Annalisa Panati

SPECTRAL AND SCATTERING THEORY FOR SOME ABSTRACT QFT HAMILTONIANS

We introduce an abstract class of bosonic QFT Hamiltonians and study their spectral and scattering theories. These Hamiltonians are of the form H = dΓ(ω) + V acting on the bosonic Fock space Γ(𝔥), where ω is a massive one-particle Hamiltonian acting on 𝔥 and V is a Wick polynomial Wick(w) for a kernel w satisfying some decay properties at infinity. We describe the essential spectrum of H, prove a Mourre estimate outside a set of thresholds and prove the existence of asymptotic fields. Our main result is the asymptotic completeness of the scattering theory, which means that the CCR representations given by the asymptotic fields are of Fock type, with the asymptotic vacua equal to the bound states of H. As a consequence, H is unitarily equivalent to a collection of second quantized Hamiltonians.

Removal of UV Cutoff for the Nelson Model with Variable Coefficients

We consider the Nelson model with variable coefficients. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric, allowing also the boson mass to depend on position. We study the removal of the ultraviolet cutoff.

Full statistics of energy conservation in two-time measurement protocols.

The first law of thermodynamics states that the average total energy current between different reservoirs vanishes at large times. In this paper we examine this fact at the level of the full statistics of two-time measurement protocols, also known as the Full Counting Statistics. Under very general conditions, we establish a tight form of the first law asserting that the fluctuations of the total energy current computed from the energy variation distribution are exponentially suppressed in the large time limit. We illustrate this general result using two examples: the Anderson impurity model and a two-dimensional spin lattice model.