91 research outputs found
Chiral charge dynamics in Abelian gauge theories at finite temperature
We study fermion number non-conservation (or chirality breaking) in Abelian
gauge theories at finite temperature. We consider the presence of a chemical
potential for the fermionic charge, and monitor its evolution with
real-time classical lattice simulations. This method accounts for short-scale
fluctuations not included in the usual effective magneto-hydrodynamics (MHD)
treatment. We observe a self-similar decay of the chemical potential,
accompanied by an inverse cascade process in the gauge field that leads to a
production of long-range helical magnetic fields. We also study the chiral
charge dynamics in the presence of an external magnetic field , and extract
its decay rate . We provide in this way a
new determination of the gauge coupling and magnetic field dependence of the
chiral rate, which exhibits a best fit scaling as . We confirm numerically the fluctuation-dissipation relation
between and , the Chern-Simons diffusion rate,
which was obtained in a previous study. Remarkably, even though we are outside
the MHD range of validity, the dynamics observed are in qualitative agreement
with MHD predictions. The magnitude of the chiral/diffusion rate is however a
factor times larger than expected in MHD, signaling that we are in
reality exploring a different regime accounting for short scale fluctuations.
This discrepancy calls for a revision of the implications of fermion number and
chirality non-conservation in finite temperature Abelian gauge theories, though
not definite conclusion can be made at this point until hard-thermal-loops
(HTL) are included in the lattice simulations.Comment: 32 pages, 11 figures. V2: Improved introduction, added some
discussions and references. Corrected typos. Corresponds to published versio
Thermal Simulations, Open Boundary Conditions and Switches
gauge theories on compact spaces have a non-trivial vacuum structure
characterized by a countable set of topological sectors and their topological
charge. In lattice simulations, every topological sector needs to be explored a
number of times which reflects its weight in the path integral. Current lattice
simulations are impeded by the so-called freezing of the topological charge
problem. As the continuum is approached, energy barriers between topological
sectors become well defined and the simulations get trapped in a given sector.
A possible way out was introduced by L\"uscher and Schaefer using open boundary
condition in the time extent. However, this solution cannot be used for thermal
simulations, where the time direction is required to be periodic. In this
proceedings, we present results obtained using open boundary conditions in
space, at non-zero temperature. With these conditions, the topological charge
is not quantized and the topological barriers are lifted. A downside of this
method are the strong finite-size effects introduced by the boundary
conditions. We also present some exploratory results which show how these
conditions could be used on an algorithmic level to reshuffle the system and
generate periodic configurations with non-zero topological charge.Comment: 7 pages, 4 figures, 35th International Symposium on Lattice Field
Theor
Gibbs entropy from entanglement in electric quenches
In quantum electrodynamics with charged chiral fermions, a background
electric field is the source of the chiral anomaly which creates a chirally
imbalanced state of fermions. This chiral state is realized through the
production of entangled pairs of right-moving fermions and left-moving
antifermions (or vice versa, depending on the orientation of the electric
field). Here we show that the statistical Gibbs entropy associated with these
pairs is equal to the entropy of entanglement between the right-moving
particles and left-moving antiparticles. We then derive an asymptotic expansion
for the entanglement entropy in terms of the cumulants of the multiplicity
distribution of produced particles and explain how to re-sum this asymptotic
expansion. Finally, we study the time dependence of the entanglement entropy in
a specific time-dependent pulsed background electric field, the so-called
"Sauter pulse", and illustrate how our re-summation method works in this
specific case. We also find that short pulses (such as the ones created by high
energy collisions) result in an approximately thermal distribution for the
produced particles.Comment: 12 pages, 4 figure
Open-Boundary Conditions in the Deconfined Phase
In this work, we consider open-boundary conditions at high temperatures, as
they can potentially be of help to measure the topological susceptibility. In
particular, we measure the extent of the boundary effects at and
. In the first case, it is larger than at while we find it to
be smaller in the second case. The length of this "boundary zone" is controlled
by the screening masses. We use this fact to measure the scalar and
pseudo-scalar screening masses at these two temperatures. We observe a mass gap
at but not at . Finally, we use our pseudo-scalar channel
analysis to estimate the topological susceptibility. The results at
are in good agreement with the literature. At , they appear to suffer
from topological freezing, impeding us from providing a precise determination
of the topological susceptibility. It still provides us with a lower bound,
which is already in mild tension with some of the existing results.Comment: 12 pages, 16 figures. V2: Improved a lot the introduction and
discussion on topological susceptibility. Added a figure. Corresponds to
published versio
Higher-form symmetry and chiral transport in real-time lattice gauge theory
We study classical lattice simulations of theories of electrodynamics coupled
to charged matter at finite temperature, interpreting them using the
higher-form symmetry formulation of magnetohydrodynamics (MHD). We compute
transport coefficients using classical Kubo formulas on the lattice and show
