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Displaced negative-binomial mixed states: Generalized thermo-field-dynamics

Apostol Vourdas, R. F. Bishop

Displaced negative-binomial mixed states are introduced and their properties are studied. It is shown that they may be used to construct a resolution of the identity operator and, therefore, that they can be used as a ``basis'' in the Hilbert space. Generalized P and Q representations with respect to these states are introduced and their properties are discussed. The pure SU(1,1) coherent states discussed by Perelomov are considered in the two-mode harmonic oscillator Hilbert space and it is shown that the partial trace with respect to one of the modes leads to negative-binomial mixed states. Using this observation, the formalism of thermo-field-dynamics is generalized in a corresponding negative-binomial field dynamics.Displaced negative-binomial mixed states are introduced and their properties are studied. It is shown that they may be used to construct a resolution of the identity operator and, therefore, that they can be used as a ``basis'' in the Hilbert space. Generalized P and Q representations with respect to these states are introduced and their properties are discussed. The pure SU(1,1) coherent states discussed by Perelomov are considered in the two-mode harmonic oscillator Hilbert space and it is shown that the partial trace with respect to one of the modes leads to negative-binomial mixed states. Using this observation, the formalism of thermo-field-dynamics is generalized in a corresponding negative-binomial field dynamics.

Physical Review AMar 1, 199514 citations

Generalized Coherent States and Their Applications

A. M. Perelomov

Springer eBooksJan 1, 19863,507 citations

Generalized Coherent States: A Novel Approach

Вадим Васильевич Борзов, Eugeniy Viktorovich Damaskinsky

Journal of Mathematical SciencesJun 8, 20057 citations

THERMAL COHERENT STATES, A BROADER CLASS OF MIXED COHERENT STATES, AND GENERALIZED THERMO-FIELD DYNAMICS

R. F. Bishop, Apostol Vourdas

We introduce coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at nonzero temperature (T ≠ 0), as a "random" (or "thermal" or "noisy") basis in Hilbert space. A resolution of the identity for these states is proven and is used to generalize the usual pure (T = 0) coherent state formalism to the mixed (T ≠ 0) case. This new formalism for thermal coherent states is then further generalized to a broader class of so-called negative-binomial mixed states. It is known that the negative-binomial distribution is itself intimately related to the discrete series of SU(1,1) representations. We consider the pure SU(1,1) coherent states in the two-mode harmonic oscillator space, and show how our negative-binomial mixed states arise from taking the partial trace with respect to one of these two modes. This observation is then used to show how the formalism of thermo-field dynamics may be generalized to a correspondingly much broader negative-binomial-field dynamics, which we expect to have many uses.We introduce coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at nonzero temperature (T ≠ 0), as a "random" (or "thermal" or "noisy") basis in Hilbert space. A resolution of the identity for these states is proven and is used to generalize the usual pure (T = 0) coherent state formalism to the mixed (T ≠ 0) case. This new formalism for thermal coherent states is then further generalized to a broader class of so-called negative-binomial mixed states. It is known that the negative-binomial distribution is itself intimately related to the discrete series of SU(1,1) representations. We consider the pure SU(1,1) coherent states in the two-mode harmonic oscillator space, and show how our negative-binomial mixed states arise from taking the partial trace with respect to one of these two modes. This observation is then used to show how the formalism of thermo-field dynamics may be generalized to a correspondingly much broader negative-binomial-field dynamics, which we expect to have many uses.

International Journal of Modern Physics BMay 30, 20072 citations

Quantum properties of the binomial state field interacting with a two-level atom

DaoLai Jiang, Xuezao Ren, HongLu Cong +1 more

Science China Physics Mechanics and AstronomyMay 1, 20101 citation

Effects of Atomic Coherence on Collapses and Revivals in the Binomial State of the Field

Amitabh Joshi, Ravinder Rupchand Puri

The effects of the coherence between the states of a two-level atom on the phenomenon of collapses and revivals in an undamped binomial state of the electromagnetic field are investigated. It is found that the Rabi oscillations exhibit qualitatively different behaviour for different phases of coherence between the levels. This behaviour in the binomial state of the field is in contrast with that in a coherent state field, in which case the Rabi oscillations are qualitatively the same for all values of the coherence between the two atomic levels.The effects of the coherence between the states of a two-level atom on the phenomenon of collapses and revivals in an undamped binomial state of the electromagnetic field are investigated. It is found that the Rabi oscillations exhibit qualitatively different behaviour for different phases of coherence between the levels. This behaviour in the binomial state of the field is in contrast with that in a coherent state field, in which case the Rabi oscillations are qualitatively the same for all values of the coherence between the two atomic levels.

Journal of Modern OpticsMay 1, 198950 citations

Correspondence between generalized binomial field states and coherent atomic states

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