[Paper Review] Decay Rate of Coherent Field Oscillation

M. Yoshimura|ArXiv.org|Mar 20, 1996

Cold Atom Physics and Bose-Einstein Condensates2 references3 citations

TL;DR

This paper derives the decay rate of coherent field oscillations in a general class of models with Yukawa and quartic couplings using the functional Schrödinger picture in the small amplitude limit. It shows that this analytic result corresponds to the zero-momentum limit of a physical process where n particles from the classical field decay simultaneously into two Bose particles, providing a novel resummation of perturbative amplitudes beyond standard field theory approaches.

ABSTRACT

In recent studies it has become increasingly clear that presence of infinitely many instability bands of the parametric resonance plays crucial roles in the phenomenon of particle production under periodic classical field oscillation. We extend previous works to a general class of models including both the Yukawa and the quartic type of couplings of the classical field to quantum bose fields. Decay rate from the $n-$th band is derived in the small amplitude limit using the functional Schr$\stackrel{..}{ m o}$dinger picture. It is then shown that this analytic result of the decay rate can also be derived as the zero momentum limit of a physical process, $n$ particles that comprise the classical homogeneous field decaying simultaneously into 2 bose particles. The latter approach uses ordinary perturbation theory, hence the former result is a novel resummation of many perturbative amplitudes, which usually becomes complicated for a large $n$ order.

Motivation & Objective

• To analyze particle production from periodic classical field oscillations in quantum field theory.
• To extend previous results on parametric resonance to models with both Yukawa and quartic couplings.
• To derive the decay rate from the n-th instability band in the small amplitude limit.
• To establish a connection between the functional Schrödinger picture result and physical perturbative processes.
• To demonstrate that the analytic decay rate corresponds to the zero-momentum limit of n-particle decay into two Bose particles.

Proposed method

• Uses the functional Schrödinger picture to compute the decay rate from the n-th instability band in the small amplitude limit.
• Considers a general class of models with both Yukawa and quartic interactions between the classical field and quantum Bose fields.
• Derives the decay rate analytically using the functional Schrödinger formalism, avoiding standard perturbation theory for large n.
• Compares the analytic result to the zero-momentum limit of a physical decay process: n particles decaying into two Bose particles.
• Applies ordinary perturbation theory to the physical decay process to confirm consistency with the functional Schrödinger result.
• Demonstrates that the functional Schrödinger result is a resummation of many perturbative amplitudes, especially useful for large n.

Experimental results

Research questions

• RQ1 How does the decay rate from the n-th instability band behave in models with both Yukawa and quartic couplings?
• RQ2 Can the functional Schrödinger picture result for the decay rate be physically interpreted via a perturbative decay process?
• RQ3 What is the relationship between the zero-momentum limit of n-to-2 Bose particle decay and the instability band decay rate?
• RQ4 How does the functional Schrödinger approach provide a resummation of perturbative amplitudes for large n?
• RQ5 Does the analytic decay rate derived via the functional Schrödinger method match the physical decay amplitude in the zero-momentum limit?

Key findings

• The decay rate from the n-th instability band is derived analytically using the functional Schrödinger picture in the small amplitude limit.
• The derived decay rate matches the zero-momentum limit of the physical process where n particles from the classical field decay into two Bose particles.
• This correspondence establishes that the functional Schrödinger result is a resummation of many perturbative amplitudes, simplifying large-n calculations.
• The result holds for both Yukawa and quartic coupling models, extending previous work limited to specific interaction types.
• The consistency between the non-perturbative functional approach and the perturbative zero-momentum limit validates the analytic method.
• The paper provides a unified framework linking non-perturbative field-theoretic results to physical decay processes in parametric resonance.