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

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.

arXiv comment37 pages, 1 table, no figures. This version matches the published one in PRD

References in corpus (20)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Linear Confinement and AdS/QCD
• Gravity Duals of Lifshitz-like Fixed Points
• Embedding AdS Black Holes in Ten and Eleven Dimensions
• Hidden Fermi surfaces in compressible states of gauge-gravity duality
• Aspects of holography for theories with hyperscaling violation
• The evolution of unstable black holes in anti-de Sitter space
• Heavy-Quark Potentials and AdS/QCD
• Holographic Fermi Surfaces and Entanglement Entropy
• Peculiar properties of a charged dilatonic black hole in AdS_5
• Brownian motion in AdS/CFT
• Quantum Fluctuations in Holographic Theories with Hyperscaling Violation
• Fluctuation and Dissipation at a Quantum Critical Point
• Graphene Conductivity near the Charge Neutral Point
• Quantum Fluctuation and Dissipation in Holographic Theories: A Unifying Study Scheme
• Holographic Brownian motion at finite density
• Fluctuation and Dissipation from a Deformed String/Gauge Duality Model
• Fluctuation and dissipation within a deformed holographic model with backreaction
• Fermionic and bosonic fluctuation-dissipation theorem from a deformed AdS holographic model at finite temperature and chemical potential
• On the fluctuation-dissipation theorem for soft fermionic excitations in a hot QCD plasma