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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the coherent states for a quantum particle on a circle are introduced and the Bargmann representation within the actual treatment provides the representation of the algebra, where U is unitary, which is a direct consequence of the Heisenberg algebra.
Abstract: The coherent states for a quantum particle on a circle are introduced. The Bargmann representation within the actual treatment provides the representation of the algebra , where U is unitary, which is a direct consequence of the Heisenberg algebra , but it is more adequate for the study of circular motion.
140 citations
TL;DR: In this article, the Hilbert-Schmidt distance between two arbitrary normalizable states is discussed as a measure of the similarity of the states and the connection to other definitions of the non-classicality of states are discussed.
Abstract: The Hilbert—Schmidt distance between two arbitrary normalizable states is discussed as a measure of the similarity of the states. Unitary transformations of both states with the same unitary operator (e.g. the displacement of both states in the phase plane by the same displacement vector and squeezing of both states) do not change this distance. The nearest distance of a given state to the whole set of coherent states is proposed as a quantitative measure of non-classicality of the state which is identical when considering the coherent states as the most classical ones among pure states and the deviations from them as non-classicality. The connection to other definitions of the non-classicality of states is discussed. The notion of distance can also be used for the definition of a neighbourhood of considered states. Inequalities for the distance of states to Fock states are derived. For given neighbourhoods, they restrict common characteristics of the state as the dispersion of the number operato...
123 citations
TL;DR: In this paper, the concept of even and odd nonlinear coherent states is introduced, and the statistical properties of such states are investigated with particular attention to their nonclassical effects.
121 citations
TL;DR: The stochastic master equations, that is to say, quantum filters, and master equations for an arbitrary quantum system probed by a continuous-mode bosonic input field in two types of non-classical states are derived.
Abstract: We derive the stochastic master equations, that is to say, quantum filters, and master equations for an arbitrary quantum system probed by a continuous-mode bosonic input field in two types of nonclassical states. Specifically, we consider the cases where the state of the input field is a superposition or combination of (1) a continuous-mode, single-photon wave packet and vacuum, and (2) any continuous-mode coherent states.
121 citations
TL;DR: In this paper, the q-integration is defined for q-oscillator realization of quantum groups, which is used to prove a completeness relation for the qanalogue of the usual coherent states.
Abstract: q-integration is defined for the q-oscillator realization of quantum groups. This is used to prove a completeness relation for the q-analogue of the usual coherent states. These states are overcomplete.
113 citations