Related papers: Thermodynamic Formalism for Transient Potential Fu…
We define the domain of a linear fractional transformation in a space of operators and show that both the affine automorphisms and the compositions of symmetries act transitively on these domains. Further, we show that Liouville's theorem…
We study topological transitivity/hypercyclicity and topological (weak) mixing for weighted composition operators on locally convex spaces of scalar-valued functions which are defined by local properties. As main application of our general…
I discuss the analytic structure of thermodynamic quantities for complex values of thermodynamic variables within Landau theory. In particular, the singularities connected with phase transitions of second order, first order and cross over…
The process of finding activated transitions in localized spin systems with continuous degrees of freedom is developed based on a magnetic variant of the Activation-Relaxation Technique (mART). In addition to the description of the method…
A thermodynamic framework that predicts the thermal conductivity $\lambda$ of simple fluids beyond the dilute-gas limit is introduced. By generalizing the transition-rate approach of particles on a lattice to conserved quantities in…
We reformulate the treatment of density-dependent chemical potential shifts appearing in excluded-volume implementations of the hadron resonance gas model. An auxiliary classical representation is constructed in which a common energy shift…
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
We study the potential theory of a large class of infinite dimensional L\'evy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e. excessive functions with…
We provide a condition for f-ergodicity of strong Markov processes at a subgeometric rate. This condition is couched in terms of a supermartingale property for a functional of the Markov process. Equivalent formulations in terms of a drift…
We consider additive functionals of stationary Markov processes and show that under Kipnis-Varadhan type conditions they converge in rough path topology to a Stratonovich Brownian motion, with a correction to the Levy area that can be…
In this paper we study the ergodic theory and thermodynamic formalism of the geodesic flow on non-compact pinched negatively curved manifolds. We consider two notions of entropy at infinity, the topological and the measure theoretic entropy…
We characterize the global maximizers of a certain non-local functional defined on the space of all positively curved metrics on an ample line bundle L over a Kahler manifold X. This functional is an adjoint version, introduced by…
In this paper we explore the fundamentals of the Martingale Representation Theorem (MRT) and a closely related result, the Clark-Ocone formula. We also investigate how far these theorems can be taken, notably beyond the regular Sobolev…
In this article we address a well known problem at the intersection of ergodic theory and statistical mechanics. We prove that there exists a continuous eigenfunction for the transfer operator corresponding to pair potentials that satisfy a…
The thermal ratchets model toggles a spatially periodic asymmetric potential to rectify random walks and achieve transport of diffusing particles. We numerically solve the governing equation for the full dynamics of an infinite 1D ratchet…
The goal of this paper is to study operators of the form, \[ Tf(x)= \psi(x)\int f(\gamma_t(x))K(t)\: dt, \] where $\gamma$ is a real analytic function defined on a neighborhood of the origin in $(t,x)\in \R^N\times \R^n$, satisfying…
A new technique is described by which light-induced gauge potentials allow systems of ultra-cold neutral atoms to behave like charged particles in a magnetic field. Here, atoms move in a uniform laser field with a spatially varying Zeeman…
A unified thermodynamic framework for characterization of functional materials is developed. This framework encompasses linear reversible and irreversible processes with thermal, electrical, magnetic, and/or mechanical effects coupled. The…
We review how some multianalytic inner functions of the Beurling type theorem are associated to row contractions following works of G.Popescu. Motivated by a result on weak Markov dilations, we define a notion of characteristic function for…
Given a non-invertible dynamical system with a transfer operator, we show there is a minimal cover with a transfer operator that preserves continuous functions. We also introduce an essential cover with even stronger continuity properties.…