Modeling dissipation in quantum active matter

TL;DR

The paper addresses how dissipation models influence quantum active matter driven by colored noise, examining a 1D quantum harmonic oscillator whose trap center $x_c(t)$ follows Ornstein–Uhlenbeck dynamics. It compares three time-local dissipators—static Lindblad, translated Lindblad, and Agarwal—by analyzing mean-squared displacement and Wigner-function dynamics, with the quantum state averaged over classical trajectories of $x_c(t)$. The key finding is that static Lindblad can fail to reproduce active motion at strong dissipation, while both translated Lindblad and Agarwal dissipators reproduce active-like dynamics (translated Lindblad matching the classical MSD transition from $t^6$ to $t^4$, and Agarwal yielding correct thermodynamics and classical limit). These results provide guidance for designing quantum-active experiments (e.g., moving optical traps in cold-atom setups) and clarify how different dissipative frameworks affect the quantum-to-classical transition in active systems.

Abstract

Active matter denotes a system of particles immersed in an external environment, from which the particles extract energy continuously in order to perform motion. Extending the paradigm of active matter to a quantum framework requires an open quantum system description. In this work, we consider a driven quantum particle whose external driving exhibits characteristics of classical activity. We model the dynamics with time-local master equations and analyze the particle motion at different time scales for different forms of the master equations. By systematically comparing several types of master equations, we uncover how the particle motion evolves under the interplay of quantum effects and active-like dynamics. These results are essential for guiding possible experiments aimed at realizing quantum analogues of classical active systems.

Figures (6)

• Figure 1: Schematic representation of a possible experiment -- an external parabolic potential (yellow) captures a quantum particle (blue wave function). The potential moves along a trajectory $x_c(t)$ corresponding to colored noise. Since the quantum particle is constantly driven away from the instantaneous trap center, the system never truly reaches equilibrium, and the quantum particle thereby mimics the properties of active motion.
• Figure 2: MSD of quantum-active particle with static Lindblad dissipator Eq. \ref{['eq:Lindblad-static']} for weak, intermediate and strong dissipation respectively. The parameters of $x_c$ are $D = 0.01, \tau = 10$, and the corresponding classical $\mathop{\mathrm{MSD}}\limits = \overline{x_c^2(t)}$ of these trajectories is shown as a black line. The dissipation strength $\gamma = 2(\nu_--\nu_+)$\ref{['eq:diss']} is set by $\nu_+ = 10^{-8}$ and $\nu_- = 10^{-2}$ (weak), $\nu_- = 10^0$ (intermediate), $\nu_-=10^1$ (strong).
• Figure 3: Steady-state Wigner function $W(x,p)$ for static Lindblad dissipator \ref{['eq:steady-L']}. The position of the trapping potential is fixed at $x_c = 3$ for (a) weak dissipation and (b) strong dissipation. The amplitude of the Wigner function values is given by the corresponding color representation; the graphs on the left and right correspond to the peak of the Wigner function at the extremum in $x$ and $p$, respectively. The green dashed lines indicate the position ($x=x_c$) of the fixed ($p=0$) harmonic potential. The dissipation strength $\gamma = 2(\nu_--\nu_+)$\ref{['eq:diss']} is set by $\nu_+ = 10^{-8}$ and $\nu_- = 10^{-2}$ (weak), $\nu_-=10^1$ (strong).
• Figure 4: MSD of quantum-active particle for translated Lindbald dissipator \ref{['eq:Lindblad-dynamic']} for weak, intermediate and strong dissipation respectively. The parameters of $x_c$ are $D = 0.01, \tau = 10$, and the corresponding classical $\mathop{\mathrm{MSD}}\limits = \overline{x_c^2(t)}$ of these trajectories is shown as a black line. The dissipation strength $\gamma = 2(\nu_--\nu_+)$\ref{['eq:diss']} is set by $\nu_+ = 10^{-8}$ and $\nu_- = 10^{-2}$ (weak), $\nu_- = 10^0$ (intermediate), $\nu_-=10^1$ (strong).
• Figure 5: Steady-state Wigner function $W(x,p)$ for dynamic Lindblad master equation \ref{['eq:steady']}. The position of the trapping potential is fixed at $x_c = 3$ for (a) weak dissipation, $\nu_+ = 10^{-8}, \nu_- = 10^{-2}$; and (b) strong dissipation $\nu_+ = 10^{-8}, \nu_- = 10^{1}$. The amplitude of the Wigner function values is given by the corresponding color representation; the graphs on the left and right correspond to the peak of the Wigner function at the extremum in $x$ and $p$, respectively. The green dashed lines indicate the position ($x=x_c$) of the fixed ($p=0$) harmonic potential. The dissipation strength $\gamma = 2(\nu_--\nu_+)$\ref{['eq:diss']} is set by $\nu_+ = 10^{-8}$ and $\nu_- = 10^{-2}$ (weak), $\nu_-=10^1$ (strong).