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We derive a finite set of nonlinear integral equations (NLIE) for the thermodynamics of the one-dimensional sl(4)-symmetric Uimin-Sutherland model. Our NLIE can be evaluated numerically for arbitrary finite temperature and chemical potentials. |
Unlike the classical exponential relaxation law, the widely prevailing universal law with its fractional power-law dependence of susceptibility on frequency cannot be explained in the framework of any intuitively simple physical concept. The resulting constancy of the ratio of the imaginary to the real parts of the co... |
In this paper we solve the inverse problem for a class of mean field models (Curie-Weiss model and its multi-species version) when multiple thermodynamic states are present, as in the low temperature phase where the phase space is clustered. The inverse problem consists in reconstructing the model parameters starting ... |
The phase transitions classes of reaction-diffusion systems with multi-particle reactions is an open challenging problem. Large scale simulations are applied for the 3A -> 4A, 3A -> 2A and the 3A -> 4A, 3A->0 triplet reaction models with site occupation restriction in one dimension. |
We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second moments of the particle position as inverse Laplace transforms. |
We address the question of how stock prices respond to changes in demand. We quantify the relations between price change $G$ over a time interval $\Delta t$ and two different measures of demand fluctuations: |
We compute the exponent gamma for self-avoiding walks in three dimensions. We get gamma = 1.1575 +- 0.0006 in agreement with renormalization-group predictions. |
Computational mechanics quantifies structure in a stochastic process via its causal states, leading to the process's minimal, optimal predictor---the $\epsilon$-machine. We extend computational mechanics to communication channels between two processes, obtaining an analogous optimal model---the $\epsilon$-transduc... |
The phase behavior of ionic fluids on simple cubic and tetragonal (anisotropic) lattices has been studied by grand canonical Monte Carlo simulations. Systems with both the true lattice Coulombic potential and continuous-space $1/r$ electrostatic interactions have been investigated. |
In superfluid $^3$He turbulence is carried predominantly by the superfluid component. To explore the statistical properties of this quantum turbulence and its differences from the classical counterpart we adopt the time-honored approach of shell models. |
The second layer of He-4 adsorbed on a graphite substrate is studied by Quantum Monte Carlo simulations. We make use of a microscopic model of the substrate fully accounting for its corrugation, and compare the results to those obtained with a smooth substrate. |
Motivated by certain problems of statistical physics we consider a stationary stochastic process in which deterministic evolution is interrupted at random times by upward jumps of a fixed size. If the evolution consists of linear decay, the sample functions are of the "random sawtooth" type and the level depen... |
We study the effect of particle mobility on phase transitions in a spin fluid in two dimensions. The presence of a phase transition of the BKT universality class is shown in an off-lattice model of particles with purely repulsive interaction employing computer simulations. |
We formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the distribution of the number of incoming links to a node follows a universal scaling form, ... |
We study the short time properties of a two-dimensional film growth model in which incident particles execute advective-diffusive motion with a vertical step followed by $D$ horizontal steps. The model represents some features of the deposition of anisotropic colloidal particles of the experiment in Phys. |
The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each o... |
A hybrid lattice-statistical model of doubly decorated two-dimensional lattices, which have localized Ising spins at its nodal sites and itinerant electrons delocalized over decorating sites, is exactly solved with the help of a generalized decoration-iteration transformation. Under the assumption of a quarter filling... |
The computational Projective Dynamics method is used to analyze simulations of magnetization reversal in nanoscale magnetic pillars. It is shown that this method can be used to determine the magnetizations corresponding to the metastable minimum and saddle point in the free energy, and the free-energy barrier associat... |
In this paper we compare market price fluctuations with the response to fundamental price drops within the Lux-Marchesi model which is able to reproduce the most important stylized facts of real market data. Major differences can be observed between the decay of spontaneous fluctuations and of changes due to external ... |
Driven barrier crossings are pervasive in optical-trapping experiments and steered molecular-dynamics simulations. Despite the high fidelity of control, the freedom in the choice of driving protocol is rarely exploited to improve efficiency. |
