arXiv subjects

E. P. Yukalova

Publications and source records attributed to E. P. Yukalova.

At least 19 recordsLinked to original sources

arXiv2026

Correlation measure for statistical systems

A measure of correlations for statistical systems is advanced, called correlation index. The measure is general, being applicable to quantum and classical, equilibrium and nonequilibrium statistical systems. After formulating the general notion of correlation indices for arbitrary trace-class operators, the calculation of the correlation indices are illustrated by several examples of density operators and reduced density matrices. The computation of the correlation indices for equilibrium systems is exemplified for bosonic systems with the Bose-Einstein condensate, superconducting systems, and for spin systems. Correlation indices for nonequilibrium systems are considered for nonlinear dynamics of spin and pseudospin systems.

quant-ph↗

arXiv2026

Emotions as intrinsic colored noise in biological systems

The idea that emotions in biological systems are analogous to intrinsic colored noise is advanced and justified. A model describing the dynamics of operation of biological networks under the influence of colored noise is suggested. The agents of a biological network can be represented either by biological species, such as humans and animals, or by neurons of the brain, or by the nodes of a neural network. Operational actions, or decisions, in a biological noisy network are based not only on the evaluation of utility of alternatives, but also on the agents emotions. The model is probabilistic, with the choice of alternatives characterized by the related probabilities. At the initial step, the agents make decisions individually and then start exchanging information with each other and imitating the actions of other agents, thus forming a biological network of interacting agents. Numerical simulations are accomplished for a heterogeneous society consisting of three groups of agents, one group possessing long-range memory, the other group, short-range memory, and the third group of super-rational agents acting strictly on the basis of utility, being deprived of emotions. Dynamics of opinions in different groups can be smooth, oscillatory, or chaotic. Altogether, eight types of operation are found, depending on the dynamics of group decisions. Under strong imitation effect, there appears chaotic motion in the evolution of decision choice. It is shown how the Ellsberg paradox can be resolved and how the exchange of information influences the dynamics of this paradox.

physics.soc-ph↗

arXiv2026

Measuring correlations in quantum and statistical systems

The survey discusses the problem of measuring correlations in composite quantum and statistical systems. After briefly recalling the standard methods of describing correlations, the emphasis is on the method of correlation indices. The latter method for quantifying the strength of correlations in composite physical systems is sufficiently general allowing for measuring in a unique way the correlation strength in both quantum and statistical systems, for static as well as for dynamic processes. The correlation indices, can be defined for correlation operators, reduced density matrices, and other operators containing information on correlations in the studied composite systems. The correlation indices measure all types of correlations, quantum correlations, such as entanglement, as well as classical correlations. They are applicable for characterizing static as well as dynamical processes. Examples are given of correlation indices for several quantum states and for spin and pseudospin systems. The quantification of correlations in a nonequilibrium system is exemplified by calculating the correlation index for a trapped Bose-Einstein condensate subject to the action of an alternating field.

quant-ph↗

arXiv2026

Dynamic probabilistic decision networks

A new type of decision networks is suggested and its operation is analyzed. The network nodes are represented by intelligent agents who can denote either some biological beings, like humans, or neurons of the brain, or the nodes of artificial intelligence. The specifics of the network are in the following: It is probabilistic in the sense that the choice, accomplished by each agent, is characterized by the related probability. It is dynamic, with the probabilities varying in time due to the exchange of information between the agents. It is affective, because the agents choose between alternatives by taking account of utility as well as of biases and emotions. In general, it is heterogeneous, being composed of the groups of agents with different properties, for instance having long-term memory and short-term memory. The network dynamics, caused by the information exchange, results in decision error decrease. The network operation is illustrated by the example starting with the Allais paradox, its resolution, and the decision error diminution in the process of decision dynamics with information exchange. Resorting to machine-learning techniques it is possible to regulate the behavior of the network agents forcing them to choose particular alternatives.

physics.soc-ph↗

arXiv2026

Self-similar summation of virial expansions

Virial expansions are the series in powers of density assumed to be small. However, the equations of state require to consider finite densities for which virial expansions, as a rule, diverge. In order to extrapolate a virial expansion to the values, where this expansion diverges, one uses summation methods. The most often used method is the Padé summation, which has several deficiencies. First of all, Padé approximants are not uniquely defined, suggesting a large table of admissible variants. Second, often there appear spurious unphysical poles. On the contrary, in those cases where the existence of a pole is physically motivated, Padé approximants do not necessarily exhibit it. A new approach for the summation of virial expansions is suggested, based on self-similar approximation theory. The method is regular and uniquely defined. It allows for the determination of physically motivated poles. The accuracy of self-similar approximants is not worse than that of the best Padé approximants with fitting parameters or of Monte Carlo simulations. The self-similar summation is based solely on virial expansions, involving no fitting parameters. In some cases, self-similar summation allows for reconstructing the sought functions exactly. The approach is illustrated by summing virial expansions for hard-disk fluids, hard-sphere fluids, and systems with power-law potentials.

