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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 article, a modification to the standard construction, based on the recently introduced (non-commutative) flux representation, was introduced, and the resulting quantum states have some welcome features, in particular, concerning peakedness properties, when compared to other coherent states in the literature.
Abstract: As part of a wider study of coherent states in (loop) quantum gravity, we introduce a modification to the standard construction, based on the recently introduced (non-commutative) flux representation. The resulting quantum states have some welcome features, in particular, concerning peakedness properties, when compared to other coherent states in the literature.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ?Coherent states: mathematical and physical aspects?.
33 citations
TL;DR: In this paper, the authors demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of reproducing kernel Hilbert space, which resembles an analogous duality in Bayesian statistics, a discrete probability distribution and a discretely parametrized family of continuous distributions.
Abstract: We demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of a reproducing kernel Hilbert space. Each family of coherent states is shown to contain, in a sort of duality, which resembles an analogous duality in Bayesian statistics, a discrete probability distribution and a discretely parametrized family of continuous distributions. It turns out that nonlinear coherent states, of the type widely studied in quantum optics, are a particularly useful class of coherent states from this point of view, in that they contain many of the standard statistical distributions. We also look at vector coherent states and multidimensional coherent states as carriers of mixtures of probability distributions and joint probability distributions.
33 citations
TL;DR: In this paper, it was shown that the Barut-girardello SU(1,1) coherent states of the Perelomov type do not go over to the vacuum in the large k limit.
Abstract: Recently, Markham and Vedral [Phys. Rev. A 67, 042113 (2003)] investigated the effect of beam splitting on the spin, or SU(2), coherent states for a single mode field. The spin coherent state is a binomial coherent state related to the Holstein-Primakoff realization of the su(2) Lie algebra given in terms of a set of single mode bose annihilation and creation operators. Upon beam splitting, the ordinary (or Glauber) coherent states merely split into products of ordinary coherent states with reduced amplitudes without becoming entangled, as one would expect for a classical-like field. The above authors expected the spin coherent states to go over to the ordinary coherent states in the limit of high spin, j{yields}{infinity}, and thus to become product states after beam splitting. But this expectation was not confirmed through numerical calculation of the entropy which, instead of going to zero, leveled off with increasing spin. In this paper we find similar behavior for SU(1,1) coherent states of the Perelomov type for large Bargman index k, but also find that the Barut-Girardello SU(1,1) coherent states appear to rapidly become product states after beam splitting for increasing k. We explain these results by showing that, in reality, neither the spinmore » coherent states nor the Perelomov SU(1,1) coherent states go over to ordinary coherent states in the limits of large j or k, and that the Barut-Girardello coherent states merely go over to the vacuum in the large k limit. Finally, we examine the correct limiting procedure for obtaining separable states (i.e., products of coherent states) upon beam splitting by performing contractions of the su(2) and su(1,1) Lie algebras and of their associated coherent states.« less
33 citations
06 Mar 2006
TL;DR: In this paper, the recently developed coupled coherent states theory is applied to direct full dimensional simulation of tunneling in multidimensional systems, and it is shown that the efficiency of the technique is largely due to the use of quantum averaged potentials.
Abstract: The recently developed coupled coherent states theory is applied to direct full dimensional simulation of tunneling in multidimensional systems. The approach is shown to work well for both symmetric and asymmetric tunneling in up to 20 dimensions. We show that the efficiency of the technique is largely due to the use of quantum averaged potentials to guide a moving basis of coherent states.
32 citations
TL;DR: In this article, the authors studied the existence of coherent fields in C*-Weyl algebra and proved that the set of all coherent fields with the same absolute factorizing function is a Bauer simplex.
Abstract: Specifying their (normally ordered) characteristic functions we determine all states of the boson C*-Weyl algebra which satisfy Glauber's coherence condition and are not realizable as density operators in Fock space. The pure ones are shown to be just the eigenstates of the annihilation operators in their GNS-representations (in contrast to the Fock case) and are characterized in many equivalent manners. The central decomposition of an arbitrary coherent state has the macroscopic phase variable as parameter and is supported by the pure coherent states, which is in fact the only way for a maximal decomposition. The set of all coherent states with the same absolute factorizing function is proven to be a Bauer simplex. The appearence of a classical coherent field part is studied in detail in the GNS-representations and shown to correspond to an enlargement of the set of one boson states by just one additional mode.
32 citations