[Paper Review] Quantum kinetic theory with nonlocal coherence

Matti Herranen|ArXiv.org|Jun 17, 2009

Advanced Thermodynamics and Statistical Mechanics106 references7 citations

TL;DR

This paper develops a quantum kinetic theory that incorporates nonlocal quantum coherence by identifying singular shell solutions in the phase space of 2-point correlation functions—specifically at $k_0 = 0$ for homogeneous systems and $k_z = 0$ for planar symmetric systems. These coherence modes, when embedded into the Kadanoff-Baym equations, yield a closed set of transport equations for on-shell distribution functions, extending the standard Boltzmann equation to include interference effects such as quantum reflection and coherent particle production.

ABSTRACT

In this thesis we develop a novel approximation scheme (eQPA), where the effects of nonlocal coherence are included in the kinetic approach to nonequilibrium quantum dynamics. The key element in our formalism is the finding of new singular shell solutions, located at $k_{0,z} = 0$ in the phase space of 2-point Wightman function, which describe the nonlocal quantum coherence between the ``opposite'' mass-shell excitations for spatially homogeneous and static planar symmetric problems, respectively. This phase space structure leads to a closed set of transport equations for the corresponding on-shell distribution functions $f$, providing an extension to the standard quantum Boltzmann equation. We have considered a number of applications to demonstrate the use of our formalism, including the Klein problem, quantum reflection from a CP-violating mass wall and coherent production of (fermionic and scalar) particles in an oscillating background. Our formalism should be of relevance for many problems in particle physics and cosmology, including baryogenesis and neutrino flavour oscillations in an inhomogeneous background.

Motivation & Objective

• To develop a kinetic theory framework that consistently includes nonlocal quantum coherence effects, which are lost in standard Boltzmann approaches.
• To address the limitations of traditional quantum kinetic theory in describing interference phenomena such as quantum reflection and coherent particle production.
• To derive a closed set of transport equations that include both coherent and incoherent (collisional) dynamics in a self-consistent manner.
• To enable realistic simulations of fermionic and scalar field dynamics in slowly varying, nonequilibrium backgrounds with decohering interactions.
• To provide a first-principles derivation of the extended quasiparticle approximation (eQPA) from the two-particle irreducible (2PI) effective action formalism.

Proposed method

• Formulates the problem using the two-particle irreducible (2PI) effective action formalism to derive Schwinger-Dyson equations for 2-point correlation functions.
• Applies a partial Fourier transform to obtain Kadanoff-Baym equations in mixed position-momentum representation.
• Identifies new singular shell solutions in the phase space of the Wightman function: $k_0 = 0$ for spatially homogeneous systems and $k_z = 0$ for planar symmetric systems.
• Introduces an extended quasiparticle approximation (eQPA) that includes both standard mass-shell and coherence-shell contributions to the spectral function.
• Derives closed transport equations for on-shell distribution functions by inserting the full phase space structure into the Kadanoff-Baym equations.
• Performs a resummation of the gradient expansion in the collision term to systematically include coherence effects in leading order in interaction width $\Gamma$ and background gradients.

Experimental results

Research questions

• RQ1 How can nonlocal quantum coherence be consistently incorporated into quantum kinetic theory beyond the standard Boltzmann approximation?
• RQ2 What are the phase space structures of the 2-point correlation function that support nonlocal coherence in systems with slowly varying backgrounds?
• RQ3 Can the Kadanoff-Baym equations be closed into a tractable set of transport equations when coherence shells are included?
• RQ4 How do decohering collisions affect coherent particle production and quantum reflection in nonequilibrium field theory?
• RQ5 Can the formalism be applied to realistic problems such as electroweak baryogenesis with $CP$-violating walls and coherent particle production from decaying particles?

Key findings

• The identification of $k_0 = 0$ and $k_z = 0$ shell solutions in the phase space of the Wightman function provides a new mechanism to describe nonlocal quantum coherence in quantum kinetic theory.
• The extended quasiparticle approximation (eQPA) emerges from first principles in the 2PI formalism and includes both mass-shell and coherence-shell contributions to the spectral function.
• The formalism reproduces exact results for the collisionless Klein problem and fermionic quantum reflection from a smooth mass wall, validating its consistency with standard field theory.
• In the presence of collisions, the coherent production of decaying particles is suppressed due to thermalization and decoherence, with a quantitative reduction observed in numerical examples.
• A resummation procedure for the gradient expansion of the collision term yields a controlled leading-order result in $\Gamma$ and background gradients, enabling systematic inclusion of coherence effects.
• The framework is well-suited for studying electroweak baryogenesis with $CP$-violating phase transition walls, where nonlocal reflection effects are critical but previously unaccounted for in kinetic theory.