Searcharxiv⌕ Search

SEARCH · Searcharxiv

Results for “cond-mat.stat-mech”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 541 records · Page 30Linked to original sources
arXiv2013

Message-Passing Algorithms for Optimal Utilization of Cognitive Radio Networks

Cognitive Radio has been proposed as a key technology to significantly improve spectrum usage in wireless networks by enabling unlicensed users to access unused resource. We present new algorithms that are needed for the implementation of opportunistic scheduling policies that maximize the throughput utilization of resources by secondary users, under maximum interference constraints imposed by existing primary users. Our approach is based on the Belief Propagation (BP) algorithm, which is advantageous due to its simplicity and potential for distributed implementation. We examine convergence properties and evaluate the performance of the proposed BP algorithms via simulations and demonstrate that the results compare favorably with a benchmark greedy strategy.

cs.IT↗
arXiv2013

Relaxation of surface tension in the liquid-solid interfaces of Lennard-Jones liquids

We have established the surface tension relaxation time in the liquid-solid interfaces of Lennard-Jones (LJ) liquids by means of direct measurements in molecular dynamics (MD) simulations. The main result is that the relaxation time is found to be weakly dependent on the molecular structures used in our study and lies in such a range that in slow hydrodynamic motion the interfaces are expected to be at equilibrium. The implications of our results for the modelling of dynamic wetting processes and interpretation of dynamic contact angle data are discussed.

cond-mat.soft↗
arXiv2013

UV-IR transmutation for hybrid realizations of Z_k parafermion systems

Recent experiments brought Majorana particles closer to reality and raised interest in realizing $\mathbb{Z}_k$ parafermions for general value of $k$ in hybrid structures. Of particular interest is the prospect of realizing a two dimensional system with the edge states described by $\mathbb{Z}_k$ parafermion conformal field theory (CFT) by coupling one dimensional hybrid systems. However in order to understand the effective perturbation due to local inter-wire coupling, it is crucial to relate short distance ultra-violet (UV) degrees of freedom to primary fields of the CFT describing long distance infra-red (IR) physics. Here we consider two recent proposals for realizing a one dimensional system described by $\mathbb{Z}_k$ parafermion CFT upon tuning to quantum critical points: a parafermion chain and a pair of $ν=2/k$ quantum Hall chiral edge states under uniform backscattering and pairing, where the latter is represented by self-dual sine-Gordon model. We explicitly derive the relation between distinct UV degrees of freedom relevant for each proposals and the primary fields of $\mathbb{Z}_3$ parafermion CFT. Our results point to a marked difference in the effect of local coupling between wires represented by each proposals, regarding robustness of the edge states in the resulting two dimensional systems.

cond-mat.str-el↗
arXiv2013

Two distinct spin liquid states in a layered cubic lattice

We construct a family of short-range resonating-valence-bond wave functions on a layered cubic lattice, allowing for a tunable anisotropy in the amplitudes assigned to nearest-neighbour valence bonds along one axis. Monte Carlo simulations reveal that four phases are stabilized over the full range of the anisotropy parameter. They are separated from one another by a sequence of continuous quantum phase transitions. An antiferromagnetic phase, centred on the perfect isotropy point, intervenes between two distinct quantum spin liquid states. One of them is continuously deformable to the two-dimensional U(1) spin liquid, which is known to exhibit critical bond correlations. The other has both spin and bond correlations that decay exponentially. The existence of this second phase is proof that, contrary to expectations, neither a bipartite lattice structure nor a conventional Marshall sign rule is an impediment to realizing a fully gapped quantum spin liquid.

cond-mat.str-el↗
arXiv2013

On the typical properties of inverse problems in statistical mechanics

In this work we consider the problem of extracting a set of interaction parameters from an high-dimensional dataset describing T independent configurations of a complex system composed of N binary units. This problem is formulated in the language of statistical mechanics as the problem of finding a family of couplings compatible with a corresponding set of empirical observables in the limit of large N. We focus on the typical properties of its solutions and highlight the possible spurious features which are associated with this regime (model condensation, degenerate representations of data, criticality of the inferred model). We present a class of models (complete models) for which the analytical solution of this inverse problem can be obtained, allowing us to characterize in this context the notion of stability and locality. We clarify the geometric interpretation of some of those aspects by using results of differential geometry, which provides means to quantify consistency, stability and criticality in the inverse problem. In order to provide simple illustrative examples of these concepts we finally apply these ideas to datasets describing two stochastic processes (simulated realizations of a Hawkes point-process and a set of time-series describing financial transactions in a real market).