cond-mat.stat-mech↗

arXiv2026

Ordering in statistical systems on the way to the thermodynamic limit

It is well known that the mathematically accurate description of ordering and related symmetry breaking in statistical systems requires to consider the thermodynamic limit. But the order does not appear from nowhere, and yet before the thermodynamic limit is reached, there should exist some kind of preordering that appears and grows in the process of increasing the system size. The quantitative description of growing order, under the growing system size, is developed by introducing the notion of {\it order indices}. The rigorous proof of the phase transition existence is a separate difficult problem that is not the topic of the present paper. We illustrate the approach resorting to several models in the mean-field approximation, which makes it possible to demonstrate the notion of order indices for finite systems in a clear way. We show how the order grows on the way to the thermodynamic limit for Bose-Einstein condensation, arising superconductivity, magnetization, and crystallization phenomena.

cond-mat.stat-mech↗

arXiv2026

Mesoscopic Fluctuations in Statistical Systems

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.

cond-mat.stat-mech↗

arXiv2025

Dynamical Transitions in Trapped Superfluids Excited by Alternating Fields

The paper presents a survey of some dynamical transitions in nonequilibrium trapped Bose-condensed systems subject to the action of alternating fields. Nonequilibrium states of trapped systems can be realized in two ways, resonant and nonresonant. Under resonant excitation, several coherent modes are generated by external alternating fields, whose frequencies are tuned to resonance with some transition frequencies of the trapped system. A Bose system of trapped atoms with Bose-Einstein condensate can display two types of the Josephson effect, the standard one, when the system is separated into two or more parts in different locations or when there are no any separation barriers, but the system becomes nonuniform due to the coexistence of several coherent modes interacting with each other, which is termed internal Josephson effect. The mathematics in both these cases is similar. We concentrate on the internal Josephson effect. Systems with nonlinear coherent modes demonstrate rich dynamics, including Rabi oscillations, Josephson effect, and chaotic motion. Under Josephson effect, there exist dynamic transitions that are similar to phase transitions in equilibrium systems. The bosonic Josephson effect is shown to be realizable not only for weakly interacting systems, but also in superfluids, with not necessarily weak interactions. Sufficiently strong nonresonant excitation can generate several types of nonequilibrium states comprising vortex germs, vortex rings, vortex lines, vortex turbulence, droplet turbulence, and wave turbulence. Nonequilibrium states can be characterized and distinguished by effective temperature, effective Fresnel number, and dynamic scaling laws.

cond-mat.quant-gas↗

arXiv2025

Measure of entanglement production by quantum operations

A measure of entanglement production by quantum operations is suggested. This measure is general, being valid for operations over pure states as well as over mixed states, for equilibrium as well as for nonequilibrium processes. The measure of entanglement production satisfies all properties typical of such a characteristic. Systems of arbitrary nature can be treated, described by field operators, spin operators, or any other operators, which is realized by defining generalized correlation matrices. Particular cases of entanglement production are considered.

quant-ph↗

arXiv2025

Self-similar renormalization for nonlinear problems

A new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory. It allows for the effective extrapolation of asymptotic series in powers of small variables to the finite and even to infinite variables. The approach is proved to be regular. It is illustrated by several examples demonstrating good agreement with numerical calculations. The method is shown to provide accurate approximate solutions to complex nonlinear problems. In some cases, the method allows for the reconstruction of exact solutions on the basis of rather short perturbative series.

math-ph↗

arXiv2025

Self-Similar Bridge between Regular and Critical Regions

In statistical and nonlinear systems, two qualitatively distinct parameter regions are typically identified: the regular region, characterized by smooth behavior of key quantities, and the critical region, where these quantities exhibit singularities or strong fluctuations. Due to their starkly different properties, these regions are often perceived as being weakly related, if at all. However, we demonstrate that these regions are intimately connected, a relationship that can be explicitly revealed using self-similar approximation theory. This framework enables the prediction of observable quantities near the critical point based on information from the regular region and vice versa. Remarkably, the method relies solely on asymptotic expansions with respect to a parameter, regardless of whether the expansion originates in the regular or critical region. The mathematical principles of self-similar theory remain consistent across both cases. We illustrate this connection by extrapolating from the regular region to predict the existence, location, and critical indices of a critical point of an equation of state for a statistical system, even when no direct information about the critical region is available. Conversely, we explore extrapolation from the critical to the regular region in systems with discrete scale invariance, where log-periodic oscillations in observables introduce additional complexity. Our findings provide insights and solutions applicable to diverse phenomena, including material fracture, stock market crashes, and earthquake forecasting.

cond-mat.stat-mech↗

arXiv2025

Quantum systems of atoms with highly singular interaction potentials

Quantum statistical systems, composed of atoms or molecules interacting with each other through highly singular non-integrable potentials, are considered. The treatment of such systems cannot start with the standard approximations such as Hartree, Hartree-Fock or Hartree-Fock-Bogolubov approximations because of non-integrability of the interaction potentials leading to divergences. It is shown that the iterative procedure for Green functions can be rearranged so that the starting approximation takes into account regularizing atomic correlations. Then all the following approximation orders contain only the regularized interaction potential producing no divergences. The method of constructing the regularizing correlation function is suggested, based on the solution of the scattering equation in the form of asymptotic series at short distance, which can be extrapolated to arbitrary spatial variables by means of self-similar approximation theory. Regularizing correlation functions for several kinds of atomic systems are exemplified.

