Showing papers on "Coherent states in mathematical physics published in 1998"
TL;DR: In this paper, a careful study of the physical properties of a family of coherent states on the circle, introduced some years ago by de Bievre and Gonzalez (in 1992 Semiclassical behaviour of the Weyl correspondence on the Circle Group Theoretical Methods in Physics vol I (Madrid: Ciemat)), is carried out.
Abstract: A careful study of the physical properties of a family of coherent states on the circle, introduced some years ago by de Bievre and Gonzalez (in 1992 Semiclassical behaviour of the Weyl correspondence on the circle Group Theoretical Methods in Physics vol I (Madrid: Ciemat)), is carried out. They were obtained from the Weyl-Heisenberg coherent states in by means of the Weil-Brezin-Zak transformation, they are labelled by the points of the cylinder , and they provide a realization of by entire functions (similar to the well known Fock-Bargmann construction). In particular, we compute the expectation values of the position and momentum operators on the circle and we discuss the Heisenberg uncertainty relation.
96 citations
TL;DR: In this article, the authors give an explicit construction of coherent states for an arbitrary irreducible representation and construct the symplectic structure on the manifold of coherent state, find canonical variables and discuss various classical limits of quantum-mechanical systems with relevant observables that obey commutation relations.
Abstract: We give an explicit construction of the coherent states for an arbitrary irreducible representation. We also construct the symplectic structure on the manifold of coherent states, find canonical variables and discuss various classical limits of quantum-mechanical systems with relevant observables that obey commutation relations.
54 citations
TL;DR: In this paper, the authors define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q-functions), which fulfils the axioms of a metric and satisfies the following semiclassical property: the distance between two coherent states is equal to the Euclidean distance between correspondences in the classical phase space.
Abstract: We define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q-functions). This quantity fulfils the axioms of a metric and satisfies the following semiclassical property: the distance between two coherent states is equal to the Euclidean distance between corresponding points in the classical phase space. We compute analytically distances between certain states (coherent, squeezed, Fock and thermal) and discuss a scheme for numerical computation of Monge distance for two arbitrary quantum states.
51 citations
TL;DR: In this article, a generalization of the square integrability theorem for unitary irreducible representations of locally compact groups is presented, which covers the case of representations admitting vector coherent states, and is illustrated by an example drawn from the isochronous Galilei group.
Abstract: We derive a generalization of the well-known theorem for the square integrability of a unitary irreducible representation of a locally compact group. The generalization covers the case of representations admitting vector coherent states. The result is illustrated by an example drawn from the isochronous Galilei group. The construction yields a wide variety of coherent states, labeled by phase space points, which satisfy a resolution of the identity condition, and incorporate spin degrees of freedom.
32 citations
TL;DR: In this article, a specific basis of Fock states was constructed by including a real (continuous) parameter in the generators of the Heisenberg algebra, which formed new bases with respect to harmonic oscillator-like developments.
22 citations
TL;DR: In this paper, a classical limit based on the harmonic-oscillator coherent-state classical limit is developed and applied to the Po ̈schl-Teller minimum-uncertainty states.
Abstract: Coherent states in the harmonic oscillator may be defined in several equivalent ways. One definition describes coherent states as special states satisfying a minimum-uncertainty requirement in position and momentum spaces. This definition is generalized for other potentials according to a method developed by Nieto et al. @Phys. Rev. D20, 1321~1979!# and is herein applied to the Po ̈schl-Teller potential. A classical limit based on the harmonic-oscillator coherent-state classical limit is then developed and applied to the Po ̈schl-Teller minimum-uncertainty states. In this limit, classical behavior may be obtained from these quantum states. Together with a completeness argument for the generalized coherent states, this result provides insight into quantum classical correspondence through the statistical interpretation of quantum mechanics. @S1050-2947 ~98!05001-X#
19 citations
TL;DR: In this article, a harmonic oscillator in a finite-dimensional Hilbert space spanned by orthogonal polynomials of a discrete variable was considered and coherent states as well as even and odd coherent states of this oscillator were examined.
