arXiv subjects
Publications and source records attributed to E. P. Yukalova.
Evolutional entanglement production is defined as the amount of entanglement produced by the evolution operator. This quantity is analyzed for systems whose Hamiltonians are characterized by spin operators. The evolutional entanglement production at the initial stage grows quadratically in time. For longer times, it oscillates, being quasiperiodic or periodic depending on the system parameters.
We propose a reduced form set of two coupled continuous time equations linking the price of a representative asset and the price of a bond, the later quantifying the cost of borrowing. The feedbacks between asset prices and bonds are mediated by the dependence of their "fundamental values" on past asset prices and bond themselves. The obtained nonlinear self-referencing price dynamics can induce, in a completely objective deterministic way, the appearance of periodically exploding bubbles ending in crashes. Technically, the periodically explosive bubbles arise due to the proximity of two types of bifurcations as a function of the two key control parameters $b$ and $g$, which represent, respectively, the sensitivity of the fundamental asset price on past asset and bond prices and of the fundamental bond price on past asset prices. One is a Hopf bifurcation, when a stable focus transforms into an unstable focus and a limit cycle appears. The other is a rather unusual bifurcation, when a stable node and a saddle merge together and disappear, while an unstable focus survives and a limit cycle develops. The lines, where the periodic bubbles arise, are analogous to the critical lines of phase transitions in statistical physics. The amplitude of bubbles and waiting times between them respectively diverge with the critical exponents $γ= 1$ and $ν= 1/2$, as the critical lines are approached.
A wide class of materials acquires magnetic properties due to particle interactions through exchange forces. These can be atoms and molecules composing the system itself, as in the case of numerous magnetic substances. Or these could be different defects, as in the case of graphene, graphite, carbon nanotubes, and related materials. The theory is suggested describing fast magnetization reversal in magnetic systems, whose magnetism is caused by exchange interactions. The effect is based on the coupling of a magnetic sample with an electric circuit producing a feedback magnetic field. This method can find various applications in spintronics. The magnetization reversal can be self-organized, producing spin superradiance. A part of radiation is absorbed by a resonator magnetic coil. But an essential part of radiation can also be emitted through the coil sides.
Spin dynamics of assemblies of magnetic nanomolecules and nanoclusters can be made coherent by inserting the sample into a coil of a resonant electric circuit. Coherence is organized through the arising feedback magnetic field of the coil. The coupling of a magnetic sample with a resonant circuit induces fast spin relaxation and coherent spin radiation, that is, superradiance. We consider spin dynamics described by a realistic Hamiltonian, typical of magnetic nanomolecules and nanoclusters. The role of magnetic anisotropy is studied. A special attention is paid to geometric effects related to the mutual orientation of the magnetic sample and resonator coil.
Nuclear matter at finite temperature and barion density exhibits several phase transitions that could happen at the early stages of the Universe evolution and could be realized in heavy-ion or hadron-hadron collisions. Microscopic description of phase transitions is notoriously difficult because of the absence of small parameters. Here we present a general approach allowing to treat situations, when there are no small parameters. The approach is based on optimized perturbation theory and self-similar approximation theory. It allows, starting with divergent perturbation series in powers of an asymptotically small parameter, to construct expressions extrapolating asymptotic series to arbitrary values of the parameter, including its infinite limit. Examples of such approximants are: right root approximants, left root approximants, continued root approximants, exponential approximants, and factor approximants. The approach is illustrated by the phase transition of gauge symmetry breaking in a multicomponent field theory. The found critical indices are in very good agreement with Monte Carlo simulations as well as with complicated methods of Pade-Borel summation, while our approach is much simpler. The nice feature of the approach is that it gives exact values for the cases where exact solutions are known.
The idea is advanced that strong perturbations of an initially equilibrium Bose-condensed gas lead to the sequence of nonequilibrium states whose order is inverse to the sequence of states arising in the process of the Bose-gas relaxation from an initial nonequilibrium state. An approach is described for constructing statistical models of nonequilibrium Bose gases. The method is based on the averaging over heterogenous configurations of a nonequilibrium system. A statistical model of grain turbulence is suggested. A simple model is analyzed consisting of a mixture of two phases, one gauge symmetric and the other with broken gauge symmetry.
The possibility is considered for the formation in optical lattices of a heterogeneous state characterized by a spontaneous mesoscopic separation of the system into the spatial regions with different atomic densities. It is shown that such states can arise, if there are repulsive interactions between atoms in different lattice sites and the filling factor is less than one-half.
The ground state of a homogeneous Bose gas of hard spheres is treated in self-consistent mean-field theory. It is shown that this approach provides an accurate description of the ground state of a Bose-Einstein condensed gas for arbitrarily strong interactions. The results are in good agreement with Monte Carlo numerical calculations. Since all other mean-field approximations are valid only for very small gas parameters, the present self-consistent theory is a unique mean-field approach allowing for an accurate description of Bose systems at arbitrary values of the gas parameter.
We suggest a novel approach to treating symbiotic relations between biological species or social entities. The main idea is the characterisation of symbiotic relations of coexisting species through their mutual influence on their respective carrying capacities, taking into account that this influence can be quite strong and requires a nonlinear functional framework. We distinguish three variants of mutual influence, representing the main types of relations between species: (i) passive symbiosis, when the mutual carrying capacities are influenced by other species without their direct interactions; (ii) active symbiosis, when the carrying capacities are transformed by interacting species; and (iii) mixed symbiosis, when the carrying capacity of one species is influenced by direct interactions, while that of the other species is not. The approach allows us to describe all kinds of symbiosis, mutualism, commensalism, and parasitism within a unified scheme. The case of two symbiotic species is analysed in detail, demonstrating several dynamical regimes of coexistence, unbounded growth of both populations, growth of one and elimination of the other population, convergence to evolutionary stable states, and everlasting population oscillations. The change of the dynamical regimes occurs by varying the system parameters characterising the destruction or creation of the mutual carrying capacities. The regime changes are associated with several dynamical system bifurcations.