Polymerized phantom membranes are revisited using a nonperturbative renormalization group approach. This allows one to investigate both the crumpling transition and the low-temperature, flat, phase in any internal dimension D and embedding dimension d, and to determine the lower critical dimension. |
We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d=1+1, for both flat and curved geometries. We analyzed two classes of models. |
We study the influence of entanglement on the relation between the statistical entropy of an open quantum system and the heat exchanged with a low temperature environment. A model of quantum Brownian motion of the Caldeira-Leggett type - for which a violation of the Clausius inequality has been stated by Th.M. |
Using thermodynamic arguments treatment it is shown that, independently on whether Fisher renormalization changes the critical exponents near a phase transition in a constrained system or not, new corrections to scaling with correction exponents proportional to the specific heat index $\alpha$ appear. Because of the s... |
We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. |
We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. |
A recent proposal for practical calculation of vibrational mode lifetimes is tested on simple, low-dimensional anharmonic models. The proposed scheme approximates the mode lifetime in terms of ensemble averages of specific functions in phase-space; various levels of approximation correspond to ensemble moments of the ... |
How much time does it take two molecules to react? If a reaction occurs upon contact, the answer to this question boils down to the classic first-passage time problem: find the time it takes the two molecules to meet. |
We investigate the phase diagram of a two-species Bose-Hubbard model describing atoms and molecules on a lattice, interacting via a Feshbach resonance. We identify a region where the system exhibits an exotic super-Mott phase and regions with phases characterized by atomic and/or molecular condensates. |
Magnetic relaxation in large spin molecular paramagnets is often found to behave as the square root of time at short times t. This behaviour was explained by Prokofiev & Stamp as arising from dipole interactions between molecular spins. |
We have analyzed the cross-correlations of daily fluctuations for N=6 358 US stock prices during the year 1999. From those $N(N-1)/2$ correlations coefficients, the Minimum Spanning Tree (MST) has been built. |
We consider the ground state energy of the Lieb-Liniger gas with $\delta$ interaction in the weak coupling regime $\gamma\to0$. For bosons with repulsive interaction, previous studies gave the expansion $e_{\text{B}}(\gamma)\simeq\gamma-4\gamma^{3/2}/3\pi+(1/6-1/\pi^{2})\gamma^{2}$. |
In this work, we show a connection between superstatistics and position-dependent mass (PDM) systems in the context of the canonical ensemble. The key point is to set the fluctuation distribution of the inverse temperature in terms od the system PDM. |
The probability that a randomly accelerated particle in two dimensions has not yet left a simply connected domain ${\cal A}$ after a time $t$ decays as $e^{-E_0t}$ for long times. The same quantity $E_0$ also determines the confinement free energy per unit length $\Delta f=k_BT\thinspace E_0$ of a semiflexible polymer... |
We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the spectral problem used to obtain the large deviations of current-type observables for r... |
We investigate the phenomenon of producing vibration-induced rotational motion in a cylinder filled with achiral rods and being vibrated by an external drive. The arrangement of the rods develops chirality as a result of the interaction of gravity and steric hindrance, which is responsible for the induced motion. |
In this text, we implement a monte carlo algorithm to study thermodynamic properties of ice. Our program, written in Python, is open-sourced and available at <a href="https://github.com/AKnightWing/ColdAsIce" rel="external noopener nofollow" class="link-external link-https">this https URL</a>. |
Classical spin Hamiltonians are a powerful tool to model complex systems, characterised by a local structure given by the local Hamiltonians. One of the best understood local structures is the grammar of formal languages, which are central in computer science and linguistics, and have a natural complexity measure give... |
We present a standard form of master equations (ME) for general one-dimensional non-Markovian (history-dependent) jump processes, complemented by an asymptotic solution derived from an expanded system-size approach. The ME is obtained by developing a general Markovian embedding using a suitable set of auxiliary field ... |
A one-dimensional driven diffusive system with two types of particles and nearest neighbors interactions has been considered on a finite lattice with open boundaries. The particles can enter and leave the system from both ends of the lattice and there is also a probability for converting the particle type at the bound... |
