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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: In this paper, the α-deformed Weyl-heisenberg algebra is used to obtain the su(2)- and su(1, 1)-algebras whenever α has specific values.
Abstract: At first, we introduce α-deformed algebra as a kind of generalization of the Weyl–Heisenberg algebra so that we get the su(2)- and su(1, 1)-algebras whenever α has specific values. After that, we construct coherent states of this algebra. Third, a realization of this algebra is given in the system of a harmonic oscillator confined at the center of a potential well. Then, we introduce two-boson realization of the α-deformed Weyl–Heisenberg algebra and use this representation to write α-deformed coherent states in terms of the two modes number states. Following these points, we consider mean number of excitations (we call them in general photons) and Mandel parameter as statistical properties of the α-deformed coherent states. Finally, the Fubini–Study metric is calculated for the α-coherent states manifold.

13 citations

Posted Content
TL;DR: A survey of the p-mechanical construction can be found in this article, which is a consistent physical theory suitable for a simultaneous description of classical and quantum mechanics Observables in pmechanics are defined to be convolution operators on the Heisenberg group and states are defined as positive linear functionals on p-observables.
Abstract: This is an up-to-date survey of the p-mechanical construction (see funct-an/9405002, quant-ph/9610016, math-ph/0007030, quant-ph/0212101, quant-ph/0303142), which is a consistent physical theory suitable for a simultaneous description of classical and quantum mechanics Observables in p-mechanics are defined to be convolution operators on the Heisenberg group H^n Under irreducible representations of H^n the p-observables generate corresponding observables in classical and quantum mechanics p-States are defined as positive linear functionals on p-observables It is shown that both states and observables can be realised as certain sets of functions/distributions on the Heisenberg group The dynamical equations for both p-observables and p-states are provided The construction is illustrated by the forced and unforced harmonic oscillators Connections with the contextual interpretation of quantum mechanics are discussed Keywords: Classical mechanics, quantum mechanics, Moyal brackets, Poisson brackets, commutator, Heisenberg group, orbit method, deformation quantisation, symplectic group, representation theory, metaplectic representation, Berezin quantisation, Weyl quantisation, Segal--Bargmann--Fock space, coherent states, wavelet transform, Liouville equation, contextual interpretation, interaction picture, forced harmonic oscillator

13 citations

ReportDOI
01 Jan 2000
TL;DR: In this paper, it is shown that the standard SU(1,1) and SU(2) coherent states are the unique states which minimize the second order characteristic inequality for the three generators.
Abstract: The three ways of generalization of canonical coherent states are briefly reviewed and compared with the emphasis laid on the (minimum) uncertainty way. The characteristic uncertainty relations, which include the Schroedinger and Robertson inequalities, are extended to the case of several states. It is shown that the standard SU(1,1) and SU(2) coherent states are the unique states which minimize the second order characteristic inequality for the three generators. A set of states which minimize the Schroedinger inequality for the Hermitian components of the su_q(1,1) ladder operator is also constructed. It is noted that the characteristic uncertainty relations can be written in the alternative complementary form.

13 citations

Posted Content
TL;DR: In this paper, it was shown that quantum computation circuits with coherent states as the logical qubits can be constructed using very simple linear networks, conditional measurements and coherent superposition resource states.
Abstract: We show that quantum computation circuits with coherent states as the logical qubits can be constructed using very simple linear networks, conditional measurements and coherent superposition resource states.

12 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20236
202214
20201
20182
201710
201612