WITP Summer Student Symposium 2016
25 Aug 2016, Room 3M69, Manitoba Hall, University of Winnipeg
Abstracts
Philipp Jaeger
Measuring Topological Invariants: Lohschmidt echo in the SSH-Model
Topological systems have been of rising interest in the last few
years. Although the theoretical understanding of these systems
suggests a wide range of applications, experimental methods do not
provide easy access to the topological invariants which determine the
behaviour of a system at given conditions.
The Lohschmidt echo (LE) measures the overlap between a given ground
state and the time evolved state after a quench. We show a connection
between the LE and topological phase transitions (TPT), and how
information about the topological phases can be extracted from the LE.
As a sample system, we use the Su-Schrieffer-Heeger model, which
describes a one-dimensional fermionic quantum chain with modulated
hopping amplitudes. This system is exactly solvable and thus provides
a very simple way to verify our numerical algorithms. We expect that
these algorithms can be applied to more complex systems, where no
explicit solutions are known. Thus, we are able to elucidate TPT
in various classes of topological systems.
Ben Guest
Peering deeper into the plerionic supernova remnant G21.5-0.9
The supernova remnant G21.5-0.9 has been observed regularly with the
Chandra X-ray observatory since its launch in 1999. The remnant hosts
a bright pulsar wind nebula (PWN), powered by a 61.8 ms pulsar (PSR
J1833-1034), and a faint limb-brightened shell revealed in X-rays with
Chandra. The nature of the X-ray emission from the shell (thermal
versus non-thermal) and knots within the nebula (ejecta?) remain a
puzzle. We present a follow-up X-ray analysis of G21.5-0.9 utilizing
the deepest (> 1 Msec total) exposure to date, including ~780 ks with
the Advanced CCD Imaging Spectrometer (ACIS) and ~310 ks with the High
Resolution Camera (HRC). These observations spanning ~15 years allow
for the study of variability and tracking the motion of small-scale
structures within the PWN.
L.J. Zhou
Model for Spherical Firewall Creation
We discuss the possibility to create a wall that cuts off
correlation/entanglement between two regions of spacetime. This
creation of a wall mimics the firewall proposal in AMPS, which
is dedicated to the ultimate purpose of understanding blackhole
radiation and the information loss conundrum. We start with spherical
wall creation with fixed flat spacetime background, then further into
the corresponding case in CGHS model. Our results to day support the
idea of a firewall formation at blackhole event horizon but more.
Paul Mikula
Gradient flow in the Ginzburg‑Landau model for superconductivity
The Ginzburg‑Landau model for superconductivity provides a
phenomenological description of superconductors near the critical
temperature where a phase transition between superconducting and
regular states occurs. The model has a single dimensionless free
parameter κ that has a critical value separating type I and
type II superconductors. Of particular interest are the vortex
solutions (which are known to occur in type II superconductors) where
we have some quantized magnetic flux through the material. We study
the dynamics of the vortices using the gradient flow of the free
energy. The gradient flow gives a system of coupled partial
differential equations whose stationary points are given by the
solutions to the Ginzburg‑Landau equations. Far from equilibrium, the
flow equations provide a description of the dynamics of a
configuration with multiple vortices that evolves as quickly as
possible to minimize the energy. Close to equilibrium the flow
equations tell us about the stability of the vortices. We solve the
equations numerically to study the interactions between vortices as
well as the decay of larger vortices into multiple smaller ones. We
find two different timescales, a short timescale where vortices
form, and a longer timescale where the vortices interact with
eachother.
Donovan Allum
Modeling the Formation of Non-Singular Black Holes in Spherical Symmetry
This work is based on theories developed by Dr. Gabor Kunstatter,
using code developed by Tim Taves. This model aims to show the
formation of Non-Singular black holes under the assumption of
spherical symmetry. The Schwarzschild metric, which governs the
curvature of spacetime, is one of the most famous results derived from
Einstein's Theory of General Relativity. While this metric is smooth
for any non-zero radius, it predicts a singularity - which would
represent an infinite mass/energy density build up - at the origin.
