Amin Naseri
Title: Interacting Electrons in Quantum Dots with Strong Rashba Spin-Orbit Coupling

We study a two-dimensional interacting system of electrons which are harmonically trapped and endowed with strong Rashba spin-orbit coupling. The low energy physics is described by almost degenerate states of Landau like bands, where the kinetic energy is suppressed by strong spin-orbit coupling and hence the role of interactions is enhanced. We predict an orbital ferromagnetism in the few-electron dots. The state is akin to the persistent current in quantum rings though requires no external magnetic field.

Darian Mclaren
Title: Perfect Quantum State Transfer on Weighted Paths

A quantum spin chain is a proposed method for transferring a quantum state over small distances. Our main focus is on perfect state transfer (PST) in which one particle is encoded with the desired state and after the spin chain evolves over some time the same state emerges in a different particle. These systems can be modeled using graph theory and of particular interest to us is the case where the system is a weighted path with a potential. We explore PST on these weighted paths through the use of orthogonal polynomials associated to the corresponding tridiagonal matrix.

Raphael Hoult
Title: Time-Varying Boundary Conditions in AdS

In recent years, the stability of Anti-de Sitter space (AdS) against black hole collapse has become an issue of interest. In this talk, we will discuss the consequences of pumping energy into AdS using time-varying boundary conditions. While we will focus primarily on four-dimensional AdS, we will also briefly discuss ongoing research into the physically intriguing 5D AdS, and talk about why it is so interesting.

Andrew Frey
Title: Gravitational Collapse in AdS

Through the AdS/CFT correspondence, black hole formation in anti-de Sitter spacetime equals thermalization of energy in a strongly coupled field theory. This talk will introduce this study of black hole formation in AdS and when black holes may not form.

Angel Barria Comicheo
Title: Hahn Banach theorem on Banach spaces over non-Archimedean valued fields.

The Hahn Banach theorem is a fundamental tool in classical Functional Analysis. When we replace the base field by a non-Archimedean valued field, the theorem is not always true and its validity depends greatly in the kind of base field we choose. We will study the sufficient and necessary conditions for the validity of the Hahn Banach Theorem for Banach spaces over a non-Archimedean valued field.

LJ Zhou
Title: Model for Spherical Firewall Creation

Recently, Brown and Louko (JHEP 1508 (2015) 061) proposed a 1+1 dimensional mechanism for evolving boundary condition that mimic the creation of firewalls, which are thought by some to be needed to resolve the black hole information loss conundrum. We extend this calculation to the more physical case of 3+1 dimensions. In particular, we consider a spherically symmetric scalar field with specifically designed time dependent boundary conditions at the origin. These boundary conditions correspond to the creation at the origin of a point-like source that produces a null energy pulse. In contrast to what happens in 1+1, the 3+1 dimensional pulse of energy is singular enough to break correlations that happen near the horizon of an evaporating black hole and may provide a viable model for firewalls. The detector response is finite except in the instantaneous creation limit where the energy density blows up everywhere in the future of the creation event.

Christopher Phillips
Title: Analysis of Numerical Methods Used to Perform Calculations Within a Strongly Interacting System

In this presentation I will talk about strongly interacting field theories. I will briefly explain what they are and try to motivate why they are interesting. The main problem is to determine the bare coupling and bare mass necessary to correctly renormalize the theory. The numerical calculation involves Gauss Legendre integration, linear interpolation, and Pade approximants. We calculate the propagator and vertex function, which can then be used to calculate a physical quantity like the pressure. One can compare results at different orders of the approximation as a function of the strength of interactions. We work at 4 loop order, and show that at small coupling our results reduce to those obtained previously at lower orders.

Paul Mikula
Title: Gradient Flow in Holographic Superconductors

The AdS/CFT correspondence provides an equivalence between a gravity theory in some bulk anti-deSitter spacetime and a conformal field theory (CFT) in one fewer dimensions on the boundary. A superconductor that can be described by a gravity theory through this correspondence is refered to as a 'holographic superconductor'. Gradient flow equations will evolve any given initial field configuration towards one that is a solution to the equations of motion, this allows us to study stability of solutions as well as the behaviour of a system far from equilibrium. Through the AdS/CFT correspondence, the gradient flow in the gravity theory should have a corresponding flow in the CFT and vice-versa. We focus on the flow of the matter fields in a gravity theory containing a charged black hole and a charged scalar field, and study the effect of the flow on the boundary superconducting theory.

