The proposed research is aimed at studying the dynamics of strongly correlated low-dimensional quantum systems, mainly quantum field theories and spin chains.
Due to experimental advances, the dynamics of strongly correlated systems is at the forefront of interest in contemporary research. In low-dimensional systems, quantum fluctuations are enhanced, and strong correlations often occur. Despite these complications, a number of such systems are integrable, which allows derivation of many exact results, and also leads to very powerful non-perturbative techniques which can be used even when integrability is broken. Recently there has been a large progress in understanding equilibration and thermalisation in such systems, as well as the special equilibrium states (generalised Gibbs ensemble) that characterise the equilibrium state of integrable ones. However, much less is understood concerning the temporal unfolding of out-of-equilibrium dynamics, and the construction of correlation functions is also quite a challenge, both in and out of equilibrium.
Our specific aims include
- extend methods to simulate the time evolution to new systems (cf. e.g  and references therein);
- finding an efficient construction for correlation functions in and out of equilibrium and use them to study the physical properties of these systems ;
- understanding the effect of non-perturbative phenomena on dynamics such as confinement [3,4] and the presence of bound states , and the presence of long-lived metastable excitations;
- to understand the limits of the quasi-particle description, to extend it and/or develop alternative approaches.
We shall apply existing, and also develop new analytic and numerical methods to investigate these issues, and to obtain a full quantum description of the dynamics both in the continuum and on the lattice.
Besides solving theoretical problems, we also aim to obtain results that are directly relevant in the experimental context.
- D. X. Horváth, I. Lovas, M. Kormos, G. Takács and G. Zaránd: Non-equilibrium time evolution and rephasing in the quantum sine-Gordon model, Phys. Rev. A 100, 013613 (2019), arXiv:1809.06789 [cond-mat.quant-gas]
- I. Kukuljan, S. Sotiriadis and G. Takács: Correlation functions of the quantum sine-Gordon model in and out of equilibrium, Phys. Rev. Lett. 121, 110402 (2018), arXiv:1802.08696
- M. Kormos, M. Collura, G. Takács and P. Calabrese: Real time confinement following a quantum quench to a non-integrable model, Nature Physics 13, 246 (2017), arXiv:1604.03571
- M. Lencsés and G. Takács: Confinement in the q-state Potts model: an RG-TCSA study, JHEP 1509, 146 (2015), arXiv:1506.06477
- M. Collura, M. Kormos and G. Takács: Dynamical manifestation of Gibbs paradox after a quantum quench, Phys. Rev. A 98, 053610 (2018), arXiv:1801.05817
To be successful in this endeavour, a strong background in theoretical physics, especially quantum theory and statistical physics is required, including familiarity with fundamentals of quantum field theory. In addition, the candidate must have affinity for both analytic and numerical computations.