We present a dequantization procedure based on a variational approach whereby quantum fluctuations latent in the quantum momentum are suppressed. This is done by adding generic local deformations to the quantum momentum operator which give rise to a deformed kinetic term quantifying the amount of ``fuzzyness'' caused by such fluctuations. Considered as a functional of such deformations, the deformed kinetic term is shown to possess a unique minimum which is seen to be the classical kinetic energy. Furthermore, we show that extremization of the associated deformed action functional introduces an essential nonlinearity to the resulting field equations which are seen to be the classical Hamilton-Jacobi and continuity equations. Thus, a variational procedure determines the particular deformation that has the effect of suppressing the quantum fluctuations, resulting in dequantization of the system.We present a dequantization procedure based on a variational approach whereby quantum fluctuations latent in the quantum momentum are suppressed. This is done by adding generic local deformations to the quantum momentum operator which give rise to a deformed kinetic term quantifying the amount of ``fuzzyness'' caused by such fluctuations. Considered as a functional of such deformations, the deformed kinetic term is shown to possess a unique minimum which is seen to be the classical kinetic energy. Furthermore, we show that extremization of the associated deformed action functional introduces an essential nonlinearity to the resulting field equations which are seen to be the classical Hamilton-Jacobi and continuity equations. Thus, a variational procedure determines the particular deformation that has the effect of suppressing the quantum fluctuations, resulting in dequantization of the system.

arXiv:quant-ph/0511068Journal of Physics A Mathematical and GeneralMar 22, 200612 citations

Kinetic equations for quantum information

Bi Qiao, X.S. Xing, Harry E. Ruda

Physica A Statistical Mechanics and its ApplicationsMar 22, 20057 citations

Kinetic Energy of a Trapped Fermi Gas at Finite Temperature

Jacek Grela, Satya N. Majumdar, Grégory Schehr

We study the statistics of the kinetic (or, equivalently, potential) energy for N noninteracting fermions in a 1d harmonic trap of frequency ω at finite temperature T. Remarkably, we find an exact solution for the full distribution of the kinetic energy, at any temperature T and for any N, using a nontrivial mapping to an integrable Calogero-Moser-Sutherland model. As a function of temperature T and for large N, we identify (i) a quantum regime, for T∼ℏω, where quantum fluctuations dominate and (ii) a thermal regime, for T∼Nℏω, governed by thermal fluctuations. We show how the mean and the variance as well as the large deviation function associated with the distribution of the kinetic energy cross over from the quantum to the thermal regime as T increases.We study the statistics of the kinetic (or, equivalently, potential) energy for N noninteracting fermions in a 1d harmonic trap of frequency ω at finite temperature T. Remarkably, we find an exact solution for the full distribution of the kinetic energy, at any temperature T and for any N, using a nontrivial mapping to an integrable Calogero-Moser-Sutherland model. As a function of temperature T and for large N, we identify (i) a quantum regime, for T∼ℏω, where quantum fluctuations dominate and (ii) a thermal regime, for T∼Nℏω, governed by thermal fluctuations. We show how the mean and the variance as well as the large deviation function associated with the distribution of the kinetic energy cross over from the quantum to the thermal regime as T increases.

arXiv:1704.01628Physical Review LettersSep 26, 201716 citations

Information Theory and Quantum Wave Functions

N. Canosa, R. Rossignoli, Angelo Plastino

Springer eBooksJan 1, 19921 citation

Momentum flux density, kinetic energy density, and their fluctuations for one-dimensional confined gases of noninteracting fermions

Anna Minguzzi, Patrizia Vignolo, Monica Tosi

We present a Green's-function method for the evaluation of the particle density profile and of the higher moments of the one-body density matrix in mesoscopic systems containing a large number N of Fermi particles moving independently on a line under an external potential. The usefulness of the method is illustrated by applications to a Fermi gas confined in a harmonic potential well, for which we evaluate the momentum flux density, entering the equations of generalized hydrodynamics, and the kinetic energy density, which is relevant to the density-functional theory. As a further application of the method we explicitly display the quantum mean square fluctuations of these quantities. We also study some properties of the kinetic energy functional ${E}_{\mathrm{kin}}[n(x)]$ in the same system. Whereas a local approximation to the kinetic energy density is demonstrably wrong, an exact single-valued relationship between the density derivative of ${E}_{\mathrm{kin}}[n(x)]$ and the particle density $n(x)$ is demonstrated and evaluated for various values of the number of particles in the system.We present a Green's-function method for the evaluation of the particle density profile and of the higher moments of the one-body density matrix in mesoscopic systems containing a large number N of Fermi particles moving independently on a line under an external potential. The usefulness of the method is illustrated by applications to a Fermi gas confined in a harmonic potential well, for which we evaluate the momentum flux density, entering the equations of generalized hydrodynamics, and the kinetic energy density, which is relevant to the density-functional theory. As a further application of the method we explicitly display the quantum mean square fluctuations of these quantities. We also study some properties of the kinetic energy functional ${E}_{\mathrm{kin}}[n(x)]$ in the same system. Whereas a local approximation to the kinetic energy density is demonstrably wrong, an exact single-valued relationship between the density derivative of ${E}_{\mathrm{kin}}[n(x)]$ and the particle density $n(x)$ is demonstrated and evaluated for various values of the number of particles in the system.

arXiv:cond-mat/0011331Physical Review AMay 9, 200110 citations

{E}_{\mathrm{kin}}[n(x)]

in the same system. Whereas a local approximation to the kinetic energy density is demonstrably wrong, an exact single-valued relationship between the density derivative of

{E}_{\mathrm{kin}}[n(x)]

and the particle density

n(x)

is demonstrated and evaluated for various values of the number of particles in the system.