2,581 research outputs found
On entanglement spreading from holography
A global quench is an interesting setting where we can study thermalization
of subsystems in a pure state. We investigate entanglement entropy (EE) growth
in global quenches in holographic field theories and relate some of its aspects
to quantities characterizing chaos. More specifically we obtain four key
results:
1. We prove holographic bounds on the entanglement velocity and the
butterfly effect speed that arises in the study of chaos.
2. We obtain the EE as a function of time for large spherical entangling
surfaces analytically. We show that the EE is insensitive to the details of the
initial state or quench protocol.
3. In a thermofield double state we determine analytically the two-sided
mutual information between two large concentric spheres separated in time.
4. We derive a bound on the rate of growth of EE for arbitrary shapes, and
develop an expansion for EE at early times.
In a companion paper arXiv:1608.05101, we put these results in the broader
context of EE growth in chaotic systems: we relate EE growth to the chaotic
spreading of operators, derive bounds on EE at a given time, and compare the
holographic results to spin chain numerics and toy models. In this paper, we
perform holographic calculations that provide the basis of arguments presented
in that paper.Comment: v2: presentation improved, typos fixed, 54 pages, 17 figures v1: 53
pages, 16 figure
Probing renormalization group flows using entanglement entropy
In this paper we continue the study of renormalized entanglement entropy
introduced in [1]. In particular, we investigate its behavior near an IR fixed
point using holographic duality. We develop techniques which, for any static
holographic geometry, enable us to extract the large radius expansion of the
entanglement entropy for a spherical region. We show that for both a sphere and
a strip, the approach of the renormalized entanglement entropy to the IR fixed
point value contains a contribution that depends on the whole RG trajectory.
Such a contribution is dominant, when the leading irrelevant operator is
sufficiently irrelevant. For a spherical region such terms can be anticipated
from a geometric expansion, while for a strip whether these terms have
geometric origins remains to be seen.Comment: 58 pages, 6 figure
Solving a family of -like theories
We deform two-dimensional quantum field theories by antisymmetric
combinations of their conserved currents that generalize Smirnov and
Zamolodchikov's deformation. We obtain that energy levels on a
circle obey a transport equation analogous to the Burgers equation found in the
case. This equation relates charges at any value of the deformation
parameter to charges in the presence of a (generalized) Wilson line. We
determine the initial data and solve the transport equations for antisymmetric
combinations of flavor symmetry currents and the stress tensor starting from
conformal field theories. Among the theories we solve is a conformal field
theory deformed by and simultaneously. We check our
answer against results from AdS/CFT.Comment: 42 page
Lectures on holographic non-Fermi liquids and quantum phase transitions
In these lecture notes we review some recent attempts at searching for
non-Fermi liquids and novel quantum phase transitions in holographic systems
using gauge/gravity duality. We do this by studying the simplest finite density
system arising from the duality, obtained by turning on a nonzero chemical
potential for a U(1) global symmetry of a CFT, and described on the gravity
side by a charged black hole. We address the following questions of such a
finite density system:
1. Does the system have a Fermi surface? What are the properties of low
energy excitations near the Fermi surface?
2. Does the system have an instability to condensation of scalar operators?
What is the critical behavior near the corresponding quantum critical point?
We find interesting parallels with those of high T_c cuprates and heavy
electron systems. Playing a crucial role in our discussion is a universal
intermediate-energy phase, called a "semi-local quantum liquid", which
underlies the non-Fermi liquid and novel quantum critical behavior of a system.
It also provides a novel mechanism for the emergence of lower energy states
such as a Fermi liquid or a superconductor.Comment: 70 pages. Based on lectures given by Hong Li
Reservoir-scale transdimensional fracture network inversion
The Waiwera aquifer hosts a structurally complex geothermal groundwater system, where a localized thermal anomaly feeds the thermal reservoir. The temperature anomaly is formed by the mixing of waters from three different sources: fresh cold groundwater, cold seawater and warm geothermal water. The stratified reservoir rock has been tilted, folded, faulted, and fractured by tectonic movement, providing the pathways for the groundwater. Characterization of such systems is challenging, due to the resulting complex hydraulic and thermal conditions which cannot be represented by a continuous porous matrix.
By using discrete fracture network models (DFNs) the discrete aquifer features can be modelled, and the main geological structures can be identified. A major limitation of this modelling approach is that the results are strongly dependent on the parametrization of the chosen initial solution. Classic inversion techniques require to define the number of fractures before any interpretation is done.
In this research we apply the transdimensional DFN inversion methodology that overcome this limitation by keeping fracture numbers flexible and gives a good estimation on fracture locations. This stochastic inversion method uses the reversible-jump Markov chain Monte Carlo algorithm and was originally developed for tomographic experiments. In contrast to such applications, this study is limited to the use of steady-state borehole temperature profiles – with significantly less data. This is mitigated by using a strongly simplified DFN model of the reservoir, constructed according to available geological information.
We present a synthetic example to prove the viability of the concept, then use the algorithm on field observations for the first time. The fit of the reconstructed temperature fields cannot compete yet with complex three-dimensional continuum models, but indicate areas of the aquifer where fracturing plays a big role. This could not be resolved before with continuum modelling. It is for the first time that the transdimensional DFN inversion was used on field data and on borehole temperature logs as input.DFG, 318763901, SFB 1294, Data Assimilation - The seamless integration of data and models, Assimilating data with different degrees of uncertainty into statistical models for earthquake occurrence (B04)TU Berlin, Open-Access-Mittel - 201
- …