Abstract We study the dynamics of a macroscopic object interacting with a dissipative stochastic environment using an adiabatic perturbation theory. The perturbation theory reproduces known expressions for the friction coefficient and, surprisingly, gives an additional negative mass correction. The effect of the negative mass correction is illustrated by studying a harmonic oscillator interacting with a dissipative stochastic environment. While it is well known that the friction coefficient causes a reduction of the oscillation frequency, we show that the negative mass correction can lead to its enhancement . By studying an exactly solvable model of a magnet coupled to a spin environment evolving under standard non-conserving dynamics we show that the effect is present even beyond the validity of the adiabatic perturbation theory.
We consider a finite two-dimensional Heisenberg triangular spin lattice coupled to a dissipative Markovian environment at finite temperature in the presence of an external uniform magnetic field. We show how inserting a magnetic impurity in the spin system can be used to effectively control the dynamics and asymptotic state of the system. A strong impurity, at a border or central site, was found to enhance its entanglement with the other spins and their thermal robustness to the dissipative environment reaching an asymptotic state that is independent of the system initial state. However, it reduces the entanglement among the other spins in the lattice and their thermal robustness and may diminish them depending on its strength and the environment temperature. Moreover, the effect of the impurity increases significantly as the degree of anisotropy of the spin system increases. Therefore, the entanglement distribution over the different sites of the lattice can be modulated by tuning the impurity strength, system anisotropy and environment temperature. The impurity can be used as a switch that turns the entanglement on among specific spins and off among others simultaneously.
In this thesis, we consider the forms of non-equilibrium phenomena that can arise in atoms or polar molecules trapped in a deep optical lattice and coupled by dipolar internal degrees of freedom. We specifically focus on only two internal states, which results in the systems studied behaving as spin
−1/2 models with long-range interactions. We first study a closed system with both static and resonant near-field dipole interactions under an external drive. By studying the uniform mean-field dynamics of the system, we find the dynamics are given by Rabi oscillations, with a bifurcation in the dynamics as a function of drive strength between small scale and large scale oscillations. Analysing the stability of these oscillations to small fluctuations reveals that interactions tend to cause the oscillations to decohere. However, we find parameter regimes where coherent oscillations can persist for high enough intensity drive. We then consider the effects of an environment on the non-equilibrium dynamics of the near-field dipole model. We find that within the mean-field approximation, an environment causes the system to relax to many novel steady state spin configurations, such as spin density waves, antiferromagnetism and long-time oscillations, as well as bistabilities between these phases. To assess the validity of the mean-field approximation, we compare our mean-field results to small quantum systems. We carry out a similar analysis on a system with far-field dipole interactions, where it is necessary to introduce nonlocal dissipation, which results in several decay modes into the environment. These decay modes lead to instabilities of many of the steady state phases that occurred in the near-field dipole system, leading to the emergence of more spin density wave and oscillatory phases. Finally, we examine the dynamics on the approach to steady state in a dissipative dipolar system by studying Rydberg atoms coupled to a photonic crystal waveguide, which mediates an effective dipole-dipole interaction between the atoms. We find that if two excitations exist in the system, then bound states can form, with nonlocal dissipation resulting in a momentum dependent decay rate of the bound states and also greater freedom in engineering the bound state energy dispersion.