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

We obtain lower and upper bounds on the heat kernel and Green functions of the Schroedinger 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 the lower bound is decreasing exponentially fast for large distances and a large time.Comment: some technical improvements, new references, to appear in Journ.Phys.

Hyperentangled States

We investigate a new class of entangled states, which we call 'hyperentangled',that have EPR correlations identical to those in the vacuum state of a relativistic quantum field. We show that whenever hyperentangled states exist in any quantum theory, they are dense in its state space. We also give prescriptions for constructing hyperentangled states that involve an arbitrarily large collection of systems.Comment: 23 pages, LaTeX, Submitted to Physical Review

Gentle Perturbations of the Free Bose Gas I

It is demonstrated that the thermal structure of the noncritical free Bose Gas is completely described by certain periodic generalized Gaussian stochastic process or equivalently by certain periodic generalized Gaussian random field. Elementary properties of this Gaussian stochastic thermal structure have been established. Gentle perturbations of several types of the free thermal stochastic structure are studied. In particular new models of non-Gaussian thermal structures have been constructed and a new functional integral representation of the corresponding euclidean-time Green functions have been obtained rigorously.Comment: 51 pages, LaTeX fil