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arXiv2009

Statistical Mechanics of the Cosmological Many-body Problem and its Relation to Galaxy Clustering

The cosmological many-body problem is effectively an infinite system of gravitationally interacting masses in an expanding universe. Despite the interactions' long-range nature, an analytical theory of statistical mechanics describes the spatial and velocity distribution functions which arise in the quasi-equilibrium conditions that apply to many cosmologies. Consequences of this theory agree well with the observed distribution of galaxies. Further consequences such as thermodynamics provide insights into the physical properties of this system, including its robustness to mergers, and its transition from a grand canonical ensemble to a collection of microcanonical ensembles with negative specific heat.

astro-ph.CO↗

arXiv2009

Sub-critical model of damage evolution as a phase transition

Many studies investigated the application of statistical mechanics to damage phenomena. However, so far the association of damage with statistical mechanics is far from completely developed. One of the most successful approaches maps the strength elements onto the spins of a lattice. This allows applying the formalism extensively developed for spin systems to damage phenomena. To improve the model the interactions of spins at the crack tips are introduced. Further, statistical mechanics of the model is developed for different external boundary constraints.

cond-mat.stat-mech↗

arXiv2009

A Blume-Capel Ising Ferromagnet with Annealed Vacancies on a Hierarchical Lattice

A dilute Ising ferromagnet is considered in this study using renormalization group techniques with a hierarchical lattice. A series of phase diagrams have been produced that probe the effects of varying the temperature and concentration of nonmagnetic impurities. Each phase diagram corresponds to a different strength for the internal coupling coefficients on our lattice. Phases have been interpreted and critical exponents calculated for the higher order transitions.

cond-mat.stat-mech↗

arXiv2010

Transport Properties of a Non-relativistic Delta-Shell Gas with Long Scattering Lengths

The coefficients of diffusion, thermal conductivity, and shear viscosity are calculated for a system of non-relativistic particles interacting via a delta-shell potential V(r)=-v δ(r-R) when the average distance between particles is smaller than R. The roles of resonances and long scattering lengths including the unitary limit are examined. Results for ratios of diffusion to viscosity and viscosity to entropy density are presented for varying scattering lengths.

quant-ph↗

arXiv2009

Shot noise in electron transport through a double quantum dot: A master equation approach

We study shot noise in tunneling current through a double quantum dot connected to two electric leads. We derive two master equations in the occupation-state basis and the eigenstate basis to describe the electron dynamics. The approach based on the occupation-state basis, despite widely used in many previous studies, is valid only when the interdot coupling strength is much smaller than the energy difference between the two dots. In contrast, the calculations using the eigenstate basis are valid for an arbitrary interdot coupling. We show that the master equation in the occupation-state basis includes only the low-order terms with respect to the interdot coupling compared with the more accurate master equation in the eigenstate basis. Using realistic model parameters, we demonstrate that the predicted currents and shot-noise properties from the two approaches are significantly different when the interdot coupling is not small. Furthermore, properties of the shot noise predicted using the eigenstate basis successfully reproduce qualitative features found in a recent experiment.

cond-mat.mes-hall↗

arXiv2010

Spatial Correlation of the Dynamic Propensity in a Glass-Forming Liquid

We present computer simulation results on the dynamic propensity [as defined by Widmer- Cooper, Harrowell, and Fynewever, Phys. Rev. Lett. 93, 135701 (2004)] in a Kob-Andersen binary Lennard-Jones liquid system consisting of 8788 particles. We compute the spatial correlation function of the dynamic propensity as a function of both the reduced temperature T, and the time scale on which the particle displacements are measured. For T\leq0.6, we find that nonzero correlations occur at the largest length scale accessible in our system. We also show that a cluster-size analysis of particles with extremal values of the dynamic propensity, as well as 3D visualizations, reveal spatially correlated regions that approach the size of our system as T decreases, consistent with the behavior of the spatial correlation function. Next, we define and examine the "coordination propensity", the isoconfigurational average of the coordination number of the minority B particles around the majority A particles. We show that a significant correlation exists between the spatial fluctuations of the dynamic and coordination propensities. In addition, we find non-zero correlations of the coordination propensity occurring at the largest length scale accessible in our system for all T in the range 0.466<T<1.0. We discuss the implications of these results for understanding the length scales of dynamical heterogeneity in glass-forming liquids.

