53 research outputs found
Exact thermostatic results for the n-vector model on the harmonic chain
Revised Version with corrections of misprints.Comment: LaTeX, 6 pages, 1 Figure upon reques
Energetic and dynamic properties of a quantum particle in a spatially random magnetic field with constant correlations along one direction
We consider an electrically charged particle on the Euclidean plane subjected
to a perpendicular magnetic field which depends only on one of the two
Cartesian co-ordinates. For such a ``unidirectionally constant'' magnetic field
(UMF), which otherwise may be random or not, we prove certain spectral and
transport properties associated with the corresponding one-particle
Schroedinger operator (without scalar potential) by analysing its ``energy-band
structure''. In particular, for an ergodic random UMF we provide conditions
which ensure that the operator's entire spectrum is almost surely absolutely
continuous. This implies that, along the direction in which the random UMF is
constant, the quantum-mechanical motion is almost surely ballistic, while in
the perpendicular direction in the plane one has dynamical localisation. The
conditions are verified, for example, for Gaussian and Poissonian random UMF's
with non-zero mean-values. These results may be viewed as ``random analogues''
of results first obtained by A. Iwatsuka [Publ. RIMS, Kyoto Univ. 21 (1985)
385] and (non-rigorously) by J. E. Mueller [Phys. Rev. Lett. 68 (1992) 385]
Simple diamagnetic monotonicities for Schroedinger operators with inhomogeneous magnetic fields of constant direction
Under certain simplifying conditions we detect monotonicity properties of the
ground-state energy and the canonical-equilibrium density matrix of a spinless
charged particle in the Euclidean plane subject to a perpendicular, possibly
inhomogeneous magnetic field and an additional scalar potential. Firstly, we
point out a simple condition warranting that the ground-state energy does not
decrease when the magnetic field and/or the potential is increased pointwise.
Secondly, we consider the case in which both the magnetic field and the
potential are constant along one direction in the plane and give a genuine
path-integral argument for corresponding monotonicities of the density-matrix
diagonal and the absolute value of certain off-diagonals. Our results
complement to some degree results of M. Loss and B. Thaller [Commun. Math.
Phys. 186 (1997) 95] and L. Erdos [J. Math. Phys. 38 (1997) 1289]
Lowest Landau level broadened by a Gaussian random potential with an arbitrary correlation length: An efficient continued-fraction approach
For an electron in the plane subjected to a perpendicular constant magnetic
field and a homogeneous Gaussian random potential with a Gau{ss}ian covariance
function we approximate the averaged density of states restricted to the lowest
Landau level. To this end, we extrapolate the first 9 coefficients of the
underlying continued fraction consistently with the coefficients' high-order
asymptotics. We thus achieve the first reliable extension of Wegner's exact
result [Z. Phys. B {\bf 51}, 279 (1983)] for the delta-correlated case to the
physically more relevant case of a non-zero correlation length.Comment: 9 pages ReVTeX, three figure
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