There is a wide-spread belief in the literature on Bose-Einstein condensation of interacting atoms that all variants of mean-field theory incorrectly describe the condensation phase transition, exhibiting, instead of the necessary second-order transition, a first-order transition, even for weakly interacting Bose gas. In the present paper, it is shown that a self-consistent mean-field approach is the sole mean-field theory that provides the correct second-order condensation transition for Bose systems with atomic interactions of arbitrary strength, whether weak or strong.
Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain measurements, and for entangled composite events. The role of the prospect and state entanglement is emphasized. Numerical modeling is presented for a two-mode Bose-condensed system of trapped atoms. The interference factor is calculated by invoking the channel-state duality.
The assemblies of either quantum dots or magnetic nanoclusters are studied. It is shown that such assemblies can produce coherent radiation. A method is developed for solving the systems of nonlinear equations describing the dynamics of such assemblies. The method is shown to be general and applicable to systems of different physical nature. Despite mathematical similarities of dynamical equations, the physics of the processes for quantum dots and magnetic nanoclusters is rather different. In a quantum dot assembly, coherence develops due to the Dicke effect of dot interactions through the common radiation field. For a system of magnetic clusters, coherence in the spin motion appears due to the Purcell effect caused by the feedback action of a resonator. Self-organized coherent spin radiation cannot arise without a resonator. This principal difference is connected with the different physical nature of dipole forces between the objects. Effective dipole interactions between the radiating quantum dots, appearing due to photon exchange, collectivize the dot radiation. While the dipolar spin interactions exist from the beginning, yet before radiation, and on the contrary, they dephase spin motion, thus destroying the coherence of moving spins. In addition, quantum dot radiation exhibits turbulent photon filamentation that is absent for radiating spins.
Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations. A general approach is described for treating statistical properties of such materials with nanoscale phase separation. Averaging over the random phase configurations, it is possible to reduce the problem to the set of homogeneous phase replicas, with additional equations defining the geometric weights of different phases in the mixture. The averaging over phase configurations is mathematically realized as the functional integration over the manifold indicator functions. This procedure leads to the definition of an effective renormalized Hamiltonian taking into account the existence of competing phases. Heterophase systems with mesoscopic phase separation can occur for different substances. The approach is illustrated by the model of a high-temperature superconductor with non-superconducting admixture and by the model of a ferroelectric with paraelectric random inclusions.
We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation where the carrying capacity is linearly dependent on the population with a time delay, which we refer to as the "linear delayed carrying capacity" model. Here, we generalize it to the case of a nonlinear delayed carrying capacity. The nonlinear functional form of the carrying capacity characterizes the delayed feedback of the evolving population on the capacity of their surrounding by either creating additional means for survival or destroying the available resources. The previously studied linear approximation for the capacity assumed weak feedback, while the nonlinear form is applicable to arbitrarily strong feedback. The nonlinearity essentially changes the behavior of solutions to the evolution equation, as compared to the linear case. All admissible dynamical regimes are analyzed, which can be of the following types: punctuated unbounded growth, punctuated increase or punctuated degradation to a stationary state, convergence to a stationary state with sharp reversals of plateaus, oscillatory attenuation, everlasting fluctuations, everlasting up-down plateau reversals, and divergence in finite time. The theorem is proved that, for the case characterizing the evolution under gain and competition, solutions are always bounded, if the feedback is destructive. We find that even a small noise level profoundly affects the position of the finite-time singularities. Finally, we demonstrate the feasibility of predicting the critical time of solutions having finite-time singularities from the knowledge of a simple quadratic approximation of the early time dynamics.
We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about 10% each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita.
The method of defining quantum joint probabilities of two events is applied to a multimode system of trapped Bose-condensed atoms. The coherent modes are generated by modulating the trapping potential with an alternating field with a frequency in resonance with a transition frequency between two coherent modes. The system is subjected to nondestructive measurements randomly influencing the phase difference of the modes. The joint probability of observing two events, corresponding to the observation of two states, is calculated by employing the channel-state duality. The interference term in the joint probability can arise when the composite events form an entangled prospect and the system state is also entangled. This interference is due to the uncertainty induced by nondestructive measurements.
The problem of the possible creation of mixed hadron-quark-gluon matter, that can arise at nuclear or heavy-ion collisions, is addressed. It is shown that there can exist several different kinds of such a mixed matter. The main types of this matter can be classified onto macroscopic mixture, mesoscopic mixture, and microscopic mixture. Different types of these mixtures require principally different descriptions. Before comparing theoretical results with experiments, one has to analyze thermodynamic stability of all these mixed states, classifying them onto unstable, metastable, and stable. Only the most stable mixed state should be compared with experiment. Mixed states also need to be checked with regard to stratification instability. In addition to the static stratification instability, there can happen dynamic instability occurring in a mixture of components moving with respect to each other. This effect, called counterflow instability, has also to be taken into account, since it can lead to the stratification of mixed matter.
The definition of order indices for density matrices is extended to finite systems. This makes it possible to characterize the level of ordering in such finite systems as macromolecules, nanoclusters, quantum dots, or trapped atoms. The general theory is exemplified by explicit calculations of the order index for the first-order density matrix of bosonic atoms confined in a finite box at zero temperature.