Understanding looping probabilities, including the particular case of ring-closure or cyclization, of fluctuating polymers (eg DNA) is important in many applications in molecular biology and chemistry. In a continuum limit the configuration of a polymer is a curve in the group SE(3) of rigid body displacements, whose ... |
Using a simple lattice model for granular media, we present a scenario of self-organization that we term self-organized structuring where the steady state has several unusual features: (1) large scale space and/or time inhomogeneities and (2) the occurrence of a non-trivial peaked distribution of large events which pro... |
We study the symmetry of large deviation functions associated with time-integrated currents in Markov pure jump processes. One current known to have this symmetry is the fluctuating entropy production and this is the content of the fluctuation theorem. |
We present a detailed account of a first-order localization transition in the Discrete Nonlinear Schrödinger Equation, where the localized phase is associated to the high energy region in parameter space. We show that, due to ensemble inequivalence, this phase is thermodynamically stable only in the microcanonical ens... |
The effect of the anisotropy in the exchange interaction on the critical temperature and the order parameter of the anisotropic Heisenberg model on a core-shell structured nanotube geometry has been investigated. As a formulation, effective field theory with the differential operator technique and decoupling approxima... |
We study the formation of large-scale coherent structures (a condensate) for a system of two weakly interacting classical waves. Using the coupled defocusing nonlinear Schrödinger (NLS) equations as a representative model, we focus on condensation in the phase mixing regime. |
We perform a Wang-Landau Monte Carlo simulation of a Cu0.5Zn0.5 order-disorder transition using 250 atoms and pairwise atom swaps inside a 5 x 5 x 5 BCC supercell. Each time step uses energies calculated from density functional theory (DFT) via the all-electron Korringa-Kohn- Rostoker method and self-consistent potent... |
We investigated the yield stress and the apparent viscosity of sand with and without small amounts of liquid. By pushing the sand through a tube with an enforced Poiseuille like profile we minimize the effect of avalanches and shear localization. |
Critical phenomena near continuous phase transitions are typically observed on the scale of wavelengths of visible light[1]. Here we report similar phenomena for atmospheric precipitation on scales of tens of kilometers. |
This work measures the time to equilibrium for the multicanonical method on the 2D-Ising system by using a new criterion, proposed here, to find the time to equilibrium, teq, of any sampling procedure based on a Markov process. Our new procedure gives the same results that the usual one, based on the magnetization, fo... |
The theory of large deviations has been applied successfully in the last 30 years or so to study the properties of equilibrium systems and to put the foundations of equilibrium statistical mechanics on a clearer and more rigorous footing. A similar approach has been followed more recently for nonequilibrium systems, e... |
We explicitly calculate the moments $t_n$ of general Heisenberg Hamiltonians up to eighth order. They have the form of finite sums of products of two factors. |
Despite the fact that the theory of mixtures has been part of non-equilibrium thermodynamics and engineering for a long time, it is far from complete. While it is well formulated and tested in the case of mechanical equilibrium (where only diffusion-like processes take place), the question how to properly describe hom... |
We have computed the two and three-particle contribution to the entropy of a Weeks-Chandler-Andersen fluid via molecular dynamics simulations. The three-particle correlation function and entropy were computed with a new method which simplified calculation. |
The infinite time-evolving block decimation (iTEBD) algorithm [Phys. Rev. Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute the ground state of one-dimensional quantum lattice systems in the thermodynamic limit. Here we extend the algorithm to tackle a much broader class of problems, namely ... |
We discuss similarities and differencies between systems of many interacting players maximizing their individual payoffs and particles minimizing their interaction energy. We analyze long-run behavior of stochastic dynamics of many interacting agents in spatial and adaptive population games. |
We study a social network consisting of over $10^4$ individuals, with a degree distribution exhibiting two power scaling regimes separated by a critical degree $k_{\rm crit}$, and a power law relation between degree and local clustering. We introduce a growing random model based on a local interaction mechanism that r... |
Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and nonequilibrium systems, but their experimental observation has remained elusiv... |
The spin 1/2 XXZ chain driven out of equilibrium by coupling with boundary reservoirs targeting perpendicular spin orientations in XY plane, is investigated. The existence of an anomaly in the nonequilibrium steady state (NESS) at the isotropic point $\Delta=1$ is demonstrated both in the weak coupling and weak drivin... |
