995 research outputs found
Complexity & wormholes in holography
Holography has proven to be a highly successful approach in studying quantum gravity, where a non-gravitational quantum field theory is dual to a quantum gravity theory in one higher dimension. This doctoral thesis delves into two key aspects within the context of holography: complexity and wormholes. In Part I of the thesis, the focus is on holographic complexity. Beginning with a brief review of quantum complexity and its significance in holography, the subsequent two chapters proceed to explore this topic in detail. We study several proposals to quantify the costs of holographic path integrals. We then show how such costs can be optimized and match them to bulk complexity proposals already existing in the literature. In Part II of the thesis, we shift our attention to the study of spacetime wormholes in AdS/CFT. These are bulk spacetime geometries having two or more disconnected boundaries. In recent years, such wormholes have received a lot of attention as they lead to interesting implications and raise important puzzles. We study the construction of several simple examples of such wormholes in general dimensions in the presence of a bulk scalar field and explore their implications in the boundary theory
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
A modern analytic method to solve singular and non-singular linear and non-linear differential equations
This article circumvents the Laplace transform to provide an analytical solution in a power series form for singular, non-singular, linear, and non-linear ordinary differential equations. It introduces a new analytical approach, the Laplace residual power series, which provides a powerful tool for obtaining accurate analytical and numerical solutions to these equations. It demonstrates the new approach’s effectiveness, accuracy, and applicability in several ordinary differential equations problem. The proposed technique shows the possibility of finding exact solutions when a pattern to the series solution obtained exists; otherwise, only rough estimates can be given. To ensure the accuracy of the generated results, we use three types of errors: actual, relative, and residual error. We compare our results with exact solutions to the problems discussed. We conclude that the current method is simple, easy, and effective in solving non-linear differential equations, considering that the obtained approximate series solutions are in closed form for the actual results. Finally, we would like to point out that both symbolic and numerical quantities are calculated using Mathematica software
Quantum Optimal Transport: Quantum Couplings and Many-Body Problems
This text is a set of lecture notes for a 4.5-hour course given at the
Erd\"os Center (R\'enyi Institute, Budapest) during the Summer School "Optimal
Transport on Quantum Structures" (September 19th-23rd, 2023). Lecture I
introduces the quantum analogue of the Wasserstein distance of exponent
defined in [F. Golse, C. Mouhot, T. Paul: Comm. Math. Phys. 343 (2016),
165-205], and in [F. Golse, T. Paul: Arch. Ration. Mech. Anal. 223 (2017)
57-94]. Lecture II discusses various applications of this quantum analogue of
the Wasserstein distance of exponent , while Lecture III discusses several
of its most important properties, such as the triangle inequality, and the
Kantorovich duality in the quantum setting, together with some of their
implications.Comment: 81 pages, 7 figure
Effective theories of phase transitions
In this thesis we study systems undergoing a superfluid phase transition at finite temperature and chemical potential. We construct an effective description valid
at late times and long wavelengths, using both the holographic duality and the Schwinger-Keldysh formalism for non-equilibrium field theories. In particular, in
chapter 2 we employ analytic techniques to find the leading dissipative corrections
to the energy-momentum tensor and the electric current of a holographic superfluid,
away from criticality. Our method is based on the symplectic current of Crnkovic
and Witten [1] and extends on previous results [2, 3]. We assume a general black
hole background in the bulk, with finite charge density and scalars fields turned
on. We express one-point functions of the boundary field theory solely in terms
of thermodynamic quantities and data related to the black hole horizon in the
bulk spacetime. Matching our results with the expected constitutive relations of
superfluid hydrodynamics, we obtain analytic expressions for the five transport
coefficients characterising superfluids with small superfluid velocities. In chapter 3
we examine the hydrodynamics of holographic superfluids arbitrarily close to the
critical point. The main difference in this case is that, close to the critical point, the
amplitude of the order parameter is an additional hydrodynamic degree of freedom
and we have to include it in our effective theory. For simplicity, we choose to work
in the probe limit. Utilising the symplectic current once again, we find the equations
that govern the critical dynamics of the order parameter and the charge density
and show that our holographic results are in complete agreement with Model F of
Hohenberg and Halperin [4]. Through this process, we find analytic expressions for
all the parameters of Model F, including the dissipative kinetic coefficient, in terms
of thermodynamics and horizon data. In addition, we perform various numerical
checks of our analytic results. Finally, in chapter 4 we consider critical superfluid
dynamics within the Schwinger-Keldysh formalism. As in chapter 3, we focus on
the complex order parameter and the conserved current of the spontaneously broken
global symmetry, ignoring temperature and normal fluid velocity fluctuations. We
construct an effective action up to second order in the a-fields and compare the
resulting stochastic system with Model F and our holographic results in chapter 3.
