arXiv subjects

V. I. Yukalov

Publications and source records attributed to V. I. Yukalov.

At least 91 records · Page 5Linked to original sources

arXiv2018

Characterization of nonequilibrium states of trapped Bose-Einstein condensates

Generation of different nonequilibrium states in trapped Bose-Einstein condensates is studied by numerically solving nonlinear Schrodinger equation. Inducing nonequilibrium states by shaking the trap, the following states are created: weak nonequilibrium, the state of vortex germs, the state of vortex rings, the state of straight vortex lines, the state of deformed vortices, vortex turbulence, grain turbulence, and wave turbulence. A characterization of nonequilibrium states is advanced by introducing effective temperature, Fresnel number, and Mach number.

cond-mat.quant-gas↗

arXiv2018

Dipolar and spinor bosonic systems

The main properties and methods of describing dipolar and spinor atomic systems, composed of bosonic atoms or molecules, are reviewed. The general approach for the correct treatment of Bose-condensed atomic systems with nonlocal interaction potentials is explained. The approach is applied to Bose-condensed systems with dipolar interaction potentials. The properties of systems with spinor interaction potentials are described. Trapped atoms and atoms in optical lattices are considered. Effective spin Hamiltonians for atoms in optical lattices are derived. The possibility of spintronics with cold atom is emphasized. The present review differs from the previous review articles by concentrating on a thorough presentation of basic theoretical points, helping the reader to better follow mathematical details and to make clearer physical conclusions.

cond-mat.quant-gas↗

arXiv2018

Local condensate depletion at trap center under strong interactions

Cold trapped Bose-condensed atoms, interacting via hard-sphere repulsive potentials are considered. Simple mean-field approximations show that the condensate distribution inside a harmonic trap always has the shape of a hump with the maximum condensate density occurring at the trap center. However Monte Carlo simulations at high density and strong interactions display the condensate depletion at the trap center. The explanation of this effect of local condensate depletion at trap center is suggested in the frame of self-consistent theory of Bose-condensed systems. The depletion is shown to be due to the existence of the anomalous average that takes into account pair correlations and appears in systems with broken gauge symmetry.

cond-mat.quant-gas↗

arXiv2018

Quantitative Predictions in Quantum Decision Theory

Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the theory of quantum measurements, which makes this approach relevant both for the description of decision making of humans and the creation of artificial quantum intelligence. General rules are formulated allowing for the explicit calculation of quantum probabilities representing the fraction of decision makers preferring the considered prospects. This provides a method to quantitatively predict decision-maker choices, including the cases of games with high uncertainty for which the classical expected utility theory fails. The approach is applied to experimental results obtained on a set of lottery gambles with gains and losses. Our predictions, involving no fitting parameters, are in very good agreement with experimental data. The use of quantum decision making in game theory is described. A principal scheme of creating quantum artificial intelligence is suggested.

physics.soc-ph↗

arXiv2018

Effects of Symmetry Breaking in Resonance Phenomena

We show that resonance phenomena can be treated as nonequilibrium phase transitions. Resonance phenomena, similar to equilibrium phase transitions, are accompanied by some kind of symmetry breaking and can be characterized by order parameters. This is demonstrated for spin-wave resonance, helicon resonance, and spin-reversal resonance.

cond-mat.mes-hall↗

arXiv2017

Critical indices from self-similar root approximants

The method of self-similar root approximants has earlier been shown to provide accurate interpolating formulas for functions for which small-variable expansions are given and the behaviour of the functions at large variables is known. Now this method is generalized for the purpose of extrapolating small-variable expansions to the region of finite and large variables, where the sought function exhibits critical behaviour. The procedure of calculating critical indices is formulated and illustrated by a variety of physical problems.

cond-mat.stat-mech↗

arXiv2017

Information Processing by Networks of Quantum Decision Makers

We suggest a model of a multi-agent society of decision makers taking decisions being based on two criteria, one is the utility of the prospects and the other is the attractiveness of the considered prospects. The model is the generalization of quantum decision theory, developed earlier for single decision makers realizing one-step decisions, in two principal aspects. First, several decision makers are considered simultaneously, who interact with each other through information exchange. Second, a multistep procedure is treated, when the agents exchange information many times. Several decision makers exchanging information and forming their judgement, using quantum rules, form a kind of a quantum information network, where collective decisions develop in time as a result of information exchange. In addition to characterizing collective decisions that arise in human societies, such networks can describe dynamical processes occurring in artificial quantum intelligence composed of several parts or in a cluster of quantum computers. The practical usage of the theory is illustrated on the dynamic disjunction effect for which three quantitative predictions are made: (i) the probabilistic behavior of decision makers at the initial stage of the process is described; (ii) the decrease of the difference between the initial prospect probabilities and the related utility factors is proved; (iii) the existence of a common consensus after multiple exchange of information is predicted. The predicted numerical values are in very good agreement with empirical data.

physics.soc-ph↗

arXiv2017

Bose-Einstein condensation temperature of weakly interacting atoms

The critical temperature of Bose-Einstein condensation essentially depends on internal properties of the system as well as on the geometry of a trapping potential. The peculiarities of defining the phase transition temperature of Bose-Einstein condensation for different systems are reviewed, including homogenous Bose gas, trapped Bose atoms, and bosons in optical lattices. The method of self-similar approximants, convenient for calculating critical temperature, is briefly delineated.

