Semiclassical Approximations in Phase Space with Coherent States

We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial value representation for the semiclassical propagator, based on an initial gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed gaussian approximation. It is very different from the Herman--Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.Comment: 80 pages, 4 figure

Semiclassical quantization of a system with mixed regular/chaotic dynamics

The quasienergy spectrum of a periodically driven quantum system is constructed from classical dynamics by means of the semiclassical initial value representation using coherent states. For the first time, this method is applied to explicitly time-dependent systems. For an anharmonic-oscillator system with mixed chaotic and regular classical dynamics, the entire quantum spectrum (both regular and chaotic states) is reproduced semiclassically with surprising accuracy. In particular, the method is capable to account for the very small tunneling splittings

Semiclassical Quantization of a System with Mixed Regular/Chaotic Dynamics

The quasienergy spectrum of a periodically driven quantum system is constructed from classical dynamics by means of the semiclassical initial value representation using coherent states. For the first time, this method is applied to explicitly time dependent systems. For an anharmonic oscillator system with mixed chaotic and regular classical dynamics, the entire quantum spectrum (both regular and chaotic states) is reproduced semiclassically with surprising accuracy. In particular, the method is capable to account for the very small tunneling splittings

Semiclassical Quantization of a System with Mixed Regular/Chaotic Dynamics

The quasienergy spectrum of a periodically driven quantum system is constructed from classical dynamics by means of the semiclassical initial value representation using coherent states. For the first time, this method is applied to explicitly time dependent systems. For an anharmonic oscillator system with mixed chaotic and regular classical dynamics, the entire quantum spectrum (both regular and chaotic states) is reproduced semiclassically with surprising accuracy. In particular, the method is capable to account for the very small tunneling splittings

Cognitive Behavioral Therapy and Acceptance and Commitment Therapy for the Discontinuation of Long-Term Benzodiazepine Use in Insomnia and Anxiety Disorders.

Benzodiazepines have proven to be highly effective for treating insomnia and anxiety. Although considered safe when taken for a short period of time, a major risk-benefit dilemma arises in the context of long-term use, relating to addiction, withdrawal symptoms, and potential side effects. For these reasons, benzodiazepines are not recommended for treating chronic sleep disorders, anxiety disorders, nor for people over the age of 65, and withdrawal among long-term users is a public health issue. Indeed, only 5% of patients manage to discontinue using these drugs on their own. Even with the help of a general practitioner, this rate does not exceed 25 to 30% of patients, of which approximately 7% manage to remain drug-free in the long term. Cognitive Behavioral Therapies (CBT) offer a crucial solution to this problem, having been shown to increase abstinence success to 70-80%. This article examines traditional and novel CBT techniques in this regard, such as Acceptance and Commitment Therapy, which address both the underlying condition (insomnia/anxiety) and the substance-related disorder. The theoretical framework and evidence supporting the use of these approaches are reviewed. Finally, current research gaps are discussed, and key research perspectives are proposed