Next to the harmonic oscillator and the Coulomb potential the class of two-body models with
point interactions is the only one where complete solutions are available. All mathematical …

Investigation of the differential operators with the generalized coefficients having singular
support on a disjoint set of points requires the consideration of the distribution theory with …

The reaction-diffusion master equation (RDME) has recently been used as a model for
biological systems in which both noise in the chemical reaction process and diffusion in …

The monograph is devoted mainly to the analytical study of the differential, pseudo-
differential and stochastic evolution equations describing the transition probabilities of …

The transformations of all the Schrödinger operators with point interactions in dimension one
under space reflection P, time reversal T and (Weyl) scaling W λ are presented. In particular …

We consider a quantum mechanical particle living on a graph and discuss the behaviour of
its wavefunction at graph vertices. In addition to the standard (or-type) boundary conditions …

The quantum dynamics of a free particle on a circle with point interaction is described by a U
(2) family of self-adjoint Hamiltonians. We provide a classification of the family by introducing …

We characterize w*-continuous, Markovian semigroups on a von Neumann algebra M,
which areφ0-symmetric wrt a faithful, normal stateφ0in M*+, in terms of quadratic forms on …

In order to give a dual, annealed description of the two-dimensional stochastic heat equation
(SHE) from regularizing the noise, we consider the Schrödinger semigroup of the many …

The critical two-dimensional Stochastic Heat Flow (SHF) is the scaling limit of the directed
polymers in random environments and the noise-mollified Stochastic Heat Equation (SHE) …