We performed a network traffic simulation to clarify the mechanism producing self-similar traffic originating in the transport layer level. Self-similar behavior could be observed without assuming a long-tailed distribution of the input file size. |
We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quan... |
In this paper a viewpoint that time is an informational and thermal entity is shown. We consider a model for a simple relaxation process for which a relationship among event, time and temperature is mathematically formulated. |
We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundary-driven XXZ spin-chain. Studying the evolution of the spin current density $\mathcal J^s$ as a function of the system size $L$, we show that, accounting for boundary effects, the transition has a non-trivial unive... |
The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic fluctuations. |
Using the Monte Carlo simulation method for bosonic reaction-diffusion systems introduced recently [S. -C. |
An extrinsic curvature surface model is investigated by Monte Carlo simulations on a disk. We found that the model undergoes a first-order transition separating the smooth phase from the collapsed phase. |
Brownian particles suspended in disordered crowded environments often exhibit non-Gaussian normal diffusion (NGND), whereby their displacements grow with mean square proportional to the observation time and non-Gaussian statistics. Their distributions appear to decay almost exponentially according to "universal... |
We investigate piecewise-linear stochastic models as with regards to the probability distribution of functionals of the stochastic processes, a question which occurs frequently in large deviation theory. The functionals that we are looking into in detail are related to the time a stochastic process spends at a phase s... |
A surface model on compartmentalized spheres is studied by using the Monte Carlo simulation technique with dynamical triangulations. We found that the model exhibits a variety of phases: the spherical phase, the tubular phase, the planar phase, the wormlike planar phase, the wormlike long phase, the wormlike short pha... |
Universal aspects of the thermodynamic Casimir effect in wetting films of 3He-4He mixtures near their bulk tricritical point are studied within suitable models serving as representatives of the corresponding universality class. The effective forces between the boundaries of such films arising from the confinement are ... |
We have obtained by Monte Carlo NVT simulations the constant-volume excess heat capacity of square-well fluids for several temperatures, densities and potential widths. Heat capacity is a thermodynamic property much more sensitive to the accuracy of a theory than other thermodynamic quantities, such as the compressibi... |
Densely packed, motile bacteria can adopt collective states not seen in conventional, passive materials. These states remain in many ways mysterious, and their physical characterization can aid our understanding of natural bacterial colonies and biofilms as well as materials in general. |
We present exact calculations of the zero-temperature partition function of the $q$-state Potts antiferromagnet on arbitrarily long strips of the square, triangular, and kagomé lattices with width $L_y=2$ or 3 vertices and with periodic longitudinal boundary conditions. From these, in the limit of infinite length, we ... |
We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). |
We derive a relationship for the electric field dependent ionic conductivity in terms of fluctuations of time integrated microscopic variables. We demonstrate this formalism with molecular dynamics simulations of solutions of differing ionic strength with implicit solvent conditions and molten salts. |
We revisit a simple lattice model of aggregation in which masses diffuse and coalesce upon contact with rate 1 and every nonzero mass chips off a single unit of mass to a randomly chosen neighbour with rate $w$. The dynamics conserves the average mass density $\rho$ and in the stationary state the system undergoes a n... |
We consider the Bose-Hubbard model of atoms in an optical lattice potential when the atom-atom interactions are attractive. If the lowest energy lattice sites are degenerate (such as in the homogeneous case), then, at a critical value of the interaction strength, a phase-coherent condensate becomes unstable to a quant... |
We analyze numerically the out-of-equilibrium relaxation dynamics of a long-range Hamiltonian system of $N$ fully coupled rotators. For a particular family of initial conditions, this system is known to enter a particular regime in which the dynamic behavior does not agree with thermodynamic predictions. |
We study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium, nonequilibrium, and manmade stochastic systems. We give conditions for the convergence of these estimators with sample size, based on the boundedness or unboundedness of th... |
We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting Yang-Baxter integrable models. |
