Nonlinear Langevin dynamics via holography

Abstract

In this work, we consider non-linear corrections to the Langevin effective theory of a heavy quark moving through a strongly coupled CFT plasma. In AdS/CFT, this system can be identified with that of a string stretched between the boundary and the horizon of an asymptotically AdS black-brane solution. We compute the Feynman-Vernon influence functional for the heavy quark by evaluating the Nambu-Goto action on a doubled string configuration. This configuration is the linearised solution of the string motion in the doubled black-brane geometry which has been proposed as the holographic dual of a thermal Schwinger-Keldysh contour of the CFT. Our expression for the influence phase passes non-trivial consistency conditions arising from the underlying unitarity and thermality of the bath. The local effective theory obeys the recently proposed non-linear fluctuation dissipation theorem relating the non-Gaussianity of thermal noise to the thermal jitter in the damping constant. This furnishes a non-trivial check for the validity of these relations derived in the weak coupling regime. Contents

Open quantum systems and Schwinger-Keldysh holograms

“…In this context, we capture in the influence functionals, not only the known dissipative physics contained in response functions, gravitationally encoded in the quasinormal modes, but also at the same time, learn about their interactions with the outgoing Hawking quanta. While earlier works, [33], demonstrated this in the context of a single Brownian particle degree of freedom, the present discussion generalizes this to scalar probes of the black hole environment. We should note that earlier attempts to understand fluctuations of the outgoing Hawking quanta, as for example in [51], where the authors studied an interacting scalar model in an ersatz two-dimensional black hole were plagued by infra-red divergences.…”

“…The authors of [31] already demonstrated the efficacy of their prescription by obtaining the quadratic influence functional in a low frequency and momentum expansion for a bulk scalar field in the probe limit. 2 Subsequently, [33] explored how this prescription may be employed to study nonlinear Langevin dynamics of a single particle degree of freedom in quantum mechanics. Their analysis subjected the prescription to the test of dealing with self-interacting fields in the bulk and demonstrated that it continues to give reasonable answers.…”

“…Their analysis subjected the prescription to the test of dealing with self-interacting fields in the bulk and demonstrated that it continues to give reasonable answers. Specifically, the authors of [33] modeled the Brownian particle using the holographic construction described in [21,34]. Using the complex holographic geometry of [31] to compute influence functionals, they demonstrated that general expectations of non-linear Langevin dynamics explored in earlier [35,36] was borne out.…”

“…However, the Schwinger-Keldysh construction has a Z 2 involution that can be thought of as time-reversal (cf., [17] for a discussion). As described in [33] the geometry does indeed have an involution which can be used to map ingoing solutions to outgoing ones. In the coordinates used in (2.4) the transformation takes the form:…”

“…The particle analogues of non-linear FDTs for a Brownian particle have for instance appeared in[33,35,36,45].…”