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Coherent states in mathematical physics

About: Coherent states in mathematical physics is a research topic. Over the lifetime, 732 publications have been published within this topic receiving 32024 citations.


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TL;DR: In this paper, it was shown that the previously introduced algebraic approach to the self-similar potentials can be generalized to the q-algebras and the associated coherent states were investigated.
Abstract: Self-similar potentials generalize the concept of shape invariance which was originally introduced to explore exactly solvable potentials in quantum mechanics. In this paper it is shown that the previously introduced algebraic approach to the latter can be generalized to the former. The infinite Lie algebras introduced in this context are shown to be closely related to the q-algebras. The associated coherent states are investigated.

76 citations

Journal ArticleDOI
TL;DR: A generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space is predicted and compared to exact quantum evolution probabilities in Bose-Hubbard models to confirm their relevance in the context of many- body thermalization.
Abstract: We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space. This enhancement is robust with respect to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition principle in Fock space. It is a genuine quantum many-body effect that lies beyond the reach of any mean-field approach. Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss their relevance in the context of many-body thermalization.

74 citations

Journal ArticleDOI
TL;DR: In this article, the concept of algebra eigenstates is introduced, which are defined for an arbitrary Lie group as eigen states of elements of the corresponding complex Lie algebra and applied to the SU(2) and SU(1,1) simple Lie groups.
Abstract: We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states associated with a dynamical symmetry group. On the one hand, algebra eigenstates include different sets of Perelomov's generalized coherent states. On the other hand, intelligent states (which are squeezed states for a system of general symmetry) also form a subset of algebra eigenstates. We develop the general formalism and apply it to theSU(2) andSU(1,1) simple Lie groups. Complete solutions to the general eigenvalue problem are found in both cases by a method that employs analytic representations of the algebra eigenstates. This analytic method also enables us to obtain exact closed expressions for quantum statistical properties of an arbitrary algebra eigenstate. Important special cases such as standard coherent states and intelligent states are examined and relations between them are studied by using their analytic representations.

74 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the dynamical algebra associated with a family of isospectral oscillator Hamiltonians through the analysis of its representation in the basis of energy eigenstates.
Abstract: The dynamical algebra associated with a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates. It is shown that this representation becomes similar to that of the standard Heisenberg algebra, and it is dependent on a parameter omega >or=0. We call it the distorted Heisenberg algebra, where omega is the distortion parameter. The corresponding coherent states for an arbitrary omega are derived, and some particular examples are discussed in detail. A prescription to produce the squeezing, by adequately selecting the initial state of the system, is given.

73 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20236
202214
20201
20182
201710
201612