Kinetics of Phase Transitions

Lifshitz, E.M.; Pitaevski, L.P.

doi:10.1016/b978-0-08-057049-5.50017-5

Cited by 395 publications

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“…the Boltzmann equation). The intensity of the noise spectrum can then found employing a related approach, known as the kinetic theory of fluctuations (KTF) [7,8,9]. The appeal of this approach is its intuitive transparency, yet traditionally it was constructed to describe pair correlation functions, hence was limited to finding the second current cumulant.…”

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“…Indeed, a static electric field E = −∂ x φ(x) can be eliminated from Eqs. (7), (8) by redefining the energy, ǫ+eφ(x) → ǫ. This implies that the counting statistics is the same in the interacting and non-interacting problems for frequencies much smaller than the inverse Thouless time, ω ≪ D/L 2 .…”

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confidence: 99%

“…1 The operatorÎ =Î dis +Î e−ph +Î e−e is the collision integral [8] with the respective contributions coming from disorder, electron-phonon and electron-electron scattering. The Langevin random source δJ(p, x, t) in (1) represents the fluctuations of the net flux of particle in phase space at (p, x).…”

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confidence: 99%

“…Explicit expressions for the collision integrals and the pair correlation functions of the random fluxes are available [8,15].…”

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confidence: 99%

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Kinetic theory of fluctuations in conducting systems

2005

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We propose an effective field theory describing the time dependent fluctuations of electrons in conducting systems, generalizing the well known kinetic theory of fluctuations. We apply then the theory to analyze the effects of strong electron-electron and electron-phonon scattering on the statistics of current fluctuations. We find that if the electron-electron scattering length is much shorter than the transport mean free path the higher cumulants of current are parametrically enhanced.Fluctuations of electric current in time have been the subject of fundamental and applied research since the time of Schottky. They have been a centerpiece in the study of systems ranging from vacuum tubes to quantum Hall bars (for a review see [1]). More recently noise has been recognized as an important diagnostic probe for the nature of disorder and interactions. Traditionally the number of electrons taking part in transport in macroscopic systems is large; for that reason current fluctuations obey nearly Gaussian statistics. Under such circumstances it is the power spectrum which is the object of primary interest when addressing the fluctuations. However, as the sample size shrinks down from a vacuum tube to a nanojunction, and the currents involved become correspondingly smaller, the central limit theorem does not apply any more, and information concerning higher current cumulants may be needed. Various techniques have been applied to address this issue [1,2,3,4,5,6].There is an interesting and relevant class of systems out of equilibrium in which the effect of quantum interference on transport quantities is negligible. Transport through such systems is often described by classical kinetic equations (e.g. the Boltzmann equation). The intensity of the noise spectrum can then found employing a related approach, known as the kinetic theory of fluctuations (KTF) [7,8,9]. The appeal of this approach is its intuitive transparency, yet traditionally it was constructed to describe pair correlation functions, hence was limited to finding the second current cumulant. In a recent insightful work Nagaev [10] has proposed a generalization of the KTF, expressing higher order cumulants in terms of pair correlators. Using this idea (which was termed the "cascade approach"), Nagaev calculated the third and the fourth cumulants of the current. While this approach was shown to successfully address a number of problems, its (quantum-mechanical) microscopic foundations, as well as its formulation in terms of an effective field theory (which would allow for further generalization, such as including interactions or calculating the full counting statistics (FCS)) were not fully understood. An important step in the latter direction was an introduction of a stochastic path integral by Pilgram, Jordan, Sukhorukov, and Büttiker [11].In the present paper we propose a phenomenological effective field theory describing the time dependent fluctuations in phase space of electrons in conducting systems. This is a field-theoretical implementation of the Nagae...

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confidence: 99%

“…Explicit expressions for the collision integrals and the pair correlation functions of the random fluxes are available [8,15].…”

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confidence: 99%

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Kinetic theory of fluctuations in conducting systems

2005

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“…The integral on the r.h.s. is the radial-radial element of the momentum flux tensor δΠ rr (r, ω) for the nuclear quantum liquid [8]. The radial velocity v r (r) is 6) while the radial momentum is p r = mv r .…”

Section: Three-dimensional (Spherical) Casementioning

confidence: 99%

Kinetic-theory approach to low-energy collective modes in nuclei

1999

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Two different solutions of the linearized Vlasov equation for finite systems, characterized by fixed and moving-surface boundary conditions, are discussed in a unified perspective. A condition determining the eigenfrequencies of collective nuclear oscillations, that can be obtained from the moving-surface solution, is studied for isoscalar vibrations of lowest multipolarity. Analytic expressions for the friction and mass parameters related to the low-enegy surface excitations are derived and their value is compared to values given by other models. Both similarities and differences are found with respect to the other approaches, however the close agreement obtained in many cases with one of the other models suggests that, in spite of some important differences, the two approaches are substantially equivalent. The formalism based on the Vlasov equation is more transparent since it leads to analytical expressions that can be a basis for further improvement of the model.

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The Influence of Strain on Point Defect Dynamics

Britton¹,

Härting

2002

Adv. Eng. Mater.

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Stress migration of point and open‐volume defects is already an important problem in a wide variety of applications. These range from the degradation of metallic interconnects in semiconductor devices to smart‐cut processing of Semiconductor‐on‐Insulator structures in semiconductor technology; and from basic metallurgical problems of fatigue and precipitation hardening to radiation damage profiles in ion implantation and surface modification. Often the driving force of the drift is the local stress field of other defects in the material, although other sources of residual stress as well as external loads play an important role. This paper concentrates on the behaviour of non‐equilibrium vacancies in a non‐uniformly strained material. Firstly the basics of defect dynamics, in equilibrium and under the influence of an external driving force, are presented. From these simple illustrative models of one‐ dimensional problems are developed and compared to available experimental results in different ion implanted materials.

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Kinetics of Phase Transitions

Cited by 395 publications

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Kinetic theory of fluctuations in conducting systems

Kinetic theory of fluctuations in conducting systems

Kinetic-theory approach to low-energy collective modes in nuclei

The Influence of Strain on Point Defect Dynamics

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