The PhD project is centered around the non-equilibrium phenomena in one dimensional quantum systems (integrable quantum field theories, spin chains, Bose gases).
The significance of low dimensional quantum systems stems from various different aspects. On the one hand, the low dimensionality enhances quantum fluctuations, so these systems are often strongly correlated. On the other hand, distinguished members of this group of models are the so-called integrable systems which allow for the non-perturbative or exact description of strongly interacting quantum systems. Apart from their theoretical significance, these systems can be studied experimentally both in condensed matter systems (spin chains, carbon nanotubes etc.), and with trapped ultra-cold atoms. The latter technique makes it possible to tune the parameters of the system in a wide range even in a time-dependent manner, which opens the way to the experimental observation of the exotic non-equilibrium dynamics of low dimensional quantum systems.
Mostly due the cold atom experiments, the out of equilibrium dynamics of isolated quantum systems have been in the forefront of research in the past years. Do these systems reach an equilibrium after a sufficiently long time? If they do, does the stationary state correspond to thermal equilibrium? How do these systems reach their stationary state? What are the universal aspects of the non-equilibrium dynamics? These questions that touch upon the foundations of quantum mechanics and statistical physics can now be studied experimentally.
The integrable systems have a distinguished role in this context: thanks to their special dynamics they do not thermalize. It is a subject of intensive research to explore how the relaxation of these systems can be described and whether their stationary state can be captured with the toolkit of statistical physics, using only macroscopic observables. Since real life systems are never perfectly integrable, it is of paramount importance to understand the effects of integrability breaking perturbations.
One of the main goals of our research is to unveil the universal aspects of the dynamics of isolated quantum systems. In close connection with this, we aim at the non-perturbative description of the non-equilibrium ("post-quench") dynamics and the effects of integrability breaking perturbations. We use both numerical and analytic methods. One of the main numerical tool is the so-called truncated Hilbert space method and the related numerical renormalization group. Based on this, a semi-analytic renormalization procedure has been developed recently which we would like to extend to the description of out-of-equilibrium time evolution. The analytic methods are based on conformal field theory, Bethe Ansatz and form factor perturbation theory, among others.
The PhD student will join this line of work to investigate the emerging questions via analytic calculations and numerical simulations. The results are expected to contribute to the description of experimentally relevant strongly correlated systems and to the resolution of fundamental theoretical issues (thermalization, universality out of equilibrium, integrability breaking).
- M. Kormos, M. Collura, G. Takács, P. Calabrese: Real time confinement following a quantum quench to a non-integrable model, Nature Physics 13, 246 (2017), arXiv:1604.03571
- T. Rakovszky, M. Mestyán, M. Collura, M. Kormos, and G. Takács: Hamiltonian truncation approach to quenches in the Ising field theory, Nucl. Phys. B 911, 805 (2016), arXiv:1607.01068
- P. Moca, M. Kormos, and G. Zaránd: Semi-semiclassical theory of quantum quenches in one dimensional systems, preprint arXiv:1609.00974
Excellent grades in theoretical physics subjects.