cond-mat.quant-gas↗

arXiv2017

Entanglement production by evolution operator

Entanglement production, generated by an evolution operator, is considered. The measure of entanglement production, introduced earlier by one of the authors, is employed. As an illustration, a two-qubit register is studied and the corresponding measure of evolutional entanglement production is calculated. Such two-qubit registers can be realized by atomic systems in a double well or by trapped atoms with two coherent modes.

quant-ph↗

arXiv2017

Dynamic Transition in Symbiotic Evolution Induced by Growth Rate Variation

In a standard bifurcation of a dynamical system, the stationary points (or more generally attractors) change qualitatively when varying a control parameter. Here we describe a novel unusual effect, when the change of a parameter, e.g. a growth rate, does not influence the stationary states, but nevertheless leads to a qualitative change of dynamics. For instance, such a dynamic transition can be between the convergence to a stationary state and a strong increase without stationary states, or between the convergence to one stationary state and that to a different state. This effect is illustrated for a dynamical system describing two symbiotic populations, one of which exhibits a growth rate larger than the other one. We show that, although the stationary states of the dynamical system do not depend on the growth rates, the latter influence the boundary of the basins of attraction. This change of the basins of attraction explains this unusual effect of the quantitative change of dynamics by growth rate variation.

q-bio.PE↗

arXiv2017

Critical Temperature in Weakly Interacting Multicomponent Field Theory

A method is suggested for calculating the critical temperature in multicomponent field theory with weak interactions. The method is based on self-similar approximation theory allowing for the extrapolation of series in powers of asymptotically small coupling to finite and even infinite couplings. The extrapolation for the critical temperature employs self-similar factor approximants. The found results are in perfect agreement with Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2017

Quantum Probabilities as Behavioral Probabilities

We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.

q-bio.NC↗

arXiv2017

Additive self-similar approximants

A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical convergence is demonstrated for the cases that can be compared with exact solutions, when these are available. The method is shown to be not less and as a rule essentially more accurate than that of Pade approximants. Comparison with other approximation methods is also given.

math-ph↗

arXiv2016

Quantum decision theory in simple risky choices

Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker's choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) data, and find that the results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. This article revisits the formalism of QDT along a concrete example and offers a practical guide to researchers who are interested in applying QDT to a dataset of binary lotteries in the domain of gains.

physics.soc-ph↗

arXiv2016

Nanoscale Phase Separation in Ferroelectric Materials

Many materials exhibit nanoscale phase separation, when inside the host thermodynamic phase there arise nanosize embryos of another thermodynamic phase. A prominent example of this phenomenon is provided by ferroelectric materials. The theoretical description of such phase heterogeneous materials is quite challenging, since they are essentially nonuniform, the nonuniformity is random, and often they are quasiequilibrium, but not absolutely equilibrium. An approach is suggested for the theoretical description of phase separated ferroelectrics, consisting of a ferroelectric matrix with nanoscale paraelectric inclusions. The properties of the heterophase ferroelectrics are studied.

cond-mat.mes-hall↗

arXiv2016

Statistical systems with nonintegrable interaction potentials

Statistical systems composed of atoms interacting with each other trough nonintegrable interaction potentials are considered. Examples of these potentials are hard-core potentials and long-range potentials, for instance, the Lennard-Jones and dipolar potentials. The treatment of such potentials is known to confront several problems, e.g., the impossibility of using the standard mean-field approximations, such as Hartree and Hartree-Fock approximations, the impossibility of directly introducing coherent states, the difficulty in breaking the global gauge symmetry, which is required for describing Bose-Einstein condensed and superfluid systems, the absence of a correctly defined Fourier transform, which hampers the description of uniform matter as well as the use of local-density approximation for nonuniform systems. A novel iterative procedure for describing such systems is developed, starting from a correlated mean-field approximation, allowing for a systematic derivation of higher orders, and meeting no problems listed above. The procedure is applicable to arbitrary systems, whether equilibrium or nonequilibrium. The specification for equilibrium systems is presented. The method of extrapolating the expressions for observable quantities from weak coupling to strong coupling is described.

cond-mat.stat-mech↗

arXiv2016

Theory of cold atoms: Bose-Einstein statistics

This Tutorial is the continuation of the previous tutorial part, published in Laser Phys. 23, 062001 (2013), where the basic mathematical techniques required for an accurate description of cold atoms for both types of quantum statistics are expounded. In the present part, the specifics of the correct theoretical description of atoms obeying Bose-Einstein statistics are explained, including trapped Bose atoms. In the theory of systems exhibiting the phenomenon of Bose-Einstein condensation, there exists a number of delicate mathematical points, whose misunderstanding often results in principally wrong conclusions. This is why the consideration in the present Tutorial is sufficiently detailed in order that the reader could clearly understand the underlying mathematics and would avoid confusions.

cond-mat.quant-gas↗

arXiv2016

Inconclusive quantum measurements and decisions under uncertainty

We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in Quantum Decision Theory, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluation of the considered prospect, and of an attraction factor, characterizing irrational, subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a general way of evaluation, based on the use of non-informative priors. As an example, we suggest the explanation of the decoy effect. Our quantitative predictions are in very good agreement with experimental data.

quant-ph↗