Large Deviations from a Stationary Measure for a Class of Dissipative PDEs with Random Kicks

We study a class of dissipative PDEs perturbed by a bounded random kick force. It is assumed that the random force is nondegenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique stationary measure. The main result of the paper is a large deviations principle for occupation measures of the Markov process in question. The proof is based on Kifer's large‐deviation criterion, a coupling argument for Markov processes, and an abstract result on large‐time asymptotic for generalized Markov semigroups.© 2015 Wiley Periodicals, Inc.     

On the Nature of Fermi Golden Rule for Open Quantum Systems

We consider a general class of models consisting of a small quantum system $S$ interacting with a reservoir $R$ . We compare three applications of 2nd order perturbation theory (the Fermi Golden Rule) to the study of such models: (1) the van Hove (weak coupling) limit for the dynamics reduced to $S$ ; (2) the Fermi Golden Rule applied to the Liouvillean—an argument that was used in recent papers on the return to equilibrium; (3) the Fermi Golden Rule applied to the so-called C-Liouvillean. These three applications lead to three Level Shift Operators. As our main result, we prove that if the reservoir $R$ is thermal (if it satisfies the KMS condition), then the Level Shift Operator obtained in (1) (often called the Davies generator) and the Level Shift Operator constructed in (2) are connected by a similarity transformation. We also show that the Davies generator coincides with the Level Shift Operator obtained in (3) for a general $R$ .     

Spectral Theory of Pauli–Fierz Operators

We study spectral properties of Pauli–Fierz operators which are commonly used to describe the interaction of a small quantum system with a bosonic free field. We give precise estimates of the location and multiplicity of the singular spectrum of such operators. Applications of these estimates, which will be discussed elsewhere, concern spectral and ergodic theory of non-relativistic QED. Our proof has two ingredients: the Feshbach method, which is developed in an abstract framework, and Mourre theory applied to the operator restricted to the sector orthogonal to the vacuum.     

The Green–Kubo Formula for Locally Interacting Fermionic Open Systems

We consider a model describing finitely many free Fermi gas reservoirs coupled by local interactions and prove the Green–Kubo formulas and the Onsager reciprocity relations for heat and charge fluxes generated by temperature and chemical potential differentials. Submitted: September 2, 2006. Accepted: November 21, 2006.     

Reversed-Phase Thin-Layer Chromatography of Some Foodstuff Dyes

JPC – Journal of Planar Chromatography – Modern TLC - The chromatographic behavior of nine frequently used water-soluble food dyes has been studied by TLC on RP-18 silica gel....     

On the Spectrum of the Surface Maryland Model

We study spectral properties of the discrete Laplacian H on the half space Z₊ ^d+1 = Z^d× Z₊ with a boundary condition (n,-1) = tan( ... n + )(n,0), where [0,1]^d. We denote by H₀ the Dirichlet Laplacian on Z₊ ^d+1. Whenever is independent over rationals (H) = R. Khoruzenko and Pastur have shown for a set of 's of Lebesgue measure 1, the spectrum of H on R\ (H₀) is pure point and that corresponding eigenfunctions decay exponentially. In this Letter we show that if is independent over rationals, then the spectrum of H on the set (H₀) is purely absolutely continuous.     

Mean‐Field Evolution of Fermionic Mixed States

In this paper we study the dynamics of fermionic mixed states in the mean‐field regime. We consider initial states that are close to quasi‐free states and prove that, under suitable assumptions on the initial data and on the many‐body interaction, the quantum evolution of such initial data is well approximated by a suitable quasi‐free state. In particular, we prove that the evolution of the reduced one‐particle density matrix converges, as the number of particles goes to infinity, to the solution of the time‐dependent Hartree‐Fock equation. Our result holds for all times and gives effective estimates on the rate of convergence of the many‐body dynamics towards the Hartree‐Fock evolution.© 2015 Wiley Periodicals, Inc.     

Localization of Surface Spectra

We study spectral properties of the discrete Laplacian H on the half-space with random boundary condition ; the V(n) are independent random variables on a probability space and λ is the coupling constant. It is known that if the V(n) have densities, then on the interval [-2(d+1), 2(d+1)] (=σ(H ₀), the spectrum of the Dirichlet Laplacian) the spectrum of H is P-a.s. absolutely continuous for all λ [JL1]. Here we show that if the random potential P satisfies the assumption of Aizenman–Molchanov [AM], then there are constants λ _d and Λ _d such that for |λ|<lambda; _d and |λ|> Λ _d the spectrum of H outside σ(H ₀) is P-a.s. pure point with exponentially decaying eigenfunctions. Received: 3 December 1998 / Accepted: 27 May 1999     

The Spectral Structure of the Electronic Black Box Hamiltonian

We give results on the absence of singular continuous spectrum of the one-particle Hamiltonian underlying the electronic black box model.