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Mesoscopic Phase Fluctuations: General Phenomenon in Condensed Matter

Vyacheslav I. Yukalov

Published Jan 1, 2003• 25 citations
OpenAlex

Abstract

General conditions for the occurrence of mesoscopic phase fluctuations in condensed matter are considered. The description of different thermodynamic phases, which coexist as a mixture of mesoscopically separated regions, is based on the theory of heterophase fluctuations. The spaces of states, typical of the related phases, are characterized by weighted Hilbert spaces. Several models illustrate the main features of heterophase condensed matter.

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General conditions for the occurrence of mesoscopic phase fluctuations in condensed matter are considered. The description of different thermodynamic phases, which coexist as a mixture of mesoscopically separated regions, is based on the theory of heterophase fluctuations. The spaces of states, typical of the related phases, are characterized by weighted Hilbert spaces. Several models illustrate the main features of heterophase condensed matter.
The fluctuations are termed mesoscopic, when their typical size is essentially larger then the average distance between the nearest neighbors, while being much smaller than the overall system size. Since the features of mesoscopic fluctuations are essentially different from those of the surrounding matter, they can be interpreted as fluctuations of one phase occurring inside another host phase. In condensed matter, these fluctuations are of nanosize. They can occur in many-body systems of different nature, for instance, they are typical for condensed matter, can appear in systems of trapped atoms, and also arise in biological and social systems. A survey of the experimental evidence for the occurrence of mesoscopic fluctuations in different materials and systems is given. The main attention is paid to a general theoretical approach for describing them. Applications of the approach are also discussed.
The fluctuations are termed mesoscopic, when their typical size is essentially larger then the average distance between the nearest neighbors, while being much smaller than the overall system size. Since the features of mesoscopic fluctuations are essentially different from those of the surrounding matter, they can be interpreted as fluctuations of one phase occurring inside another host phase. In condensed matter, these fluctuations are of nanosize. They can occur in many-body systems of different nature, for instance, they are typical for condensed matter, can appear in systems of trapped atoms, and also arise in biological and social systems. A survey of the experimental evidence for the occurrence of mesoscopic fluctuations in different materials and systems is given. The main attention is paid to a general theoretical approach for describing them. Applications of the approach are also discussed.
The fluctuations are termed mesoscopic, when their typical size is essentially larger than the average distance between the nearest neighbors, while being much smaller than the overall system size. Since the features of mesoscopic fluctuations are essentially different from those of the surrounding matter, they can be interpreted as fluctuations of one phase occurring inside another host phase. In condensed matter, these fluctuations are of nanosize. They can occur in many-body systems of different nature, for instance, they are typical for condensed matter, can appear in systems of trapped atoms, and also arise in biological and social systems. A survey of the experimental evidence for the occurrence of mesoscopic fluctuations in different materials and systems is given. The main attention is paid to a general theoretical approach for describing them. Applications of the approach are also discussed.
The analytical theory of Bose–Einstein condensation of an ideal gas in mesoscopic systems has been briefly reviewed in application to traps with arbitrary shapes and dimension. This theory describes the phases of the classical gas and the formed Bose–Einstein condensate, as well as the entire vicinity of the phase transition point. The statistics and thermodynamics of Bose–Einstein condensation have been studied in detail, including their self-similar structure in the critical region, transition to the thermodynamic limit, effect of boundary conditions on the properties of a system, and nonequivalence of the description of Bose–Einstein condensation in different statistical ensembles. The complete classification of universality classes of Bose–Einstein condensation has been given.
The review is devoted to the elucidation of the basic problems arising in the theoretical investigation of systems with Bose-Einstein condensate. Understanding these challenging problems is necessary for the correct description of Bose-condensed systems. The principal problems considered in the review are as follows: (i) What is the relation between Bose-Einstein condensation and global gauge symmetry breaking? (ii) How to resolve the Hohenberg-Martin dilemma of conserving versus gapless theories? (iii) How to describe Bose-condensed systems in strong spatially random potentials? (iv) Whether thermodynamically anomalous fluctuations in Bose systems are admissible? (v) How to create nonground-state condensates? Detailed answers to these questions are given in the review. As examples of nonequilibrium condensates, three cases are described: coherent modes, turbulent superfluids, and heterophase fluids.