相关论文: Recent developments in quantum mechanics with magn…
We provide sufficient conditions for the discreteness of spectrum for magnetic Schr\"odinger operators. They generalize the classical result by K.Friedrichs (1934) and earlier results by J.Avron, I.Herbst and B.Simon (1978), A.Dufresnoy…
We consider the Schr\"odinger operator with a periodic potential on quasi-1D models of zigzag single-wall carbon nanotubes in magnetic field. The spectrum of this operator consists of an absolutely continuous part (intervals separated by…
The objective of this paper is to report on recent progress on Strichartz estimates for the Schr\"odinger equation and to present the state-of-the-art. These estimates have been obtained in Lebesgue spaces, Sobolev spaces and, recently, in…
We study the motion of a spin 1/2 particle in a scalar as well as a magnetic field within the framework of supersymmetric quantum mechanics(SUSYQM). We also introduce the concept of shape invariant scalar and magnetic fields and it is shown…
We review some recent results of the so-called quasi-hermitian quantum mechanics, with particular focus on the quantum dynamics both in the Schr\"odinger and in the Heisenberg representations. The role of Krein spaces is also discussed.
We study two seminal approaches, developed by B. Simon and J. Kisy\'nski, to the well-posedness of the Schr\"odinger equation with a time-dependent Hamiltonian. In both cases the Hamiltonian is assumed to be semibounded from below and to…
We review from a theoretical perspective the emerging field of spintronics where active control of spin transport and dynamics in electronic materials may provide novel device application possibilities. In particular, we discuss the quantum…
I review Chandra's achievements in the last two years in AGN research. I concentrate on some topics of my interest; some others are reviewed in an accompanying article by K. Nandra. I comment briefly on the need to allow for the discovery…
We review selected achievements of the late Bogdan Mielnik in the field of theoretical physics, with an emphasis on his attempts to go beyond quantum mechanics. Some of his original views on the problems of contemporary society and…
We review the most recent results from experiments studying systems containing charmed quarks. The selection reflects the presenter's bias, and there is an emphasis on decays of open charm. We discuss precision measurements of various…
Schr\"odinger operators often display singularities at the origin, the Coulomb problem in atomic physics or the various matter coupling terms in the Friedmann-Robertson-Walker problem being prominent examples. For various applications it…
I review recent progress achieved on the lattice in the quantitative comprehension of chiral symmetry breaking in QCD. Emphasis is given to the recent precise computations of the spectral density of the Dirac operator in the continuum…
We show that the knowledge of the set of the Cauchy data on the boundary of a $C^1$ bounded open set in $\R^n$, $n\ge 3$, for the Schr\"odinger operator with continuous magnetic and bounded electric potentials determines the magnetic field…
We revisit the problem of semiclassical spectral asymptotics for a pure magnetic Schr\"odinger operator on a two-dimensional Riemannian manifold. We suppose that the minimal value $b_0$ of the intensity of the magnetic field is strictly…
We give a mathematically rigorous construction of a magnetic Schr\"odinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating at…
We have advocated in a previous paper (Godart M. arXiv: 1206.2917v2[quant-ph] ) a version of the stochastic theory of quantum mechanics. It is indirectly based on a method proposed by Nelson to associate a Markov process with any solution…
A review over recent experimental progress in the physics of the fifth quark is given.
Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.
Old studies on supersymmetric quantum mechanics and its deformations, that were initiated by the 1988 joint paper with V. Rubakov, are retrospectively discussed. In the modern circumstances, corresponding results can be related to…
We discover a new version of the celebrated Montgomery identity via quantum integral operators and establish certain quantum integral inequalities of Ostrowski type by using this identity. Relevant connections of the results obtained in…