quant-ph↗

arXiv2024

Nonlinear coherent modes and atom optics

By pumping energy into a trapped Bose-Einstein condensate it is possible to generate nonlinear coherent modes representing non-ground-state condensates. A Bose-condensed system of trapped atoms with nonlinear coherent modes is analogous to a finite-level atom considered in optics which can be excited by applying external fields. The excitation of finite-level atoms produces a variety of optical phenomena. In the similar way, the generation of nonlinear coherent modes in a trapped condensate results in many phenomena studied in what is termed atom optics. For example, there occur such effects as interference patterns, interference current, Rabi oscillations, harmonic generation, parametric conversion, Ramsey fringes, mode locking, and a dynamic transition between Rabi and Josephson regimes. The possibility of creating mesoscopic entangled states of trapped atoms and entanglement production by atomic states in optical lattices are studied.

cond-mat.quant-gas↗

arXiv2024

Strong-Coupling Extrapolation of Gell-Mann--Low Functions

Gell-Mann-Low functions can be calculated by means of perturbation theory and expressed as truncated series in powers of asymptotically small coupling parameters. However, it is necessary to know there behavior at finite values of the parameter and, moreover, their behavior at asymptotically large coupling parameters is also important. The problem of extrapolation of weak-coupling expansions to the region of finite and even infinite coupling parameters is considered. A method is suggested allowing for such an extrapolation. The basics of the method are described and illustrations of its applications are given for the examples where its accuracy and convergence can be checked. It is shown that in some cases the method allows for the exact reconstruction of the whole functions from their weak-coupling asymptotic expansions. Gell-Mann-Low functions in multicomponent field theory, quantum electrodynamics, and quantum chromodynamics are extrapolated to their strong-coupling limits.

hep-ph↗

arXiv2024

Atom Optics with Cold Bosons

Trapped bosonic atoms can be cooled down to temperatures where the atomic cloud experiences Bose-Einstein condensation. Almost all atoms in a dilute gaseous system can be Bose-condensed, which implies that this system is in a coherent state. The coherent atomic system enjoys many properties typical of coherent optical systems. It is possible to generate different condensate coherent modes similarly to the generation of optical modes. Several effects can be observed, such as interference patterns, interference current, Rabi oscillations, harmonic generation, parametric conversion, Ramsey fringes, mode locking, dynamic transition between Rabi and Josephson regimes, and atomic squeezing.

cond-mat.quant-gas↗

arXiv2024

Regulating spin dynamics of dipolar and spinor atoms

Systems of atoms or molecules can possess nonzero total spins that can be employed in spintronics, for instance for creating memory devices, which requires to be able to efficiently regulate spin directions. This article presents some methods of regulating spin dynamics, developed by the authors. These methods can be applied for different physical systems, described by different Hamiltonians including the interactions of spins with magnetic fields. The principal feature of the methods is the use of the feedback fields formed by moving spins.

cond-mat.mes-hall↗

arXiv2024

Strong-coupling limits induced by weak-coupling expansions

A method is described for the extrapolation of perturbative expansions in powers of asymptotically small coupling parameters or other variables onto the region of finite variables and even to the variables tending to infinity. The method involves the combination of ideas from renormalization group theory, approximation theory, dynamical theory, and optimal control theory. The extrapolation is realized by means of self-similar factor approximants, whose control parameters can be uniquely defined. The method allows to find the large-variable behavior of sought functions knowing only their small-variable expansions. Convergence and accuracy of the method are illustrated by explicit examples, including the so-called zero-dimensional field theory and anharmonic oscillator. Strong-coupling behavior of Gell-Mann-Low functions in multicomponent field theory, quantum electrodynamics, and quantum chromodynamics is found, being based on their weak-coupling perturbative expansions.

hep-ph↗

arXiv2023

Trapped Bose-Einstein condensates with nonlinear coherent modes

The review presents the methods of generation of nonlinear coherent excitations in strongly nonequilibrium Bose-condensed systems of trapped atoms and their properties. Non-ground-state Bose-Einstein condensates are represented by nonlinear coherent modes. The principal difference of nonlinear coherent modes from linear collective excitations is emphasized. Methods of generating nonlinear modes and the properties of the latter are described. Matter-wave interferometry with coherent modes is discussed, including such effects as interference patterns, internal Josephson current, Rabi oscillations, Ramsey fringes, harmonic generation, and parametric conversion. Dynamic transition between mode-locked and mode-unlocked regimes is shown to be analogous to a phase transition. Atomic squeezing and entanglement in a lattice of condensed atomic clouds with coherent modes are considered. Nonequilibrium states of trapped Bose-condensed systems, starting from weakly nonequilibrium state, vortex state, vortex turbulence, droplet or grain turbulence, and wave turbulence, are classified by means of effective Fresnel and Mach numbers. The inverse Kibble-Zurek scenario is described. A method for the formation of directed beams from atom lasers is reported.

cond-mat.quant-gas↗