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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),…
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Existence and nonexistence of a ground state for the massless Nelson model under binding condition
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Energy Conservation, Counting Statistics, and Return to Equilibrium
We study a microscopic Hamiltonian model describing an N-level quantum system $${\mathcal{S}}$$S coupled to an infinitely extended thermal reservoir $${\mathcal{R}}$$R. Initially, the system…
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Full statistics of energy conservation in two-time measurement protocols.
TLDR
Under very general conditions, 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 is established.
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Control of Fluctuations and Heavy Tails for Heat Variation in the Two-Time Measurement Framework
We study heat fluctuations in the two-time measurement framework. For bounded perturbations, we give sufficient ultraviolet regularity conditions on the perturbation for the moments of the heat…
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Reflection Probabilities of One-Dimensional Schrödinger Operators and Scattering Theory
The dynamic reflection probability of Davies and Simon (Commun Math Phys 63(3):277–301, 1978) and the spectral reflection probability of Gesztesy et al. (Diff Integral Eqs 10(3):521–546, 1997) and…
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Infrared Problem for the Nelson Model on Static Space-Times
We consider the Nelson model on some static space-times and investigate the problem of existence of a ground state. Nelson models with variable coefficients arise when one replaces in the usual…
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Heat conservation and fluctuations for open quantum systems in the Two-Time Measurement picture
This work concerns the statistics of the Two-Time Measurement definition of heat variation in each thermal bath of a thermodynamic quantum system. We study the cumulant generating function of the…
Absence of ground state for the Nelson model on static space-times
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Infrared Divergence of a Scalar Quantum Field Model on a Pseudo Riemannian Manifold
A scalar quantum field model defined on a pseudo Riemannian manifold is considered. The model is unitarily transformed to the one with a variable mass. By means of a Feynman-Kac-type formula, it is…
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