Large Time Behavior of the Heat Kernel of Two-dimensional Magnetic Schrödinger Operators

An Estimate on the Heat Kernel of Magnetic Schrödinger Operators and Unformly Elliptic Operators with Non–negative Potentials

Bounds on the heat kernel of the Schrödinger operator in a random electromagnetic field

We obtain lower and upper bounds on the heat kernel and Green functions of the Schrödinger operator in a random Gaussian magnetic field and a fixed scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic upper bounds and the Jensen inequality for the lower bound. We show that if the covariance of the electromagnetic (vector) potential is increasing at large distances then ...

Resolvent Expansions and Trace Regularizations for Schrödinger Operators

We provide a direct approach to a study of regularized traces for long range Schrödinger operators and small time asymptotics of the heat kernel on the diagonal. The approach does not depend on multiple commutator techniques and improves upon earlier treatments by Agmon and Kannai, Melin, and the authors.

Effects of variations in magnetic Reynolds number on magnetic field distribution in electrically conducting fluid under magnetohydrodynamic natural convection

In this study the effect of magnetic Reynolds number variation on magnetic distribution of natural convection heat transfer in an enclosure is numerically investigated. The geometry is a two dimensional enclosure which the left wall is hot, the right wall is cold and the top and bottom walls are adiabatic. Fluid is molten sodium with Pr=0.01 and natural convection heat transfer for Rayleigh num...

On the Spectral Estimates for the Schrödinger-like Operators: the Case of Small Local Dimension

The behavior of the discrete spectrum of the Schrödinger operator −∆ − V , in quite a general setting, up to a large extent is determined by the behavior of the corresponding heat kernel P (t;x, y) as t → 0 and t → ∞. If this behavior is powerlike, i.e., ‖P (t; ·, ·)‖L∞ = O(t), t → 0; ‖P (t; ·, ·)‖L∞ = O(t), t → ∞, then it is natural to call the exponents δ,D ”the local dimension” and ”the dime...