Spectral and scattering theory of massive Pauli–Fierz Hamiltonians is studied. Asymptotic
completeness of these Hamiltonians is shown. The proof consists of three parts. The first is a …

We present a selective overview of the current state of our knowledge (more precisely of our
ignorance) regarding the derivation of Fourier's Law, J (r)=− κ∇ T (r); J the heat flux, T the …

Unifying topics that are scattered throughout the literature, this book offers a definitive review
of mathematical aspects of quantization and quantum field theory. It presents both basic and …

We consider a system of finitely many nonrelativistic, quantum mechanical electrons bound
to static nuclei. The electrons are minimally coupled to the quantized electromagnetic field; …

The renewed interest in the foundations of quantum statistical mechanics in recent years has
led us to study John von Neumann's 1929 article on the quantum ergodic theorem. We have …

We study an atom with finitely many energy levels in contact with a heat bath consisting of
photons blackbody radiation at a temperature T 0. The dynamics of this system is described …

A generalization of the standard spin-boson model is considered. The HamiltonianH (α) of
the model with a coupling parameterα∈ Racts in the tensor product H⊕ F bof a Hilbert …

Quantum systems coupled to environments exhibit intricate dynamics. The master equation
gives a Markov approximation of the dynamics, allowing for analytic and numerical …

We review and further develop a mathematical framework for non-equilibrium quantum
statistical mechanics recently proposed in refs. 1–7. In the algebraic formalism of quantum …

We study spectral and scattering properties of the discrete Laplacian H on the half-space
with boundary condition ψ (n,-1)= V (n) ψ (n, 0). We consider cases where V is a …