Quantum Fluctuation and Dissipation in Holographic Theories: A Unifying Study Scheme

TL;DR

This paper develops a universal framework for analyzing quantum and thermal fluctuations, dissipation, and Brownian motion in strongly coupled quantum field theories using holographic methods, emphasizing the role of Bessel function orders.

Contribution

It introduces a unified analytic scheme based on Bessel function orders to study fluctuation and dissipation phenomena across various holographic theories.

Findings

Universal verification of the fluctuation-dissipation theorem.

Late time fluctuation behaviors depend on Bessel function order.

Stochastic observables for Dp-branes can be derived from string fluctuations.

Abstract

Motivated by the wide range of applicability of the fluctuation and dissipation phenomena in non-equilibrium systems, we provide a universal study scheme for the dissipation of the energy and the corresponding Brownian motion analysis of massive particles due to quantum and thermal fluctuations in a wide class of strongly coupled quantum field theories. The underlying reason for the existence of such unified study scheme, is that our analytic methods turn out to heavily depend on the order of the Bessel functions $\nu$, describing the string fluctuations attached to the particle. Different values of the order are associated to different theories. The two-point function of the fluctuations exhibits two different late time behaviors, depending purely on the value of the order of Bessel functions. We then find that the coefficients and observables associated with the stochastic motion at zero and finite temperature, depend on the scales of the theory through powers of the order $\nu$. Moreover, the fluctuation-dissipation theorem is verified from the bulk perspective to be universally satisfied for the whole class of theories. Finally, we show that the analysis of certain types of Dp-brane fluctuations can be mapped one-to-one to the string fluctuations and therefore the stochastic brane observables can be read from the string ones. In the closing remarks we demonstrate how our analysis accommodates known results as special cases and provide more applications.