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

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2529-2545
Author(s):  
RAYMOND F. BISHOP ◽  
APOSTOLOS VOURDAS
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Negative Binomial ◽  
Discrete Series ◽  
Nonzero Temperature ◽  
Mixed States ◽  
Partial Trace ◽  
New Formalism ◽  
Thermo Field Dynamics ◽  
Resolution Of The Identity

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.

A COMPARISON BETWEEN WEHRL–LIEB AND VON NEUMANN ENTROPIES FOR TIME-EVOLVING SPIN-1/2 MIXED STATES

1994 ◽  
Vol 08 (16) ◽  
pp. 995-1006 ◽  
Author(s):  
S. S. MIZRAHI ◽  
V. V. DODONOV ◽  
D. OTERO
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Quantum States ◽  
Alternative Formulation ◽  
Spin States ◽  
Continuous Representation ◽  
Commun Math Phys ◽  
Mixed States ◽  
Von Neumann ◽  
Math Phys

Years ago, A. Wehrl (Rev. Mod. Phys.50, 221 (1978)) introduced the concept of classicallike entropy of quantum states when a two-label continuous representation is used; for instance, the harmonic oscillator coherent states. Subsequently, E. H. Lieb (Commun. Math. Phys.62, 35 (1978)) extended that concept of entropy to the Bloch coherent spin states. Here, we consider spin-1/2 systems and calculate both the Wehrl–Lieb and von Neumann entropies, and then we compare the results and discuss the Wehrl–Lieb entropy as an alternative formulation to von Neumann's. As illustration, three examples are worked out: (i) the decoherence of a quantum state in a measurement process, (ii) the conservation of coherence, and (iii) the recoherence phenomena that appear in the solutions of a specific master equation that originates from a nonlinear Schrödinger equation.

scholarly journals NON-HERMITIAN OSCILLATOR-LIKE HAMILTONIANS AND λ-COHERENT STATES REVISITED

2001 ◽  
Vol 16 (02) ◽  
pp. 91-98 ◽  
Author(s):  
JULES BECKERS ◽  
NATHALIE DEBERGH ◽  
JOSÉ F. CARIÑENA ◽  
GIUSEPPE MARMO
Keyword(s):  
Harmonic Oscillator ◽  
Hilbert Spaces ◽  
Coherent States ◽  
Scalar Product ◽  
Points Of View ◽  
Usual Scalar ◽  
Usual Scalar Product

Previous λ-deformed non-Hermitian Hamiltonians with respect to the usual scalar product of Hilbert spaces dealing with harmonic oscillator-like developments are (re)considered with respect to a new scalar product in order to take into account their property of self-adjointness. The corresponding deformed λ-states lead to new families of coherent states according to the DOCS, AOCS and MUCS points of view.

scholarly journals Lewis-Riesenfeld quantization and SU(1, 1) coherent states for 2D damped harmonic oscillator

2018 ◽  
Vol 59 (11) ◽  
pp. 112101 ◽  
Author(s):  
Latévi M. Lawson ◽  
Gabriel Y. H. Avossevou ◽  
Laure Gouba
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Damped Harmonic Oscillator

scholarly journals An Ethology of Adaptation: Dolphins Stop Feeding but Continue Socializing in Construction-Degraded Habitat

2021 ◽  
Vol 8 ◽  
Author(s):  
Ann Weaver
Keyword(s):  
Linear Models ◽  
Negative Binomial ◽  
Environmental Changes ◽  
Bottlenose Dolphins ◽  
Observation Time ◽  
Mixed States ◽  
The West ◽  
Behavioral Adaptations ◽  
Construction Zone ◽  
Free Ranging

Adaptation is a biological mechanism by which organisms adjust physically or behaviorally to changes in their environment to become more suited to it. This is a report of free-ranging bottlenose dolphins’ behavioral adaptations to environmental changes from coastal construction in prime habitat. Construction was a 5-year bridge removal and replacement project in a tidal inlet along west central Florida’s Gulf of Mexico coastline. It occurred in two consecutive 2.5-year phases to replace the west and east lanes, respectively. Lane phases involved demolition/removal of above-water cement structures, below-water cement structures, and reinstallation of below + above water cement structures (N = 2,098 photos). Data were longitudinal (11 years: 2005–2016, N = 1,219 surveys 2–4 times/week/11 years, N = 4,753 dolphins, 591.95 h of observation in the construction zone, 126 before-construction surveys, 568 during-construction surveys, 525 after-construction surveys). The dependent variable was numbers of dolphins (count) in the immediate construction zone. Three analyses examined presence/absence, total numbers of dolphins, and numbers of dolphins engaged in five behavior states (forage-feeding, socializing, direct travel, meandering travel, and mixed states) across construction. Analyses were GLIMMIX generalized linear models for logistic and negative binomial regressions to account for observation time differences as an exposure (offset) variable. Results showed a higher probability of dolphin presence than absence before construction began, more total dolphins before construction, and significant decreases in the numbers of feeding but not socializing dolphins. Significant changes in temporal rhythms also revealed finer-grained adaptations. Conclusions were that the dolphins adapted to construction in two ways, by establishing feeding locations beyond the disturbed construction zone and shifting temporal rhythms of behaviors that they continued to exhibit in the construction zone to later in the day when construction activities were minimized. This is the first study to suggest that the dolphins learned to cope with coastal construction with variable adjustments.

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