In this review recent investigations are summarized of many-body quantum systems with
long-range interactions, which are currently realized in Rydberg atom arrays, dipolar …

The theory of large deviations is concerned with the exponential decay of probabilities of
large fluctuations in random systems. These probabilities are important in many fields of …

For systems with long-range interactions, the two-body potential decays at large distances
as V (r)∼ 1/rα, with α≤ d, where d is the space dimension. Examples are: gravitational …

We review what is known, unknown, and expected about the mathematical properties of
Coulomb and Riesz gases. Those describe infinite configurations of points in R d interacting …

In locally interacting quantum many-body systems, the velocity of information propagation is
finitely bounded, and a linear light cone can be defined. Outside the light cone, the amount …

The theoretical study of the self-organization of two-dimensional and geophysical turbulent
flows is addressed based on statistical mechanics methods. This review is a self-contained …

Statistical mechanics constitutes one of the pillars of contemporary physics. Recognized as
such-together with mechanics (classical, quantum, relativistic), electromagnetism and …

Phase transitions are among the most impressive phenomena occurring in nature. They are
an example of emergent behavior, ie, of collective properties having no direct counterpart in …

By considering generalized logarithm and exponential functions used in nonextensive
statistics, the four usual algebraic operators: addition, subtraction, product and division, are …

The ground-state phase diagram of a two-dimensional Bose system with dipole-dipole
interactions is studied by means of a quantum Monte Carlo technique. Our calculation …