Maggie Lawrence

Quantum transport in disordered systems poses intriguing fundamental questions, such as the interplay of disorder, interactions, and decoherence, and has attracted significant interest. These fundamental aspects also have important implications in real-world scenarios, such as energy transfer in nanoscale systems (e.g., light-harvesting complexes) and quantum information transfer. This large body of work spanning broad research areas in physics, chemistry, and nanotechnology has led to major insights and advances, yet open questions remain, namely, in terms of the emergence of multiple timescales observed in the dynamics of such systems. Here, we investigate the emergence of multiple transport timescales in the dissipative dynamics of a spin impurity coupled to a small, spatially disordered network of spins. Using a two-dimensional tight-binding model with dipolar interactions and local dephasing, we demonstrate that geometric heterogeneity leads to hierarchical coupling strengths. This results in pronounced separation of dynamical timescales, far beyond those expected in homogeneous environments. By analyzing different metrics for dynamics, we identify distinct relaxation timescales associated with cluster-level equilibration and global equilibration. A minimal three-site model reveals the physical origin of the longest timescale: Strong internal hybridization generates an effective detuning that suppresses transfer to other weakly coupled sites, yielding a parametrically enhanced relaxation time in the weak dephasing regime. We corroborate this picture with nonequilibrium steady-state transport calculations and extensive simulations of disordered spin configurations, demonstrating orders-of-magnitude slowing of relaxation when hierarchical couplings are present. Our results highlight the central role of geometry and connectivity in spin networks and open quantum systems in general, and provide experimentally relevant predictions for relaxation times in small spin baths.

Carrier transport in quantum networks is governed by a variety of factors, including network dimensionality and connectivity, on-site energies, couplings between sites and whether they are short or long range, leakage processes, and environmental effects. In this work, we identify classes of quasi-one-dimensional chains with energy profiles that optimize carrier transport under such influences. Specifically, we optimize on-site energies using Optax’s optimistic gradient descent and AdaMax algorithms, enabled by the JAX automatic differentiation framework. Focusing on nonequilibrium steady-state transport, we study the system’s behavior under combined unitary and nonunitary (dephasing and dissipative) effects using the Lindblad quantum master equation. After validating our optimization scheme on short chains, we extend the study to larger systems where we identify systematic patterns in energy profiles. Our analysis reveals that different types of energy landscapes enhance transport, depending on whether intersite tunneling couplings in the chain are short or long range, the existence of environmental interactions, and the temperature of the environment. Our classification and insights of optimal energy landscapes offer guidance for designing efficient transport systems for electronic, photovoltaic, and quantum communication applications.

Laminar flow velocity profiles are directly related to the rheological properties of the flowing fluids. Magnetic resonance spin echo measurements at complete polarization, with a flow-oriented magnetic field gradient, can be utilized to determine the velocity profile of laminar flow in a circular pipe. However, fluids with a long spin-lattice relaxation time will not have time to completely polarize before signal acquisition in typical applications. This will restrict applications of the method, and modification of the original methodology is required to work with the general case of incomplete polarization. In this paper, magnetic resonance spin echo measurements at incomplete polarization with a flow-oriented magnetic field gradient are employed to determine the velocity profile of laminar flow in a circular pipe. The governing equations describing phase shifts and magnitude changes of odd echoes for laminar flows were derived, at incomplete polarization, based on the flow behavior index, an effective polarization length, spin-lattice relaxation time, and the average velocity. The objective function for least squares minimization was constructed, based on the first odd echo phase shifts and magnitude changes at different echo times, to solve for the flow behavior index and average velocity. The Nelder–Mead algorithm was employed to minimize the objective function. Discrete simulations for three kinds of laminar flows in a circular pipe, that is, shear-thickening flow, Poiseuille flow, and shear-shinning flow, were employed to validate the proposed method. Magnetic resonance experiments for Poiseuille flow were undertaken for further verification.

Laminar flow velocity profiles depend heavily on fluid rheology. Developing methods of laminar flow characterization, based on low-field magnetic resonance (MR), contribute to the widespread industrial application of the MR technique in rheology. In this paper, we outline the design of a low-cost, palm-sized permanent magnet with a ¹H resonance frequency of 20.48 MHz to measure the laminar flow. The magnet consists of two disk magnets, which were each tilted at an angle of 1° from an edge separation of 1.4 cm to generate a constant gradient, 65 G/cm, in the direction of flow. Subsequently, a series of process methods, for MR measurements, were proposed to characterize Newtonian and non-Newtonian fluid flows in a pipe, including phase-based method, magnitude-based method, and a velocity spectrum method. The accuracy of the proposed methods was validated by simulations, and experiments in Poiseuille flow and shear-thinning flow with the designed magnet. The new velocity profile methods proposed are advantageous because the MR hardware and measurement methods are simple and will result in a portable instrument. Although the governing equations are complicated, the data analysis is straightforward.