Related papers: Estimates on trapped modes in deformed quantum lay…
This paper together with the previous one (arXiv:hep-th/0604146) presents the detailed description of all quantum deformations of D=4 Lorentz algebra as Hopf algebra in terms of complex and real generators. We describe here in detail two…
The Lieb-Thirring inequalities give a bound on the negative eigenvalues of a Schr\"odinger operator in terms of an $L^p$ norm of the potential. This is dual to a bound on the $H^1$-norms of a system of orthonormal functions. Here we extend…
We propose a method for measuring entangled vibronic quantum states of a trapped atom. It is based on the nonlinear dynamics of the system that appears by resonantly driving a weak electronic transition. The proposed technique allows the…
A new and elementary proof of a recent result of Laptev and Weidl is given. It is a sharp Lieb-Thirring inequality for one dimensional Schroedinger operators with matrix valued potentials.
A numerical method is presented which allows to compute the spectrum of the Schroedinger operator for a particle constrained on a two dimensional flat torus under the combined action of a transverse magnetic field and any conservative…
In this paper we approximate a Schr\"odinger operator on $L^2(\R)$ by Jacobi operators on $\ell^2(\Z)$ to provide new proofs of sharp Lieb-Thirring inequalities for the powers $\gamma=1/2$ and $\gamma=3/2$. To this end we first investigate…
We derive conditional stability estimates for inverse scattering problems related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic type estimates for retrieving the magnetic (up to a gradient) and electric potentials…
We prove L^1 --> L^\infty estimates for the linear Schroedinger equation in three dimensions. The potential is assumed to belong to certain L^p spaces, but no pointwise decay estimates and no additional regularity is required.
We present a method to extract the phase shift of a scattering process using the real-time evolution in the early and intermediate stages of the collision in order to estimate the time delay of a wave packet. This procedure is convenient…
To achieve high-fidelity operations on a large-scale quantum computer, the parameters of the physical system must be efficiently characterized with high accuracy. For trapped ions, the entanglement between qubits are mediated by the…
The Schr\"odinger equation is investigated in the Euclidean Taub-NUT geometry. The bound states are degenerate and an extra degeneracy is due to the conserved Runge-Lenz vector. The existence of the extra conserved quantities, quadratic in…
We prove Lieb-Thirring-type bounds for fractional Schr\"odinger operators and Dirac operators with complex-valued potentials. The main new ingredient is a resolvent bound in Schatten spaces for the unperturbed operator, in the spirit of…
We investigate quantum entanglement in a non-relativistic critical system by calculating the logarithmic negativity of a class of mixed states in the quantum Lifshitz model in one and two spatial dimensions. In 1+1 dimensions we employ a…
We obtain $L^p$ estimates of the maximal Schr\"odinger operator in $\mathbb R^n$ using polynomial partitioning, bilinear refined Strichartz estimates, and weighted restriction estimates.
In this paper we present two different problems within the framework of shift-invariant theory. First, we develop a triangular form for shift-preserving operators acting on finitely generated shift-invariant spaces. In case of the normal…
In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twisting operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values $z_L$ measure the…
The study of dispersive properties of Schr\"odinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be…
We consider the Schroedinger operator with a complex delta interaction supported by two parallel hypersurfaces in the Euclidean space of any dimension. We analyse spectral properties of the system in the limit when the distance between the…
We develop a general approach to study three-dimensional Schroedinger operators with confining potentials depending on the distance to a surface. The main idea is to apply parallel coordinates based on the surface but outside its cut locus…
Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one-dimension. This allow us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative…