Analyzing the dependence of finite-fold approximations of the harmonic oscillator equilibrium density matrix and of the Wigner function on the quantization prescription

2015 ◽  
Vol 184 (1) ◽  
pp. 986-995 ◽  
Author(s):  
L. A. Borisov ◽  
Yu. N. Orlov
Keyword(s):  
Density Matrix ◽  
Harmonic Oscillator ◽  
Wigner Function ◽  
Equilibrium Density

SOME FEATURES OF SQUEEZED NEGATIVE BINOMIAL STATE

1992 ◽  
Vol 06 (03n04) ◽  
pp. 409-415 ◽  
Author(s):  
AMITABH JOSHI ◽  
S. V. LAWANDE
Keyword(s):  
Electromagnetic Field ◽  
Density Matrix ◽  
Wigner Function ◽  
Negative Binomial ◽  
Thermal State ◽  
Photon Number ◽  
Binomial State ◽  
Relationship Of ◽  
The Relationship ◽  
Photon Number Distribution

Properties of electromagnetic field in the squeezed negative binomial state are investigated in terms of photon number distribution and Wigner function. The relationship of the density matrix of the squeezed negative binomial state to the density matrix of the squeezed thermal state is shown explicitly. The possibility of generation of the negative binomial state is also discussed.

scholarly journals Equilibrium Wigner Function for Fermions and Bosons in the Case of a General Energy Dispersion Relation

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1023
Author(s):  
Vito Dario Camiola ◽  
Liliana Luca ◽  
Vittorio Romano
Keyword(s):  
Wigner Function ◽  
Natural Generalization ◽  
Bloch Equation ◽  
Equilibrium Density ◽  
Diagonal Form ◽  
Energy Dispersion ◽  
Unitary Evolution ◽  
Von Neumann ◽  
General Energy

The approach based on the Wigner function is considered as a viable model of quantum transport which allows, in analogy with the semiclassical Boltzmann equation, to restore a description in the phase-space. A crucial point is the determination of the Wigner function at the equilibrium which stems from the equilibrium density function. The latter is obtained by a constrained maximization of the entropy whose formulation in a quantum context is a controversial issue. The standard expression due to Von Neumann, although it looks a natural generalization of the classical Boltzmann one, presents two important drawbacks: it is conserved under unitary evolution time operators, and therefore cannot take into account irreversibility; it does not include neither the Bose nor the Fermi statistics. Recently a diagonal form of the quantum entropy, which incorporates also the correct statistics, has been proposed in Snoke et al. (2012) and Polkovnikov (2011). Here, by adopting such a form of entropy, with an approach based on the Bloch equation, the general condition that must be satisfied by the equilibrium Wigner function is obtained for general energy dispersion relations, both for fermions and bosons. Exact solutions are found in particular cases. They represent a modulation of the solution in the non degenerate situation.

scholarly journals Extended Wigner function for the harmonic oscillator in the phase space

2020 ◽  
Vol 19 ◽  
pp. 103546
Author(s):  
E.E. Perepelkin ◽  
B.I. Sadovnikov ◽  
N.G. Inozemtseva ◽  
E.V. Burlakov
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Wigner Function

PATH INTEGRAL DERIVATION OF AN EXACT MASTER EQUATION

1995 ◽  
Vol 09 (02) ◽  
pp. 87-94 ◽  
Author(s):  
S. V. LAWANDE ◽  
Q. V. LAWANDE
Keyword(s):  
Density Matrix ◽  
Harmonic Oscillator ◽  
Master Equation ◽  
Path Integral ◽  
Open System ◽  
Coherent States ◽  
Reduced Density Matrix ◽  
Feynman Propagator ◽  
Reduced Density

The Feynman propagator in coherent states representation is obtained for a system of a single harmonic oscillator coupled to a reservoir of N oscillators. Using this propagator, an exact master equation is obtained for the evolution of the reduced density matrix for the open system of the oscillator.

On the generalization of moyal equation for an arbitrary linear quantization

2021 ◽  
Vol 24 (01) ◽  
pp. 2150003
Author(s):  
Leonid A. Borisov ◽  
Yuriy N. Orlov
Keyword(s):  
Characteristic Function ◽  
Harmonic Oscillator ◽  
Linear Combination ◽  
Stationary Solution ◽  
Wigner Function ◽  
Inverse Operator ◽  
Stationary Solutions ◽  
Weyl Quantization ◽  
Quantization Rule ◽  
Arbitrary Linear Combination

For an arbitrary linear combination of quantizations, the kernel of the inverse operator is constructed. An equation for the evolution of the Wigner function for an arbitrary linear quantization is derived and it is shown that only for Weyl quantization this equation does not contain a source of quasi-probability. Stationary solutions for the Wigner function of a harmonic oscillator are constructed, depending on the characteristic function of the quantization rule. In the general case of Hermitian linear quantization these solutions are real but not positive. We found the representation of Weyl quantization in the form of the limit of a sequence of linear Hermitian quantizations, such that for each element of this sequence the stationary solution of the Moyal equation is positive.

Sign in / Sign up

Export Citation Format

Share Document