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.
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TL;DR: In this article, a quantum-mechanical model of a damped harmonic oscillator with time-independent and time-dependent parameters is studied in the framework of the linear Schr\"odinger equation with a Hermitian nonstationary Hamiltonian.
Abstract: A quantum-mechanical model of a damped harmonic oscillator (both with time-independent and time-dependent parameters) is studied in the framework of the linear Schr\"odinger equation with a Hermitian nonstationary Hamiltonian. Integrals of the motion of this equation and their eigenstates, including coherent states, are constructed. The influence of an external harmonic force to the time evolution of various average values calculated over coherent states is considered, including the resonance case. The specific symmetry of the Hamiltonian leading to the new concept of loss-energy states is discussed.
215 citations
TL;DR: In this paper, the authors define coherent states for general potentials, requiring that they have the physically interesting properties of the harmonic-oscillator coherent states, and show that they obey a quantum approximation to the classical motion.
Abstract: We define coherent states for general potentials, requiring that they have the physically interesting properties of the harmonic-oscillator coherent states. We exhibit these states for several solvable examples and show that they obey a quantum approximation to the classical motion.
212 citations
TL;DR: In this paper, a review of entanglement in quantum systems is presented, focusing on the mathematical and physical aspects of entangling coherent states, which are in a sense the most classical states of a dynamical system.
Abstract: We review entangled coherent state research since its first implicit use in 1967 to the present. Entangled coherent states are important to quantum superselection principles, quantum information processing, quantum optics and mathematical physics. Despite their inherent fragility, entangled coherent states have been produced in a conditional propagating-wave quantum optics realization. Fundamentally the states are intriguing because they entangle the coherent states, which are in a sense the most classical of all states of a dynamical system.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.
210 citations
TL;DR: A survey of the theory of coherent states (CS) and some of their generalizations, with emphasis on the mathematical structure, rather than on physical applications, can be found in this paper.
Abstract: We present a survey of the theory of coherent states (CS); and some of their generalizations, with emphasis on the mathematical structure, rather than on physical applications. Starting from the standard theory of CS over Lie groups, we develop a general formalism, in which CS are associated to group representations which are square integrable over a homogeneous space. A further step allows us to dispense with the group context altogether, and thus obtain the so-called reproducing triples and continuous frames introduced in some earlier work. We discuss in detail a number of concrete examples, namely semisimple Lie groups, the relativity groups and various types of wavelets. Finally we turn to some physical applications, centering on quantum measurement and the quantization/dequantization problem, that is, the transition from the classical to the quantum level and vice versa.
173 citations
170 citations