Narrow Results

An approach to the description of the Gibbs states of lattice models of interacting quantum anharmonic oscillators, based on integration in infinite dimensional spaces, is described in a systematic way. Its main feature is the representation of the local Gibbs states by means of certain probability measures (local Euclidean Gibbs measures). This makes it possible to employ the machinery of conditional probability distributions, known in classical statistical physics, and to define the Gibbs state of the whole system as a solution of the equilibrium (Dobrushin–Lanford–Ruelle) equation. With the help of this representation the Gibbs states are extended to a certain class of unbounded multiplication operators, which includes the order parameter and the fluctuation operators describing the long range ordering and the critical point respectively. It is shown that the local Gibbs states converge, when the mass of the particle tends to infinity, to the states of the corresponding classical model. A lattice approximation technique, which allows one to prove for the local Gibbs states analogs of known correlation inequalities, is developed. As a result, certain new inequalities are derived. By means of them, a number of statements describing physical properties of the model are proved. Among them are: the existence of the long-range order for low temperatures and large values of the particle mass; the suppression of the critical point behavior for small values of the mass and for all temperatures; the uniqueness of the Euclidean Gibbs states for all temperatures and for the values of the mass less than a certain threshold value, dependent on the temperature.

This paper is concerned with the following Kirchhoff–Schrödinger–Poisson system:

The model of Bonabeau explains the emergence of social hierarchies from the memory of fights in an initially egalitarian society. Introducing a feedback from the social inequality into the probability to win a fight, we find a sharp transition between an egalitarian society at low population density and a hierarchical society at high population density.

Using the new supercomputer JUMP at the Research Center Jülich, we were able to simulate large lattices (up to L=2·10⁶, a new world record) for long times (up to T=6000 for L=1.5·10⁵). Using this data, we examined the dynamical critical exponent z. The old assumption of z=2 with logarithmic corrections seems very unlikely according to our data, leaving the asymptotic value of z≃2.167.

Monte Carlo simulations with up to 176⁵ spins show no significant deviations between four different random number generators in multispin coding, as opposed to multiplication with 16807 for one-word-per-spin coding for 32⁵. Also world record sizes 1000192², 9984³, 880⁴ and 48⁶ spins were simulated.

The hypothesis z=2 with logarithmic corrections seems inconsistent with one way of simulation but not with a different one, for the same Ising model.

When the cosmological constant, Λ, is interpreted as a thermodynamic variable in the study of black hole thermodynamics a very rich structure emerges. It is natural to interpret Λ as a pressure and define the thermodynamically conjugate variable to be the thermodynamic volume of the black hole (which need not bear any relation to the geometric volume). Recent progress in this new direction for black hole thermodynamics is reviewed.

This work deals with dynamical system analysis of Holographic Dark Energy (HDE) cosmological model with different infra-red (IR)-cutoff. By suitable transformation of variables, the Einstein field equations are converted to an autonomous system. The critical points are determined and the stability of the equilibrium points are examined by Center Manifold Theory and Lyapunov function method. Possible bifurcation scenarios have also been explained.

In this work, cosmological implications of a non-canonical scalar field model have been studied in the background of homogeneous and isotropic flat FLRW spacetime by using dynamical system analysis. By suitable change of variables, the field equations are transformed to an autonomous system and the stability of the system of critical points are examined. For hyperbolic critical points, the analysis of the system is done by using Hartman–Grobman theorem, while the center manifold theory is used to study non-hyperbolic critical points. It is found that the parameters in the autonomous system play a crucial role for phase transition of the Universe. Finally, possible bifurcation scenarios are discussed to identify the point of phase transition.

The equation of the $\gamma$-unstable Bohr Hamiltonian, with particular forms of the sextic potential in the $\beta$ shape variable, is exactly solved for a finite number of states. The shape of the quasi-exactly solvable potential is then defined by the number of exactly determined states. The effect of exact solvability order on the spectral characteristics of the model is closely investigated, especially, concerning the critical point of the phase transition from spherical to deformed shapes. The energy spectra and the $B(E2)$ transition probabilities, up to a scaling factor, depend only on a single-free parameter, while for the critical point, parameter-free results are available. Several numerical applications are done for nuclei undergoing a $\gamma$-unstable shape phase transition in order to identify critical nuclei based on the most suitable exact solvability order.

In this paper, a search for power-law fluctuations with fractality and intermittency analysis to explore the QCD phase diagram and the critical point is summarized. Experimental data on self-similar correlations and fluctuations with respect to the size of phase–space volume in various high energy heavy-ion collisions are presented, with special emphasis on background subtraction and efficiency correction of the measurement. Phenomenological modeling and theoretical work on the subject are discussed. Finally, we highlight possible directions for future research.

The ultimate aim of high energy heavy ion collisions is to study quark deconfinement and the quark–gluon plasma predicted by quantum chromodynamics. This requires the identification of observables calculable in QCD and measurable in heavy ion collisions. I concentrate on three such phenomena, related to specific features of strongly interacting matter. The observed pattern of hadrosynthesis corresponds to that of an ideal resonance gas in equilibrium at the pseudo-critical temperature determined in QCD. The critical behavior of QCD is encoded in the fluctuation patterns of conserved quantum numbers, which are presently being measured. The temperature of the quark–gluon plasma can be determined by the dissociation patterns of the different quarkonium states, now under study at the LHC for both charmonia and bottomonia.

Understanding the phase diagram of the QCD matter is one of the ultimate goals in high-energy nuclear physics. Event-by-event fluctuations of conserved charges are believed to be sensitive to the QCD phase structures. In this paper, we will review the measurements carried out in the Beam Energy Scan program at RHIC. Our focus will be on the technical details to overcome various difficulties of the measurements. We will also discuss about the current interpretations on the results and future prospects.

The most relevant thermal perturbation of the continuous d=2 minimal conformal theory with c=7/10 (Tricritical Ising Model) is treated here. This model describes the scaling region of the ϕ⁶ universality class near the tricritical point. The problematic IR divergences of the naive perturbative expansion around conformal theories are dealt within the OPE approach developed at all orders by the authors. The main result is a description of the short distance behavior of correlators that is compared with existing long distance expansion (form factors approach) related to the integrability of the model.

Based on the general adiabatic theory for the evolutionary minority game (EMG) that we proposed earlier,¹ we perform a detail analysis of the EMG limited to three groups of agents. We derive a formula for the critical point of the transition from segregation (into opposing groups) to clustering (towards cautious behaviors). Particular to the three-group EMG, the strategy switching in the "extreme" group does not occur at every losing step and is strongly intermittent. This leads to an correction to the critical value of the number of agents at the transition, N_c. Our expression for N_c is in agreement with the results obtained from our numerical simulations.

In this work, we present a review of the results obtained in the exploitation of percolation theory and the renormalization group method in the study of soil moisture spatial patterns.

In order to capture critical point in soil moisture spatio-temporal dynamics, we developed an algorithm consisting of three steps: (i) dichotomization, i.e., transforming the soil moisture maps into binary maps; (ii) identification of the largest wet cluster; (iii) scaling transformation, i.e., applying an ad hoc implemented coarse-graining procedure to the binary maps.

The methodology was explored by means of several applications on soil moisture data coming from field measurement, remote sensing, and hydrological modelling over a wide range of spatial scales. From the relations between the occupation probability in soil moisture spatial patterns and the normalized size of the largest cluster at different scales, as well as the scaling behaviour, it is possible to argue that also for this physical system the critical point theory applies.

The critical probability seems to be a structural feature of the catchment, being insensitive to the scale of the analysis, as well as to the parameterization of the methodology.

