The project is focused on the investigation of the dynamical properties of one dimensional quantum systems (spin chains and quantum field theories).

The significance of low dimensional quantum systems stems from various aspects. On the one hand low dimensionality enhances quantum fluctuations, so these systems are often strongly correlated. On the other hand, distinguished members of this class 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.

If the density of the (quasi-)particles present in the system is low (e.g. at low temperature or for small quantum quenches), the particles move classically between collisions and quantum mechanics enters only in their collisions. This is the basis of the so-called semiclassical approach [1] which has been used successfully to describe the dynamics of various systems in [2] and out of equilibrium [3,4].

The task is to improve the method through the more accurate quantum mechanical description of collisions and to apply it to different finite temperature and non-equilibrium systems. The work requires analytic calculations as well as numerical simulations. The project gives an opportunity to learn about spin chains and quantum field theories and to master several analytic and numerical techniques.

[1] S. Sachdev, A. P. Young, Low Temperature Relaxational Dynamics of the Ising Chain in a Transverse Field, Phys. Rev. Lett. 78, 2220 (1997), http://arxiv.org/abs/cond-mat/9609185

[2] S. Sachdev, K. Damle, Low Temperature Spin Diffusion in the One-Dimensional Quantum O3 Nonlinear σ Model, Phys. Rev. Lett. 78, 943 (1997), http://arxiv.org/abs/cond-mat/0507380

[3] M. Kormos, G. Zaránd, Quantum quenches in the sine--Gordon model: a semiclassical approach, Phys. Rev. E 93, 062101 (2016), http://arxiv.org/abs/1507.02708

[4] C. P. Moca, M. Kormos, G. Zaránd, Hybrid Semiclassical Theory of Quantum Quenches in One-Dimensional Systems, Phys. Rev. Lett. 119, 100603 (2017), http://arxiv.org/abs/1609.00974