Related papers: Determining the potential and the gradient couplin…
We prove a conditional theorem on the positivity of the Lyapunov exponent for a Schr\"odinger cocycle over a skew shift base with a cosine potential and the golden ratio as frequency. For coupling below 1, which is the threshold for…
We study an analog of the anisotropic Calder\'on problem for fractional Schr\"odinger operators $(-\Delta_g)^\alpha + V$ with $\alpha \in (0,1)$ on closed Riemannian manifolds of dimensions two and higher. We prove that the knowledge of a…
This paper presents an energy estimate in terms of the total variation of the control for bilinear infinite dimensional quantum systems with unbounded potentials. These estimates allow a rigorous construction of propagators associated with…
This paper deals with an inverse problem for a non-self-adjoint Schr\"odinger equation on a compact Riemannian manifold. Our goal is to stably determine a real vector field from the dynamical Dirichlet-to Neumann map. We establish in…
This note presents a sufficient condition for partial approximate ensemble controllability of a set of bilinear conservative quantum systems in an infinite dimensional Hilbert space. The proof relies on classical geometric and averaging…
The isotropic harmonic oscillator and the Kepler-Coulomb system are pivotal models in the Sciences. They are two examples of second-order (maximally) superintegrable (Hamiltonian) systems. These systems are classified in dimension two. A…
We study the inverse problem of determining the coefficients of the fractional power of a general second order elliptic operator given in the exterior of an open subset of the Euclidean space. We show the problem can be reduced into…
Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending.…
The relativistic fermion-antifermion bound state vector potential of constraint theory is calculated, in perturbation theory, by means of the Lippmann-Schwinger type equation that relates it to the scattering amplitude. Leading…
We first show that partial transposition for pure and mixed two-particle states in a discrete $N$-dimensional Hilbert space is equivalent to a change in sign of the momentum of one of the particles in the Wigner function for the state. We…
In this paper, we study the partial data inverse problem for nonlinear magnetic Schr\"odinger equations. We show that the knowledge of the Dirichlet-to-Neumann map, measured on an arbitrary part of the boundary, determines the…
Inverse scattering theory is extended to one-dimensional Schr\"odinger problems with near-boundary singularities of the form $v(z\to 0)\simeq -z^{-2}/4+v_{-1}z^{-1}$. Trace formulae relating the boundary value $v_0$ of the nonsingular part…
We investigate coherent electron-switching transport in a double quantum waveguide system in a perpendicular static or vanishing magnetic field. The finite symmetric double waveguide is connected to two semi-infinite leads from both ends.…
We study a one-dimensional extended Hubbard model with longer-range Coulomb interactions at quarter-filling in the strong coupling limit. We find two different charge-ordered (CO) ground states as the strength of the longer range…
The Schr\"odinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics. We demonstrate how simple transformations of the Schr\"odinger equation leads to a coupled linear system, whereby…
This paper is mainly concerned with the inverse scattering problem of determining the unknown potential for the classical Schr\"odinger equation in two and three dimensions. We establish the increasing stability of the inverse scattering…
A hierarchy of infinite-dimensional systems of hydrodynamic type is considered and a general scheme for classifying its reductions is provided. Wide families of integrable systems including, in particular, those associated with…
The potential between heavy quarks can be rigorously defined in a QCD effective field theories framework. I discuss the general situation when the coupling constant may not be considered small and provide an explicit expression for the…
The initial value problem for some coupled nonlinear Schrodinger system with unbounded potential is investigated. In the defocusing case, global well-posedness is obtained. For the focusing sign, existence of global and non global solutions…
We investigate numerically parametrically driven coupled nonlinear Schrodinger equations modelling the dynamics of coupled wavefields in a periodically oscillating double-well potential. The equations describe among other things two coupled…