We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of Caldeira-Leggett type, where the collective coordinate is coupled to an internal bath of phonons. In contrast to the usual Caldeira-Leggett model, the bath in the present case is part of the system. We derive an equation of motion for the collective coordinate which takes the form of a damped harmonic oscillator. We show that the distribution of quantum transition strengths induced by the collective mode is determined by its classical dynamics.
We study the interplay between collective and incoherent single-particle motion in a model of two chains of particles whose interaction comprises a non-integrable part. In the perturbative regime, but for a general form of the interaction, we calculate the spectral density for collective excitations. We obtain the remarkable result that it always has a unique semiclassical interpretation. We show this by a proper renormalization procedure which allows us to map our system to a Caldeira-Leggett-type of model in which the bath is part of the system.
We derive a geometric representation of couplings between spin degrees of
freedom and gauge fields within the worldline approach to quantum field theory.
We combine the string-inspired methods of the worldline formalism with elements
of the loop-space approach to gauge theory. In particular, we employ the loop
(or area) derivative operator on the space of all holonomies which can
immediately be applied to the worldline representation of the effective action.
This results in a spin factor that associates the information about spin with
"zigzag" motion of the fluctuating field. Concentrating on the case of quantum
electrodynamics in external fields, we obtain a purely geometric representation
of the Pauli term. To one-loop order, we confirm our formalism by rederiving
the Heisenberg-Euler effective action. Furthermore, we give closed-form
worldline representations for the all-loop order effective action to lowest
nontrivial order in a small-N_f expansion.Comment: 18 pages, v2: references added, minor changes, matches PRD versio
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