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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: The case of a compact, connected, simply connected Lie group of symmetry, having the same rank as the stationary group of the coherent states, such that the manifold of coherent states is a Kahlerian C-space, is considered in this article.
Abstract: Perfect Morse functions on the manifold of coherent states are effectively constructed. The case of a compact, connected, simply connected Lie group of symmetry, having the same rank as the stationary group of the manifold of coherent states, such that the manifold of coherent states is a Kahlerian C‐space, is considered. It is proved that the set of perfect Morse functions is dense in the set of energy functions for linear Hamiltonians in the elements of the Cartan algebra of the Lie algebra of the representation of the group considered. It is proved that the maximum number of orthogonal vectors on a coherent vector manifold is equal to the Euler–Poincare characteristic of the manifold.
21 citations
TL;DR: A model for interferometric GW antennas without dissipative or active elements is discussed, predicted that the even and odd coherent states may play an alternative role to squeezed vacuum states in reducing the optimal power of the input laser.
Abstract: We discuss a model for interferometric GW antennas without dissipative or active elements.
It is predicted that the even and odd coherent states may play an alternative role to squeezed vacuum states in reducing the optimal power of the input laser.
21 citations
TL;DR: In this paper, the authors investigated the connection between quasi-classical (pointer) states and generalized coherent states (GCSs) within an algebraic approach to Markovian quantum systems (including bosons, spins, and fermions).
Abstract: We investigate the connection between quasi-classical (pointer) states and generalized coherent states (GCSs) within an algebraic approach to Markovian quantum systems (including bosons, spins, and fermions). We establish conditions for the GCS set to become most robust by relating the rate of purity loss to an invariant measure of uncertainty derived from quantum Fisher information. We find that, for damped bosonic modes, the stability of canonical coherent states is confirmed in a variety of scenarios, while for systems described by (compact) Lie algebras, stringent symmetry constraints must be obeyed for the GCS set to be preferred. The relationship between GCSs, minimum-uncertainty states, and decoherence-free subspaces is also elucidated.
21 citations
TL;DR: In this paper, a quantum exponential process acting on the Fock space based on the finite-difference algebra of P. J. Feinsilver was constructed, which is a quantum Poisson process.
Abstract: In [3],R. L. Hudson andK. R. Parthasarathy showed that the Fock space based on the Heisenberg—Weyl algebra hosts Brownian motion and Poisson processes. In this paper we construct a quantum exponential process acting on the Fock space based on the finite-difference algebra ofP. J. Feinsilver ([2]).
21 citations
TL;DR: Using second-order differential operators as a realization of the su(1,1) Lie algebra by the associated Laguerre functions, it is shown that the quantum states of the Calogero-Sutherland, half-oscillator and radial part of a 3D harmonic oscillator constitute the unitary representations for the same algebra as discussed by the authors.
Abstract: Using second-order differential operators as a realization of the su(1,1) Lie algebra by the associated Laguerre functions, it is shown that the quantum states of the Calogero-Sutherland, half-oscillator and radial part of a 3D harmonic oscillator constitute the unitary representations for the same algebra. This su(1,1) Lie algebra symmetry leads to derivation of the Barut-Girardello and Klauder-Perelomov coherent states for those models. The explicit compact forms of these coherent states are calculated. Also, to realize the resolution of the identity, their corresponding positive definite measures on the complex plane are obtained in terms of the known functions. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
21 citations