Research
Uncovering the mechanisms of equilibration and transport in quantum systems
Do quantum systems tend to equilibrium when starting from an arbitrary initial state? Is the equilibrium state always of thermal type? How does energy and particles flow in an inhomogeneous quantum system? My goal is to address these questions explaining how the macroscopic behaviour of out-of-equilibrium quantum systems emerges from the fundamental laws of quantum physics. I use a combination of exact mathematical methods, physical arguments and numerical simulation methods.
Violation of horizon by topological excitations
One of the fundamental principles of relativity is that a physical observable at any space-time point is determined only by events within its past light-cone. In non-equilibrium quantum field theory this is manifested in the way correlations spread through space-time: starting from an initial state that has short range correlations, measurements of two observers at distant points are expected to remain independent until their past light-cones overlap. This is called the "horizon effect". Surprisingly we find that when topological excitations are present, correlations can develop outside of the horizon, even between infinitely distant points. We demonstrate this effect in the quantum sine-Gordon model, showing that it can be attributed to the non-local nature of soliton and breather excitations.
Non-Gaussianity of quantum states in interacting systems
Complete information on the equilibrium behaviour and dynamics of a quantum field theory is given by multipoint correlation functions. However, their theoretical calculation is a challenging problem, even for exactly solvable models. Using the so-called Truncated Conformal Space Approach, we numerically compute correlation functions of the quantum sine-Gordon model, a prototype integrable model of central interest from both theoretical and experimental point of view. We measure deviations from Gaussianity due to interaction, as expressed by the kurtosis of thermal states, and analyse their dependence on temperature, explaining recent experimental observations.
Quantum gas expansion in one dimension
The expansion of an ultra-cold atomic gas from a confining trap is a common experiment for the study of quantum dynamics. We analytically derive the non-equilibrium dynamics of a hard-core boson gas released from a parabolic trap to a circle, showing that at large times it equilibrates locally to a generalized Gibbs ensemble, a non-thermal statistical ensemble characterised by an extensive number of conserved quantities.
Quantum transport through a defect
The presence of a defect obstructs the energy and particle flow through a system with an initial imbalance between left and right. We study quantum transport after an inhomogeneous quantum quench in a free fermion lattice system in the presence of a localised defect. Using a novel exact analytical approach we derive the asymptotic profiles of particle density and current at large times and distances, verifying the predictions of a semiclassical approach.
Determining initial states after a quantum quench
A standard way of bringing a quantum system away from equilibrium is by abruptly changing a dynamical parameter, i.e. by performing what is known as a "quantum quench". Such processes induce complex and highly-energetic excitations into the system. We develop a diagrammatic method for determining the excitation content of quench initial states in integrable quantum field theories from first principles. Our method is essentially based on the form-factor bootstrap, a set of rules dictated by fundamental requirements and consistency criteria applicable to relativistically invariant integrable models.
Selected conference talks
"Quantum Simulation - from Theory to Application" thematic programme
Erwin Schrödinger International Institute for Mathematics and Physics (ESI), Vienna (17/09/2019)
"Emergent Hydrodynamics In Low Dimensional Quantum Systems" workshop
International Institute of Physics (IIP), Natal, Brazil (13/05/2019)
"Mathematical Aspects of Quantum Integrable Models in and out of Equilibrium" workshop
Isaac Newton Institute, Cambridge (02/02/2016)