arXiv subjects

V. I. Yukalov

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

At least 163 records · Page 9Linked to original sources

arXiv2012

Statistical Outliers and Dragon-Kings as Bose-Condensed Droplets

A theory of exceptional extreme events, characterized by their abnormal sizes compared with the rest of the distribution, is presented. Such outliers, called "dragon-kings", have been reported in the distribution of financial drawdowns, city-size distributions (e.g., Paris in France and London in the UK), in material failure, epileptic seizure intensities, and other systems. Within our theory, the large outliers are interpreted as droplets of Bose-Einstein condensate: the appearance of outliers is a natural consequence of the occurrence of Bose-Einstein condensation controlled by the relative degree of attraction, or utility, of the largest entities. For large populations, Zipf's law is recovered (except for the dragon-king outliers). The theory thus provides a parsimonious description of the possible coexistence of a power law distribution of event sizes (Zipf's law) and dragon-king outliers.

physics.soc-ph↗

arXiv2012

Extreme events in population dynamics with functional carrying capacity

A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations between populations can be realized not merely through direct interactions, as in the usual predator-prey Lotka-Volterra model, but also through the influence of species on the carrying capacities of each other. This includes the self-influence of each kind of species on its own carrying capacity with delays. Several examples of such evolution equations with functional carrying capacities are analyzed. The emphasis is given on the conditions under which the solutions to the equations display extreme events, such as finite-time death and finite-time singularity. Any destructive action of populations, whether on their own carrying capacity or on the carrying capacities of co-existing species, can lead to the instability of the whole population that is revealed in the form of the appearance of extreme events, finite-time extinctions or booms followed by crashes.

q-bio.PE↗

arXiv2012

Fast magnetization reversal of nanoclusters in resonator

An effective method for ultrafast magnetization reversal of nanoclusters is suggested. The method is based on coupling a nanocluster to a resonant electric circuit. This coupling causes the appearance of a magnetic feedback field acting on the cluster, which drastically shortens the magnetization reversal time. The influence of the resonator properties, nanocluster parameters, and external fields on the magnetization dynamics and reversal time is analyzed. The magnetization reversal time can be made many orders shorter than the natural relaxation time. The reversal is studied for both the cases of a single nanocluster as well as for the system of many nanoclusters interacting through dipole forces.

cond-mat.mes-hall↗

arXiv2012

Decoherence and equilibration under nondestructive measurements

The evolution of observable quantities of finite quantum systems is analyzed when the latter are subject to nondestructive measurements. The type and number of measurements characterize the level of decoherence produced in the system. A finite number of instantaneous measurements leads to only a partial decoherence. But infinite number of such measurements yields complete decoherence and equilibration. Continuous measurements result in partial decoherence in finite time, but produce complete decoherence and equilibration as time tends to infinity. Resulting equilibrium states are characterized by representative statistical ensembles that, generally, retain information on initial conditions. Any system, to be observable, necessarily requires the presence of measurements, whose large number leads to the system equilibration and decoherence.

quant-ph↗

arXiv2012

Equilibration of quasi-isolated quantum systems

The evolution of a quasi-isolated finite quantum system from a nonequilibrium initial state is considered. The condition of quasi-isolation allows for the description of the system dynamics on the general basis, without specifying the system details and for arbitrary initial conditions. The influence of surrounding results in (at least partial) equilibration and decoherence. The resulting equilibrium state bears information on initial conditions and is characterized by a representative ensemble. It is shown that the system average information with time does not increase. The partial equilibration and non-increase of average information explain the irreversibility of time.

quant-ph↗

arXiv2012

Possibility of superradiance by magnetic nanoclusters

The possibility of realizing spin superradiance by an assembly of magnetic nanoclusters is analyzed. The known obstacles for realizing such a coherent radiation by magnetic nanoclusters are their large magnetic anisotropy, strong dephasing dipole interactions, and an essential nonuniformity of their sizes. In order to give a persuasive conclusion, a microscopic theory is developed, providing an accurate description of nanocluster spin dynamics. It is shown that, despite the obstacles, it is feasible to organize such a setup that magnetic nanoclusters would produce strong superradiant emission.

cond-mat.mes-hall↗

arXiv2012

Nonequilibrium representative ensembles for isolated quantum systems

An isolated quantum system is considered, prepared in a nonequilibrium initial state. In order to uniquely define the system dynamics, one has to construct a representative statistical ensemble. From the principle of least action it follows that the role of the evolution generator is played by a grand Hamiltonian, but not merely by its energy part. A theorem is proved expressing the commutators of field operators with operator products through variational derivatives of these products. A consequence of this theorem is the equivalence of the variational equations for field operators with the Heisenberg equations for the latter. A finite quantum system cannot equilibrate in the strict sense. But it can tend to a quasi-stationary state characterized by ergodic averages and the appropriate representative ensemble depending on initial conditions. Microcanonical ensemble, arising in the eigenstate thermalization, is just a particular case of representative ensembles. Quasi-stationary representative ensembles are defined by the principle of minimal information. The latter also implies the minimization of an effective thermodynamic potential.

cond-mat.stat-mech↗

arXiv2012

Equilibration and thermalization in finite quantum systems

Experiments with trapped atomic gases have opened novel possibilities for studying the evolution of nonequilibrium finite quantum systems, which revived the necessity of reconsidering and developing the theory of such processes. This review analyzes the basic approaches to describing the phenomena of equilibration, thermalization, and decoherence in finite quantum systems. Isolated, nonisolated, and quasi-isolated quantum systems are considered. The relations between equilibration, decoherence, and the existence of time arrow are emphasized. The possibility for the occurrence of rare events, preventing complete equilibration, are mentioned.

