Related papers: On weak interaction between a ground state and a n…
We consider ground states of the $N$ coupled fermionic nonlinear Schr\"{o}dinger systems with the Coulomb potential $V(x)$ in the $L^2$-subcritical case. By studying the associated constraint variational problem, we prove the existence of…
In this paper, the incremental stability of interconnected switched nonlinear systems is discussed. The nature of switching considered is state-dependent. The incremental stability of the switched interconnected system is a stronger…
In this paper, we explore the metastable behavior of the Glauber dynamics associated with the three-state Potts model with an asymmetrical external field at a low-temperature regime. The model exhibits three monochromatic configurations: a…
We study the stationary nonequilibrium states of N point particles moving under the influence of an electric field E among fixed obstacles (discs) in a two dimensional torus. The total kinetic energy of the system is kept constant through a…
We consider two types of non linear fast diffusion equations in R^N:(1) External drift type equation with general external potential. It is a natural extension of the harmonic potential case, which has been studied in many papers. In this…
An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then…
We consider a Nonlinear Schr\"odinger Equation with a very general non linear term and with a trapping $\delta $ potential on the line. We then discuss the asymptotic behavior of all its small solutions, generalizing a recent result by…
Candidate homogeneous, isotropic superfluid or superconducting states of paired fermion species with different chemical potentials, can lead to quasiparticle excitation energies that vanish at either zero, one, or two spheres in momentum…
Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p))…
As an application of the finite-rank Lieb-Thirring inequality established in [R. L. Frank, D. Gontier and M. Lewin, Comm. Math. Phys., 2021], we study ground states of mass-critical N-coupled Fermi nonlinear Schr\"{o}dinger systems with…
We analyze the stability of standing pulse solutions of a neural network integro-differential equation. The network consists of a coarse-grained layer of neurons synaptically connected by lateral inhibition with a non-saturating nonlinear…
A preceding paper demonstrated that explicit asymptotic methods generally work much better for extremely stiff reaction networks than has previously been shown in the literature. There we showed that for systems well removed from…
The ground state entanglement of the system, both in discrete-time and continuous-time cases, is quantified through the linear entropy. The result shows that the entanglement increases as the interaction between the particles increases in…
We show that a localized quantum system following an arbitrary stationary trajectory and weakly interacting with a stationary thermal bath of a massless scalar field is generically driven into a non-Gibbs steady state by relative motion…
Small oscillations of an elastic system of point masses (particles) with a nonlocal interaction are considered. We study the asymptotic behavior of the system, when number of particles tends to infinity, and the distances between them and…
We study the Little-Parks effect for mesoscopic loops with very nonuniform thickness. The results follow the trend of the phase diagram obtained for almost uniform thickness. In particular, the singly-connected state is stable on a line…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
This paper discusses about solutions of the nonlocal nonlinear Schrodinger equation. We prove that the solution remains close to the orbit of the soliton for a large-time, if the initial data is close to the ground state solitons. The proof…
We provide a short proof of $L^3$-asymptotic stability around vector fields that are small in weak-$L^3$, including small Landau solutions. We show that asymptotic stability also holds for vector fields in the range of Lorentz spaces…
We construct a normal form suited to {\it fast driven systems}. We call so systems including actions ${\rm I}$, angles {$\psi$}, and one fast coordinate $y$, moving under the action of a vector--field $N$ depending only on ${\rm I}$ and $y$…