Journal of Statistical Physics最新文献

We propose an extension of the preferential attachment scheme by allowing the connecting probability to depend on time t. We estimate the parameters involved in the model by minimizing the expected squared difference between the number of vertices of degree one and its conditional expectation. The asymptotic properties of the estimators are also investigated when the parameters are time-varying by establishing the central limit theorem (CLT) of the number of vertices of degree one. We propose a new statistic to test whether the parameters have change points. We also offer some methods to estimate the number of change points and detect the locations of change points. Simulations are conducted to illustrate the performances of the above results.

The simplified approach to the Bose gas was introduced by Lieb in 1963 to study the ground state of systems of interacting Bosons. In a series of recent papers, it has been shown that the simplified approach exceeds earlier expectations, and gives asymptotically accurate predictions at both low and high density. In the intermediate density regime, the qualitative predictions of the simplified approach have also been found to agree very well with quantum Monte Carlo computations. Until now, the simplified approach had only been formulated for translation invariant systems, thus excluding external potentials, and non-periodic boundary conditions. In this paper, we extend the formulation of the simplified approach to a wide class of systems without translation invariance. This also allows us to study observables in translation invariant systems whose computation requires the symmetry to be broken. Such an observable is the momentum distribution, which counts the number of particles in excited states of the Laplacian. In this paper, we show how to compute the momentum distribution in the simplified approach, and show that, for the simple equation, our prediction matches up with Bogolyubov’s prediction at low densities, for momenta extending up to the inverse healing length.

In coalescing ballistic annihilation, infinitely many particles move with fixed velocities across the real line and, upon colliding, either mutually annihilate or generate a new particle. We compute the critical density in symmetric three-velocity systems with four-parameter reaction equations.

We prove the Thouless–Anderson–Palmer (TAP) equations for the local magnetization in the multi-species Sherrington–Kirkpatrick (MSK) spin glass model. One of the key ingredients is based on concentration results established in Dey and Wu (J Stat Phys 185(3):22, 2021). The equations hold at high temperature for general MSK model without positive semi-definite assumption on the variance profile matrix (mathbf {Delta }^2).

The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is derived from various microscopic models, and to establish a robust way to derive the KPZ equation is a fundamental problem both in mathematics and in physics. As a microscopic model, we consider multi-species interacting diffusion processes, whose dynamics is driven by a nonlinear potential which satisfies some regularity conditions. In particular, we study asymptotic behavior of fluctuation fields associated with the processes in the high temperature regime under equilibrium. As a main result, we show that when the characteristic speed of each species is the same, the family of the fluctuation fields seen in moving frame with this speed converges to the coupled KPZ equations. Our approach is based on a Taylor expansion argument which extracts the harmonic potential as a main part. This argument works without assuming a specific form of the potential and thereby the coupled KPZ equations are derived in a robust way.

Our work is dedicated to the introduction and investigation of a new asymptotic correlation relation in the field of mean field models and limits. This new notion, order (as opposed to chaos), revolves around a tendency for self organisation in a given system and is expected to be observed in biological and societal models. Beyond the definition of this new notion, our work will show its applicability, and propagation, in the so-called choose the Leader model.

This paper proposes an improved cumulant collision model for the pseudo-potential lattice Boltzmann method (LBM) to increase the stability of multiphase flow simulations involving low viscosities. This model is based on the work of Kharmiani et al. in (J Stat Phys 175: 47, 2019), which can be extended regardless of the collision model. The original cumulant collision model (Geier et al. in Comput Math Appl 70:507, 2015) causes a non-physical shape of droplets in pseudo-potential LBM because only the first-order central moments are considered in the forcing scheme. The improved cumulant collision model proposed in this paper applies the central moment forcing scheme to the original cumulant model to cover the high-order central moments. Several numerical simulations were carried out to validate the proposed model. First, the problem of a stationary liquid layer was solved, where the proposed model was demonstrated to be thermodynamically consistent. Second, the problem of a stationary droplet was solved, where the result agreed well with Laplace’s law. Third, the problem of a droplet impact on a liquid film was solved, where the crown radius agreed well with the analytical and numerical results available. Fourth, the simulation results carried out with the raw moment, central moment, and the proposed improved cumulant collision models were compared, as the liquid and vapor viscosities were gradually lowered. With all else being equal, only the lattice Boltzmann method with the proposed improved cumulant collision model was able to successfully simulate a density ratio of 720 and a Reynolds number of ({mathbf {8.7}}{mathbf {times 10}}^{{textbf{4}}}).

Resistance distance in electrical circuits measures how much a component or an entire circuit resists the flow of electric current. When dealing with intricate circuits, this term explicitly denotes the total resistance observed between any two points, which varies based on the configuration and resistance values of the components within the circuit. The Kirchhoff index is a metric used to quantify the mean resistance distance across all pairs of nodes in an electrical network. In graph theory, these networks are depicted as graphs with nodes representing electrical components and edges symbolizing the connecting wires. The resistance distance between any two nodes is calculated as if the graph were an electrical circuit, with each edge functioning as a resistor. We focus on a particular type of graph known as a cacti graph, denoted by (mathcal {C}(n,s)), which features interconnected cycles that share a single common vertex, with n representing the total number of nodes and s the number of cycles. This paper explores cacti networks to establish the maximum possible values of the Kirchhoff index for these structures.

We show, without relying on any unproven assumptions, that a low-density free fermion chain exhibits thermalization in the following (restricted) sense. We choose the initial state as a pure state drawn randomly from the Hilbert space in which all particles are in half of the chain. This represents a nonequilibrium state such that the half chain containing all particles is in equilibrium at infinite temperature, and the other half chain is a vacuum. We let the system evolve according to the unitary time evolution determined by the Hamiltonian and, at a sufficiently large typical time, measure the particle number in an arbitrary macroscopic region in the chain. In this setup, it is proved that the measured number is close to the equilibrium value with probability very close to one. Our result establishes the presence of thermalization in a concrete model in a mathematically rigorous manner. The key for the proof is a new strategy to show that a randomly generated nonequilibrium initial state typically has a large enough effective dimension by using only mild verifiable assumptions. In the present work, we first give general proof of thermalization based on two assumptions, namely, the absence of degeneracy in energy eigenvalues and a property about the particle distribution in energy eigenstates. We then justify these assumptions in a concrete free-fermion model, where the absence of degeneracy is established by using number-theoretic results. This means that our general result also applies to any lattice gas models in which the above two assumptions are justified. To confirm the potential wide applicability of our theory, we discuss some other models for which the essential assumption about the particle distribution is easily verified, and some non-random initial states whose effective dimensions are sufficiently large.

By the dimension reduction idea, overshoot for random walks, coupling and martingale arguments, we obtain a simpler and easily computable expression for the first-order correction constant between discrete harmonic measures for random walks with rotationally invariant step distribution in (mathbb {R}^d (dge 2)) and the corresponding continuous counterparts. This confirms and extends a conjecture in Jiang and Kennedy (J Theor Probab 30(4):1424–1444, 2017), and simplifies the related expression of Wang et al. (Bernoulli 25(3):2279–2300, 2019). Furthermore, we propose a universality conjecture on high-order corrections for error estimation between generalized discrete harmonic measures and their continuous counterparts, which generalizes the universality conjecture of the first-order correction in Kennedy (J Stat Phys 164(1):174–189, 2016); and we prove this conjecture heuristically for the rotationally invariant case, and also provide several examples of second-order error corrections to check the conjecture by a numerical simulation argument.