arXiv subjects

Z. A. Mayzelis

Publications and source records attributed to Z. A. Mayzelis.

9 recordsLinked to original sources

arXiv2008

Non-additive properties of finite 1D Ising chains with long-range interactions

We study the statistical properties of Ising spin chains with finite (although arbitrary large) range of interaction between the elements. We examine mesoscopic subsystems (fragments of an Ising chain) with the lengths comparable with the interaction range. The equivalence of the Ising chains and the multi-step Markov sequences is used for calculating different non-additive statistical quantities of a chain and its fragments. In particular, we study the variance of fluctuating magnetization of fragments, magnetization of the chain in the external magnetic field, etc. Asymptotical expressions for the non-additive energy and entropy of the mesoscopic fragments are derived in the limiting cases of weak and strong interactions.

cond-mat.stat-mech↗

arXiv2008

Hysteretic jumps in the response of layered superconductors to electromagnetic fields

We consider here a layered superconductor subject to an externally applied moderately-strong electromagnetic field. We predict hysteretic jumps in the dependence of the surface reactance of the superconductor on the amplitude of the incident electromagnetic wave. This very unusual nonlinear phenomenon can be observed in thin superconducting slabs at not very strong ac amplitudes, if the frequency of the irradiating field is close to the Josephson plasma frequency. Using the set of coupled sine-Gordon equations, we derive the expression for the phase shift of the reflected wave and obtain the conditions for the appearance of hysteresis.

cond-mat.supr-con↗

arXiv2007

Signum Function Method for Generation of Correlated Dichotomic Chains

We analyze the signum-generation method for creating random dichotomic sequences with prescribed correlation properties. The method is based on a binary mapping of the convolution of continuous random numbers with some function originated from the Fourier transform of a binary correlator. The goal of our study is to reveal conditions under which one can construct binary sequences with a given pair correlator. Our results can be used in the construction of superlattices and waveguides with selective transport properties.

cond-mat.dis-nn↗

arXiv2007

Non-extensive thermodynamics of 1D systems with long-range interaction

A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov chains. This general approach is applied to the Ising spin chain with long-range interaction between its elements. The asymptotical expressions for the energy and entropy of the system are derived for the limiting case of weak interaction. These thermodynamical quantities are found to be non-proportional to the length of the system (number of its particle).

physics.data-an↗

arXiv2006

High-Order Correlation Functions of Binary Multi-Step Markov Chains

Two approaches to studying the correlation functions of the binary Markov sequences are considered. The first of them is based on the study of probability of occurring different ''words'' in the sequence. The other one uses recurrence relations for correlation functions. These methods are applied for two important particular classes of the Markov chains. These classes include the Markov chains with permutative conditional probability functions and the additive Markov chains with the small memory functions. The exciting property of the self-similarity (discovered in Phys. Rev. Lett. 90, 110601 (2003) for the additive Markov chain with the step-wise memory function) is proved to be the intrinsic property of any permutative Markov chain. Applicability of the correlation functions of the additive Markov chains with the small memory functions to calculating the thermodynamic characteristics of the classical Ising spin chain with long-range interaction is discussed.

physics.data-an↗

arXiv2006

Isotropy Properties of the Multi-Step Markov Symbolic Sequences

A new object of the probability theory, the two-sided chain of symbols (introduced in Ref. arXiv:physics/0306170) is used to study isotropy properties of binary multi-step Markov chains with the long-range correlations. Established statistical correspondence between the Markov chains and certain two-sided sequences allows us to prove the isotropy properties of three classes of the Markov chains. One of them is the important class of weakly correlated additive Markov chains, which turned out to be equivalent to the additive two-sided sequences.

physics.data-an↗

arXiv2006

Additive N-Step Markov Chains as Prototype Model of Symbolic Stochastic Dynamical Systems with Long-Range Correlations

A theory of symbolic dynamic systems with long-range correlations based on the consideration of the binary N-step Markov chains developed earlier in Phys. Rev. Lett. 90, 110601 (2003) is generalized to the biased case (non equal numbers of zeros and unities in the chain). In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function of the number of unities (zeros) among the preceding N symbols. The correlation and distribution functions as well as the variance of number of symbols in the words of arbitrary length L are obtained analytically and verified by numerical simulations. A self-similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented. The diffusion Fokker-Planck equation governing the distribution function of the L-words is explored. If the persistent correlations are not extremely strong, the distribution function is shown to be the Gaussian with the variance being nonlinearly dependent on L. An equation connecting the memory and correlation function of the additive Markov chain is presented. This equation allows reconstructing a memory function using a correlation function of the system. Effectiveness and robustness of the proposed method is demonstrated by simple model examples. Memory functions of concrete coarse-grained literary texts are found and their universal power-law behavior at long distances is revealed.

physics.data-an↗

arXiv2006

Equivalence of Markov's Symbolic Sequences to Two-Sided Chains

A new object of the probability theory, two-sided chain of events (symbols), is introduced. A theory of multi-steps Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to establish the correspondence between these chains and two-sided ones. The Markov chain is proved to be statistically equivalent to the definite two-sided one and vice versa. The results obtained for the binary chains are generalized to the chains taking on the arbitrary number of states.

physics.data-an↗

arXiv2006

Memory functions and Correlations in Additive Binary Markov Chains

A theory of additive Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such systems, a memory function, and its relation to the correlation properties of the systems are examined. Various methods for finding the memory function via the correlation function are proposed. The inverse problem (calculation of the correlation function by means of the prescribed memory function) is also solved. This is demonstrated for the analytically solvable model of the system with a step-wise memory function.

physics.data-an↗