Transport Properties of Discrete Time-dependent Quantum Dynamical Systems

Andrei Yu. Khrennikov, Yaroslav Volovich

Andrzej Grudka, Marcin Karczewski, Paweł Kurzyński +3 more

Abstract This paper investigates Rabi transport and finite-size effects in one-dimensional discrete-time topological quantum walks. We demonstrate the emergence of localized states at boundaries between topologically distinct phases and analyze how finite system sizes influence quantum walk dynamics. For finite lattices, we show that topology induces localized and bilocalized states, leading to Rabi-like transport as a result of degeneracy breaking due to finite-size effects. The study bridges the gap between topological protection and size-dependent dynamics, revealing transitions from ballistic motion to localized or oscillatory behavior based on the system’s topological properties. Analytical and numerical methods are employed to explore the spectra and dynamics of quantum walks, highlighting the robustness of Rabi transport against disorder. The findings provide insights into controlled quantum transport and potential applications in quantum information processing.

Yasuhiro Saiga, Yusuke S. Kato, Yoshio Kuramoto +3 more

Sayumi Takei, Akira Ishikawa, Kiyoshi Kobayashi

Alessandro Summer, Alexander Nico-Katz, Shane Dooley +1 more

Abstract In this work we investigate discrete-time transport in a generic U(1)-symmetric disordered model tuned across an array of different dynamical regimes. We develop an aggregate quantity, a circular statistical moment, which is a simple function of the magnetization profile and which elegantly captures transport properties of the system. From this quantity we extract transport exponents, revealing behaviors across the phase diagram consistent with localized, diffusive, and - most interestingly for a disordered system - superdiffusive regimes. Investigation of this superdiffusive regime reveals the existence of a prethermal ''swappy'' regime unique to discrete-time systems in which excitations propagate coherently; even in the presence of strong disorder.

Yutaka Shikano, Tatsuaki Wada, Junsei Horikawa

Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a quantum-mechanical cellular automaton, a discrete-time quantum walk is defined to include various quantum dynamical behavior. Here we generalize a discrete-time quantum walk on a line into the feed-forward quantum coin model, which depends on the coin state of the previous step. We show that our proposed model has an anomalous slow diffusion characterized by the porous-medium equation, while the conventional discrete-time quantum walk model shows ballistic transport.