cond-mat.mtrl-sci↗

arXiv2009

Critical behavior of slider-block model

This paper applies the theory of continuous phase transitions of statistical mechanics to a slider-block model. The slider-block model is chosen as a representative of systems with avalanches. Similar behavior can be observed in a forest-fire model and a sand-pile model. Basing on the well-developed theory of critical phenomena for percolating systems a strong analogy for the slider-block model is investigated. It is found that the slider-block model has a critical point when the stiffness of the model is infinite. Critical exponents are found and it is shown that the behavior of the slider-block model, particularly, the occurrence of system-wide events is strongly dominated by the finite-size effects. Also the unknown before behavior of the frequency-size distributions is found for large statistics of events.

cond-mat.stat-mech↗

arXiv2009

Communities in Networks

We survey some of the concepts, methods, and applications of community detection, which has become an increasingly important area of network science. To help ease newcomers into the field, we provide a guide to available methodology and open problems, and discuss why scientists from diverse backgrounds are interested in these problems. As a running theme, we emphasize the connections of community detection to problems in statistical physics and computational optimization.

physics.soc-ph↗

arXiv2012

Brownian dynamic simulation by reticular mapping matrix method

This work proposes a method for the two-dimensional simulation of Brownian particles in a fluid with restrictions. The method is based on simple numerical rules between two matrices. One of the matrix represent the identification of all particles over which are adapted statistics rules for particles movement, the results are mapped over other matrix which represent the particles positions. The rules for the movement are established by a statistic mechanism allowing assign random or non-random movement direction. The same probably of movement for each direction for each time step is assumed, in order to be agreed with the physics conditions of Brownian movement in a two dimensional network. The root mean square displacement of all particles was calculated in a large number of simulations, together with the translational velocity of particles in order to compare with theoretical values of diffusion coefficient and the validation of model. Also, the time duration for some simulations vs. the number of particles and concentration was calculated.

cond-mat.stat-mech↗

arXiv2009

Wavenumber dependence of the structural relaxation time in the crossover regime of supercooled liquid dynamics

As a liquid is progressively supercooled an intriguing weakening of the wavenumber ($q$) dependence of the structural relaxation time $τ(q)$ in the large q limit is observed both in experiments and simulation studies. Neither the continuous Brownian diffusive dynamics nor the discontinuous activated events can alone explain the anomalous wavenumber dependence. Here we use our recently developed theory that unifies the mode coupling theory (MCT) for continuous dynamics and the random first order transition theory (RFOT) treatment of activated discontinuous motion as a nucleation (instanton) process, to understand the wavenumber dependence of density relaxation. The predicted smooth change in mechanism of relaxation from diffusive to activated, in the crossover regime, is wavevector dependent and is eventually responsible for sub-quadratic, almost linear, $q$ dependence of the relaxation time.

cond-mat.soft↗

arXiv2009

Tricritical Points and Liquid-Solid Critical Lines

Tricritical points separate continuous and discontinuous symmetry breaking transitions. They occur in a variety of physical systems and their mathematical models. A tricritical point is used to determine a liquid-solid phase transition line in the pressure-temperature plane [Aitta, J. Stat. Mech., 2006]. Excellent experimental agreement has been obtained for iron, the material having the most high pressure data. This allows extrapolation to much higher pressures and temperatures than available experimentally. One can predict the temperature at the liquid-solid boundary in the core of the Earth where the pressure is 329 GPa. Light matter, present as impurities in the core fluid, is found to generate about a 600 K reduction of this temperature.

cond-mat.stat-mech↗

arXiv2009

Mesophases of soft-sphere aggregates

Soft spheres interacting via a hard core and range of attractive and repulsive "soft-shoulder" potentials self-assemble into clusters forming a variety of mesophases. We combine a mean field theory developed from a lattice model with a level surface analysis of the periodic structures of soft-sphere aggregates to study stable morphologies for all clustering potentials. We develop a systematic approach to the thermodynamics of mesophase assembly in the low-temperature, strong-segregation and predict a generic sequence of phases including lamella, hexagonal-columnar and body-center cubic phases, as well as the associated inverse structures. We discuss the finite-temperature corrections to strong segregation theory in terms of Sommerfeld-like expansion and how these corrections affect the thermodynamic stability of bicontinuous mesophase structures, such as gyroid. Finally, we explore the opposite limit of weakly-segregated particles, and predict the generic stability of a bicontinuous cluster morphology within the mean-field phase diagram.

cond-mat.soft↗

arXiv2011

An analytical application of Niedermayer's algorithm to the Edwards-Anderson model: analytical results for the multicritical point on the Nishimori line

