Bosonic and Fermionic Holographic Fluctuation and Dissipation at finite temperature and density

TL;DR

This paper explores fluctuation and dissipation phenomena for bosons and fermions in holographic models at finite temperature and density, revealing ballistic and ultraslow diffusive behaviors and applying these to specific black hole backgrounds.

Contribution

It provides a comprehensive holographic analysis of fluctuation and dissipation for both bosonic and fermionic probes at finite temperature and density, including new results on diffusion behaviors.

Findings

Short-time mean square displacement shows ballistic behavior.

Large-time dynamics exhibit ultraslow diffusion, except at zero chemical potential.

Fermionic diffusion analyzed in models with Fermi surfaces.

Abstract

In this paper we investigate some general aspects of fluctuation and dissipation in the holographic scenario at zero and finite density. We model this situation with a probe string in a diagonal metric representing a black brane. The string stretches from the black brane to a probe brane thus simulating a stochastic driven particle. In this scenario, we compute the admittance, the diffusion coefficient, the correlation functions and the regularized mean square displacement, for bosons and fermions, all from the metric components. We check these calculations with the fluctuation-dissipation theorem. Further, we show that at finite temperature and density, the mean square displacement in the limit of short times reproduces the usual quadratic (ballistic) behavior, for bosons and fermions. For large times, we find ultraslow diffusive processes in various cases, except for bosons at zero chemical potential. We apply this general analysis in two different models: hyperscaling violation at finite temperature and a charged dilatonic AdS black hole, both for bosons and fermions. This is important because we found the fermionic diffusion in systems which allow the appearance of Fermi surfaces and Fermi liquids.