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arXiv:1001.3607 · Physics of Particles and Nuclei

Thermal Bogoliubov transformation in nuclear structure theory

A. I. Vdovin, A. A. Dzhioev

Published Nov 25, 2010• 3 citations
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Abstract

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.

DOI
10.1134/s1063779610070336

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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 coupling of elementary excitation modes in hot nuclei is studied. For this aim the quasiparticle-phonon nuclear model (QPM) is extended to a finite temperature by using the formalism of the thermofield dynamics. First the energies and structures of one-phonon states are calculated in the thermal random phase approximation and then the thermal QPM Hamiltonian HQPM is expressed in terms of thermal quasiparticles and thermal RPA-phonons. The equation for the energies taking into account mixing of one-and two-thermal phonon states is derived. The expression of the coupling matrix element between thermal phonons is given.
The approach in a theory of collective excitations in hot nuclei exploring the formalism of thermo field dynamics and the model Hamiltonian consisting of a mean field, the BCS paring interaction, and long-range particle–hole effective forces is reexamined. In contrast with earlier studies, it is found that a wave function of a thermal phonon is depended not only on the Fermi–Dirac thermal occupation numbers of the Bogoliubov quasiparticles consisting the phonon but also on the Bose thermal occupation numbers of the phonon. This strongly affects a thermal phonon coupling due to the renormalization of a phonon–phonon interaction and enlarging the number of thermal two-phonon configurations coupled with one-phonon ones. Moreover, it is shown that the formulation of the double tilde conjugation rule for fermions proposed by I. Ojima is more appropriate in the context of the present study than the original one by H. Umezawa and co-workers.
The approach in a theory of collective excitations in hot nuclei exploring the formalism of thermo field dynamics and the model Hamiltonian consisting of a mean field, the BCS paring interaction and long-range particle-hole effective forces is reexamined. In contrast with earlier studies it is found that a wave function of a thermal phonon is depended not only on the Fermi-Dirac thermal occupation numbers of Bogoliubov quasiparticles consisting the phonon but on the Bose thermal occupation numbers of the phonon as well. This strongly affects a thermal phonon couplings due to renormalizing of a phononphonon interaction and enlarging the number of thermal two-phonon configurations coupled with one-phonon ones. Moreover, it is shown that the formulation of the double tilde conjugation rule for fermions proposed by I. Ojima is more appropriate in the context of the present study than the original one by H. Umezawa and coworkers. 1.
Abstract We develop a wave‐function‐based method for the simulation of quantum dynamics of systems with many degrees of freedom at finite temperature. The method is inspired by the ideas of Thermo Field Dynamics (TFD). As TFD, our method is based on the doubling of the system's degrees of freedom and thermal Bogoliubov transformation. As distinct from TFD, our method implements the doubling of thermalized degrees of freedom only, and relies upon the explicitly constructed generalized thermal Bogoliubov transformation, which is not restricted to fermionic and bosonic degrees of freedom. This renders the present approach computationally efficient and applicable to a large variety of systems.
We present a comprehensive review of the most fundamental and practical aspects of thermo-field dynamics (TFD), including some of the most recent developments in the field. To make TFD fully consistent, some suitable changes in the structure of the thermal doublets and the Bogoliubov transformation matrices have been made. A close comparison between TFD and the Schwinger-Keldysh closed time path formalism (SKF) is presented. We find that TFD and SKF are in many ways the same in form; in particular, the two approaches are identical in stationary situations. However, TFD and SKF are quite different in time-dependent nonequilibrium situations. The main source of this difference is that the time evolution of the density matrix itself is ignored in SKF while in TFD it is replaced by a time-dependent Bogoliubov transformation. In this sense TFD is a better candidate for time-dependent quantum field theory. Even in equilibrium situations, TFD has some remarkable advantages over the Matsubara approach and SKF, the most notable being the Feynman diagram recipes, which we will present. We will show that the calculations of two-point functions are simplified, instead of being complicated, by the matrix nature of the formalism. We will present some explicit calculations using TFD, including space-time inhomogeneous situations and the vacuum polarization in equilibrium relativistic QED.