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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: Hall and Mitchell as discussed by the authors described a family of heat kernels (or equivalently coherent states) and associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S d J.
Abstract: Hall and Mitchell described a family of heat kernels (or equivalently coherent states) and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S d J. Math. Phys.43(3), 1211 (2002). These heat kernels were chosen intelligently but in the case of d = 2, “one” of the formulas for the heat kernel must be corrected.
TL;DR: In this paper, a general approach to building photon-added generalized Peremolov coherent states (PAGPCSs) associated to generalized su(1, 1) algebra is developed.
Abstract: We develop a general approach to building photon-added generalized Peremolov coherent states (PAGPCSs) and photon-added generalized Barut–Girardello coherent states (PA-GBGCSs) associated to generalized su(1, 1) algebra. We study the problem of completeness of these coherent states for some particular cases and investigate the physical properties of these states through the evaluation of the Mandel parameter using an alteration of the Holstein–Primakoff realization of the su(1, 1) algebra. We show that these states exhibit sub-Poissonian, Poissonian, or super-Poissonian statistics. These features make the photon-added approach a good candidate for implementation of quantum optics schemes and coherent information processing.
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TL;DR: In this article, the authors studied the interaction between several fields initially in coherent states and gave a completely algebraic solution to explain why coherent states remain coherent states when subject to non-Markovian dissipation.
Abstract: We study the interaction between several fields initially in coherent states. The solution allows us to explain why coherent states remain coherent states when subject to non-Markovian dissipation. We first study the interaction between two fields and show that this is the building block of the total interaction. We give a completely algebraic solution of this system.
14 Aug 1992
TL;DR: The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite-mode squeezed coherent states is introduced in this article, which provides an interesting geometrical interpretation of quantum nonequilibrium phenomena.
Abstract: The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite-mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena.
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TL;DR: In this paper, the Schrodinger cat states, constructed from Glauber coherent states and applied for description of qubits, are generalized to the kaleidoscope of coherent states related with regular n-polygon symmetry and the roots of unity.
Abstract: The Schr\"odinger cat states, constructed from Glauber coherent states and applied for description of qubits, are generalized to the kaleidoscope of coherent states related with regular n-polygon symmetry and the roots of unity. The cases of the trinity states and the quartet states are described in details. Normalization formula for these states requires introduction of specific combinations of exponential functions with mod 3 and mod 4 symmetry. We show that for an arbitrary $n$, these states can be generated by the Quantum Fourier transform and can provide qutrits, ququats and in general, qudit units of quantum information. Relations with quantum groups and quantum calculus are discussed.