Active matter denotes a system of particles immersed in an external environment, from which the particles extract energy continuously in order to perform directed motion. Extending the paradigm of active matter to a quantum framework requires an appropriate description of the 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.
Active matter denotes a system of particles immersed in an external environment, from which the particles extract energy continuously in order to perform directed motion. Extending the paradigm of active matter to a quantum framework requires an appropriate description of the 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.
The dynamics of a mixed quantum-classical system, in which the classical subsystem interacts with a dissipative bath, is investigated. This description of the dynamics will be appropriate if the details of the bath dynamics are unimportant but its presence plays an important role in the dissipation of energy to the environment. In this dynamical description, which can be simulated employing an ensemble of stochastic surface-hopping trajectories, the strength of the dissipation is controlled by a friction coefficient. We show that if decoherence, whose effects are controlled by the bath friction, is sufficiently rapid, the equation of motion can be reduced to a master equation. Thus, decoherence and the validity of master equation models may be explored as a function of bath friction. We use this framework to study the mechanism of decoherence in a simple model nonadiabatic chemical reaction.
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.
The theory of open quantum systems represents one of the major developments of quantum mechanics over the last 50 years. Its central object of study is constituted by quantum systems that cannot be regarded as fully isolated, but instead interact with additional degrees of freedom, giving rise to irreversible phenomena such as dissipation and decoherence. The tools provided by this framework are nowadays of paramount importance across many active areas of research, including quantum computation, thermodynamics, metrology and biology. In this thesis, we investigate three main topics within the field. The first contribution concerns the microscopic derivation of the evolution equations, socalled quantum master equations, for open systems which are also subject to external driving fields. Standard techniques developed for time-independent Hamiltonians encounter several difficulties in the time-dependent case, largely restricting their applicability to specific instances, such as periodic or adiabatic drivings. In contrast, a core result of the derivation presented in the thesis is that, when the environment is sufficiently Markovian (essentially, memoryless), the non-adiabatic contributions to the driving field can be neglected in a controlled fashion, yielding an accurate master equation with time-dependent generator, capable of correctly reproducing the open dynamics even for strong drivings. This result is further supported by benchmarks against numerically exact simulations. The second contribution addresses the long-time behavior of general types of (Markovian) quantum master equations, including those of the form introduced above. While this problem has been extensively analyzed in the time-independent setting, virtually no results are known for time-dependent generators. In particular, we establish the foundations of a general theory of relaxation, that is, convergence towards an asymptotic trajectory in the long-time limit, independently of the initial state. The main results include a theorem guaranteeing sufficient conditions for relaxation and the derivation of a rate function governing the convergence to the asymptotic trajectory. The analysis is further extended to a simple non-Markovian case. Moreover, we treat in detail the specific master equation derived in the first part, connecting the aforementioned relaxation property directly to the underlying microscopic dynamics. The third contribution investigates chirality-induced spin selectivity (CISS) effects from the perspective of open quantum systems. Although the majority of theoretical studies aiming to model CISS are based on a coherent description of the spin dynamics, such effects have been observed also for electrons subject to incoherent transport across molecular networks. In this regard, we provide a rigorous ab initio derivation of the microscopic Hamiltonian describing the electronic transport, incorporating electron spin effects and contributions stemming from the nuclear vibrations. Within this result, we critically revise a master equation approach aiming to explain the origin of CISS effects observed in photosynthetic complexes. Taken together, these contributions offer fresh insights and original results on the interplay between driving fields and dissipation, relaxation phenomena, and electronic spin transport in the presence of incoherent dynamics. More broadly, these results provide new theoretical tools with several potential applications in quantum technologies, from modeling of control pulses in noisy environments to quantum reservoir engineering, and contribute to a deeper understanding of the role of quantum effects in biological 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.
An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature. In contrast to previous claims, we found that all initial states of two-level atoms undergo finite-time disentanglement. We were also able to access regimes which cannot be described by Lindblad equations and other simpler methods, such as near resonance. Finally we revisit the infamous Abraham-Lorentz force, wherein a single particle in motion experiences backreaction from the electromagnetic field. This leads to a number of well-known problems including pre-acceleration and runaway solutions. We found a more a more-suitable open-system treatment of the nonrelativistic particle to be perfectly causal and dissipative without any extraneous requirements for finite size of the particle, weak coupling to the field, etc..
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.