Related papers: On the Wegner orbital model
We consider operators with random potentials on graphs, such as the lattice version of the random Schroedinger operator. The main result is a general bound on the probabilities of simultaneous occurrence of eigenvalues in specified distinct…
In this paper, we consider a class of two-particle tight-binding Hamiltonians, describing pairs of interacting quantum particles on the lattice $\Z^d$, $d\ge 1$ subject to a common external potential $V(x)$ which we assume quasi-periodic…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic $\sigma$-model approach. We analyze conditions of…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
We characterize the limiting second order distributions of certain independent complex Wigner and deterministic matrices using Voiculescu's notions of freeness over the diagonal. If the Wigner matrices are Gaussian, Mingo and Speicher's…
Optimal transport has found widespread applications in signal processing and machine learning. Among its many equivalent formulations, optimal transport seeks to reconstruct a random variable/vector with a prescribed distribution at the…
The delocalized non-ergodic phase existing in some random $N \times N$ matrix models is analyzed via the Wigner-Weisskopf approximation for the dynamics from an initial site $j_0$. The main output of this approach is the inverse…
We study the eigenvector mass distribution for generalized Wigner matrices on a set of coordinates $I$, where $N^\varepsilon \le | I | \le N^{1- \varepsilon}$, and prove it converges to a Gaussian at every energy level, including the edge,…
We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…
We consider a quantum two-particle system on a d-dimensional lattice with interaction and in presence of an IID external potential. We establish Wegner-typer estimates for such a model. The main tool used is Stollmann's lemma.
We study the time evolution of the reduced Wigner function for a class of quantum Brownian motion models. We derive two generalized uncertainty relations. The first consists of a sharp lower bound on the uncertainty function, $U = (\Delta…
We prove a Wegner estimate for discrete Schr\"odinger operators with a potential given by a Gaussian random process. The only assumption is that the covariance function decays exponentially, no monotonicity assumption is required. This…
We consider the time-independent Wigner functions of phase-space quantum mechanics (a.k.a. deformation quantization) for a Morse potential. First, we find them by solving the $\ast$-eigenvalue equations, using a method that can be applied…
We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…
We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from the basic localized modes in various collective models arising from the quantum hierarchy described by Wigner-like…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
The Gibbons-Werner method for the gravitational deflection angle of unbound particles in static spherically symmetric spacetimes is based on Jacobi metric and Gauss-Bonnet theorem. When it is extended to bound massive particles, there…
We study $N \times N$ random band matrices $H = (H_{xy})$ with mean-zero complex Gaussian entries, where $x,y$ lie on the discrete torus $(\mathbb{Z} / \sqrt[d]{N} \mathbb{Z})^d$ in dimensions $d \ge 3$. The variance profile satisfies…
We describe a quantum system consisting of a one-dimensional linear chain of n identical harmonic oscillators coupled by a nearest neighbor interaction. Two boundary conditions are taken into account: periodic boundary conditions (where the…