Topic
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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01 Aug 2008
TL;DR: In this article, a new class of Bogoliubov transformations is introduced, which generalize the notion of squeezed states, and the transformation of the ordinary annihilation and creation operators under this unitary transformation leads to the introduction of multi-photon coherent states.
Abstract: Using Lie algebra methods, we find a new class of Bogoliubov transformations which generalize the notion of squeezed states. The Hamiltonians for the simple harmonic and anharmonic oscillators, turn out to be the generators of a Lie group, whose other generators may be found exactly, or up to any desired order of the perturbation parameter. An element of this Lie group, which is realized as the multi-photon operator, transforms the anharmonic Hamiltonian to the harmonic one. The transformation of the ordinary annihilation and creation operators under this unitary transformation leads to the introduction of multi-photon coherent states. We specifically consider four-photon coherent states in detail and study the time dependent position and momentum uncertainties in these states.
1 citations
TL;DR: In this article, a weak deformation approximation of the Weyl-Heisenberg algebra is proposed, where the corresponding generalized coherent states and displacement operator are constructed in the Bargmann Fock representation.
Abstract: In the weak deformation (WD) approximation of the Weyl-Heisenberg algebra, the corresponding generalized coherent states and displacement operator are constructed. It is shown that those states, and contrary to the non-deformed Weyl-Heisenberg algebra, are not eigenstates of the annihilation operator. Moreover, and as an alternative to the Chaichian et al. Q-deformed path integral approach (where Qis the deformation parameter), using the Bargmann Fock representation, we propose in the WD approximation, a general simple formalism. As an application, we calculate the propagator and the wave function of the harmonic oscillator.
1 citations
01 May 1994
TL;DR: In this paper, the authors propose a method for obtaining generalized minimum-uncertainty squeezed states, giving examples, and relates it to known concepts, such as ladder-operator and displacement-operator squeezed states.
Abstract: Both the coherent states and also the squeezed states of the harmonic oscillator have long been understood from the three classical points of view: the (1) displacement operator, (2) annihilation- (or ladder-) operator, and (3) minimum-uncertainty methods. For general systems, there is the same understanding except for ladder-operator and displacement-operator squeezed states. After reviewing the known concepts, the author proposes a method for obtaining generalized minimum-uncertainty squeezed states, gives examples, and relates it to known concepts. He comments on the remaining concept, that of general displacement-operator squeezed states.
1 citations
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TL;DR: In this paper, it was shown that many interesting type of wavelets arise from group representations which are not square integrable or vacuum vectors, and thus are not admissible.
Abstract: The purpose of this paper is to articulate an observation that many interesting type of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not admissible. This extends an applicability of the popular wavelets construction to classic examples like the Hardy space.
Keywords: Wavelets, coherent states, group representations, Hardy space, functional calculus, Berezin calculus, Radon transform, Moebius map, maximal function, affine group, special linear group, numerical range.
1 citations
TL;DR: Geometric positions of square roots of coherent states of CCR algebras are investigated in this paper along with an explicit formula for transition amplitudes among them, which is a natural extension of our previous results on quasifree states and will provide a new insight into quasi-equivalence problems of quasIFree states.
Abstract: Geometric positions of square roots of coherent states of CCR algebras are investigated along with an explicit formula for transition amplitudes among them, which is a natural extension of our previous results on quasifree states and will provide a new insight into quasi-equivalence problems of quasifree states.
1 citations