We investigate the dissipative adaptation hypothesis in a quantum regime using a system-reservoir approach. This hypothesis proposes that self-organization arises from a system's ability to dissipate the work transiently absorbed from an external drive. We analyze the quantum dynamics of a driven open system described by a time-dependent spin-boson Hamiltonian modeling a particle in a metastable double-well potential with controllable asymmetry. We explore how the work provided by the dynamic potential is related to the transition probability between the two ground states of the double well. These studies motivate further investigations of the driven spin-boson model toward an understanding of the system's evolution and its thermodynamic implications.
We investigate the dissipative adaptation hypothesis in a quantum regime using a system-reservoir approach. This hypothesis proposes that self-organization arises from a system's ability to dissipate the work transiently absorbed from an external drive. We analyze the quantum dynamics of a driven open system described by a time-dependent spin-boson Hamiltonian modeling a particle in a metastable double-well potential with controllable asymmetry. We explore how the work provided by the dynamic potential is related to the transition probability between the two ground states of the double well. These studies motivate further investigations of the driven spin-boson model toward an understanding of the system's evolution and its thermodynamic implications.
The study of dissipative systems holds significant interest in physics.This thesis aims to explore these phenomena in both classical and quantum regimes.In the first part, we utilize the system-reservoir approach to investigate the dynamics of two Brownian particles immersed in the same bath.Two methods are employed to address this problem: one with bilinear coupling and the other with nonlinear coupling between the particles and the bath.The extension of the system to include two particles with bilinear coupling yields unphysical results, such as free-particle motion for the relative coordinate and a lack of interaction between closely spaced particles.To address this issue, authors have been introduced an exponential coupling.In this work, we propose a method to reconcile both linear and nonlinear couplings.We demonstrate how to derive the same nonlinear dissipation rates starting from the bilinear Lagrangian, achieved through a modified spectral function that explicitly depends on the distance between the particles.Additionally, we implement a modified spectral function to mitigate anomalous diffusion observed in the standard nonlinear model, along with a phenomenological model describing hydrodynamic interaction between a pair of Brownian particles in a viscous fluid.In the quantum regime, we adopt the same system-reservoir approach to investigate the dissipative adaptation hypothesis proposed by Jeremy England.This hypothesis proposes a general thermodynamic mechanism that explains the self-organization of systems through the dissipation of work absorbed from an external drive.In the second part of this thesis, we explore the quantum dynamics of systems subjected to an external drive, evaluating the thermodynamic quantities of a self-organization process.To do so, we utilize a time-dependent spin-boson Hamiltonian that characterizes a particle subject to a metastable double potential with time-dependent parameters controlling the asymmetry of the wells.Our objective is to demonstrate that the asymmetric potential can localize the particle in the unstable side of the well and verify that this transition results in the highest energy absorption.In conclusion, we propose further investigations into the driven spin-boson model to establish a comprehensive theory of the system's evolution and its thermodynamic implications.
The study of dissipative systems holds significant interest in physics. This thesis aims to explore these phenomena in both classical and quantum regimes. In the first part, we utilize the system-reservoir approach to investigate the dynamics of two Brownian particles immersed in the same bath. Two methods are employed to address this problem: one with bilinear coupling and the other with nonlinear coupling between the particles and the bath. The extension of the system to include two particles with bilinear coupling yields unphysical results, such as free-particle motion for the relative coordinate and a lack of interaction between closely spaced particles. To address this issue, authors have been introduced an exponential coupling. In this work, we propose a method to reconcile both linear and nonlinear couplings. We demonstrate how to derive the same nonlinear dissipation rates starting from the bilinear Lagrangian, achieved through a modified spectral function that explicitly depends on the distance between the particles. Additionally, we implement a modified spectral function to mitigate anomalous diffusion observed in the standard nonlinear model, along with a phenomenological model describing hydrodynamic interaction between a pair of Brownian particles in a viscous fluid. In the quantum regime, we adopt the same system-reservoir approach to investigate the dissipative adaptation hypothesis proposed by Jeremy England. This hypothesis proposes a general thermodynamic mechanism that explains the self-organization of systems through the dissipation of work absorbed from an external drive. In the second part of this thesis, we explore the quantum dynamics of systems subjected to an external drive, evaluating the thermodynamic quantities of a self-organization process. To do so, we utilize a time-dependent spin-boson Hamiltonian that characterizes a particle subject to a metastable double potential with time-dependent parameters controlling the asymmetry of the wells. Our objective is to demonstrate that the asymmetric potential can localize the particle in the unstable side of the well and verify that this transition results in the highest energy absorption. In conclusion, we propose further investigations into the driven spin-boson model to establish a comprehensive theory of the systems evolution and its thermodynamic implications.
Metastability in many-body quantum systems and its associated exponentially-long timescales have been the subject of considerable recent interest. Here, we focus on a class of driven-dissipative many-body open quantum systems described by a Lindbladian having hidden time-reversal symmetry (a form of quantum detailed balance). Examples include boundary-driven interacting spin chains, bosonic lattice models and driven-dissipative collective spin models. We suggest that for such systems, slow timescales in the vicinity of a dissipative first-order phase transition can be analytically predicted using a special purification of the non-equilibrium steady state. We show the accuracy of our conjecture through detailed studies of a dissipative transverse-field Ising model with collective and local decay, and a driven-dissipative nonlinear cavity model. Our results allow quantitative insights into metastability and slow dynamics for a range of systems, including cases where semiclassical or path-integral instanton approaches are intractable.
Abstract Dissipative adaptation is a general thermodynamic mechanism that explains self-organization in a broad class of driven classical many-body systems. It establishes how the most likely (adapted) states of a system subjected to a given drive tend to be those following trajectories of highest work absorption, followed by dissipated heat to the reservoir. Here, we extend the dissipative adaptation phenomenon to the quantum realm. We employ a fully-quantized exactly solvable model, where the source of work on a three-level system is a single-photon pulse added to a zero-temperature infinite environment, a scenario that cannot be treated by the classical framework. We find a set of equalities relating adaptation likelihood, absorbed work, heat dissipation and variation of the informational entropy of the environment. Our proof of principle provides the starting point towards a quantum thermodynamics of driven self-organization.
In this work, I study the dynamics of spin-1/2 systems in contact with dissipative bosonic reservoirs. Investigations are motivated by recent progress in designing and controling atomic and solid state structures of growing complexity. The interplay between the bare system and the environment is of substantial importance for understanding the dynamics of such devices. Spin systems that are embedded in bosonic reservoirs are described by the famous spin-boson model and have been studied for several decades. Recent work has shown that two-level systems in contact with sub-Ohmic reservoirs are of fundamental interest in view of both theoretical considerations and their experimental relevance. This is why I focus on the dynamics of systems that couple to a sub-Ohmic environment. Additionally, impressive experimental progress in embedding quantum dots into photonic crystals encouraged me to investigate the dynamics of two-level systems coupled to surroundings with spectral gaps.
Classical dissipative adaptation is a hypothetical non-equilibrium thermodynamic principle of self-organization in driven matter, and it relates transition probabilities with the non-equilibrium work performed by an external drive on dissipative matter. Recently, the dissipative adaptation hypothesis was extended to a quantum regime with a theoretical model where only one single-photon pulse drives each atom of an ensemble. Here, we further generalize that quantum model by analytically showing that N cascaded single-photon pulses driving each atom still fulfill a quantum dissipative adaptation. Interestingly, we find that the level of self-organization achieved with two pulses can be matched with a single effective pulse only up to a threshold, above which the presence of more photons provides unparalleled degrees of self-organization.