Proposal of a quantum version of active particles via a nonunitary quantum walk

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 the differences and similarities of quantum and classical active matter. Although the field of active matter has been expanding, most research has been conducted on classical systems. Here, we propose a truly deterministic quantum active-particle model with a nonunitary quantum walk as the minimal model of quantum active matter. We aim to reproduce results obtained previously with classical active Brownian particles; that is, a Brownian particle, with finite energy take-up, becomes active and climbs up a potential wall. We realize such a system with nonunitary quantum walks. We introduce new internal states, the ground state and the excited state, and a new nonunitary operator $N(g)$ for an asymmetric transition between the two states. The non-Hermiticity parameter $g$ promotes the transition to the excited state; hence, the particle takes up energy from the environment. For our quantum active particle, we successfully observe that the movement of the quantum walker becomes more active in a nontrivial manner as we increase the non-Hermiticity parameter $g$, which is similar to the classical active Brownian particle. 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 and the excited state both in one and two dimensions.

28 pages, 17 figures

References in corpus (14)

• Novel type of phase transition in a system of self-driven particles
• Self-motile colloidal particles: from directed propulsion to random walk
• Motility-Induced Phase Separation
• Quantum trajectories and open many-body quantum systems
• Exploring Topological Phases With Quantum Walks
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• A self-propelled particle in an external potential: is there an effective temperature?
• Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
• Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
• Active Particle Diffusion in Convection Roll Arrays
• Delocalization of non-Hermitian Quantum Walk on Random Media in One Dimension
• Diffraction and interference with run-and-tumble particles
• Multi-Dimensional Quantum Walks: a Playground of Dirac and Schrödinger Particles
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk

Cited by in corpus (8)

• Engineering active motion in quantum matter
• Propelling Ferrimagnetic Domain Walls by Dynamical Frustration
• Active quantum flocks
• Measurement-Induced Phase Transitions in Informational Active Matter
• Heat-to-motion conversion for quantum active matter
• Motion from Measurement: The Role of Symmetry of Quantum Measurements
• Modeling dissipation in quantum active matter
• Dissipative Generation of Currents by Nonreciprocal Local and Global Environments