Related papers: A duality method for mean-field limits with singul…
A discrete system constituted of particles interacting by means of a centroid-based law is numerically investigated. The elements of the system move in the plane, and the range of the interaction can be varied from a more local form…
Exactly solvable many-body systems are few and far between, and the utility of approximate methods cannot be overestimated. Entanglement mean field theory is an approximate method to handle such systems. While mean field theories reduce the…
We develop the `duality approach', that has been extensively studied for classical models of transport, for quantum systems in contact with a thermal `Lindbladian' bath. The method provides (a) a mapping of the original model to a simpler…
The mean-field approximations of many-boson dynamics are known to be effective in many physical relevant situations. The mathematical justifications of such approximations rely generally on specific considerations which depend too much on…
An inversion method is formulated for extracting entanglement-related information on two-particle interactions in a one-dimensional system from measurable one-particle position- and momentum-distribution functions. The method is based on a…
Understanding quantum many-body systems with long-range or infinite-range interactions is of relevance across a broad set of physical disciplines, including quantum optics, nuclear magnetic resonance and nuclear physics. From a theoretical…
Recently, the paper [12] introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This…
Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field…
Strongly-interacting systems consisting of particles that interact through a large scattering length satisfy universal relations that relate many of their central properties to the contact, which measures the number of pairs with small…
We study the random-field Ising model with long-range interactions and show the exactness of the mean-field theory under certain mild conditions. This is a generalization of the result of Mori for the non-random and spin-glass cases. To…
The generally accepted view in quantum theory is that information about which way the quantum system traveled and interference visibility are complementary. In all which-way experiments, however, an intervention takes place in the…
Ionic liquids are solvent-free electrolytes, some of which possess an intriguing self-assembly property. Using a mean-field framework (based on Onsager's relations) we show that bulk nano-structures arise via type-I and II phase transitions…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
Using fourth-order perturbation theory, a general formula for the van der Waals potential of two neutral, unpolarized, ground-state atoms in the presence of an arbitrary arrangement of dispersing and absorbing magnetodielectric bodies is…
We propose a family of lower bounds for concurrence in quantum systems using mutually unbiased measurements, which prove more effective in entanglement estimation compared to existing methods. Through analytical and numerical examples, we…
In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform in the number of particles, and uniform-in-time propagation of chaos for the…
In general, the system of $2$nd-order partial differential equations made of the Euler-Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the so-called second-order problem. The first aim of…
We consider a field theory describing interacting nonrelativistic particles of two types, which map to each other under time reversal, with point-like interaction. We identify a new type of interaction which depends on the relative velocity…
We consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions. We prove that the (mollified) empirical process converges, uniformly in time and space variables, to the…
Theories which have been used to describe the quantized electromagnetic field interacting with a nonlinear dielectric medium are either phenomenological or derived by quantizing the macroscopic Maxwell equations. Here we take a different…