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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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17 Feb 2011
4 citations
TL;DR: In this article, a reference state for finite-dimensional coherent states is proposed, which is easy to deal with in comparison to former suggestions which we briefly review here, and explicit calculations which show that the phase of the overlap of finite coherent state has a structure analogous to the usual infinite-dimensional continuous coherent states.
Abstract: We propose a reference state for finite-dimensional coherent states, which is easy to deal with in comparison to former suggestions which we briefly review. We also advance explicit calculations which shows that the phase of the overlap of finite coherent state has a structure analogous to the usual infinite-dimensional continuous coherent states.
4 citations
Posted Content•
TL;DR: In this article, the Bargmann Fock construction can also be done in the quantum group symmetric case, which leads to a 'q-deformed quantum mechanics' in which the basic concepts, Hilbert space of states and unitarity of time evolution, are preserved.
Abstract: Usually in quantum mechanics the Heisenberg algebra is generated by operators of position and momentum. The algebra is then represented on an Hilbert space of square integrable functions. Alternatively one generates the Heisenberg algebra by the raising and lowering operators. It is then natural to represent it on the Bargmann Fock space of holomorphic functions. In the following I show that the Bargmann Fock construction can also be done in the quantum group symmetric case. This leads to a 'q- deformed quantum mechanics' in which the basic concepts, Hilbert space of states and unitarity of time evolution, are preserved.
4 citations
TL;DR: In this article, a general theoretical formalism is presented to compute the fidelity of transformations of unknown quantum states, and the theory is applied to Gaussian transformations of continuous variable quantum systems.
Abstract: We present a general theoretical formalism to compute the fidelity of transformations of unknown quantum states, and we apply our theory to Gaussian transformations of continuous variable quantum systems. For the case of a Gaussian distribution of displaced coherent states, the theory is readily tractable by a covariance matrix formalism, and a wider class of states, exemplified by Fock states, can be treated efficiently by the Wigner function formalism. Given the distribution of input states, the optimum feedback gain is identified, and analytical results for the fidelities are presented for recently implemented teleportation and memory storage protocols for continuous variables.
4 citations
TL;DR: In this paper, shape-invariant trigonometric potentials for the displacement-operator-derived effective mass Hamiltonian were derived by linearizing the algebra resulting from SUSY-QM factorization of the constructed systems.
Abstract: Applying the supersymmetric quantum mechanics approach, we derive shape-invariant trigonometric potentials for the displacement-operator-derived effective mass Hamiltonian. By linearizing the algebra resulting from SUSY-QM factorization of the constructed systems, their coherent states are defined and shown to be exponentially dependent on a function of the quantum numbers.
4 citations