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We study analytically and numerically the stability of the standing waves for a nonlinear Schr\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the…

Employing the Bloch eigenmode matching approach, we numerically study the evolution of individual quantum Hall edge states with respect to disorder. As shown by the two-parameter renormalization group flow of the Hall and Thouless…

The nonequilibrium steady state (NESS) of integrable spin chains experiencing strong boundary dissipation is accounted by introducing quasiparticles with a renormalized -- dissipatively dressed -- dispersion relation. This allows us to…

It is proved that the eigenvalues in the N--particle system are absorbed at zero energy threshold, if none of the subsystems has a bound state with $E \leq 0$ and none of the particle pairs has a zero energy resonance. The pair potentials…

Voltage instability is a major threat in power system operation. The growing presence of constant power loads significantly aggravates this issue, hence motivating the development of new analysis methods for both existence and stability of…

Many-body localization provides a mechanism to avoid thermalization in isolated interacting quantum systems. The breakdown of thermalization may be complete, when all eigenstates in the many-body spectrum become localized, or partial, when…

The boundary modes of one dimensional quantum systems can play host to a variety of remarkable phenomena. They can be used to describe the physics of impurities in higher dimensional systems, such as the ubiquitous Kondo effect or can…

The stability of nonaxisymmetric perturbations in differentially rotating astrophysical accretion disks is analyzed by fully incorporating the properties of shear flows. We verify the presence of discrete unstable eigenmodes with complex…

A novel class of nonequilibrium phase-transitions at zero temperature is found in chains of nonlinear oscillators.For two paradigmatic systems, the Hamiltonian XY model and the discrete nonlinear Schr\"odinger equation, we find that the…

We consider the existence and stability of the hole, or dark soliton, solution to a Ginzburg-Landau perturbation of the defocusing nonlinear Schroedinger equation (NLS), and to the nearly real complex Ginzburg-Landau equation (CGL). By…

We investigate the decoherence dynamics of continuous variable entanglement as the system-environment coupling strength varies from the weak-coupling to the strong-coupling regimes. Due to the existence of localized modes in the…

Natural convection is ubiquitous throughout the physical sciences and engineering, yet many of its important properties remain elusive. To study convection in a novel context, we derive and solve a quasilinear form of the Rayleigh-B\'enard…

We study both analytically and numerically metastability and nucleation in a two-dimensional nonequilibrium Ising ferromagnet. Canonical equilibrium is dynamically impeded by a weak random perturbation which models homogeneous disorder of…

We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…

In this study we are concerned with a class of generalized BVP' s consisting of eigendependent boundary conditions and supplementary transmission conditions at finite number interior points. By modifying some techniques of classical…

We consider a diffusive Rosenzweig-MacArthur predator-prey model in the situation when the prey diffuses at the rate much smaller than that of the predator. In a certain parameter regime, the existence of fronts in the system is known: the…

An active Brownian particle is a minimal model for a self-propelled colloid in a dissipative environment. Experiments and simulations show that, in the presence of boundaries and obstacles, active Brownian particle systems approach…

The statistical properties of the dynamics of energy levels are investigated in the case of two two-dimensional disordered quantum dot models with nearest neighbor hopping subjected to external time-dependent perturbations. While in the…

It was shown previously that the current-carrying state of a Field Effect Transistor with asymmetric source and drain boundary conditions may become unstable against spontaneous generation of plasma waves [1]. By extending the analysis to…

Many physical systems can be described by nonlinear eigenvalues and bifurcation problems with a linear part that is non-selfadjoint e.g. due to the presence of loss and gain. The balance of these effects is reflected in an antilinear…