We study relaxation time T_c of time-delayed bistable system driven by two cross-correlated Gaussian white noises that one is multiplicative and the other is additive. By means of numerical calculations, the results indicate that: (i) Combination of noise and time delay can induce two critical points about the relaxation time at some certain noise cross-correlation strength λ under the condition that the multiplicative intensity D equals to the additive noise intensity α. (ii) For each fixed D or α, there are two symmetrical critical points which locates in the regions of positive and negative correlations, respectively. Namely, as λ equals to the critical value λ_c, T_c is independent of the delay time and the result of T_c versus τ is a horizontal line, but as |λ|>|λ_c| (or |λ|<|λ_c|), the relaxation time T_c monotonically increases (or decreases) with the delay time increasing. (iii) In the presence of D = α, the change of λ_c with D is two symmetrical curves about the axis of λ_c = 0, and the critical value λ_c is close to zero for a smaller D, which approaches to +1 or -1 for a greater D.

The flow regimes of liquids encountered in engineering practice are mainly turbulent due to their structure, with which the features of such flows at supercritical pressure are considered in the work and some results are compared with similar ones obtained at low Reynolds numbers. Under these conditions, the physical properties of the fluid change sharply in the parietal layer and, depending on the values of the heat flux density and temperature, the area of sharp changes in physical properties can move along the flow cross section. Depending on the influence of these factors, the nature of the fluid flow can change, which affects the patterns of heat transfer and, accordingly, the nature of the distribution of wall temperature. In particular, conditions were identified for the appearance of a primary and secondary improved heat transfer regime. The possibility of the existence of an anomalous behavior of heat transfer during a turbulent flow of aromatic hydrocarbons was revealed, the nature of the distribution of the wall temperature along the length of the experimental tube is examined, and the influence of changes in the thermophysical properties of the substance on it is analyzed. The experimental data for water and toluene with a deteriorated heat transfer mode deviate from the calculated by $\pm$25%.

As is known, the flow regime of fluids in engineering practice is mainly turbulent in structure. Therefore, it is very important to study the characteristics of such flows at supercritical pressure and compare some results with similar results obtained at low Reynolds numbers.

Experiments suggest that localization via self-trapping plays a central role in the behavior of equilibrated low mass particles in both liquids and in supercritical fluids. In the latter case, the behavior is dominated by the liquid-vapor critical point which is difficult to probe, both experimentally and theoretically. Here, for the first time, we present the results of path-integral computations of the characteristics of a self-trapped particle at the critical point of a Lennard-Jones fluid for a positive particle-atom scattering length. We investigate the influence of the range of the particle-atom interaction on trapping properties, and the pick-off decay rate for the case where the particle is ortho-positronium. We find that, at the critical point, the transition from the self-trapped inhomogeneity to the density of the surrounding fluid is more gradual than in the liquid, or dense gas, away from the critical point. In addition the "shell structure" in fluid density surrounding the droplet is effaced.

The nature of the fixed points of the Carotid–Kundalini (C–K) map was studied and the boundary equation of the first bifurcation of the C–K map in the parameter plane is presented. Using the quantitative criterion and rule of chaotic system, the paper reveals the general features of the C–K Map transforming from regularity to chaos. The following conclusions are obtained: (i) chaotic patterns of the C–K map may emerge out of double-periodic bifurcation; (ii) the chaotic crisis phenomena are found. At the same time, the authors analyzed the orbit of critical point of the complex C–K Map and put forward the definition of Mandelbrot–Julia set of the complex C–K Map. The authors generalized the Welstead and Cromer's periodic scanning technique and using this technology constructed a series of the Mandelbrot–Julia sets of the complex C–K Map. Based on the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing, we investigated the symmetry of the Mandelbrot–Julia set and studied the topological inflexibility of distribution of the periodic region in the Mandelbrot set, and found that the Mandelbrot set contains abundant information of the structure of Julia sets by finding the whole portray of Julia sets based on Mandelbrot set qualitatively.