Statistical Mechanics
The Fredrickson-Andersen model with hyperparameter $K=1$ is a severely constrained kinetic lattice spin system, such that any site is temporarily blocked from changing its packing state (empty or occupied) if there is one or more occupied…
In this review we discuss semi-classical methods that are traditionally used to describe many-body systems in physics, but may also be used to describe partitions of integers in analytic number theory. Specifically, we explore the…
We show that in a reciprocal Brownian motor the entropy production hidden behind a mechanically stalled coordinate can be reconstructed exactly from measurements of that coordinate alone. We introduce a minimal, analytically solvable…
We investigate the completion dynamics of an overdamped dimer moving in a bistable potential under thermal fluctuations and a weak periodic force. Both monomers start in one of the two wells separated by a barrier. The transition is…
We develop a general method, based on the construction of a kinetic potential acting as a Lyapunov function, to establish when diffusion necessarily equilibrates in non-ideal reaction-diffusion systems, under arbitrary driving by autonomous…
The Ramsey community number $r_k$ is the smallest size at which a network is better described by communities than by none, under a Bayesian detection rule. On the diamond hierarchical lattice we show that $r_k$ is an exact…
More than 80 years ago Kramers published a paper calculating how fast a Brownian particle escapes from a potential well over an activation barrier. Since then Kramers' model has been widely adopted by nuclear physics, biophysics and…
We consider random sequential adsorption (RSA) of aligned squares and derive the low-coverage expansion of the availability function alpha(q), the fraction of positions accessible to an additional square, up to fourth order in the coverage…
Level statistics in non-integrable quantum many-body systems with time reversal symmetry are expected to follow the Gaussian Orthogonal Ensemble (GOE), a hallmark of quantum chaos. However, we show that the interacting Su-Schrieffer-Heeger…
We introduce the notion of an Ising emulator for two-dimensional Ising models: flat, unit-edge-length lattices can be represented as site- or bond-diluted supercells of a single host lattice, for which the Feynman--Vdovichenko/Kac--Ward…
Classical nucleation theory (CNT) describes the formation of a stable phase from a metastable one in terms of a single reaction coordinate that corresponds to the radius of a nucleating droplet. In this work, we provide a full account of…
We study a Brownian particle in a harmonic trap whose stiffness switches between two values with arbitrary waiting-time statistics, generating semi-Markovian dynamics. To treat the resulting temporal memory, we formulate the problem in an…
Ising machines are heuristic solvers for combinatorial optimization, but their solution quality can degrade when large-scale constrained problems are solved directly. Ising-machine-assisted large neighborhood search (LNS) instead repeatedly…
We propose a numerical algorithm to construct a Markov model with an extended list of variables to parameterize the equation of motion of a multidimensional coarse-grained physical system in an external potential, when memory effects are…
We complete the phase diagram of the macroscopic Curie-Weiss magnet in a time-periodic external field, as a function of temperature and driving parameters. There is a regime (large enough driving amplitude and frequency, at low…
Large-scale quadratic unconstrained binary optimization (QUBO) formulations of constrained combinatorial optimization problems often exceed the input-size limit of present Ising machines or suffer from degraded solution quality as the…
Random exploration is usually quantified by how fast new space is found, from the range of a single walker to the territory collectively covered by many walkers. In competitive exploration, first arrival secures an exclusive resource, as…
Reweighting of probability measures provides a unifying perspective on conditioning, exponential tilting, and, more generally, ensemble transformations in statistical mechanics. We show that exponential tilting and conditioning arise as the…
The quantum tunneling Mpemba effect is investigated within a continuous one-dimensional symmetric double-well potential open to external environmental sinks at the boundaries ($x=\pm L$). Using a non-Hermitian spectral decomposition of the…
We study continuously monitored dynamics of a quasiperiodic free-fermion chain defined on a Fibonacci lattice. We focus on fluctuations of the local particle number, which exhibit a spatially uniform distribution in the unitary limit.…