相关论文: Recent developments in quantum mechanics with magn…

We discuss modern numerical methods for quantum spin systems and their application to magnetic molecules.

We review Bohr's atomic model and its extension by Sommerfeld from a mathematical perspective of wave mechanics. The derivation of quantization rules and energy levels is revisited using semiclassical methods. Sommerfeld-type integrals are…

The Schr\"odinger-type formalism of the Klein-Gordon quantum mechanics is adapted for the case of the $SL(2,\R)$ spacetime. The free particle case is solved, the results of a recent work are reproduced while all the other, topologically…

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which…

Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting…

One-dimensional Schr\"odinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized…

Substantial progress has been achieved over the last decade in studies of stellar magnetism due to the improvement of magnetic field measurement methods. We review recent results on the magnetic field characteristics of early B- and O-type…

Decomposition of (finite-dimensional) operators in terms of orthogonal bases of matrices has been a standard method in quantum physics for decades. In recent years, it has become increasingly popular because of various methodologies applied…

The results of measurements with a gradient magnet arranged with the help of current sheets are represented and analyzed

In honor of S.G.Dani's 65th birthday, we describe some of his many contributions to the theory and applications of dynamical systems on homogeneous spaces, with emphasis on unipotent flows.

We establish new necessary and sufficient conditions for the discreteness of spectrum and strict positivity of magnetic Schr\"odinger operators with a positive scalar potential. They extend earlier results by Maz'ya and Shubin (2005), which…

I present a brief review on some of the recent developments in topological quantum field theory. These include topological string theory, topological Yang-Mills theory and Chern-Simons gauge theory. It is emphasized how the application of…

In writing this report we had two goals in mind. The first is to provide a survey of a subset of discoveries from recent experiments performed on quantum matter in high magnetic fields, and to anticipate the scientific opportunities to be…

We investigate the efficiency of the recently proposed Restricted Boltzmann Machine (RBM) representation of quantum many-body states to study both the static properties and quantum spin dynamics in the two-dimensional Heisenberg model on a…

An approximate analytic solution for the ground electron state are found to the Schroedinger equation for a combination of a uniform magnetic field and single attractive delta-potential. Effect of the magnetic field on this bound localized…

What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…

We study the existence of negative eigenvalues for two-dimensional Schr\"odinger operators with real-valued potentials in the weak coupling regime. In his pioneering paper [Simon 1976] from half a century ago, Simon was the first to…

This paper discusses the phenomenon of spontaneous symmetry breaking in the Schr\"odinger representation formulation of quantum field theory. The analysis is presented for three-dimensional space-time abelian gauge theories with either…

In this paper we will present very recent results obtained in the ambit of quantum electrodynamics in curved spacetime. We utilize a newly developed non-perturbative heat kernel asymptotic expansion on homogeneous Abelian bundles over…

After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions…