Coherent states: Theory and some applications

Zhang, Wei Min; Feng, Da Hsuan; Gilmore, Robert

doi:10.1103/revmodphys.62.867

Cited by 1,462 publications

(1,492 citation statements)

References 175 publications

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“…34 The multiphonon operators appearing in the nonadiabatic terms of the transformed Holstein Hamiltonian assume such form, with c 2 ϭϪc 1 * , characteristic of the displacement operator which generates coherent states when acting on the linear-harmonic-oscillator vacuum. 35 However, in our case one is confronted with the more complicated thermal expectation values. One type of thermal average we have to perform is…”

Section: ͑A2͒mentioning

confidence: 99%

Nonlocal electron-phonon coupling: Consequences for the nature of polaron states

2004

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We develop a variational approach to an extended Holstein model, comprising both local and nonlocal electron-phonon coupling. The approach is based on the minimization of a Bogoliubov bound to the Helmholtz free energy. The ambivalent character of nonlocal coupling, which both promotes and hinders transport, is clearly observed. Furthermore, a salient feature of our results is that the local and nonlocal couplings can compensate each other, leading to a reduction of polaronic effects and a quasi-free character of the excitation. Our findings have implications for organic crystals of -conjugated molecules, where this electron-phonon coupling mechanism plays an important role.

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Section: ͑A2͒mentioning

confidence: 99%

Nonlocal electron-phonon coupling: Consequences for the nature of polaron states

2004

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“…A family of generalized coherent states consists of an orbit of a dynamical group acting on a state space [23,24]. According to this definition, every state is in a family of generalized coherent states.…”

Section: The Lie-algebraic Settingmentioning

confidence: 99%

“…To show that the ideas of entanglement, separability and product states do not critically depend on the two subsystems, we provide several ways in which product states can be characterized in terms of h alone. All of these ways lead to the same concept for general semisimple Lie algebras, namely that of generalized coherent states [22,23,24]. It is therefore natural to consider product states to be special kinds of coherent states.…”

Section: Introductionmentioning

confidence: 99%

“…The recognition that incoherence naturally generalizes entanglement makes explicit the dependence of the notion of entanglement on the relevant Lie algebra and makes available the tools of the theory of generalized coherent states [23,24] for investigating aspects of entanglement. To extend the power of this perspective to the information-theoretic applications of entanglement requires introducing measures of entanglement, generalizing the ways in which entanglement can be manipulated and providing a means for using states as a resource.…”

Section: Introductionmentioning

confidence: 99%

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Generalizations of entanglement based on coherent states and convex sets

et al. 2003

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Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence and (non-)entanglement. To a large extent, these concepts can be defined and studied in the even more general setting of convex cones of states. Based on the idea that entanglement is relative, we suggest considering these notions in the context of partially ordered families of Lie algebras or convex cones, such as those that arise naturally for multipartite systems. The study of entanglement includes notions of local operations and, for information-theoretic purposes, entanglement measures and ways of scaling systems to enable asymptotic developments. We propose ways in which these may be generalized to the Lie-algebraic setting, and to a lesser extent to the convex-cones setting. One of our motivations for this program is to understand the role of entanglement-like concepts in condensed matter. We discuss how our work provides tools for analyzing the correlations involved in quantum phase transitions and other aspects of condensed-matter systems. * barnum@lanl.gov † knill@lanl.gov ‡ g ortiz@lanl.gov § lviola@lanl.gov 2 Contents

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“…To extract the time-evolution equation of carrier wavefunction only, we expand jWðtÞi in the basis set of the unnormalized Bargmann coherent states [50,51] for phonon motions…”

Section: The Mtdpwd Methodsmentioning

confidence: 99%

Time‐dependent wavepacket diffusion method and its applications in organic semiconductors

Han

Zhong

et al. 2014

Int J of Quantum Chemistry

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Although the carriers in organic semiconductors commonly follow the hopping-type motions caused by strong carrierphonon interactions, they can also present a band-like behavior in well-performed organic crystals. In this article, we review a unified model to describe the carrier dynamics covering from the hopping-type to band-like motions, the timedependent wavepacket diffusion method proposed in our group recently. In the method, the effects of vibrational motions of organic molecules and inter or intramolecular electronic couplings are considered as the fluctuations to the carrier dynamics. Numerical simulations demonstrate that the computational cost of present method is similar to that of mixed quantum-classical methods, but it overcomes the deficiency in those methods that the detailed balance principle is not satisfied. We further present how to combine electronic structure calculations and molecular dynamics simulations with the present model to reveal the carrier dynamics in realistic organic semiconductors.

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Coherent states: Theory and some applications

Cited by 1,462 publications

References 175 publications

Nonlocal electron-phonon coupling: Consequences for the nature of polaron states

Nonlocal electron-phonon coupling: Consequences for the nature of polaron states

Generalizations of entanglement based on coherent states and convex sets

Time‐dependent wavepacket diffusion method and its applications in organic semiconductors

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