Related papers: Semiclassical analysis for the Kramers-Fokker-Plan…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
We study the pseudospectral properties of general pseudodifferential operators around a doubly characteristic point and provide necessary and sufficient conditions for semiclassical hypoelliptic a priori estimates with a big loss of…
In the past decade there has been a flurry of activity at the intersection of spectral theory and symplectic geometry. In this paper we review recent results on semiclassical spectral theory for commuting Berezin-Toeplitz and…
We prove semi-classical resolvent estimates for the Schr{\"o}dinger operator with a real-valued L $\infty$ potential on non-compact, connected Riemannian manifolds which may have a compact smooth boundary. We show that the resolvent bound…
We consider a Trotter-type-product formula for approximating the solution of a linear abstract Cauchy problem (given by a strongly continuous semigroup), where the underlying Banach space is a product of two spaces. In contrast to the…
Error estimates are rigorously derived for a semi-discrete version of a conservative spectral method for approximating the space-homogeneous Fokker-Planck-Landau (FPL) equation associated to hard potentials. The analysis included shows that…
We study spectral properties of the Schroedinger operator with an imaginary sign potential on the real line. By constructing the resolvent kernel, we show that the pseudospectra of this operator are highly non-trivial, because of a blow-up…
We study the resonant set of a two-level Schr\"odinger operator with a linear conical intersection. This model operator can be decomposed into a direct sum of first order systems on the real half-line. For these ordinary differential…
The semi-classical approximation is an explicit formula of mathematical physics for the sum of Feynman diagrams with a single circuit.In this paper, we study the same problem in the setting of modular operads (see dg-ga/9408003); instead of…
We study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over R^d and in L^p-spaces with respect to tight evolution systems of measures. Here, the linear part…
We study the behaviour of the norm of the resolvent for non-self-adjoint operators of the form $A := -\partial_x + W(x)$, with $W(x) \ge 0$, defined in $L^2(\mathbb{R})$. We provide a sharp estimate for the norm of its resolvent operator,…
We show that solutions of nonlinear nonlocal Fokker--Planck equations in a bounded domain with no-flux boundary conditions can be approximated by Cauchy problems with increasingly strong confining potentials defined in the whole space. Two…
In this article we study the semiclassical spectral measures associated with Schr\"odinger operators on $R^n$. In particular we compute the first few coefficients of the asymptotic expansions of these measures and, as an application, give…
The abstract theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic operator on $\mathbb{R}^{n}$ with linear boundary conditions on (a relatively open part of) a…
We define a class of pseudo-differential operators in a completely new way, which is called the abstract operators and expounded systematically the theory of abstract operators. By combining abstract operators with the Laplace transform, we…
In this paper we examine the semiclassical behaviour of the scattering data of a non-self-adjoint Dirac operator with analytic potential decaying at infinity. In particular, employing the exact WKB method, we provide the complete rigorous…
We study exact solutions of the steady state behaviour of several non-linear open quantum systems which can be applied to the field of circuit quantum electrodynamics. Using Fokker-Planck equations in the generalised P-representation we…
In $L_2 (\mathbb{R}^d; \mathbb{C}^n)$, we consider a selfadjoint matrix strongly elliptic second order differential operator $\mathcal{A}_\varepsilon$ with periodic coefficients depending on $\mathbf{x}/\varepsilon$. We find approximations…
We study Cauchy problems associated to elliptic operators acting on vector-valued functions and coupled up to the first-order. We prove pointwise estimates for the spatial derivatives of the semigroup associated to these problems in the…
In this article we try to bridge the gap between the quantum dynamical semigroup and Wigner function approaches to quantum open systems. In particular we study stationary states and the long time asymptotics for the quantum Fokker-Planck…