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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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06 May 2022
TL;DR: In this article , the generalized coherent states for an electron in monolayer or bilayer graphene placed in an external magnetic field were constructed. But the authors focused on the conditions leading to the mutual equivalence between coherent states.
Abstract: In this paper we construct the generalized coherent states for an electron in monolayer or bilayer graphene placed in an external magnetic field. At first we define an appropriate set of ladder operators acting on the eigenfunctions for each Hamiltonian, afterwards we derive the generalized coherent states through several definitions and analyze the commutation relationship between the ladder operators. Then we determine the conditions leading to the mutual equivalence between coherent states. Finally, some physical quantities are calculated and we study the time evolution for the generalized graphene coherent states.
TL;DR: A new construction of Perelomov's generalised coherent states for one-dimensional harmonic oscillators admitting the Heisenberg-Weyl group as invariance Lie group is considered in this paper.
Abstract: A new construction of Perelomov's generalised coherent states (1986) is considered for one-dimensional harmonic oscillators admitting the Heisenberg-Weyl group as invariance Lie group. Exploiting the Niederer maximal kinematical invariance group (1973) for such physical systems, the author deduce further characteristics on the Heisenberg states through the use of the fundamental Perelomov state mod k, k) with k=3/4. The author explicitly gets new normalisation factor and measure for the Heisenberg generalised coherent states. The real Lie algebras so(2, 1) Square Operator h(2), so(2, 1) and h(2) play a prominent role in this study.
TL;DR: In this article, it was shown that the suitably doubled Fock representations of the Heisenberg algebra do not need to be introduced by hand but can be canonically handed down from deformations of the extended Heisenburg bialgebra.
Abstract: In Thermal Field Dynamics, thermal states are obtained from restrictions of vacuum states on a doubled field algebra. It is shown that the suitably doubled Fock representations of the Heisenberg algebra do not need to be introduced by hand but can be canonically handed down from deformations of the extended Heisenberg bialgebra. The relationship between quantum symmetries and doublings is discussed.
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TL;DR: Agarwal and Tara as discussed by the authors derived the ECS wave function as a blend of Coherent States and Fock States and thus established them as a result of Quantum fluctuations represented by Fock states on Coherent states.
Abstract: Agarwal and Tara, in 1991 introduced a new class of states defined as m times application of creation operator to Coherent States known as Excited Coherent States (ECS) or Photon Added Coherent States (PACS). They are neither completely quantum nor completely classical. Here we present and develop these Excited Coherent Sates from a basic and more approachable Wave-function approach. We have derived the ECS wave function as a blend of Coherent States and Fock States and thus established them as a result of Quantum fluctuations (represented by Fock states) on Coherent States. We further derived and analyzed basic relations such as wave packet width and uncertainty relation in a more generalized form and presented their development with time. Another important property of ECS is Quadrature Squeezing. Here we also present a general analysis of squeezing in ECS and derived conditions on parameters for squeezing.