Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0809.1294 · International Journal of Modern Physics E

ON THE TFD TREATMENT OF COLLECTIVE VIBRATIONS IN HOT NUCLEI

ALAN A. DZHIOEV, A. I. VDOVIN

Published Aug 1, 2009• 20 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/s0218301309013695

Related papers

ON THE TFD TREATMENT OF COLLECTIVE VIBRATIONS IN HOT NUCLEI

Alan A. Dzhioev, A.I. Vdovin

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.

•Dec 4, 2012•13 citations

Thermal Bogoliubov transformation in nuclear structure theory

A. I. Vdovin, A. A. Dzhioev

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.

arXiv:1001.3607•Physics of Particles and Nuclei•Nov 25, 2010•3 citations

THE TFD TREATMENT OF THE QUASIPARTICLE-PHONON INTERACTION AT FINITE TEMPERATURE

Daniel S. Kosov, A.I. Vdovin

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.

Modern Physics Letters A•Jun 21, 1994•18 citations

Nuclear Many-Body Problem at Finite Temperature: A TFD Approach

Daniel S. Kosov, Vdovin, A. I., Jochen Wambach

Based on the formalism of thermo-field dynamics a new approach for studying collective excitations in hot finite Fermi systems is presented. Two approximations going beyond the thermal RPA namely renormalized thermal RPA and thermal second RPA are formulated.

arXiv:nucl-th/9710002•Oct 1, 1997•0 citations

On fermionic tilde conjugation rules and thermal bosonization. Hot and cold thermofields

S. É. Korenblit, V. V. Semenov

A generalization of Ojima tilde conjugation rules is suggested, which is useful for the thermofield bosonization. The notion of hot and cold thermofields is introduced to distinguish different thermofield representations giving the correct normal form of thermofield solution for finite temperature Thirring model with correct renormalization and anticommutation properties.

arXiv:1108.5392•Physics of Particles and Nuclei Letters•Dec 1, 2011•1 citation

QUANTUM GROUPS AND THERMO FIELD DYNAMICS

S. De Martino, Silvio De Siena, Giuseppe Vitiello

The algebraic structure of Thermo Field Dynamics for bosons can be fully incorporated in the q-deformation of the Weyl-Heisenberg algebra hq (1) . The doubling of the degrees of freedom, the set of the tilde-conjugation rules, the Bogoliubov transformation and its generator have a direct and simple interpretation in terms of operators and of properties of hq (1) . The notion of “thermal degree of freedom” introduced by Umezawa also finds a more specific formalization since the corresponding “thermal conjugate momentum” can be formally introduced, thus providing us with a set of canonical “thermal” variables.

International Journal of Modern Physics B•Jun 30, 1996•9 citations
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.
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 algebraic structure of Thermo Field Dynamics for bosons can be fully incorporated in the q-deformation of the Weyl-Heisenberg algebra hq (1) . The doubling of the degrees of freedom, the set of the tilde-conjugation rules, the Bogoliubov transformation and its generator have a direct and simple interpretation in terms of operators and of properties of hq (1) . The notion of “thermal degree of freedom” introduced by Umezawa also finds a more specific formalization since the corresponding “thermal conjugate momentum” can be formally introduced, thus providing us with a set of canonical “thermal” variables.