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We prove optimal convergence results of a stochastic particle method for computing the classical solution of a multivariate McKean-Vlasov equation, when the measure variable is in the drift, following the classical approach of [BT97,…
Uniform-in-time bounds of nonnegative classical solutions to reaction-diffusion systems in all space dimension are proved. The systems are assumed to dissipate the total mass and to have locally Lipschitz nonlinearities of at most (slightly…
Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems…
We propose a two-dimensional (2d) quantum breakdown model of hardcore bosons interacting with disordered spins which would be classical without the bosons. It resembles particles incident into supersaturated vapor. The model exhibits a set…
Whether the 3D compressible Navier-Stokes-Poisson equations admit global classical solutions for general large initial data has long been a challenging open problem. In this paper, we provide an affirmative answer to this question under…
We prove that there is off-diagonal long-range order in the symmetrised version of the one-dimensional many-body problem presented by Jain and Khare (Phys. Lett. A262 (1999)35). This model is related to the short-range Dyson model employed…
The symmetric heavy-light ansatz is a method for finding the ground state of any dilute unpolarized system of attractive two-component fermions. Operationally it can be viewed as a generalization of the Kohn-Sham equations in density…
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…
We analyze the propagation of experimentally relevant two-particle correlations for one-dimensional interacting bosons, and give evidence that many-body chaos induces the emergence of an effective diffusive regime for the fully coherent…
In this paper the conditions are investigated for the occurrence of the so-called macroscopic irreversibility property and the related phenomenon of decay to kinetic equilibrium which may characterize the $1-$body probability density…
This paper presents a thermodynamically consistent model for multicomponent electrolyte solutions. The first part of this paper derives the general governing equations for nonequilibrium systems within the theory of nonequilibrium…
In this paper, the emergence of macroscopic-scale pseudo time-irreversibility is studied in the closed classical many-body system of pair interacting particles. First, exact continuum equations are derived to the Hamiltonian dynamics…
We review recent developments in the study of out-of-equilibrium topological states of matter in isolated systems. The phenomenon of many-body localization, exhibited by some isolated systems usually in the presence of quenched disorder,…
We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional…
Modeling many-body quantum systems with strong interactions is one of the core challenges of modern physics. A range of methods has been developed to approach this task, each with its own idiosyncrasies, approximations, and realm of…
A new direct integration method is established to construct the solutions of the stationary BBGKY hierarchy, assuming the usual form of the equilibrium correlation functions, for infinite classical systems of particles interacting via a…
A new series of integrable cases of the many-body problem in many-dimensional spaces is found. That series appears as a part of the larger series of integrable problems, which are in 1-1 correspondence with Krichever-Novikov algebras of…
A lattice model with soft repulsion followed by attraction is developed for a monolayer of hybrid core-shell particles self-assembling at an interface. The model is solved exactly in one dimension. One, two or three periodic structures and…
We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a…
A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occur in a pairwise fashion. It is also…