damping which arises from collisions. We will not explicitly calculate corrections that are second-order in g to the quasiparticle energy spectrum or to the condensate chemical potential, both of which are associated with the real parts of the second-order Beliaev self-energies. The present chapter is a natural generalization of work presented in Chapter 6 for the simpler HF excitation spectrum assumed in the ZNG analysis.