Narrow Results

After a short presentation of KMS states and modular theory as the unifying description of thermalizing systems we propose the absence of transverse vacuum fluctuations in the holographic projections as the principle reason for an area behavior (the transverse area) of localization entropy as opposed to the volume dependence of ordinary heat bath entropy. Thermalization through causal localization is not a property of QM but results from the omnipresent vacuum polarization in QFT and does not require a Gibbs type ensemble avaraging (coupling to a heat bath).

In anticipation of subsequent application to QED and QCD, we consider the case of a model, high temperature, relativistic, scalar field theory. We introduce into the exact, nonperturbative, functional expressions of this "quenched" model, a new Fradkin representation, and extract the infrared/Bloch–Nordsieck/(IR/BN) contributions of every perturbative graph, in order to circumvent the lack of a clear-cut separation of energy scales of previous semiperturbative treatments. Our results are applicable to the absorption of a fast particle which enters a heat bath, as well as to the propagation of a symmetric pulse within the thermal medium due to the appearance of an instantaneous, shockwave-like source acting in the medium. In momentum space, the former case displays a propagator which decays exponentially with increasing time, in addition to a new damping factor independent of time. The latter case displays an exponential growth with time of the symmetric pulse, generating effective and increasing plasmon waves, in competition with damping independent of time. When extended to QCD, qualitative applications could be made to RHIC scattering, in which a fireball appears, expands and is damped away.

To remedy the failure of minimal coupling method in describing the quantum dynamics of two localized Brownian oscillators interacting with a common medium, a scheme is introduced to model the medium by a continuum of complex scalar fields or equivalently two independent real scalar fields. The starting point is a Lagrangian of the total system and quantization is achieved in the framework of canonical quantization. The equations of motion, memory or response functions and fluctuation–dissipation relations are obtained. An induced force between oscillators is obtained originating from the fluctuations of the medium. Ohmic and non-Ohmic regimes are discussed and the positions of oscillators are obtained approximately in large time limit and weak coupling regime. Quantum entanglement between localized oscillators is obtained in zero temperature and strong coupling regime.

An evolution equation is introduced which governs a two-sided optical cavity under spontaneous photon emission. This equation implies a system of rate equations for expectation values of combinations of operators relevant to the cavity. This system of equations closes with respect to these variables and it can be solved completely in closed form. Some of the properties of the solutions such as the large time behavior of the expectation values and other properties will be discussed.

Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a Kac–Zwanzig setting, with the initial data for the electrons stochastically perturbed from the ground state and the ratio M of nuclei and electron mass tending to infinity. The Ehrenfest nuclei dynamics is approximated by the Langevin dynamics with accuracy o(M^-1/2) on bounded time intervals and by o(1) on unbounded time intervals, which makes the small friction and o(M^-1/2) diffusion terms visible. The initial electron probability distribution is a Gibbs density at low temperature, motivated by a stability and consistency argument. The diffusion and friction coefficients in the Langevin equation satisfy the Einstein's fluctuation–dissipation relation.