cond-mat.stat-mech↗

arXiv2011

Mesoscopic disorder in double-well optical lattices

Double-well optical lattices are considered, each cite of which is formed by a double-well potential. The lattice is assumed to be in an insulating state and order and disorder are defined with respect to the displacement of atoms inside the double-well potential. It is shown that in such lattices, in addition to purely ordered and disordered states, there can exist an intermediate mixed state, where, inside a generally ordered lattice, there appear disordered regions of mesoscopic size.

cond-mat.quant-gas↗

arXiv2011

Basics of Bose-Einstein Condensation

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.

cond-mat.stat-mech↗

arXiv2011

Transition to quantum turbulence in a finite size superfluid

A novel concept of quantum turbulence in finite size superfluids, such as trapped bosonic atoms, is discussed. We have used an atomic $^{87}\mathrm{Rb}$ BEC to study the emergence of this phenomenon. In our experiment, the transition to the quantum turbulent regime is characterized by a tangled vortex lines formation, controlled by the amplitude and time duration of the excitation produced by an external oscillating field. A simple model is suggested to account for the experimental observations. The transition from the non-turbulent to the turbulent regime is a rather gradual crossover. But it takes place in a sharp enough way, allowing for the definition of an effective critical line separating the regimes. Quantum turbulence emerging in a finite-size superfluid may be a new idea helpful for revealing important features associated to turbulence, a more general and broad phenomenon.

cond-mat.quant-gas↗

arXiv2011

Route to turbulence in a trapped Bose-Einstein condensate

We have studied a Bose-Einstein condensate of $^{87}Rb$ atoms under an oscillatory excitation. For a fixed frequency of excitation, we have explored how the values of amplitude and time of excitation must be combined in order to produce quantum turbulence in the condensate. Depending on the combination of these parameters different behaviors are observed in the sample. For the lowest values of time and amplitude of excitation, we observe a bending of the main axis of the cloud. Increasing the amplitude of excitation we observe an increasing number of vortices. The vortex state can evolve into the turbulent regime if the parameters of excitation are driven up to a certain set of combinations. If the value of the parameters of these combinations is exceeded, all vorticity disappears and the condensate enters into a different regime which we have identified as the granular phase. Our results are summarized in a diagram of amplitude versus time of excitation in which the different structures can be identified. We also present numerical simulations of the Gross-Pitaevskii equation which support our observations.

cond-mat.quant-gas↗

arXiv2011

Decision Theory with Prospect Interference and Entanglement

We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage's sure-thing principle, known as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analysed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect and novel experiments testing the combined interplay between the two effects are suggested.

math-ph↗

arXiv2011

Quasiequilibrium Mixture of Itinerant and Localized Bose Atoms in Optical Lattice

Conditions are studied under which there can exist a quasiequilibrium mixture of itinerant and localized bosonic atoms in an optical lattice, even at zero temperature and at integer filling factor, when such a coexistence is impossible for an equilibrium lattice. The consideration is based on a model having the structure of a two-band, or two-component, boson Hubbard Hamiltonian. The minimal value for the ratio of on-site repulsion to tunneling parameter, necessary for the occurrence of such a mixture, is found.

cond-mat.quant-gas↗

arXiv2010

Mathematical Structure of Quantum Decision Theory

One of the most complex systems is the human brain whose formalized functioning is characterized by decision theory. We present a "Quantum Decision Theory" of decision making, based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to explain a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory describes entangled decision making, non-commutativity of subsequent decisions, and intention interference of composite prospects. We demonstrate how the violation of the Savage's sure-thing principle (disjunction effect) can be explained as a result of the interference of intentions, when making decisions under uncertainty. The conjunction fallacy is also explained by the presence of the interference terms. We demonstrate that all known anomalies and paradoxes, documented in the context of classical decision theory, are reducible to just a few mathematical archetypes, all of which finding straightforward explanations in the frame of the developed quantum approach.

cs.AI↗

arXiv2010

Self-similar extrapolation from weak to strong coupling

The problem is addressed of defining the values of functions, whose variables tend to infinity, from the knowledge of these functions at asymptotically small variables close to zero. For this purpose, the extrapolation by means of different types of self-similar approximants is employed. Two new variants of such an extrapolation are suggested. The methods are illustrated by several examples of systems typical of chemical physics, statistical physics, and quantum physics. The developed methods make it possible to find good approximations for the strong-coupling limits from the knowledge of the weak-coupling expansions.

cond-mat.stat-mech↗

arXiv2010

Fluctuation indices for atomic systems with Bose-Einstein condensate

The notion of fluctuation indices, characterizing thermodynamic stability of statistical systems, is advanced. These indices are especially useful for investigating the stability of nonuniform and trapped atomic assemblies. The fluctuation indices are calculated for several systems with Bose-Einstein condensate. It is shown that: the ideal uniform Bose-condensed gas is thermodynamically unstable; trapped ideal gases are stable for the confining dimension larger than two; trapped gases, under the confining dimension two, are weakly unstable; harmonically trapped gas is stable only for the spatial dimension three; one-dimensional harmonically trapped gas is unstable; two-dimensional gas in a harmonic trap represents a marginal case, being weakly unstable; interacting nonuniform three-dimensional Bose-condensed gas is stable. There are no thermodynamically anomalous particle fluctuations in stable Bose-condensed systems.

cond-mat.quant-gas↗

arXiv2010

Turbulent superfluid as continuous vortex mixture

A statistical model is advanced for describing quantum turbulence in a superfluid system with Bose-Einstein condensate. Such a turbulent superfluid can be realized for trapped Bose atoms subject to either an alternating trapping potential or to an alternating magnetic field modulating the atomic scattering length by means of Feshbach resonance. The turbulent system is represented as a continuous mixture of states each of which is characterized by its own vorticity corresponding to a particular vortex.

cond-mat.quant-gas↗