Abstract: We have considered a harmonic oscillator in a finite-dimensional Hilbert space spanned by orthogonal polynomials of a discrete variable and constructed coherent states as well as even and odd coherent states of this oscillator. Various properties such as squeezing and antibunching of these states have also been examined.
17 citations
TL;DR: In this paper, the authors show that coherent states are the only quantum states that recover the harmonic oscillator classical motion in a single-mode cavity with ordinary one-photon losses.
Abstract: Coherent states are the only quantum states that recover the harmonic oscillator classical motion. However, rather than being deduced as the classical limit of the theory, coherent states were introduced into physics in a different context and then found to have properties that we can identify with our familiar classical experience. If classicality is really brought about by decoherence, coherent states should emerge naturally as the unique privileged states selected by the interaction with the environment. This is shown explicitly here, for the field in a single-mode cavity with ordinary one-photon losses, by calculating them directly as the only pure state solutions of the master equation at zero temperature.
10 citations
9 citations
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TL;DR: Coherent states for general systems with discrete spectrum, such as the bound states of the hydrogen atom, are discussed in this paper, where the states in question satisfy continuity of labeling, resolution of unity, temporal stability, and an action identity.
Abstract: Coherent states for general systems with discrete spectrum, such as the bound states of the hydrogen atom, are discussed The states in question satisfy: (1) continuity of labeling, (2) resolution of unity, (3) temporal stability, and (4) an action identity This set of reasonable physical requirements uniquely specify coherent states for the (bound state portion of the) hydrogen atom
7 citations
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TL;DR: In this article, the introduction of constraints is both natural and economical in coherent state path integrals involving only the dynamical and Lagrange multiplier variables, and a preliminary indication of how these procedures may possibly be applied to quantum gravity is briefly discussed.
Abstract: Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time regularization that may involve a Wiener measure concentrated on continuous phase space paths. The introduction of constraints is both natural and economical in coherent state path integrals involving only the dynamical and Lagrange multiplier variables. A preliminary indication of how these procedures may possibly be applied to quantum gravity is briefly discussed.
TL;DR: In this paper, a new version of integration of time-adapted processes with respect to creation, annihilation and conservation processes on the full Fock space is presented, which is both simpler and more general than the known ones.
Abstract: We present a new version of integration of time-adapted processes with respect to creation, annihilation and conservation processes on the full Fock space. Among the new features, in the first place, there is a new formulation of adaptedness which is both simpler and more general than the known ones. The new adaptedness allows for processes which are not restricted to be elements of some norm closure of the ∗-algebra which is generated by the basic creation processes.
11 Mar 1998
TL;DR: In this article, the SU(1,1)-like and SU(2)-like two-photon coherent states can be combined to form a O(3, 2)-like 2D coherent state.
Abstract: It is shown that the SU(1,1)-like and SU(2)-like two-photon coherent states can be combined to form a O(3,2)-like two-photon state. Since the O(3,2) group has many subgroups, there are also many new interesting new coherent and squeezed two-photon states. Among them is the two-photon sheared state whose symmetry property is like that for the two-dimensional Euclidean group. There are now two-phonon coherent states which may exhibit symmetries not yet observed for photons, including sheared states. Let us note that both SU(1,1) and S(3,2) are isomorphic to the symplectic groups Sp(2) and Sp(4) respectively, and that symplectic transformations consist of rotations and squeeze transformations.
TL;DR: A two-parameter correlated negative binomial state is constructed and analyzed from the point of view of quantum optics theory in two-mode Fock space in this article, which can be identified as a type of correlated SU (1, 1) coherent state.
Abstract: A kind of two-parameter correlated negative binomial state is constructed and analysed from the point of view of quantum optics theory in two-mode Fock space. By choosing a suitable two-mode correlated Holstein-Primakoff-analogue transformation, the state can be identified as a type of correlated SU (1, 1) coherent state. The possible physical uses of the state are also pointed out.
