Description
Understanding and predicting the temporal evolution of quantum systems is essential for the development of theoretical physics and modern quantum technologies. A significant group of models that have been intensively researched in recent years are non-ergodic systems of interacting particles. They open the way to future technological solutions such as quantum memories. In the relaxation process, these systems do not strive for thermal states, which means that the initial quantum information encoded in the initial conditions is not lost. Attempts to understand the physical mechanisms responsible for the above-mentioned anomalous quantum dynamics constitute an important research goal in the theory of non-equilibrium processes. They are extensively studied in condensed matter and high energy physics. Such systems have an experimental implementation on the so-called cold atoms on optical lattices [1-2]. Their great advantage is that they can be easily applied to various geometries. For this purpose, a semiclassical description of time evolution within the Wigner-Weyl representation will be used [3]. In my poster, I will demonstrate that a single-trajectory version of the fermionic truncated Wigner approximation (fTWA) gives unexpectedly accurate results for the dynamics of one-dimensional (1D) systems with moderate or strong disorders. At the same time, the computational complexity of calculations carried out within this approximation is small enough to enable studies of two-dimensional (2D) systems larger than standard fTWA. Using this method, we discuss the dynamics of interacting spinless fermions propagating on disordered 1D and 2D lattices. We find for both spatial dimensions that the imbalance exhibits a universal dependence on the rescaled time, where the time-scale follows a stretched-exponential dependence on the disorder strength.
References
[1] J. Choi, S. Hild, J. Zeiher, P. Schauß, A. Rubio-Abadal, T. Yefsah, V. Khemani, D. A. Huse, I. Bloch, and C. Gross, Science, 352, 1547 (2016)
[2] P. Bordia, H. Luschen, S. Scherg, S. Gopalakrishnan nad M. Knap, U. Schneider, and I. Bloch, Physical Review X,7 (2017)
[3] A. Polkovnikov, Annals of Physics 325, 1790 (2010)
