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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TL;DR: In this article, the SU (2) and SU (1, 1, 1) algebras and their coherent states are discussed. But the definition of the coherent state of this group is not discussed.
4 citations
TL;DR: The authors showed that coherent states as defined by Mikhailov, (see Teor. Mat. Fiz., no.15, p.367 of 1974) may be considered in certain special cases as intelligent states.
Abstract: Shows that coherent states as defined by Mikhailov, (see Teor. Mat. Fiz., no.15, p.367 of 1974) may be considered in certain special cases as intelligent states.
4 citations
TL;DR: In this paper, deformed quantum Heisenberg Lie algebras are derived from the usual creation and annihilation operators of the standard harmonic oscillator and the associated algebra eigenstates are computed and give rise to new classes of deformed coherent and squeezed states.
Abstract: Starting from deformed quantum Heisenberg Lie algebras some realizations are given in terms of the usual creation and annihilation operators of the standard harmonic oscillator. Then the associated algebra eigenstates are computed and give rise to new classes of deformed coherent and squeezed states. They are parametrized by deformed algebra parameters and suitable redefinitions of them as paragrassmann numbers. Some properties of these deformed states are also analysed.
4 citations
TL;DR: In this article, a shape-invariant Lie algebra spanned by ladder operators plus the identity operator is realized using the associated Bessel functions, and two kinds of generalized coherent states as an appropriate superposition of these functions are constructed.
Abstract: Using the associated Bessel functions, a shape-invariant Lie algebra spanned by ladder operators plus the identity operator, is realized. The Hilbert space of the associated Bessel functions, representing the Lie algebra, are established and two kinds of generalized coherent states as an appropriate superposition of these functions are constructed. By implying appropriate similarity transformation on the constructed coherent states, the generalized coherent states for the Morse potential are obtained. By considering some statistical characteristics, it is revealed that the constructed coherent states indeed possess nonclassical features, such as squeezing and sub-Poissonian statistics.
4 citations
Dissertation•
25 Sep 2014
TL;DR: In this paper, the authors propose a framework to deform the phase spaces of classical particles using a non-abelian group structure by the introduction of a single deformation parameter, called Heisenberg double.
Abstract: We present a well-defined framework to deform the phase spaces of classical particles. These new phase spaces, called Heisenberg doubles, provide a laboratory to probe the effects of quantum gravity. In particular, they allow us to equip momentum space with a non-abelian group structure by the introduction of a single deformation parameter. In order to connect Heisenberg doubles with classical phase spaces we begin with a review of Hamiltonian systems, symmetries and conservation laws in the classical framework. Next, we provide a comprehensive review of the theory behind Poisson-Lie groups, including Lie bialgebras and the construction of the Drinfeld double. Lastly, we build the Heisenberg double from Poisson-Lie group components. We then identify the Heisenberg double as a deformation of the cotangent bundle of Lie groups and extend many of the notions of classical Hamiltonian systems to this new picture with Poisson-Lie symmetries. As an example, we look at a new presentation of the deformed rotator.
4 citations