Biomedical subjects

V I Yukalov

Publications and source records attributed to V I Yukalov.

6 recordsLinked to original sources

PubMed2005

Fluctuations of composite observables and stability of statistical systems.

Thermodynamic stability of statistical systems requires that susceptibilities be semipositive and finite. Susceptibilities are known to be related to the fluctuations of extensive observable quantities. This relation becomes nontrivial, when the operator of an observable quantity is represented as a sum of operators corresponding to the extensive system parts. The association of the dispersions of the partial operator terms with the total dispersion is analyzed. Special attention is paid to the dependence of dispersions on the total number of particles in the thermodynamic limit. An operator dispersion is called thermodynamically normal if it is proportional to at large values of the latter. While, if the dispersion is proportional to a higher power of , it is termed thermodynamically anomalous. The following theorem is proved: The global dispersion of a composite operator, which is a sum of linearly independent self-adjoint terms, is thermodynamically anomalous if and only if at least one of the partial dispersions is anomalous, the power of in the global dispersion being defined by the largest partial dispersion. Conversely, the global dispersion is thermodynamically normal if and only if all partial dispersions are normal. The application of the theorem is illustrated by several examples of statistical systems. The notion of representative ensembles is formulated. The relation between the stability and equivalence of statistical ensembles is discussed.

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PubMed2005

Self-similar variational perturbation theory for critical exponents.

We extend field theoretic variational perturbation theory by self-similar approximation theory, which greatly accelerates convergence. This is illustrated by recalculating the critical exponents of O (N) -symmetric phi(4) theory. From only three-loop perturbation expansions in 4-epsilon dimensions, we obtain analytic results for the exponents, which are close to those derived recently from ordinary field-theoretic variational perturbational theory to seventh order. In particular, the specific-heat exponent is found to be in good agreement with best-measured exponent alpha approximately -0.0127 of the specific-heat peak in superfluid helium, found in a satellite experiment. In addition, our analytic expressions reproduce also the exactly known large- N behavior of the exponents.

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PubMed2003

Entanglement measure for composite systems.

A general description of entanglement is suggested as an action realized by an arbitrary operator over given disentangled states. The related entanglement measure is defined. Because of its generality, this definition can be employed for any physical systems, pure or mixed, equilibrium or nonequilibrium, and characterized by any type of operators, whether these are statistical operators, field operators, spin operators, or anything else. Entanglement of any number of parts from their total ensemble forming a multiparticle composite system can be determined. Interplay between entanglement and ordering, occurring under phase transitions, is analyzed by invoking the concept of operator order indices.

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PubMed2003

Self-similar factor approximants.

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Padé approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Padé approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties.

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PubMed2002

Processing information by punctuated spin superradiance.

The possibility of realizing the regime of punctuated spin superradiance is advanced. In this regime, the number of superradiant pulses and the temporal intervals between them can be regulated. This makes it feasible to compose a kind of a Morse code alphabet and, hence, to develop a technique of processing information.

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PubMed2002

Stochastic instability of quasi-isolated systems.

The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with respect to infinite time describes the asymptotic stability of a stochastic dynamical system. Another limit of the stability index is given by the vanishing intensity of stochastic perturbations. A dynamical system is stochastically unstable when these two limits do not commute with each other. Several examples illustrate the thesis that there always exist such stochastic perturbations that render a given dynamical system stochastically unstable. The stochastic instability of quasi-isolated systems is responsible for the irreversibility of time arrow.

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