Quantum Statistics in Optics and Solid-State Physics

Graham, R. H.; Haake, Fritz

doi:10.1007/bfb0044954

Cited by 121 publications

(70 citation statements)

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“…The development of a corresponding statistical theory of states far from equilibrium is still far from being completed [2,4,5]. We will show here that there exists a special class of open systems, the so-called canonical dissipative systems, where an ensemble theory may be developed in a way which is quite similar to the Gibbs theory [6][7][8][9][10][11]. This theory is closely related to Klimontovich's statistical theory of open systems on the one hand [5] and to the theory of active Brownian particles [12][13][14][15][16][17] on the other hand.…”

Section: Introductionmentioning

confidence: 93%

“…The main new topic in this work is constructing a bridge to the semiclassical kinetic theory of quantum gases proposed first by Nordheim, Uehling and Uhlenbeck [18,19]. Our approach is based on the theory of canonical-dissipative systems which is an extension of the statistical physics of Hamiltonian systems to a special type of dissipative systems [6][7][8][9][10][11]. The term dissipative means here that the system is non-conservative and the term canonical means that the dissipative as well as the conservative parts of the dynamics are both determined by the Hamilton function H or by another invariant c W.Ebeling of motion.…”

Section: Introductionmentioning

confidence: 99%

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Canonical Nonequilibrium Statistics and Applications to Fermi-Bose Systems

Ebeling¹

2000

Condens. Matter Phys.

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The aim of this work is the study of a special class of nonequilibrium systems which admits to find exact stationary solutions of the kinetic equations. In particular we investigate canonical-dissipative systems, where the driving terms are determined by the Hamiltonian or other invariants of motion only. We construct systems which drive the system to special invariants of motion and solve the corresponding Fokker-Planck equations. Finally several applications to mean-field problems for fermion and for boson systems are discussed.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Canonical Nonequilibrium Statistics and Applications to Fermi-Bose Systems

Ebeling¹

2000

Condens. Matter Phys.

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“…The equations for optimal paths can be found using the eikonal approximation to solve the corresponding Fokker-Plank equation, or by using a path integral formulation and evaluating the path integral over the fluctuational paths in the steepest descent approximation (for details and discussion see [42,57,64,65,71,72,73,117]). The optimal path of a periodically driven system corresponds to the locus traced out by the maximum in the prehistory probability density, p h (q, φ| q f , φ f ) [60,123].…”

Section: Theorymentioning

confidence: 99%

“…Using the path-integral expression for the transition probability density [64], one can write p h in the form [60] …”

Section: Fluctuational Escape and Related Phenomenamentioning

confidence: 99%

“…Let us fix the parameter r = 24.08 in this range and consider the noise-induced escape for the chaotic attractor to the basins of attraction of the stable points. Note that in [64] the invariant measure of the noisy Lorenz attractor was found within a Hamiltonian formalism, but large deviations from a chaotic attractor were not considered.…”

Section: Fluctuational Escape From a Quasi-hyperbolic Attractormentioning

confidence: 99%

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Fluctuational Escape and Related Phenomena in Nonlinear Optical Systems

Khovanov

Luchinsky

Mannella

et al.

Modern Nonlinear Optics, Part III

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ii FLUCTUATIONAL ESCAPE AND RELATED PHENOMENA been selected mainly for their own intrinsic scientific interest, but also in order to provide an indication of the power and utility of the simulation approach as a means of focusing on, and reaching an understanding of, the essential physics underlying the phenomena under investigation; they also provide examples of different theoretical approaches and situations where numerical and analogue simulations have led to the development of new experimental techniques and new ideas with potential technological significance. Although the different Sections all share the same general theme -of fluctuational escape phenomena in model nonlinear optical systems -they deal with quite different aspects of the subject; each of them is therefore to a considerable extent self-contained (with Secs. 1.4 and 1.5 being exceptions, because they should be read after Sec. 1.3) and thus can be read almost independently of the others. Before considering particular systems, we review briefly the scientific context of the work and discuss in a general way the significance of escape phenomena in nonlinear optics.The investigation of fluctuations by means of analog or digital simulation is usually found most useful for those systems where the fluctuations of the quantities of immediate physical interest can be assumed to be due to noise. The latter perception of fluctuations goes back to Einstein, Smoluchowski, and Langevin [2, 3, 4] and has often been used in optics (cf. Refs. [5,6,7,8]). In nonlinear optics, the noise can be regarded as arising from two main sources. First there are internal fluctuations in the macroscopic system itself. These arise because spontaneous emission of light by individual atoms occurs at random, and because of fluctuations in the populations of atomic energy levels. The physical characteristics of such noise are usually closely related to the physical characteristics of the model that describes the "regular" dynamics of the system, i.e. in the absence of noise. In particular, the power spectrum of thermal noise and its intensity can be expressed in terms of the dissipation characteristics via the fluctuation-dissipation relations (cf. Ref. [9]) and, if the dissipation is non-retarded so that the corresponding dissipative forces (e.g. the friction force) depend only on the instantaneous values of dynamical variables, the noise power spectrum is independent of frequency, i.e. the noise is white. The model of noise as being white and Gaussian is one of the most commonly used in optics because the quantities of physical interest often vary slowly compared with the fast random processes that give rise to the noise, like emission or absorption of a photon [5,6,7,8]. The second very important source of noise is external: for example, fluctuations of the pump power in a laser. The physical characteristics of such noise naturally vary from one particular system to another; its correlation time is often much longer than that of the internal noise, and its effects can be larg...

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