cond-mat.stat-mech↗
arXiv2013

Phase transitions in the three-dimensional Z(N) models

Phase transitions in zero-temperature 3D Z(N) lattice gauge theories are studied. We use a cluster algorithm defined for the dual formulation of the models. We also attempt to explain the nature of the intermediate continuously symmetric phase, which appears for N>5. The critical indices are calculated. The results obtained are used to study the scaling of critical points with N, as well as the scaling of finite-temperature critical points with the lattice size in the time direction, $N_t$.

hep-lat↗
arXiv2013

Reunion probabilities of $N$ one-dimensional random walkers with mixed boundary conditions

In this work we extend the results of the reunion probability of $N$ one-dimensional random walkers to include mixed boundary conditions between their trajectories. The level of the mixture is controlled by a parameter $c$, which can be varied from $c=0$ (independent walkers) to $c\to\infty$ (vicious walkers). The expressions are derived by using Quantum Mechanics formalism (QMf) which allows us to map this problem into a Lieb-Liniger gas (LLg) of $N$ one-dimensional particles. We use Bethe ansatz and Gaudin's conjecture to obtain the normalized wave-functions and use this information to construct the propagator. As it is well-known, depending on the boundary conditions imposed at the endpoints of a line segment, the statistics of the maximum heights of the reunited trajectories have some connections with different ensembles in Random Matrix Theory (RMT). Here we seek to extend those results and consider four models: absorbing, periodic, reflecting, and mixed. In all four cases, the probability that the maximum height is less or equal than $L$ takes the form $F_N(L)=A_N\sum_{k\inΩ_{B}}\int Dz e^{-\sum_{j=1}^Nk_j^2+G_N(k)-\sum_{j,\ell=1}^N z_jV_{j\ell}(k)\overline{z}_\ell}$, where $A_N$ is a normalization constant, $G_N(k)$ and $V_{j\ell}(k)$ depend on the type of boundary condition, and $Ω_{B}$ is the solution set of quasi-momenta $k$ obeying the Bethe equations for that particular boundary condition.

cond-mat.stat-mech↗
arXiv2013

Coarse-grained description of general oscillator networks

We propose a novel and systematic method for coarse-graining oscillator networks described by phase equations. Our coarse-graining method enables us to obtain the closed coarse-grained equations for a few effective eigenmodes, which is based on the eigenvalue problem of the linearized system around the phase-locked solution and a nonlinear transformation. We demonstrate our method by applying it to oscillator dynamics on a random graph, which exhibits a saddle-node bifurcation at the bifurcation point.

nlin.AO↗
arXiv2013

Conservation laws for the Cattaneo heat propagation

In this work we determine for the Cattaneo heat propagation system all the supplementary balance laws (conservation laws) of the same order (zero) as the system itself and extract the constitutive relations (expression for the internal energy) dictated by the Entropy Principle. The space of all supplementary balance laws (having the functional dimension 8) contains four original balance laws and their deformations depending on 4 functions of temperature $θ$ - $λ(θ),K^{A}(θ),A=1,2,3$. The requirements of the II law of thermodynamics leads to the exclusion of three of these functions ($K^A$) and to further restriction to the form of internal energy. In its final formulation, entropy balance represent the deformation of the energy balance law by the functional parameter $λ(θ)$.

cond-mat.stat-mech↗
arXiv2013

Microrheology measurements with a hanging-fiber AFM probe

A method to measure the viscosity of liquids at microscales is presented. It uses a thin glass fiber fixed on the tip of the cantilever of an extremely low noise Atomic Force Microscope (AFM), which accurately measures the cantilever {deflection}. When the fiber is dipped into the liquid the dissipation of the cantilever-fiber system increases. This dissipation, linked to the liquid viscosity, is computed from the power spectral density of the thermal fluctuations of the cantilever {deflection}. The {high sensitivity of the AFM} allows us to show the existence and to develop a model of the coupling between the dynamics of the fiber and that of the cantilever. This model {accurately} fits the experimental data. The advantages and draw-backs of the method are discussed

cond-mat.soft↗
arXiv2013

On the Foundation of Statistical Mechanics under Experimentally Realistic Conditions: A Comparison between the Quantum and the Classical Case

Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail) evolve towards a stationary long-time behavior ("equilibration")? In how far is this steady state in agreement with the microcanonical ensemble as predicted by Statistical Mechanics ("thermalization")? In the first part of the paper, a recently developed quantum mechanical treatment of the problem is briefly summarized, putting particular emphasis on the realistic modeling of experimental measurements and non-equilibrium initial conditions. Within this framework, equilibration can be proven under very weak assumptions about those measurements and initial conditions, while thermalization still requires quite strong additional hypotheses. In the second part, an analogous approach within the framework of classical mechanics is developed and compared with the quantum case. In particular, the assumptions to guarantee classical equilibration are now rather strong, while thermalization then follows under relatively weak additional conditions.

cond-mat.stat-mech↗
arXiv2013

Exercises in simplest dynamical random walk, or Quantum path integral approach to true diffusion law and 1/f noise of classical particle interacting with ideal gas

Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is demostrated between results of an naturally arising simple approximation of this integral and results obtained by formally different methods, thus in a new fashion showing inevitability of scaleless 1/f-type fluctuations in rates of molecular Brownian motions and other dynamical transport and evolution processes.

cond-mat.stat-mech↗
arXiv2013

Long-range interacting systems and the Gibbs-Duhem equation

The generalized Gibbs-Duhem equation is obtained for systems with long-range interactions in $d$ spatial dimensions. We consider that particles in the system interact through a slowly decaying pair potential of the form $1/r^ν$ with $0\leqν\leq d$. The local equation of state is obtained by computing the local entropy per particle and using the condition of local thermodynamic equilibrium. This local equation of state turns out to be that of an ideal gas. Integrating the relation satisfied by local thermodynamic variables over the volume, the equation involving global magnitudes is derived. Thus, the Euler relation is found and we show that it is modified by the addition of a term proportional to the total potential energy. This term is responsible for the modification of the Gibbs-Duhem equation. We also point out a close relationship between the thermodynamics of long-range interacting systems and the thermodynamics of small systems introduced by Hill.

cond-mat.stat-mech↗
arXiv2013

Lattice Monte Carlo methods for systems far from equilibrium

We present a new numerical Monte Carlo approach to determine the scaling behavior of lattice field theories far from equilibrium. The presented methods are generally applicable to systems where classical-statistical fluctuations dominate the dynamics. As an example, these methods are applied to the random-force-driven one-dimensional Burgers' equation - a model for hydrodynamic turbulence. For a self-similar forcing acting on all scales the system is driven to a nonequilibrium steady state characterized by a Kolmogorov energy spectrum. We extract correlation functions of single- and multi-point quantities and determine their scaling spectrum displaying anomalous scaling for high-order moments. Varying the external forcing we are able to tune the system continuously from equilibrium, where the fluctuations are short-range correlated, to the case where the system is strongly driven in the infrared. In the latter case the nonequilibrium scaling of small-scale fluctuations are shown to be universal.

hep-lat↗
arXiv2013

Fundamental aspects of steady state heat to work conversion

We review theoretical approaches to analyzing efficiency of steady state heat to work conversion which is crucial in the timely problem of optimizing efficiency of small-scale heat engines and refrigerators. A rather abstract perspective of non-equilibrium statistical mechanics and dynamical system's theory is taken to view at this very practical problem. Several recently discovered general mechanisms of optimizing the figure of merit of thermoelectric efficiency are discussed, also in connection to breaking time-reversal symmetry of the microscopic equations of motion. Applications of these theoretical and mathematical ideas to practically relevant models are pointed out.

cond-mat.stat-mech↗
arXiv2013

Collective behaviours: from biochemical kinetics to electronic circuits

In this work we aim to highlight a close analogy between cooperative behaviors in chemical kinetics and cybernetics; this is realized by using a common language for their description, that is mean-field statistical mechanics. First, we perform a one-to-one mapping between paradigmatic behaviors in chemical kinetics (i.e., non-cooperative, cooperative, ultra-sensitive, anti-cooperative) and in mean-field statistical mechanics (i.e., paramagnetic, high and low temperature ferromagnetic, anti-ferromagnetic). Interestingly, the statistical mechanics approach allows a unified, broad theory for all scenarios and, in particular, Michaelis-Menten, Hill and Adair equations are consistently recovered. This framework is then tested against experimental biological data with an overall excellent agreement. One step forward, we consistently read the whole mapping from a cybernetic perspective, highlighting deep structural analogies between the above-mentioned kinetics and fundamental bricks in electronics (i.e. operational amplifiers, flashes, flip-flops), so to build a clear bridge linking biochemical kinetics and cybernetics.

cond-mat.stat-mech↗