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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, the authors introduce a class of quantum pure state models called the coherent models, which is an even-dimensional manifold of pure states whose tangent space is characterized by a symplectic structure.
Abstract: We introduce a class of quantum pure state models called the coherent models. A coherent model is an even-dimensional manifold of pure states whose tangent space is characterized by a symplectic structure. In a rigorous framework of noncommutative statistics, it is shown that a coherent model inherits and expands the original spirit of the minimum uncertainty property of coherent states.
50 citations
01 Aug 2009
TL;DR: In this paper, coherent states for non-Hermitian systems are introduced as eigenstates of pseudo-hermitian boson annihilation operators, and the wave functions of the eigen states of the two complementary number operators are found to be proportional to new polynomials, that are bi-orthogonal and can be regarded as a generalization of standard Hermite polynomial.
Abstract: Coherent states (CS) for non-Hermitian systems are introduced as eigenstates of pseudo-Hermitian boson annihilation operators. The set of these CS includes two subsets which form bi-normalized and bi-overcomplete system of states. The subsets consist of eigenstates of two complementary lowering pseudo-Hermitian boson operators. Explicit constructions are provided on the example of one-parameter family of pseudo-boson ladder operators. The wave functions of the eigenstates of the two complementary number operators, which form a bi-orthonormal system of Fock states, are found to be proportional to new polynomials, that are bi-orthogonal and can be regarded as a generalization of standard Hermite polynomials.
49 citations
48 citations
TL;DR: In this article, the eigenvalues of the annihilation operator for interacting systems in general are not analytic signals and general conditions under which the states which are initially coherent remain coherent at all times are considered.
47 citations
01 Jan 1980
TL;DR: The coherent states of the harmonic oscillator and hence the radiation field (which is considered as an assembly of oscillators) can be defined in many different, but essentially equivalent ways as mentioned in this paper.
Abstract: The coherent states of the harmonic oscillator and hence the radiation field (which is considered as an assembly of oscillators) can be defined in many different, but essentially equivalent ways.1
47 citations