Related papers: Wegner-type bounds for a two-particle continuous A…
We prove a Wegner estimate for alloy type models merely assuming that the single site potential is lower bounded by a characteristic function of a thick set, that is a particular set of positive measure. The proof is based on two…
Euclidean quantum fields obtained as solutions of stochastic partial pseudo differential equations driven by a Poisson white noise have paths given by locally integrable functions. This makes it possible to define a class of ultra-violet…
In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of…
In this paper, we develop the notion of the marginal and density atomic Wehrl entropies for two-level atom interacting with the single mode field, i.e. Jaynes-Cummings model. For this system we show that there are relationships between…
We have used different methods to obtain the bound states of a Hamiltonian of a relativistic two scalar particle system in a local potential. The potentials we are interested in are binding and confining potentials, that are associated with…
We consider a system of two discrete quasiperiodic 1D particles as an operator on $\ell^2(\mathbb Z^2)$ and establish Anderson localization at large disorder, assuming the potential has no cosine-type symmetries. In the presence of…
We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by…
We study spectral properties of Schr\"odinger operators with random potentials of alloy type on $L^2(\RR)$ and their restrictions to finite intervals. A Wegner estimate for non-negative single site potentials with small support is proven.…
The $D$-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work we…
We establish the complete spectral exponential, and the strong Hilbert-Schmidt dynamical localization for the one-dimensional multi-particle Anderson tight-binding model and for weakly interacting particles system. In other words, we show…
The one-dimensional Klein-Gordon equation is investigated with the most general Lorentz structure for the external potentials. The analysis and calculation of the reflection and transmission coefficients for the scattering of particles in a…
We study Schr\"odinger operators on $L^2 (\RR^d)$ and $\ell^2(\ZZ^d)$ with a random potential of alloy-type. The single-site potential is assumed to be exponentially decaying but not necessarily of fixed sign. In the continuum setting we…
We consider discrete random Schr\"odinger operators on $\ell^2 (\mathbb{Z}^d)$ with a potential of discrete alloy-type structure. That is, the potential at lattice site $x \in \mathbb{Z}^d$ is given by a linear combination of independent…
We study Schroedinger operators with a random potential of alloy type. The single site potentials are allowed to change sign. For a certain class of them we prove a Wegner estimate. This is a key ingredient in an existence proof of pure…
We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians which appear in certain superspaces. Some of the resulting Hamiltonians have a direct physics…
We predict hyper-entanglement generation during binary scattering of mesoscopic bound states, solitary waves in Bose-Einstein condensates containing thousands of identical Bosons. The underlying many-body Hamiltonian must not be integrable,…
Complex dielectric media often appear opaque because light traveling through them is scattered multiple times. Although the light scattering is a random process, different paths through the medium can be correlated encoding information…
A construction of a quasi-random potential for cold atoms using dark states emerging in $\Lambda$ {level configuration} is proposed. Speckle laser fields are used as a source of randomness. Anderson localisation in such potentials is…
We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key…
We prove an optimal one-volume Wegner estimate for interacting systems of $N$ quantum particles moving in the presence of random potentials. The proof is based on the scale-free unique continuation principle recently developed for the…