We apply analytically Niedermayer's algorithm to the Edwards-Anderson model on random graphs with arbitary degree distributions. The results for the multicritical point on the Nishimori line are shown. The results are shown by applying a criterion for spin models on the random graphs with arbitary degree distributions. The application of Niedermayer's algorithm makes the size of the Fortuin-Kasteleyn cluster small and shifts the percolation threshold. The results for the $\pm J$ model and the Gaussian model are respectively shown. In the present article, it is respectively shown for the $\pm J$ model and the Gaussian model that, by adjusting an introduced parameter for Niedermayer's algorithm, the percolation threshold obtained in the present article agrees with the location of the multicritical point. We naively estimate the locations of the multicritical points for the $\pm J$ model and the Gaussian model on the randam graphs with arbitary degree distributions.

cond-mat.dis-nn↗

arXiv2009

Correlation Probes of a QCD Critical Point

Critical opalescence is a characteristic experimental signature of a second order phase transition in solid state physics. A new, experimentally accessible measure of opacity and of attenuation length in heavy ion reactions is suggested, as a combination of HBT radii and nuclear modification factors. This opacity is maximal when $\sqrt{s_{NN}}$, the system size and centrality correspond to the critical point of QCD. To characterize the phase transition at this critical point, the critical exponent of the correlation function can be determined by measuring the Lévy index of stability of the Bose-Einstein or HBT correlations. The exponent of the correlation length can be determined from fits to the multiplicity distribution in various pseudorapidity intervals, also as a function of colliding energy, system size, centrality and (chemical) freeze-out temperature. These two critical exponents determine the remaining four critical exponents and the universality class of this second order phase transition. As a control experiment, the determination of the critical exponent of the specific heat capacity is proposed, from event-by-event fluctuation measurements. To measure opacity precisely, well calibrated high transverse momentum probes are needed, such as given by the excitation function of $γ$ + jet correlation functions.

nucl-th↗

arXiv2009

The sensitivity of the population of states to the value of $q$ and the legitimate range of $q$ in Tsallis statistics

In the framework of the Tsallis statistical mechanics, for the spin-1/2 and the harmonic oscillator, we study the change of the population of states when the parameter $q$ is varied; the results show that the difference between predictions of the Boltzmann--Gibbs and Tsallis Statistics can be much smaller than the precision of any existing experiment. Also, the relation between the privilege of rare/frequent event and the value of $q$ is restudied. This relation is shown to be more complicated than the common belief about it. Finally, the convergence criteria of the partition function of some simple model systems, in the framework of Tsallis Statistical Mechanics, is studied; based on this study, we conjecture that $q \leq 1$, in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2009

The Non-equilibrium Behavior of Fluctuation Induced Forces

While techniques to compute thermal fluctuation induced, or pseudo-Casimir, forces in equilibrium systems are well established, the same is not true for non-equilibrium cases. We present a general formalism that allows us to unambiguously compute non-equilibrium fluctuation induced forces by specifying the energy of interaction of the fluctuating fields with the boundaries. For a general class of classical fields with dissipative dynamics, we derive a very general relation between the Laplace transform of the time-dependent force and the static partition function for a related problem with a different Hamiltonian. In particular, we demonstrate the power of our approach by computing, for the first time, the explicit time dependence of the non-equilibrium pseudo-Casimir force induced between two parallel plates, upon a sudden change in the temperature of the system. We also show how our results can be used to determine the steady-state behavior of the non-equilibrium force in systems where the fluctuations are driven by colored noise.

cond-mat.stat-mech↗

arXiv2009

Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise

The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using Laplace analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions and its derivatives from a generalized Langevin equation. Our results show that the oscillator displays an anomalous diffusive behavior. In the strictly asymptotic limit, the dynamics of the harmonic oscillator corresponds to an oscillator driven by a noise with a pure power-law autocorrelation function. However, at short and intermediate times the dynamics has qualitative difference due to the presence of the characteristic time of the noise.

cond-mat.stat-mech↗

arXiv2011

Detection of early cluster formation in soft matter: an entropic imprint

We study model protein solutions and colloidal suspensions in the temperature range whereupon the nature of the system changes from a homogeneous fluid to a "cluster fluid". It is commonly assumed - as deduced by the behavior of the structural correlations - that this microphase separation sets as a continuous process. We challenge such assumption and demonstrate that the entropy shows a discontinuous behavior across a well-defined temperature threshold, providing a neat signature of the modifications occurring in the fluid. All predictions, obtained in the framework of a refined theory of the liquid state, are systematically assessed against extensive Monte Carlo simulations. We emphasize the broad generality of our conclusions, and the importance of accurate theoretical treatments to characterize the thermodynamic properties of soft materials.

cond-mat.stat-mech↗