Related papers: An extensive resonant normal form for an arbitrary…
We consider the Schr\"odinger equation with a Hamiltonian given by a second order difference operator with nonconstant growing coefficients, on the half one dimensional lattice. This operator appeared first naturally in the construction and…
The Klein-Fock-Gordon equation is studied on the generalized Y-junction of $N$ strings with a massive center. The corresponding formulas for wave scattering and normal modes are obtained.
We consider the massive Klein-Gordon field on the half line with and without a Robin boundary potential.The field is coupled at the boundary to a harmonic oscillator.We solve the system classically and observe the existence of classical…
$N$-body non efimovian bound or quasi-bound states for particles with short range interactions are considered in arbitrary dimensions. The different resonance regimes near the threshold are depicted by using a generalization of the…
We study the initial-boundary value problem for the coupled Klein-Gordon-Schr\"{o}dinger equations in a domain in $\mathbb R^N$ with $N \leq 4$. Under natural assumptions on the initial data, we prove the existence and uniqueness of global…
This paper is concerned with the derivative nonlinear Schr\"{o}dinger equation with periodic boundary conditions. We obtain complete Birkhoff normal form of order six. As an application, the long time stability for solutions of small…
A simple quantum mechanical model consisting of a discrete level resonantly coupled to a continuum of finite width, where the coupling can be varied from perturbative to strong (Fano-Anderson model), is considered. The particle is initially…
We construct small amplitude breathers in 1D and 2D Klein--Gordon infinite lattices. We also show that the breathers are well approximated by the ground state of the nonlinear Schroedinger equation. The result is obtained by exploiting the…
The charge spreading of ground and excited states of Klein-Gordon particles moving in a Coulomb potential is quantitatively analyzed by means of the ordinary moments and the Heisenberg measure as well as by use of the most relevant…
We develop a polymer expansion with large/small field conditions for the mean resolvent of a weakly disordered system. Then we show that we can apply our result to a two-dimensional model, for energies outside the unperturbed spectrum or in…
The stationary one dimensional Schr\"odinger-Poisson system on a bounded interval is considered in the limit of a small Debye length (or small temperature). Electrons are supposed to be in a mixed state with the Boltzmann statistics. Using…
The Klein-Gordon equation describes the wave-like behavior of spinless particles since it is Lorentz invariant. While it seemed initially ripe for explaining the electronic structure of the hydrogen atom, the lack of a unconditional…
We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon…
We describe a procedure naturally associating relativistic Klein-Gordon equations in static curved spacetimes to non-relativistic quantum motion on curved spaces in the presence of a potential. Our procedure is particularly attractive in…
We construct non-equilibrium steady states in the Klein-Gordon theory in arbitrary space dimension $d$ following a local quench. We consider the approach where two independently thermalized semi-infinite systems, with temperatures $T_{\rm…
We give the complete list of all first-order consistent interaction vertices for a set of exterior form gauge fields of form degree >1, described in the free limit by the standard Maxwell-like action. A special attention is paid to the…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
We consider nonlinear Schr\"odinger equations on flat tori satisfying a simple and explicit Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic term, we prove the almost global existence and stability of…
We establish quantitative bounds on the rate of approach to equilibrium for a system with infinitely many degrees of freedom evolving according to a one-dimensional focusing nonlinear Schr\"odinger equation with diffusive forcing.…
We analyze the behavior of the energy spectrum of the Klein-Gordon equation in the presence of a truncated hyperbolic tangent potential. From our analysis we obtain that, for some values of the potential there is embedding of the bound…