TL;DR: In this paper, coherent states are used as a time-dependent variational ansatz for a semiclassical treatment of the dynamics of anharmonic quantum oscillators, and the square variance of the Hamiltonian within coherent states is of particular interest.
Abstract: We use coherent states as a time-dependent variational ansatz for a semiclassical treatment of the dynamics of anharmonic quantum oscillators. In this approach the square variance of the Hamiltonian within coherent states is of particular interest. This quantity turns out to have natural interpretation with respect to time-dependent solutions of the semiclassical equations of motion. Moreover, our approach allows for an estimate of the decoherence time of a classical object due to quantum fluctuations. We illustrate our findings at the example of the Toda chain.
TL;DR: In this paper, an isomorphism between the space free coherent states and the space of distributions on a p-adic disk is constructed for a system with p degrees of freedom.
Abstract: Free coherent states for a system with p degrees of freedom are defined. An isomorphism between the space free coherent states and the space of distributions on p-adic disk is constructed.
TL;DR: In this paper, possible modifications of the Calogero-Vasiliev quantum condition are considered and the problem of constructing coherent states is addressed, and a solution to the problem is given.
Abstract: We consider possible modifications of the Calogero–Vasiliev quantum condition and address the problem of construction of coherent states.
TL;DR: In this paper, a set of generalized coherent states as eigenstates of the annihilation operator is proposed, which admit a resolution of identity with positive measure, guided by the classical action angle transformation and the correspondence principle.
Abstract: A set of generalized coherent states as eigenstates of the annihilation operator is proposed. These states are analytic functions of a complex variable and admit a resolution of identity with positive measure. Guided by the classical action angle transformation and the correspondence principle a formalism is developed for the construction of the annihilation operator for a given Hamiltonian.
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TL;DR: In this paper, it was shown that quantum statistics can be algebraically formalized defining the different statistics as (multi-mode) coherent states of the appropriate (but different from the usual ones) Lie-Hopf groups.
Abstract: Usual quantum statistics is written in Fock space but it is not an algebraic theory. We show that at a deeper level it can be algebraically formalized defining the different statistics as (multi-mode) coherent states of the appropriate (but different from the usual ones) Lie-Hopf groups. The traditional connection between groups and statistics, established in vacuum, is indeed subverted by the interaction with the thermal bath. We show indeed that h(1), related in quantum field theory to bosons, must be used to define in presence of a bath the Boltzmann statistics while, to build the Bose statistics, we have to take into account su(1,1). Astonishing to describe fermions we are forced to use not the superalgebra h(1|1) but su(2) in the fundamental representation. Higher representations of su(2) allow also to give a possible definition of anyon statistics with generalized Pauli principle. Physical implications are discussed; the results is more general then the usual on the discrete spectrum, but everything collapses to standard theory when the continuum limit is performed.
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TL;DR: In this paper, it is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states, such as the geodesics, the conjugate locus and the cut locus.
Abstract: The coherent states are viewed as a powerful tool in differential geometry. It is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states. The following subjects are discussed via the coherent states: the geodesics, the conjugate locus and the cut locus; the divisors; the Calabi's diastasis and its domain of definition; the Euler-Poincar\'e characteristic of the manifold, the number of Borel-Morse cells, Kodaira embeding theorem....
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TL;DR: In this article, it was proved that the Darboux transformation of the system of coherent states of a free particle leads to the states that may be treated as coherent states with soliton-like potentials.
Abstract: It is proved that the Darboux transformation of the system of coherent states of a free particle leads to the states that may be treated as coherent states of soliton-like potentials.
TL;DR: In this article, it was shown that the suitably doubled Fock representations of the Heisenberg algebra do not need to be introduced by hand but can be canonically handed down from deformations of the extended Heisenburg bialgebra.
Abstract: In Thermal Field Dynamics, thermal states are obtained from restrictions of vacuum states on a doubled field algebra. It is shown that the suitably doubled Fock representations of the Heisenberg algebra do not need to be introduced by hand but can be canonically handed down from deformations of the extended Heisenberg bialgebra. The relationship between quantum symmetries and doublings is discussed.