Title: | Out-of-equilibrium hydrodynamics with and without boost symmetry |
Author: | |
Advisor: | Lárus Thorlacius |
Date: | 2021-05 |
Language: | English |
University/Institute: | University of Iceland Háskóli Íslands |
School: | Verkfræði- og náttúruvísindasvið (HÍ) School of Engineering and Natural Sciences (UI) |
Department: | Raunvísindadeild (HÍ) Faculty of Physical Sciences (UI) |
Subject: | High Energy Physics; Mathematical Physics; Hydrodynamics; Gauge-gravity duality; Atómfræði; Stærðfræðileg eðlisfræði; Straumfræði; Eðlisfræði; Doktorsritgerðir |
URI: | https://hdl.handle.net/20.500.11815/2591 |
Abstract:In this thesis, we explore the role of symmetries in hydrodynamics by studying certain
properties of relativistic and non-relativistic fluids. In the first part of the thesis, we
examine the theory of relativistic magnetohydrodynamics (Maxwell electromagnetism
coupled to hydrodynamics) and its low temperature incarnation, force-free electrodynamics, reformulated in the language of higher-form symmetries and discuss the
advantages of such a scheme. Using this framework, we analyse the regime of validity
of force-free electrodynamics by evaluating the lifetime of the non-conserved electric
field operator via a holographic model sharing the same global symmetries as that of a
plasma. We are able to explicitly calculate the lifetime of the electric field, both parallel
and perpendicular to the magnetic field, and find that there are indeed no long-lived
modes that interfere with a hydrodynamic description of force-free electrodynamics. In
the second part of the thesis, we study the thermodynamic properties of non-relativistic
Lifshitz fluids with an arbitrary dynamic exponent z (encoding the anisotropy in the
scaling of time and space coordinates). We study energy transport in such fluids far from
equilibrium after performing a local quench between two semi-infinite fluid reservoirs.
We find that the late time energy flow is universal and accommodated via a steady
state occupying an expanding central region between outgoing shock and rarefaction
waves (a non-equilibrium steady state), as seen previously for relativistic scale invariant
fluids. Armed with an equation of state for a perfect Lifshitz fluid with an arbitrary z
and moving with a velocity v, we proceed to study its holographic dual using the well established Einstein-Maxwell-Dilaton model. We find that the fluid velocity appears
as the chemical potential, conjugate to the dual momentum density and the solutions
represent a physically distinct class of black branes possessing a linear momentum,
different from boosting a static brane.
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