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The spectrum of Schrödinger operators with random δ magnetic fields

Takuya Mine, Yuji Nomura (2009)

Annales de l’institut Fourier

We shall consider the Schrödinger operators on ℝ 2 with the magnetic field given by a nonnegative constant field plus random δ magnetic fields of the Anderson type or of the Poisson-Anderson type. We shall investigate the spectrum of these operators by the method of the admissible potentials by Kirsch-Martinelli. Moreover, we shall prove the lower Landau levels are infinitely degenerated eigenvalues when the constant field is sufficiently large, by estimating the growth order of the eigenfunctions...

The spin of the ground state of an atom.

Charles L. Fefferman, Luis A. Seco (1996)

Revista Matemática Iberoamericana

In this paper we address a question posed by M. and T. Hoffmann-Ostenhof, which concerns the total spin of the ground state of an atom or molecule. Each electron is given a value for spin, ±1/2. The total spin is the sum of the individual spins.

The spin-statistics relation in nonrelativistic quantum mechanics and projective modules

Nikolaos A. Papadopoulos, Mario Paschke, Andrés Reyes, Florian Scheck (2004)

Annales mathématiques Blaise Pascal

In this work we consider non-relativistic quantum mechanics, obtained from a classical configuration space 𝒬 of indistinguishable particles. Following an approach proposed in [8], wave functions are regarded as elements of suitable projective modules over C ( 𝒬 ) . We take furthermore into account the G -Theory point of view (cf. [HPRS,S]) where the role of group action is particularly emphasized. As an example illustrating the method, the case of two particles is worked out in detail. Previous works (cf....

The Srní lectures on non-integrable geometries with torsion

Ilka Agricola (2006)

Archivum Mathematicum

This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of...

The structure of corings with a grouplike element

Tomasz Brzeziński (2003)

Banach Center Publications

Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the Cuntz-Quillen theorem relating existence of connections in a module to projectivity of this module is proven.

The symbol of a function of a pseudo-differential operator

Alfonso Gracia-saz (2005)

Annales de l'institut Fourier

We give an explicit formula for the symbol of a function of an operator. Given a pseudo-differential operator A ^ on L 2 ( ℝ N ) with symbol A ∈ 𝒞 ∞ ( T * ℝ N ) and a smooth function f , we obtain the symbol of f ( A ^ ) in terms of A . As an application, Bohr-Sommerfeld quantization rules are explicitly calculated at order 4 in ℏ .

The symmetry algebra and conserved Currents for Klein-Gordon equation on quantum Minkowski space

MaŁgorzata Klimek (1997)

Banach Center Publications

The symmetry operators for Klein-Gordon equation on quantum Minkowski space are derived and their algebra is studied. The explicit form of the Leibniz rules for derivatives and variables for the case Z=0 is given. It is applied then with symmetry operators to the construction of the conservation law and the explicit form of conserved currents for Klein-Gordon equation.

The theory and applications of complex matrix scalings

Rajesh Pereira, Joanna Boneng (2014)

Special Matrices

We generalize the theory of positive diagonal scalings of real positive definite matrices to complex diagonal scalings of complex positive definite matrices. A matrix A is a diagonal scaling of a positive definite matrix M if there exists an invertible complex diagonal matrix D such that A = D*MD and where every row and every column of A sums to one. We look at some of the key properties of complex diagonal scalings and we conjecture that every n by n positive definite matrix has at most 2n−1 scalings...

The time-dependent Born-Oppenheimer approximation

Gianluca Panati, Herbert Spohn, Stefan Teufel (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering.

Currently displaying 1981 – 2000 of 2284