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 Physics A Mathematical and General

Multidimensional generalized coherent states

Marcel Novaes, Jean‐Pierre Gazeau

Published Dec 12, 2002• 45 citations
Publisher

Abstract

Generalized coherent states were presented recently for systems with one degree of freedom having discrete and/or continuous spectra. We extend that definition to systems with several degrees of freedom, give some examples and apply the formalism to the model of two-dimensional fermion gas in a constant magnetic field.
DOI
10.1088/0305-4470/36/1/313

Related papers

Coherent states for systems with discrete and continuous spectrum

Jean‐Pierre Gazeau, John R. Klauder

For a system with one degree of freedom, coherent states that are parametrized by classical canonical action-angle variables are introduced. These states also possess continuity of labelling, a resolution of unity, and temporal stability. The insistence on canonical action-angle variables strongly restricts any remaining arbitrariness in the coherent state definition. Such states are introduced for semibounded Hamiltonian operators having either a discrete or a continuous spectrum. Hamiltonians that have both discrete and continuous parts in their spectrum are also discussed.

Journal of Physics A Mathematical and General•Jan 1, 1999•335 citations

Coherent states for a system of an electron moving in a plane: case of discrete spectrum

Isiaka Aremua, Laure Gouba

Abstract In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and continuous spectra. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space appropriate for building the related coherent states. These latter are achieved in the context where we consider both spectra purely discrete obeying the criteria that a family of coherent states must satisfy.

arXiv:2108.09765•Journal of Physics Communications•Dec 1, 2021•2 citations

Degenerate discrete energy spectra and associated coherent states

L. Dello Sbarba, Véronique Hussin

Generalized and Gaussian coherent states constructed for quantum system with degeneracies in the energy spectrum are compared with respect to some minimal definitions and fundamental properties they have to satisfy. The generalized coherent states must be eigenstates of a certain annihilation operator that has to be properly defined in the presence of degeneracies. The Gaussian coherent states are, in the particular harmonic oscillator case, an approximation of the generalized coherent states and so the localizability in phase space of the particle in those states is very good. For other quantum systems, this last property serves as a definition of those Gaussian coherent states. The example of a particle in a two-dimensional square box is thus revisited having in mind the preceding definitions of generalized and Gaussian coherent states and also the preservation of the important property known as the resolution of the identity operator.

Journal of Mathematical Physics•Jan 1, 2007•15 citations

A characterization of coherent states from varying Planck's constant

J. C. Houard

For a quantum system with one degree of freedom we introduce some families of stats depending on the Planck's constant, that we call «classical states». We show that a definite class of these families allows to characterize the coherent states

Annales De L Institut Henri Poincare-physique Theorique•Jan 1, 1992•0 citations

Coherent states in a finite-dimensional Hilbert space

Adam Miranowicz, K. Pia̧tek, R. Tanaś

We construct, according to Glauber's definition, the coherent states in a univocally specified finite-dimensional Hilbert space. Their analytical form is obtained as an analytical solution of the problem raised by Bu\ifmmode \check{z}\else \v{z}\fi{}ek et al. [Phys. Rev. A 45, 8079 (1992)]. The phase properties of the coherent states are studied within the Pegg-Barnett formalism.

Physical Review A•Oct 1, 1994•50 citations

Continuum Limits of Quantum Lattice Systems

Tobias J. Osborne

We describe a general procedure to give effective continuous descriptions of quantum lattice systems in terms of quantum fields. There are two key novelties of our method: firstly, it is framed in the hamiltonian setting and applies equally to distinguishable quantum spins, bosons, and fermions and, secondly, it works for arbitrary variational tensor network states and can easily produce computable non-gaussian quantum field states. Our construction extends the mean-field fluctuation formalism of Hepp and Lieb (developed later by Verbeure and coworkers) to identify emergent continuous large-scale degrees of freedom - the continuous degrees of freedom are not identified beforehand. We apply the construction to to tensor network states, including, matrix product states and projected entangled-pair states, where we recover their recently introduced continuous counterparts, and also for tree tensor networks and the multi-scale entanglement renormalisation ansatz. Finally, extending the continuum limit to include dynamics we obtain a strict light cone for the propagation of information.

arXiv:1901.06124•Jan 18, 2019•9 citations
For a system with one degree of freedom, coherent states that are parametrized by classical canonical action-angle variables are introduced. These states also possess continuity of labelling, a resolution of unity, and temporal stability. The insistence on canonical action-angle variables strongly restricts any remaining arbitrariness in the coherent state definition. Such states are introduced for semibounded Hamiltonian operators having either a discrete or a continuous spectrum. Hamiltonians that have both discrete and continuous parts in their spectrum are also discussed.
Abstract In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and continuous spectra. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space appropriate for building the related coherent states. These latter are achieved in the context where we consider both spectra purely discrete obeying the criteria that a family of coherent states must satisfy.
Generalized and Gaussian coherent states constructed for quantum system with degeneracies in the energy spectrum are compared with respect to some minimal definitions and fundamental properties they have to satisfy. The generalized coherent states must be eigenstates of a certain annihilation operator that has to be properly defined in the presence of degeneracies. The Gaussian coherent states are, in the particular harmonic oscillator case, an approximation of the generalized coherent states and so the localizability in phase space of the particle in those states is very good. For other quantum systems, this last property serves as a definition of those Gaussian coherent states. The example of a particle in a two-dimensional square box is thus revisited having in mind the preceding definitions of generalized and Gaussian coherent states and also the preservation of the important property known as the resolution of the identity operator.
We describe a general procedure to give effective continuous descriptions of quantum lattice systems in terms of quantum fields. There are two key novelties of our method: firstly, it is framed in the hamiltonian setting and applies equally to distinguishable quantum spins, bosons, and fermions and, secondly, it works for arbitrary variational tensor network states and can easily produce computable non-gaussian quantum field states. Our construction extends the mean-field fluctuation formalism of Hepp and Lieb (developed later by Verbeure and coworkers) to identify emergent continuous large-scale degrees of freedom - the continuous degrees of freedom are not identified beforehand. We apply the construction to to tensor network states, including, matrix product states and projected entangled-pair states, where we recover their recently introduced continuous counterparts, and also for tree tensor networks and the multi-scale entanglement renormalisation ansatz. Finally, extending the continuum limit to include dynamics we obtain a strict light cone for the propagation of information.