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 Jan 1991
TL;DR: In this paper, the product of two operators is given for compact Lie groups, especially for SU(2), and for the non-compact Weyl-Heisenberg group, which are especially suited to discuss quantum corrections to classical results.
Abstract: To obtain a closed and consistent mathematical description of quantum systems in terms of group-related 'phase space' functions one needs counterparts for all the operations usually performed with operators. For functions related to coher ent states, so-called Q-representatives, the relation corresponding to the product of two operators is given for compact Lie groups, especially for SU(2), and for the non-compact Weyl-Heisenberg group. Equations (5-8) show that these formulas, as well as the resulting commutator relation, are especially suited to discuss quantum corrections to classical results. In addition they should simplify the calculation of expectation values for coherent states as they relate the Q-representatives of more complicated operators to those of simpler ones.
TL;DR: In this article, a complete set of harmonic oscillator orthogonal coherent states is discussed, in particular towards applications as a basis for nonstationary problems, and an orthonormal set of squeezed states is introduced.
Abstract: A complete set of harmonic oscillator orthogonal coherent states is discussed. The properties of the states are studied, in particular towards applications as a basis for nonstationary problems. To make such a basis even more flexible, an orthonormal set of squeezed states is introduced. These states share most of the properties that make the familiar coherent states useful in applications. They are also extremal states of the uncertainty product. Their particular advantage, beyond the obvious one of orthogonality, is in applications to the dynamics of excited states.
01 Jan 2011
TL;DR: In this paper, the authors present statistical properties of even and odd combinations of nonlinear coherent states associated with two nonlinear potentials, one supporting a finite number of bound states and the other supporting an infinite number of states, within the framework of an f-deformed algebra.
Abstract: In this work we present some statistical properties of even and odd combinations of nonlinear coherent states associated with two nonlinear potentials; one supporting a finite number of bound states and the other supporting an infinite number of bound states, within the framework of an f-deformed algebra. We calculate their normalized variance and the temporal evolution of their dispersion relations using nonlinear coherent states defined as (a) eigensates of the deformed annihilation operator and (b) those states created by the application of a deformed displacement operator upon the ground state of the oscillator.
13 Jun 2007
TL;DR: In this article, the authors provide experimental proposals for coherent communication with linear optics, including a linear-optical scheme for coherent superdense coding and a linearoptical coherent teleportation scheme.
Abstract: We provide experimental proposals for coherent communication with linear optics. The first proposal suggests a linear-optical scheme for coherent superdense coding. The second proposal gives a linear-optical coherent teleportation scheme.
01 Apr 2004
TL;DR: VCS theory is perhaps the simplest and most effective way known for computing the matrix elements of a Lie algebra as discussed by the authors, and it is a mathematical tool that noone who is serious about using algebraic methods in physics should be without.
Abstract: VCS theory is perhaps the simplest and most effective way known for computing the matrix elements of a Lie algebra. It is a mathematical tool that noone who is serious about using algebraic methods in physics should be without. It encorporates the mathematical theories of induced representations and geometric quantization in a physically intuitive manner that makes it easy to construct the explicit representations of a desired Lie algebra in a chosen basis in a systematic manner. Its practical utility has been confirmed in numerous applications.