Related papers: Generalized Statistics on Lattices
We consider an overdamped Brownian particle subject to an asymptotically flat potential with a trap of depth $U_0$ around the origin. When the temperature is small compared to the trap depth ($\xi=k_B T/U_0 \ll 1$), there exists a range of…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
A phase coexistence state cannot be specified uniquely by any intensive parameters, such as the temperature and the magnetic field, because they take the same values over all coexisting phases. It can be specified uniquely only by an…
Originally, quantum probability theory was developed to analyze statistical phenomena in quantum systems, where classical probability theory does not apply, because the lattice of measurable sets is not necessarily distributive. On the…
We use recent results that localized excitations in nonlinear Hamiltonian lattices can be viewed and described as multiple-frequency excitations. Their dynamics in phase space takes place on tori of corresponding dimension. For a…
We use recent results that localized excitations in nonlinear Hamiltonian lattices can be viewed and described as multiple-frequency excitations. Their dynamics in phase space takes place on tori of corresponding dimension. For a…
Lattice models are valuable tools to gain insight into the statistical physics of heteropolymers. We rigorously map the partition function of these models into a vacuum expectation value of a $\mathbb{Z}_2$ lattice gauge theory (LGT), with…
Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…
This paper introduces a new method for the efficient computation of oscillatory multidimensional lattice sums in geometries with boundaries. Such sums are ubiquitous in both pure and applied mathematics, and have immediate applications in…
We present a general procedure for constructing lattices of qubits with a Hamiltonian composed of nearest-neighbour two-body interactions such that the ground state encodes a cluster state. We give specific details for lattices in one-,…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing…
Statistical physics models ranging from simple lattice to complex quantum Hamiltonians are one of the mainstays of modern physics, that have allowed both decades of scientific discovery and provided a universal framework to understand a…
We consider sequences of symmetric $U$-statistics, not necessarily Hoeffding-degenerate, both in a one- and multi-dimensional setting, and prove quantitative central limit theorems (CLTs) based on the use of {\it contraction operators}. Our…
We consider quantum quenches in the so-called $q$-boson lattice model. We argue that the Generalized Eigenstate Thermalization Hypothesis holds in this model, therefore the Generalized Gibbs Ensemble (GGE) gives a valid description of the…
We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test function of…
The Lieb-Schultz-Mattis theorem dictates that a trivial symmetric insulator in lattice models is prohibited if lattice translation symmetry and $U(1)$ charge conservation are both preserved. In this paper, we generalize the…
We study ballistic aggregation on a two dimensional square lattice, where particles move ballistically in between momentum and mass conserving coalescing collisions. Three models are studied based on the shapes of the aggregates: in the…
Pure gauge theories are rather different from theories with pure scalar and fermionic matter, especially in terms of the nature of excitations. For example, in scalar and fermionic theories, one can create ultra-local excitations. For a…
The long-standing puzzle surrounding the statistical mechanics of self-gravitating systems has not yet been solved successfully. We formulate a systematic theoretical framework of entropy-based statistical mechanics for spherically…