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

Journal of the Physical Society of Japan

Husimi Function around Hyperbolic Point

Kin’ya Takahashi

Published Jun 15, 1986• 11 citations
Publisher

Abstract

Husimi functions for eigen states around a hyperbolic point are studied. Husimi functions for eigen states of wave forms with even and odd parity are strictly concerned with the hyperbolic point and the separatrix in classical limit (\(\hbar{\rightarrow}0\)), respectively. It is interesting that classical behavior is affected by quantum symmetry.

DOI
10.1143/jpsj.55.1783

Related papers

Eigenstate structures around a hyperbolic point

Stéphane Nonnenmacher, André Voros

Using coherent-state representations of quantum mechanics (Bargmann, Husimi, and stellar representations), we describe analytically the phase-space structure of the general eigenstates corresponding to a one-dimensional bilinear hyperbolic Hamiltonian, H = pq or equivalently . Their semiclassical behaviour is discussed for eigenvalues either near or away from the separatrix energy , especially in the phase-space vicinity of the saddle-point (q,p) = (0,0).

arXiv:chao-dyn/9609002•Journal of Physics A Mathematical and General•Jan 7, 1997•44 citations

Wigner and Husimi Functions in Quantum Mechanics

Kin’ya Takahashi

The quantum dynamics in Husimi representation is studied for the commutation relation, time development of distribution function and eigen distribution function. In the integrable system, the Husimi eigen distribution function is confined almost on the classical torus and can be approximated by Gaussian distribution with the variance \((\Delta\xi_{l})^{2}{\sim}\hbar/2\) around the torus. Further, considering the correspondence between quantum and classical mechanics, the Husimi distribution function is a better representation than the Wigner distribution function, because coarse graining is usually involved in observational process.

Journal of the Physical Society of Japan•Mar 15, 1986•130 citations

Wigner and Husimi functions in the double-well potential

Marcel Novaes

We present Wigner and Husimi functions for the stationary states of the quartic oscillator and the more general double-well potential, paying particular attention to the corresponding classical structure. We find that the qualitative behaviour of both these functions depends strongly on the height of the potential barrier, and that the Husimi function has vestiges of the classical trajectories even for states below this barrier. The zero-point energy is also seen to play an important role.

Journal of Optics B Quantum and Semiclassical Optics•Jun 1, 2003•13 citations

Quantum and classical aspects of deformation in the symmetric pairing model

Molina Santos, MARIA LUIZA CESCATO, K. Furuya +2 more

We examine the interesting physics for the Symmetric Pairing Model from the point of view of dynamical systems. The well known transition from spherical to deformed regime is shown to possess a classical analogue where we find a separatrix between the two regimes. The relevant wave functions are studied by means of Husimi distributions.

Physica Scripta•Apr 1, 1997•0 citations

Separatrix eigenfunctions

John R. Cary, Petre Rusu

Near-separatrix eigenfunctions for the double-well potential are analyzed. These functions are needed for the study of systems with perturbed or slowly varying double-well potentials. The probability density of separatrix eigenfunctions collapses to the classical result (a \ensuremath{\delta} function at the unstable fixed point) logarithmically with the number of quantum states. Matrix elements with respect to this basis are also studied. Unlike the wave functions, the unnormalized matrix elements are nonsingular in the limit of large quantum number.

Physical Review A•Jun 1, 1992•10 citations

Husimi representation for stationary states

John E. Harriman, Mark E. Casida

Abstract This paper considers a Husimi representation of quantum mechanics in which the (stationary) state of a system or ensemble is described by a Husimi function and an observable is described by a phase space function or distribution such that the expectation value of the observable is given by an integral over phase space of the product of that function or distribution and the Husimi function. The density matrix, Wigner function, and Husimi function are considered to be alternative ways of describing the state of a system or ensemble, and methods of recovering the Wigner function or density matrix from the Husimi function are discussed. The classical limits of the Wigner and Husimi functions and of the relationship between them are considered. © 1993 John Wiley & Sons, Inc.

International Journal of Quantum Chemistry•Jan 1, 1993•27 citations
Husimi functions for eigen states around a hyperbolic point are studied. Husimi functions for eigen states of wave forms with even and odd parity are strictly concerned with the hyperbolic point and the separatrix in classical limit ((\hbar{\rightarrow}0)), respectively. It is interesting that classical behavior is affected by quantum symmetry.
The quantum dynamics in Husimi representation is studied for the commutation relation, time development of distribution function and eigen distribution function. In the integrable system, the Husimi eigen distribution function is confined almost on the classical torus and can be approximated by Gaussian distribution with the variance (Δξl)2∼ℏ/2(\Delta\xi_{l})^{2}{\sim}\hbar/2(Δξl​)2∼ℏ/2 around the torus. Further, considering the correspondence between quantum and classical mechanics, the Husimi distribution function is a better representation than the Wigner distribution function, because coarse graining is usually involved in observational process.
Near-separatrix eigenfunctions for the double-well potential are analyzed. These functions are needed for the study of systems with perturbed or slowly varying double-well potentials. The probability density of separatrix eigenfunctions collapses to the classical result (a \ensuremath{\delta} function at the unstable fixed point) logarithmically with the number of quantum states. Matrix elements with respect to this basis are also studied. Unlike the wave functions, the unnormalized matrix elements are nonsingular in the limit of large quantum number.
Abstract This paper considers a Husimi representation of quantum mechanics in which the (stationary) state of a system or ensemble is described by a Husimi function and an observable is described by a phase space function or distribution such that the expectation value of the observable is given by an integral over phase space of the product of that function or distribution and the Husimi function. The density matrix, Wigner function, and Husimi function are considered to be alternative ways of describing the state of a system or ensemble, and methods of recovering the Wigner function or density matrix from the Husimi function are discussed. The classical limits of the Wigner and Husimi functions and of the relationship between them are considered. © 1993 John Wiley & Sons, Inc.