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

Physical Review A

Thermal quasiparticles with phase-space distribution

Michael R. Berman

Published Aug 1, 1989• 11 citations
Publisher

Abstract

A new Wigner phase-space distribution function is introduced for thermal quasiparticles currently in use in thermo field dynamics. The properties of this phase-space distribution are studied and compared with those of the corresponding zero-temperature distribution. Generalized uncertainty relations are implemented in order to study the explicit spreading in phase space as a function of temperature and quantum number of the thermal excitation, thereby permitting the investigation of quantum and thermal fluctuations.

DOI
10.1103/physreva.40.2057

Related papers

Wigner phase-space representation of thermal excitations

Michael R. Berman

The Wigner phase-space representation of thermal excitations used in thermo-field-dynamics (TFD) is investigated. The phase-space description is obtained by introducing a reduced density operator in which the fictitious degrees of freedom of TFD are traced over. A new closed-form expression for the Wigner function of the harmonic oscillator thermal excitation is derived, thereby showing that the thermal excitation may be described as a temperature-dependent radial spreading of the coordinates and momenta in phase space. The population distribution in these stationary excitations is determined and shown to reduce to a Boltzmann distribution for the thermal vacuum only.

Physical Review A•Aug 1, 1990•5 citations

Generalized Phase-Space Distribution Functions

Leon W. Cohen

A set of quasi-probability distribution functions which give the correct quantum mechanical marginal distributions of position and momentum is studied. The phase-space distribution does not have to be bilinear in the state function. The Wigner distribution is a special case. A general relationship between the phase-space distribution functions and the rule of associating classical quantities to quantum mechanical operators is derived. This allows the writing of correspondence rules at will,of which the ones presently known are particular cases. The dynamics and other properties of the generalized phase-space distribution are considered.

Journal of Mathematical Physics•May 1, 1966•1,105 citations

Proposal of a Computational Approach for Simulating Thermal Bosonic Fields in Phase Space

Alessandro Sergi, Roberto Grimaudo, Gabriel Hanna +1 more

When a quantum field is in contact with a thermal bath, the vacuum state of the field may be generalized to a thermal vacuum state, which takes into account the thermal noise. In thermo field dynamics, this is realized by doubling the dimensionality of the Fock space of the system. Interestingly, the representation of thermal noise by means of an augmented space is also found in a distinctly different approach based on the Wigner transform of both the field operators and density matrix, which we pursue here. Specifically, the thermal noise is introduced by augmenting the classical-like Wigner phase space by means of Nosé–Hoover chain thermostats, which can be readily simulated on a computer. In this paper, we illustrate how this may be achieved and discuss how non-equilibrium quantum thermal distributions of the field modes can be numerically simulated.

arXiv:1910.11642•Physics•Dec 3, 2019•4 citations

NEW APPROACH TO DERIVING THE THERMO-MINIMUM UNCERTAINTY STATES AND ITS WIGNER FUNCTION

Hong‐Chun Yuan, Xue-xiang Xu, Hong-Yi Fan

Based on our previous study [Mod. Phys. Lett. A18 (2003) 677] in which minimum uncertainty states for thermo-field dynamics were proposed, we use a new approach to derive the thermo-minimum uncertainty states via the relation of two-variable Hermite polynomial. In addition, the compact expression for its corresponding Wigner function is obtained analytically by using the Weyl-ordered invariance under the similar transformations, which seems a new result.

Modern Physics Letters B•Sep 17, 2010•1 citation

Spreading of a free wave packet

Hai-Woong Lee

The spreading of a free wave packet and its relation to classical and quantum dynamics are examined. The phase-space formulation using the Wigner distribution function provides a convenient representation in which each phase point of the distribution follows a classical trajectory and the spreading occurs as a result of classical dynamics. A different formulation using a different phase-space distribution function, however, does not allow this simple interpretation of the spreading.