We present a kinetic theory for inhomogeneous systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a closed kinetic equation describing the relaxation of the distribution function of the system as a whole due to resonances between different orbits... |
If the damping of a simple harmonic oscillator from a thermally random force is sufficiently strong, then the oscillator may become unstable. For a photon oscillator (radiatively damped by electric dipole moments), the instability leads to a low temperature Hepp-Lieb-Preparata super-radiant phase transition. |
We analyze the scaling of avalanche precursors in the three dimensional random fuse model by numerical simulations. We find that both the integrated and non-integrated avalanche size distributions are in good agreement with the results of the global load sharing fiber bundle model, which represents the mean-field limi... |
The geometrical approach to phase transitions is illustrated by simulating the high-temperature representation of the Ising model on a square lattice. |
When described in a grand canonical ensemble, a finite Coulomb system exhibits charge fluctuations. These fluctuations are studied in the case of a classical (i.e. non-quantum) system with no macroscopic average charge. |
Reply to the comment, <a href="https://arxiv.org/abs/cond-mat/0209398" data-arxiv-id="cond-mat/0209398" class="link-https">cond-mat/0209398</a> by by N.W. Watkins, S.C. Chapman, and G. Rowlands |
An ideal mixture of parahydrogen (with nuclear spin K=0) and orthohydrogen (with K=1), in statistical weights 1/4 and 3/4, respectively, is used as a test ground for the existence of non-extensivity in chemical physics. We report on a new bound on the non extensivity parameter q - 1 that characterizes generalized ther... |
The non-stationary relaxation and physical ageing in the diffusion-limited erosion process ({\sc dle}) is studied through the exact solution of its Langevin equation, in $d$ spatial dimensions. The dynamical exponent $z=1$, the growth exponent $\beta=\max(0,(1-d)/2)$ and the ageing exponents $a=b=d-1$ and $\lambda_C=\... |
Two significant consequences of quantum fluctuations are entanglement and criticality. Entangled states may not be critical but a critical state shows signatures of universality in entanglement. |
A master equation description of the inherent dynamics is used to calculate the frequency-dependent linear thermo-visco-elastic response functions of a glass-forming liquid. From the imaginary parts of the isobaric specific heat, isothermal bulk modulus, and isobaric thermal expansion coefficient, we define a quantity... |
The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number of dimensions, a phenomenon called the curse of dimensionality. |
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the system-environment interaction, we bound the counting observables in the environment by t... |
We prove that for a wide class of quantum spin systems with isotropic Heisenberg coupling the energy eigenvalues which belong to a total spin quantum number S have upper and lower bounds depending at most quadratically on S. The only assumption adopted is that the mean coupling strength of any spin w.r.t. its neighbour... |
Theory of solutions in energy representation (ER method) developed by Matubayasi and Nakahara provides with an approximate way of calculating solvation free energies (or, identically, the excess chemical potentials) from atomistic simulations. In this document we provide some derivation details of this, to our opinion... |
Non-local twist operators are introduced for the O(n) and Q-state Potts models in two dimensions which, in the limits n -> 0 (resp. Q -> |
A new class of models, generalizing Asymmetric Exclusion Process for many parallel interacting channels, is proposed. We couple the models with boundary reservoirs, study boundary-driven phase transitions and show that usually taken hydrodynamic description fails. |
In a single molecule assay, the motion of a molecular motor is often inferred from measuring the stochastic trajectory of a large probe particle attached to it. We discuss a simple model for this generic set-up taking into account explicitly the elastic coupling between probe and motor. |
A modified fluctuation-dissipation-theorem (MFDT) for a non-equilibrium steady state (NESS) is experimentally checked by studying the position fluctuations of a colloidal particle whose motion is confined in a toroidal optical trap. The NESS is generated by means of a rotating laser beam which exerts on the particle a... |
We provide a rigorous proof of the absence of nontrivial local conserved quantities in all spin-1/2 chains with symmetric nearest-neighbor interaction, except for known integrable systems. This result shows that there are no further integrable system that awaits to be discovered. |
From bird flocks and fish schools to migrating cell sheets, collective motion is a ubiquitous biological phenomenon that inspires quantitative modeling through self-propelled particle (SPP) frameworks. Conventional SPP models prescribe either distance-based (metric) or rank-based (topological) interactions; however, e... |
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