Probing anomalous driving
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Springer
Received: February 13, 2019 Accepted: March 19, 2019 Published: April 4, 2019
Michael Haack,a Debajyoti Sarkara,b and Amos Yaromc,d a
Arnold Sommerfeld Center for Theoretical Physics, Ludwig Maximilians Universit¨ at M¨ unchen, Theresienstrasse 37, 80333 M¨ unchen, Germany b Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland c Department of Physics, Technion, Haifa 32000, Israel d Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544, U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: We study the effects of driving a magnetically charged black brane solution of Einstein-Maxwell-Chern-Simons theory by a time dependent electric field. From a holographic perspective, we find that placing a sample in a background magnetic field and driving the system via a parallel electric field generates a charge current which may oscillate for long periods and (or) may exhibit non-Ohmic behavior. We discuss how these two effects manifest themselves in various types of quenches and in periodic driving of the sample. Keywords: (AdS/CMT)
AdS-CFT Correspondence, Holography and condensed matter physics
ArXiv ePrint: 1812.08210
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP04(2019)034
JHEP04(2019)034
Probing anomalous driving
Contents 1
2 Setting up the problem
2
3 Quasi normal modes and late time behavior 3.1 Quasi normal modes 3.2 Late time behavior
6 7 8
4 Solving the equation of motion 4.1 An oscillatory electric field 4.2 A localized disturbance 4.3 A quench-like disturbance
11 12 13 16
5 Discussion
16
1
Introduction
Thermally equilibrated gauge theories have rich and interesting phase diagrams. Many techniques and tools have been developed over the last years that help us understand the structure of such gauge theories. Be that as it may, many observable phenomena can not be captured by equilibrium dynamics. Core collapse supernova and the early stages of heavy ion collisions are but a few systems where equilibrium dynamics is, at best, an approximate description. The term out of equilibrium dynamics spans a broad range of phenomena which we will not attempt to fully classify here. In what follows we will restrict ourselves to driven systems whereby the state of the system is not thermally equilibrated due to time dependent probing by an external agent. For example, quenches exhibit interesting transient behavior before and after the quench, see, e.g., [1–6]. Holographic analyses of quenches have been studied in, for example, [7–11]. Likewise, periodically driven systems have received renewed interest. Topological phase transitions seem to be induced by an appropriate driving force [12–22], see also [23]. A holographic analysis of Floquet systems was carried out in [24–29]. The interested reader is referred to the recent review [30] on holography and out of equilibrium dynamics for more details. In the
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