We introduce a framework for engineering active quantum matter that involves mimicking the role of self-propulsion through an external trapping potential that is moving along imposed trajectories traced by classical active dynamics. This approach in the presence of dissipation not only recovers essential dynamical behavior of classical activity, including the ballistic to diffusive crossover of its mean-square displacement, but also reveals additional features of activity that are of quantum origin. These quantum-active features are revealed in nondissipative systems, and manifest as novel exponents of the mean-square displacement at short timescales.
We introduce a framework for engineering active quantum matter that involves mimicking the role of self-propulsion through an external trapping potential that is moving along imposed trajectories traced by classical active dynamics. This approach in the presence of dissipation not only recovers essential dynamical behavior of classical activity, including the ballistic to diffusive crossover of its mean-square displacement, but also reveals additional features of activity that are of quantum origin. These quantum-active features are revealed in nondissipative systems, and manifest as novel exponents of the mean-square displacement at short timescales.
We introduce and characterize different models for an active quantum particle where activity arises from engineered dissipation-- specifically, from a suitably coupled nonequilibrium environment. These include a model of a particle moving on a lattice with coherent and dissipative hopping, as well as quantum generalizations of well-studied models of active behavior, such as the active Ornstein-Uhlenbeck process, run-and-tumble dynamics, and the active Brownian particle. Despite the different microscopic mechanisms at play, we show that all these models display key features of active motion. Notably, we observe a crossover from diffusive to active-diffusive behavior at long times, leading to an effective Péclet number, as well as a strong sensitivity to boundary conditions which, in our open quantum system context, arises from the Liouville skin effect. We discuss the role of quantum fluctuations and experimental realizations with superconducting circuits or cold gases, closing with perspectives for many-body effects in quantum active matter.
Active matter is characterized by a constant influx and dissipation of energy that gives rise to directed motion. Dissipation requires interactions with an external environment, such that extending the paradigm of active matter to a quantum framework requires an appropriate description of this environment. In this work, we consider a driven quantum particle undergoing noise and dissipation, with external driving exhibiting characteristics of classical activity. We model the non-unitary dynamics with time-local master equations and analyze the particle motion at different time scales for different forms of the master equations, satisfying different criteria. We systematically compare predictions on the dynamics of particle trajectories and thereby we uncover how the particle motion evolves under the interplay of quantum effects, dissipation, and active-like dynamics. These results are essential for guiding possible experiments aimed at realizing quantum analogues of classical active systems.
Engineering dissipation has emerged as a powerful strategy for controlling quantum many-body dynamics, complementing purely coherent control for state preparation. However, finite-time driving across a quantum critical point generates nonadiabatic excitations and coherences, and existing dissipation-engineering approaches have largely characterized how a fixed environment modifies critical dynamics rather than actively steering a system toward a prescribed thermal trajectory. Here we develop a Markovian dissipative framework for finite-time thermal-state tracking based on engineered population currents with non-negative transition rates, and apply it to the transverse-field Ising model driven across its quantum critical point. Compared with unitary dynamics and a natural thermal bath, the engineered dynamics strongly suppresses thermal excitation deviations and provides additional control over coherence damping through a free common current Qk, while exhibiting a substantially steeper residual scaling, δnexth∼(v/vch)2, than the Kibble--Zurek behavior recovered for unitary evolution. These results point toward engineered dissipation as a route for controlling thermal-state preparation in driven quantum critical systems.
Abstract The main aim of the present paper is to define an active particle in a quantum framework as a minimal model of quantum active matter and investigate difference and commonalities of quantum and classical active matters. Although the research field of active matter has been expanding wider and wider, most research is conducted in classical systems. We here propose a truly deterministic quantum active-particle model with a non-unitary quantum walk as minimal models of quantum active matter. We aim to reproduce similar results obtained previously with classical active Brownian particle; that is, a Brownian particle, with a finite energy take-up, becomes active and climbs up a potential wall. We realize such a system with non-unitary quantum walks. We introduce new internal states, the ground state |G⟩ and the excited state |E⟩, and a new non-unitary operator N(g) for an asymmetric transition between |G⟩ and |E⟩. The non-Hermiticity parameter g promotes transition to the excited state and hence the particle takes up energy from the environment. With our quantum active particle, we successfully observe that the movement of the quantum walker becomes more active in a non-trivial way as we increase the non-Hermiticity parameter g, which is similar to the classical active Brownian particle. Meanwhile, we also observe three unique features of quantum walks, namely, ballistic propagation of peaks in one dimension, the walker staying on the constant energy plane in two dimensions, and oscillations originating from the resonant transition between the ground state |G⟩ and excited state |E⟩ both in one and two dimensions.
Quantum diffusion is a major topic in condensed-matter physics, and the Caldeira-Leggett model has been one of the most successful approaches to study this phenomenon. Here, we generalize this model by coupling the bath to the system through a Liouville fractional derivative. The Liouville fractional Langevin equation is then derived in the classical regime, without imposing a non-Ohmic macroscopic spectral function for the bath. By investigating the short- and long-time behavior of the mean squared displacement, we show that this model is able to describe a large variety of anomalous diffusion. Indeed, we find ballistic, sub-ballistic, and super-ballistic behavior for short times, whereas for long times, we find saturation and sub- and super-diffusion.
Active matter is driven out of equilibrium by a local influx of energy. While classical active matter has been extensively studied, the extension of active matter concepts to quantum systems has been explored far less. In this work we develop a quantum description based on the Wigner function for a quantum system influenced by a classical noise. For the model considered here, the hybrid dynamics reduces to an Ornstein--Uhlenbeck process, enabling us to compute the quantum mean-squared displacement (MSD) using established techniques from classical active matter. We analytically derive the time dependence of the MSD and clarify the conditions under which the characteristic scaling with time MSD t6 emerges, namely the regime of long persistence time and large active noise strength. We also show that, for certain parameter and initial conditions, the MSD can exhibit an even steeper scaling regime MSD t7. In addition, explicit expressions are derived that precisely predict the onset times of t6 and t7 scaling behaviors. Finally, we examine the robustness of these behaviors against quantum fluctuations of the initial state.