The main goal of this research is to test the different versions of
this metric - in Matlab - that comes with the new theory. With the
aide of my supervisor, Dr. Gabor Kunstatter, I have worked with two
types of code. One that allows for hawking radiation and one that
assumes for there to be no radiation.
Darren Flynn
Non-Archimedean Fields: A laboratory for the infinite and the
infinitesimal
The concepts of infinity and infinitesimal have puzzled humanity for
millennia; from Zeno’s paradox through Cantor’s diagonalization
argument to modern string theory it is safe to say that the infinite
and infinitesimal have been a source of astounding insight and even
more astounding problems. With this presentation I hope to convince
the audience that non-Archimedean fields in general and the
Levi-Civita field in particular are an excellent laboratory in which
to study those elusive concepts.
Will Grafton
On the Convergence and Analytical Properties of Power Series on
non-Archimedean Field Extensions of the Real Numbers
In this
talk the analytic properties of power series over a class of
non-Archimedean field extensions of the real numbers, a representative
of which will be denoted by F, are investigated.
We first review some properties of well-ordered subsets of the
rational numbers which are used in the construction of such a field.
Then, we define operations + and * which make F a field. Then we
define an order under which F is non-Archimedean with infinitely small
and infinitely large elements. We embed the real numbers as a
subfield; and the embedding is compatible with the order. Then we
define an ultrametric on F which induces the same topology as the
order. This topology will allow us to define continuity and
differentiability in the usual which we shall show are insufficient
conditions to ensure intermediate values, extreme values, et cetera.
We shall study convergence of sequences and series and then study the
analytical properties of power series, showing they have the same
smoothness properties as real power series; in particular they satisfy
the intermediate value theorem, the extreme value theorem and the mean
value theorem on any closed interval within their domain of
convergence.
Brett Meggison
Renormalization of scalar nPI effective theories in 4 dimensions
The goal of our work is to develop methods for calculating the
probability of scattering events occurring in situations where
perturbative methods are insufficient. The presentation will outline
phi-4 theory and the motivations for using it. Previous work showed that
4 loop contributions to the 2PI skeleton expansion are important at large
coupling [1]. The next step is to look at 4 loop contributions to the 4PI
theory. In order to do this effectively and accurately in fortran, a few
different numerical techniques have been explored. This includes
switching to a spherical coordinate system, employing a logarithmic
scale as apposed to a linear one for the lattice spacing in our
calculation, fast fourier transforms, and interpolation methods.
[1] arXiv:1603.02085v1
Brad Cownden
Modelling gravitational collapse in Anti-de Sitter space
Physicists currently require large experiments (e.g. CERN's LHC) to
probe the physics of high-energy, strongly coupled systems such as
quark-gluon plasmas. This is because the theories that describe the
strong force -- which dominates the physics inside an atom's nucleus
-- are not valid at all energies. Previous inquiries into physics at
this scale were only possible through approximate methods such as
lattice gauge theory. However, the advent of the gauge/gravity
correspondence has allowed for the study of strongly-coupled quantum
field theories (like that describing the strong force) via
weakly-coupled gravitational theories. A particular example of this
duality is the relation of a conformal field theory (CFT) to
Einstein's gravity in Anti-de Sitter (AdS) space. In this talk we
outline the AdS/CFT correspondence and use it to study the
thermalization of a strongly-coupled gauge theory by modelling the
formation of black holes in AdS. To do so, we numerically evolve
Einstein’s equations in the presence of a scalar field and determine
when -- or if -- a black hole is formed. We further examine the
effects of a wide range of initial data and uncover a rich landscape
of solutions that demonstrate stable, unstable, and quasi-stable
behaviours.
Raphael Hoult
Black hole formation in AdS4 with varying boundary conditions
Continuing the discussion of Black Hole formation in AdS: in this talk
we discuss an alternate method for injecting energy into Anti-de
Sitter space, by varying the boundary conditions according to a time
dependence. We investigate the consequences of doing so, and what
effect varying frequencies and amplitudes will have. Two conditions
are looked at, one in which energy is pumped in ad infinitum, and one
in which the boundary conditions return to zero after a set period of
time.