A crucial role in this construction is played by a time independent gauge symmetry,
called “chemical shift symmetry”. We also integrate out the amplitude mode and
obtain the conventional equations of superfluid hydrodynamics, valid for energies
well below the gap of the amplitude mode
Data-driven deep-learning methods for the accelerated simulation of Eulerian fluid dynamics
Deep-learning (DL) methods for the fast inference of the temporal evolution of fluid-dynamics systems, based on the previous recognition of features underlying large sets of fluid-dynamics data, have been studied. Specifically, models based on convolution neural networks (CNNs) and graph neural networks (GNNs) were proposed and discussed.
A U-Net, a popular fully-convolutional architecture, was trained to infer wave dynamics on liquid surfaces surrounded by walls, given as input the system state at previous time-points. A term for penalising the error of the spatial derivatives was added to the loss function, which resulted in a suppression of spurious oscillations and a more accurate location and length of the
predicted wavefronts. This model proved to accurately generalise to complex wall geometries not seen during training.
As opposed to the image data-structures processed by CNNs, graphs offer higher freedom on how data is organised and processed. This motivated the use of graphs to represent the state of fluid-dynamic systems discretised by unstructured sets of nodes, and GNNs to process such graphs. Graphs have enabled more accurate representations of curvilinear geometries and higher resolution placement exclusively in areas where physics is more challenging to resolve. Two novel
GNN architectures were designed for fluid-dynamics inference: the MuS-GNN, a multi-scale GNN, and the REMuS-GNN, a rotation-equivariant multi-scale GNN. Both architectures work by repeatedly passing messages from each node to its nearest nodes in the graph. Additionally, lower-resolutions graphs, with a reduced number of nodes, are defined from the original graph,
and messages are also passed from finer to coarser graphs and vice-versa. The low-resolution graphs allowed for efficiently capturing physics encompassing a range of lengthscales.
Advection and fluid flow, modelled by the incompressible Navier-Stokes equations, were the two types of problems used to assess the proposed GNNs. Whereas a single-scale GNN was sufficient to achieve high generalisation accuracy in advection simulations, flow simulation highly benefited from an increasing number of low-resolution graphs. The generalisation and long-term accuracy of these simulations were further improved by the REMuS-GNN architecture, which
processes the system state independently of the orientation of the coordinate system thanks to a rotation-invariant representation and carefully designed components. To the best of the author’s knowledge, the REMuS-GNN architecture was the first rotation-equivariant and multi-scale GNN.
The simulations were accelerated between one (in a CPU) and three (in a GPU) orders of magnitude with respect to a CPU-based numerical solver. Additionally, the parallelisation of multi-scale GNNs resulted in a close-to-linear speedup with the number of CPU cores or GPUs.Open Acces
Electron Thermal Runaway in Atmospheric Electrified Gases: a microscopic approach
Thesis elaborated from 2018 to 2023 at the Instituto de Astrofísica de Andalucía under the supervision of Alejandro Luque (Granada, Spain) and Nikolai Lehtinen (Bergen, Norway). This thesis presents a new database of atmospheric electron-molecule collision cross sections which was published separately under the DOI :
With this new database and a new super-electron management algorithm which significantly enhances high-energy electron statistics at previously unresolved ratios, the thesis explores general facets of the electron thermal runaway process relevant to atmospheric discharges under various conditions of the temperature and gas composition as can be encountered in the wake and formation of discharge channels
Strong-Field Physics in QED and QCD: From Fundamentals to Applications
We provide a pedagogical review article on fundamentals and applications of
the quantum dynamics in strong electromagnetic fields in QED and QCD. The
fundamentals include the basic picture of the Landau quantization and the
resummation techniques applied to the class of higher-order diagrams that are
enhanced by large magnitudes of the external fields. We then discuss observable
effects of the vacuum fluctuations in the presence of the strong fields, which
consist of the interdisciplinary research field of nonlinear QED. We also
discuss extensions of the Heisenberg-Euler effective theory to finite
temperature/density and to non-Abelian theories with some applications. Next,
we proceed to the paradigm of the dimensional reduction emerging in the
low-energy dynamics in the strong magnetic fields. The mechanisms of
superconductivity, the magnetic catalysis of the chiral symmetry breaking, and
the Kondo effect are addressed from a unified point of view in terms of the
renormalization-group method. We provide an up-to-date summary of the lattice
QCD simulations in magnetic fields for the chiral symmetry breaking and the
related topics as of the end of 2022. Finally, we discuss novel transport
phenomena induced by chiral anomaly and the axial-charge dynamics. Those
discussions are supported by a number of appendices.Comment: Prepared for an invited review article; Published versio
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