相关论文: Stability and correlations in dilute two-dimension…

As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…

We formulate a method to study two-body correlations in a condensate of N identical bosons. We use the adiabatic hyperspheric approach and assume a Faddeev like decomposition of the wave function. We derive for a fixed hyperradius an…

Two-time correlations are a crucial tool to probe the dynamics of many-body systems. We use these correlation functions to study the dynamics of dissipative quantum systems. Extending the adiabatic elimination method, we show that the…

We investigate the correlation properties in the steady state of driven-dissipative interacting bosonic systems in the quantum regime, as for example non-linear photonic cavities. Specifically, we consider the Bose-Hubbard model on a…

Given $\beta\in\mathbb{R}$ and $\varrho,k>0$, we analyze an abstract version of the nonlinear stationary model in dimensionless form $$\begin{cases} u"" - \Big(\beta+ \varrho\int_0^1 |u'(s)|^2\,{\rm d} s\Big)u" +k(u-v) = 0 v"" - \Big(\beta+…

This paper deals with quantitative spectral stability for Aharonov-Bohm operators with many colliding poles of whichever circulation. An equivalent formulation of the eigenvalue problem is derived as a system of two equations with real…

In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…

We study the two-dimensional paramagnetic Anderson-Hubbard model using an extension of dynamical mean-field theory that allows us to treat disorder and strong electronic correlations on equal footing. We investigate the scaling of the…

A description of a large system of particles is often sought in a derivation from the detailed behaviour of just a few of the particles. The present thesis deals with the connection between such microscopic features and the nature of a…

We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation…

We study the problem of stabilization for the acoustic system with a spatially distributed damping. Imposing various hypotheses on the structural properties of the damping term, we identify either exponential or polynomial decay of…

The soft-core boson system is one of the simplest models of supersolids, which have both off-diagonal long-range order (Bose-Einstein condensation) and diagonal long-range order (crystalline order). Although this model has been studied from…

We investigate the long-time behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not…

In this paper, we study the stabilization problem for a hyperbolic type Stokes system posed on a bounded domain. We show that when the damping effects are restricted to a subdomain satisfying the geometrical control condition the system…

We consider two-dimensional bosonic dipoles oriented perpendicularly to the plane. On top of the usual two-body contact and long-range dipolar interactions we add a contact three-body repulsion as expected, in particular, for dipoles in the…

We investigate systems of identical bosons with the focus on two-body correlations and attractive finite-range potentials. We use a hyperspherical adiabatic method and apply a Faddeev type of decomposition of the wave function. We discuss…

The dynamical evolution of self-gravitating scalar field configurations in numerical relativity is studied. The previous analysis on ground state boson stars of non-interacting fields is extended to excited states and to fields with self…

We classify and analyze the stability of all relative equilibria for the two-body problem in the hyperbolic space of dimension 2 and we formulate our results in terms of the intrinsic Riemannian data of the problem.

We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by…

We investigate the survival of symmetries in a relativistic system of two mutually interacting bosons coupled with an external field, when this field is "strongly" translation invariant in some directions and additionally remains unchanged…