Comparison between Causal and Acausal Diffusion: a Schwinger-Keldysh Effective Field Theory Perspective

TL;DR

This paper compares causal and acausal diffusion theories using Schwinger-Keldysh Effective Field Theory, revealing universal behaviors in one-loop corrections and implications for precision tests in diffusive systems.

Contribution

It introduces a detailed comparison of diffusion and quasi-diffusion within the SK-EFT framework, highlighting universal features of one-loop corrections in both regimes.

Findings

One-loop corrections are governed by two universal functions.

Overdamped behavior matches acausal diffusion theory.

Results enable precision tests in quasi-diffusive systems.

Abstract

In Fick's time-honored theory of diffusion, the system responds instantaneously to external perturbations, resulting in acausal behavior. Maxwell-Cattaneo theory addresses this issue by introducing a relaxation time, rendering the diffusion process causal. We focus on systems where this relaxation time is comparable to the diffusion time and significantly larger than the relaxation times of all other non-conserved operators. In such systems, late-time diffusion is influenced by this relaxation process, leading to a theory of quasi-diffusion. Using the Schwinger-Keldysh Effective Field Theory (SK-EFT) framework, we compare the theories of diffusion and quasi-diffusion by analyzing the real-time dynamics of correlation functions both in linear response and at one-loop order. In particular, we show that the one-loop corrections in the causal (quasi-diffusion) theory, in both the underdamped and the overdamped cases, are governed by two universal functions. In the overdamped case, the behavior mirrors that of the acausal (diffusion) theory, which has recently been applied for precision tests of SK-EFT in diffusive systems. We suggest that our results in the underdamped limit can also be used for precision tests in quasi-diffusive systems.