that the properties of the simulated plasma are in complete agreement with the
predictions from effective field theories. In particular, the higher-form
formulation allows us to understand from hydrodynamic considerations the
relaxation rate of axial charge in the chiral plasma observed in previous
simulations. A key point is that the resistivity of the plasma -- defined in
terms of Kubo formulas for the electric field in the 1-form formulation of MHD
-- remains a well-defined and predictive quantity at strong electromagnetic
coupling. However, the Kubo formulas used to define the conventional
conductivity vanish at low frequencies due to electrodynamic fluctuations, and
thus the concept of the conductivity of a gauged electric current must be
interpreted with care.Comment: 24 pages with appendix, 9 figures. Comments are welcome
Entropy Suppression through Quantum Interference in Electric Pulses
The Schwinger process in strong electric fields creates particles and
antiparticles that are entangled. The entropy of entanglement between particles
and antiparticles has been found to be equal to the statistical Gibbs entropy
of the produced system. Here we study the effect of quantum interference in
sequences of electric pulses, and show that quantum interference suppresses the
entanglement entropy of the created quantum state. This is potentially relevant
to quantum-enhanced classical communications. Our results can be extended to a
wide variety of two-level quantum systems.Comment: 4 pages, 5 figures, supplementary material: 3 pages, 1 figur
Mass gaps of a gauge theory with three fermion flavors in 1 + 1 dimensions
We consider a gauge theory coupled to three degenerate massive
flavors of fermions, which we term "QZD". The spectrum can be computed in
dimensions using tensor networks. In weak coupling the spectrum is that of the
expected mesons and baryons, although the corrections in weak coupling are
nontrivial, analogous to those of non-relativistic QED in 1+1 dimensions. In
strong coupling, besides the usual baryon, the singlet meson is a baryon
anti-baryon state. For two special values of the coupling constant, the
lightest baryon is degenerate with the lightest octet meson, and the lightest
singlet meson, respectively.Comment: 17 pages and 10 figure
The art of simulating the early Universe -- Part I
We present a comprehensive discussion on lattice techniques for the
simulation of scalar and gauge field dynamics in an expanding universe. After
reviewing the continuum formulation of scalar and gauge field interactions in
Minkowski and FLRW backgrounds, we introduce basic tools for the discretization
of field theories, including lattice gauge invariant techniques. Following, we
discuss and classify numerical algorithms, ranging from methods of
accuracy like and integration, to
methods up to accuracy, and the and
higher-order integrators, accurate up to . We adapt these methods
for their use in classical lattice simulations of the non-linear dynamics of
scalar and gauge fields in an expanding grid in dimensions, including the
case of `self-consistent' expansion sourced by the volume average of the
fields' energy and pressure densities. We present lattice formulations of
canonical cases of: Interacting scalar fields, Abelian gauge
theories, and Non-Abelian gauge theories. In all three cases we
provide symplectic integrators, with accuracy ranging from up to
. For each algorithm we provide the form of relevant observables,
such as energy density components, field spectra and the Hubble constraint.
Remarkably, all our algorithms for gauge theories respect the Gauss constraint
to machine precision, including when `self-consistent' expansion is considered.
As a numerical example we analyze the post-inflationary dynamics of an
oscillating inflaton charged under . The present manuscript
is meant as part of the theoretical basis for , a modern C++
MPI-based package for simulating the non-linear dynamics of scalar-gauge field
theories in an expanding universe, publicly available at www.cosmolattice.netComment: Minor corrections to match published version, and one more algorithm
added. Still 79 pages, 8 figures, 1 appendix, and many algorithm
CosmoLattice
This is the user manual for CosmoLattice, a modern package for lattice
simulations of the dynamics of interacting scalar and gauge fields in an
expanding universe. CosmoLattice incorporates a series of features that makes
it very versatile and powerful: it is written in C++ fully exploiting the
object oriented programming paradigm, with a modular structure and a clear
separation between the physics and the technical details, it is MPI-based
and uses a discrete Fourier transform parallelized in multiple spatial
dimensions, which makes it specially appropriate for probing scenarios with
well-separated scales, running very high resolution simulations, or simply very
long ones, it introduces its own symbolic language, defining field
variables and operations over them, so that one can introduce differential
equations and operators in a manner as close as possible to the continuum,
it includes a library of numerical algorithms, ranging from to methods, suitable for simulating global and gauge
theories in an expanding grid, including the case of `self-consistent'
expansion sourced by the fields themselves. Relevant observables are provided
for each algorithm (e.g.~energy densities, field spectra, lattice snapshots)
and we note that remarkably all our algorithms for gauge theories always
respect the Gauss constraint to machine precision. In this manual we explain
how to obtain and run CosmoLattice in a computer (let it be your laptop,
desktop or a cluster). We introduce the general structure of the code and
describe in detail the basic files that any user needs to handle. We explain
how to implement any model characterized by a scalar potential and a set of
scalar fields, either singlets or interacting with and/or gauge
fields. CosmoLattice is publicly available at www.cosmolattice.net.Comment: 111 pages, 3 figures and O(100) code file
- …