Brad Cownden
Title: Modelling the Collapse of Scalar Fields In Anti-de Sitter Space

For phases like quark-gluon plasmas, the strong-coupling nature of the system means that perturbative approximations are invalid, and therefore conventional solution methods break down. However, using a duality first established by string theory, we are able to relate strongly coupled quantum field theories to weakly coupled gravitational systems (in one higher dimension). The most common use of this hidden relationship is to map between special quantum field theories — known as Conformal Field Theories (CFTs) — and general relativity in anti-de Sitter (AdS) space. As a consequence of the AdS/CFT correspondence, the more strongly coupled a CFTs is, the more weakly curved (i.e., classically solvable) the gravitational dual is. Motivated by the AdS/CFT correspondence, we examine the conditions that lead to the formation of a black hole in 4D AdS as a dual to the thermalization of a 3D CFT under an initial energy perturbation. We numerically evolve the full Einstein equations in the presence of both massless and massive scalar fields for a variety of initial momentum profiles. The curvature of AdS is such that massless fields are able to travel to spatial infinity and back in finite time, and therefore these fields have multiple opportunities to collapse. Massive fields do not travel to infinity, but do undergo periodic motion that may lead to horizon formation at long times. In this talk, the landscape of collapse behaviour created by the interplay between the initial conditions and the geometry of the space will be explored. Using the highest resolution available, we are able to extend our numerical results into amplitude regimes that are described by a perturbative theory. For certain initial pro- les, the prediction of the perturbative theory — that AdS space is stable to black hole formation in this regime — is at odds with the numerical data. We will make preliminary comments on how this discrepancy may be resolved, and how the resolution could bring about significant improvements in modelling the formation of black holes from massless and massive scalar fields.

Jonathan Ziprick
Title: Discrete Gravity

We consider 3+1 dimensional gravity with field variables constrained to be piecewise flat. Dynamics takes the form of an evolving simplicial complex described by a countable number of variables. The theory is amenable to quantization by existing methods, and represents a possible road to the elusive goal of quantum gravity.

Lewis Chen
Title: Loschmidt echo in disordered quantum systems

We study the Loschmidt echo and extend the analysis to one dimensional, non-interacting, disordered quantum systems. For a non-interacting one-dimensional system with short-range hoppings, it is well-known that even an infinitesimal amount of disorder will lead to a localization of the single-particle wave functions. This phenomena is known as Anderson localization. We study whether the disorder-averaged Loschmidt echo show dynamical phase transitions in the presence of Anderson localization after a quench of disorder strength.

Phillip Jaeger
Title: Bulk-boundary correspondence in non-equilibrium dynamics of one-dimensional topological insulators

Dynamical phase transitions (DPT) are receiving a rising interest. They are known to behave analogously to equilibrium phase transitions (EPT) to a large extend. However, it is easy to see that DPT can occur in finite systems, while EPT are only possible in the thermodynamic limit. So far it is not clear how far the analogy of DPT and EPT goes. It was suggested, that there is a relation between topological phase transitions (TPT) and DPT. We show, that there is also an equivalent of bulk-boundary correspondence in dynamical phase transitions.

Andrew Urichuk
Title: Integrable Spin Chains and Generalized Hydrodynamics

Quantum integrable systems like the spin–1/2 XXZ chain with zero field are characterized by the methods used to solve them in addition to their infinite number of local and non–local charges. Simultaneous ballistic and diffusive transport emerges in these systems due to an overlap of the current and conserved charges, leading to part of the current that survives to long times. These overlaps are generally difficult to compute, however the recently developed framework of generalized hydrodynamics has been shown to accurately determine these properties. The generalized hydrodynamics framework can be used to study the cross-over region between integrable and non-integrable quantum system and provide further insight into quantum integrable systems.