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Thomas Epelbaum

Publications and source records attributed to Thomas Epelbaum.

14 recordsLinked to original sources
arXiv2017

Deep Learning applied to Road Traffic Speed forecasting

In this paper, we propose deep learning architectures (FNN, CNN and LSTM) to forecast a regression model for time dependent data. These algorithm's are designed to handle Floating Car Data (FCD) historic speeds to predict road traffic data. For this we aggregate the speeds into the network inputs in an innovative way. We compare the RMSE thus obtained with the results of a simpler physical model, and show that the latter achieves better RMSE accuracy. We also propose a new indicator, which evaluates the algorithms improvement when compared to a benchmark prediction. We conclude by questioning the interest of using deep learning methods for this specific regression task.

stat.AP↗
arXiv2017

Deep learning: Technical introduction

This note presents in a technical though hopefully pedagogical way the three most common forms of neural network architectures: Feedforward, Convolutional and Recurrent. For each network, their fundamental building blocks are detailed. The forward pass and the update rules for the backpropagation algorithm are then derived in full.

stat.ML↗
arXiv2016

From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on $Z^2$

In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the algebraic areas over the set of loops that have fixed number of edges in the two directions. We show that these moments are the product of a combinatorial factor that counts the number of such loops, by a polynomial in the numbers of steps in each direction. Our approach leads to an algorithm for obtaining explicit formulas for the moments of low order.

math-ph↗
arXiv2015

Heavy quark diffusion from coherent color fields in relativistic heavy-ion collisions

The diffusion coefficients of heavy quarks from the coherent color electromagnetic fields which are generated in the early stage of relativistic heavy-ion collisions are calculated at midrapidity, and compared with those obtained from collisions within a thermalized quark-gluon plasma. The coherent color fields are modeled such that they are initially longitudinal and then become isotropic. We found that the diffusion coefficients from the coherent color fields are larger than those from collisions except for very fast heavy quarks, and the color fields are less effective for heavy-quark energy loss. The importance of coherent color fields for heavy-quark diffusion decreases as energy density decreases.

nucl-th↗
arXiv2015

Kinetic theory of a longitudinally expanding system of scalar particles

A simple kinematical argument suggests that the classical approximation may be inadequate to describe the evolution of a system with an anisotropic particle distribution. In order to verify this quantitatively, we study the Boltzmann equation for a longitudinally expanding system of scalar particles interacting with a $ϕ^4$ coupling, that mimics the kinematics of a heavy ion collision at very high energy. We consider only elastic $2\to 2$ scatterings, and we allow the formation of a Bose-Einstein condensate in overpopulated situations by solving the coupled equations for the particle distribution and the particle density in the zero mode. For generic CGC-like initial conditions with a large occupation number and a moderate coupling, the solutions of the full Boltzmann equation do not follow a classical attractor behavior.

hep-ph↗
arXiv2015

Perturbative Vacuum Wavefunctional for Gauge Theories in the Milne Space

The spectrum of vacuum fluctuations in the Milne space (i.e. the tau-eta coordinate system) is an important ingredient in the thermalization studies in relativistic heavy ion collisions. In this paper, the Schrodinger functional for the gauge theory perturbative vacuum is derived for the Milne space. The Wigner-transform of the corresponding vacuum density functional is also found together with the propagators. We finally identify the fluctuation spectrum in vacuum, and show the equivalence between the present approach and the symplectic product based method.

hep-ph↗
arXiv2015

Lattice worldline representation of correlators in a background field

We use a discrete worldline representation in order to study the continuum limit of the one-loop expectation value of dimension two and four local operators in a background field. We illustrate this technique in the case of a scalar field coupled to a non-Abelian background gauge field. The first two coefficients of the expansion in powers of the lattice spacing can be expressed as sums over random walks on a d-dimensional cubic lattice. Using combinatorial identities for the distribution of the areas of closed random walks on a lattice, these coefficients can be turned into simple integrals. Our results are valid for an anisotropic lattice, with arbitrary lattice spacings in each direction.

hep-ph↗
arXiv2014

Properties of the Boltzmann equation in the classical approximation

We study the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.

hep-ph↗
arXiv2014

Isotropization of the Quark Gluon Plasma

We report here recent analytical and numerical work on the theoretical treatment of the early stages of heavy ion collisions, that amounts to solving the classical Yang-Mills equations with fluctuating initial conditions. Our numerical simulations suggest a fast isotropization of the pressure tensor of the system. This trend appears already for small values of the coupling constant $α_s$ . In addition, the system exhibits an anomalously small shear viscosity.

hep-ph↗
arXiv2014

Non-renormalizability of the classical statistical approximation

In this paper, we discuss questions related to the renormalizability of the classical statistical approximation, an approximation scheme that has been used recently in several studies of out-of-equilibrium problems in Quantum Field Theory. Although the ultraviolet power counting in this approximation scheme is identical to that of the unapproximated quantum field theory, this approximation is not renormalizable. The leading cause of this non-renormalizability is the breakdown of Weinberg's theorem in this approximation. We also discuss some practical implications of this negative result for simulations that employ this approximation scheme, and we speculate about a possible modification of the classical statistical approximation in order to systematically subtract the leading residual divergences.

hep-ph↗
arXiv2013

Pressure isotropization in high energy heavy ion collisions

The early stages of high energy heavy ion collisions are studied in the Color Glass Condensate framework, with a real-time classical lattice simulation. When increasing the coupling constant, we observe a rapid increase of the ratio of longitudinal to transverse pressure. The transient regime that precedes this behavior is of the order of 1 fm/c.

hep-ph↗
arXiv2013

Fluctuations of the initial color fields in high energy heavy ion collisions

In the Color Glass Condensate approach to the description of high energy heavy ion collisions, one needs to superimpose small random Gaussian distributed fluctuations to the classical background field, in order to resum the leading secular terms that result from the Weibel instability, that would otherwise lead to pathological results beyond leading order. In practical numerical simulations, one needs to know this spectrum of fluctuations at a proper time $τ\ll Q_s^{-1}$ shortly after the collision, in the Fock-Schwinger gauge $A^τ=0$. In this paper, we derive these fluctuations from first principles, by solving the Yang-Mills equations linearized around the classical background, with plane wave initial conditions in the remote past. We perform the intermediate steps in light-cone gauge, and we convert the results to the Fock-Schwinger gauge at the end. We obtain simple and explicit formulas for the fluctuation modes.

hep-ph↗
arXiv2012

Instability induced pressure isotropization in a longitudinally expanding system

In two previous works [arXiv:1009.4363,arXiv:1107.0668], we studied the time evolution of a system of real scalar fields with quartic coupling which shares important features with the Color Glass Condensate description of heavy ion collisions. Our primary objective was to understand how such a system, when initialized with a non-perturbatively large classical field configuration, reaches thermal equilibrium. An essential goal of these works was to highlight the role played by the quantum fluctuations. However, these studies considered only a system confined within a box of fixed volume. In the present paper, we extend this work to a system that expands in the longitudinal direction thereby more closely mimicking a heavy ion collision. We conclude that the microscopic processes that drive the system towards equilibrium are able to keep up with the expansion of the system; the pressure tensor becomes isotropic despite the anisotropic expansion.

hep-ph↗