American Journal of Physics•May 1, 1982•18 citations

Wigner function for number and phase

John A. Vaccaro, David Thomas Pegg

Various quasiprobability distributions have been developed in the past using the Hilbert space of the single-mode light field. The development of a quasiprobability distribution associated with a phase operator has previously been impossible because of the absence of a unique Hermitian phase operator defined on the Hilbert space. Recently, however, Pegg and Barnett [Europhys. Lett. 6, 483 (1988); Phys. Rev. A 39, 1665 (1989)] and Barnett and Pegg [J. Mod. Optics 36, 7 (1989)] introduced a new formalism that does allow the construction of a Hermitian phase operator and associated phase eigenstates. In this paper we develop a quasiprobability distribution associated with the number and phase operators of the single-mode light field in the new formalism. The new distribution, which we call the number-phase Wigner function, has properties analogous to the Wigner function. We also derive the number-phase Wigner representation of number states, phase states, general physical states, coherent states, and the squeezed vacuum. We find this new representation has features that are related to the number and phase properties of states. For example, the number-phase Wigner representation of a number state is nonzero only on a circle, while the representation of a phase state is only nonzero along a radial line.

Physical Review A•May 1, 1990•91 citations
A new Wigner phase-space distribution function is introduced for thermal quasiparticles currently in use in thermo field dynamics. The properties of this phase-space distribution are studied and compared with those of the corresponding zero-temperature distribution. Generalized uncertainty relations are implemented in order to study the explicit spreading in phase space as a function of temperature and quantum number of the thermal excitation, thereby permitting the investigation of quantum and thermal fluctuations.
The Wigner phase-space representation of thermal excitations used in thermo-field-dynamics (TFD) is investigated. The phase-space description is obtained by introducing a reduced density operator in which the fictitious degrees of freedom of TFD are traced over. A new closed-form expression for the Wigner function of the harmonic oscillator thermal excitation is derived, thereby showing that the thermal excitation may be described as a temperature-dependent radial spreading of the coordinates and momenta in phase space. The population distribution in these stationary excitations is determined and shown to reduce to a Boltzmann distribution for the thermal vacuum only.
A set of quasi-probability distribution functions which give the correct quantum mechanical marginal distributions of position and momentum is studied. The phase-space distribution does not have to be bilinear in the state function. The Wigner distribution is a special case. A general relationship between the phase-space distribution functions and the rule of associating classical quantities to quantum mechanical operators is derived. This allows the writing of correspondence rules at will,of which the ones presently known are particular cases. The dynamics and other properties of the generalized phase-space distribution are considered.
When a quantum field is in contact with a thermal bath, the vacuum state of the field may be generalized to a thermal vacuum state, which takes into account the thermal noise. In thermo field dynamics, this is realized by doubling the dimensionality of the Fock space of the system. Interestingly, the representation of thermal noise by means of an augmented space is also found in a distinctly different approach based on the Wigner transform of both the field operators and density matrix, which we pursue here. Specifically, the thermal noise is introduced by augmenting the classical-like Wigner phase space by means of Nosé–Hoover chain thermostats, which can be readily simulated on a computer. In this paper, we illustrate how this may be achieved and discuss how non-equilibrium quantum thermal distributions of the field modes can be numerically simulated.
Various quasiprobability distributions have been developed in the past using the Hilbert space of the single-mode light field. The development of a quasiprobability distribution associated with a phase operator has previously been impossible because of the absence of a unique Hermitian phase operator defined on the Hilbert space. Recently, however, Pegg and Barnett [Europhys. Lett. 6, 483 (1988); Phys. Rev. A 39, 1665 (1989)] and Barnett and Pegg [J. Mod. Optics 36, 7 (1989)] introduced a new formalism that does allow the construction of a Hermitian phase operator and associated phase eigenstates. In this paper we develop a quasiprobability distribution associated with the number and phase operators of the single-mode light field in the new formalism. The new distribution, which we call the number-phase Wigner function, has properties analogous to the Wigner function. We also derive the number-phase Wigner representation of number states, phase states, general physical states, coherent states, and the squeezed vacuum. We find this new representation has features that are related to the number and phase properties of states. For example, the number-phase Wigner representation of a number state is nonzero only on a circle, while the representation of a phase state is only nonzero along a radial line.