Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. 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 and pronounced separation of dynamical timescales. 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 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.Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. 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 and pronounced separation of dynamical timescales. 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 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.

quant-pharXiv:2605.08918May 12, 20260 citations

Quantum Transport in Presence of Disorder

Linda Sansoni

Springer thesesJan 1, 20140 citations

Emergent Decoherence Dynamics in Doubly Disordered Spin Networks

Cooper M. Selco, Christian Bengs, Chaitali Shah +2 more

Elucidating the emergence of irreversible macroscopic laws from reversible quantum many-body dynamics is a question of broad importance across all quantum science. Many-body decoherence plays a key role in this transition, yet connecting microscopic dynamics to emergent macroscopic behavior remains challenging. Here, in a doubly disordered electron-nuclear spin network, we uncover an emergent decoherence law for nuclear polarization, $e^{-\sqrt{R_{p}t}}e^{-R_{d}t}$ , that is robust across broad parameter regimes. We trace its microscopic origins to two interdependent decoherence channels: long-range interactions mediated by the electron network and spin transport within the nuclear network exhibiting anomalous, sub-diffusive dynamics. We demonstrate the capacity to control--and even eliminate--either channel individually through a combination of Floquet engineering and (optical) environment modulation. We find that disorder, typically viewed as detrimental, here proves protective, generating isolated electron-free clusters that localize polarization and prolong coherence lifetimes. These findings establish a microscopic framework for manipulating decoherence pathways and suggests engineered disorder as a new design principle for realizing long-lived quantum memories and sensors.Elucidating the emergence of irreversible macroscopic laws from reversible quantum many-body dynamics is a question of broad importance across all quantum science. Many-body decoherence plays a key role in this transition, yet connecting microscopic dynamics to emergent macroscopic behavior remains challenging. Here, in a doubly disordered electron-nuclear spin network, we uncover an emergent decoherence law for nuclear polarization, $e^{-\sqrt{R_{p}t}}e^{-R_{d}t}$, that is robust across broad parameter regimes. We trace its microscopic origins to two interdependent decoherence channels: long-range interactions mediated by the electron network and spin transport within the nuclear network exhibiting anomalous, sub-diffusive dynamics. We demonstrate the capacity to control--and even eliminate--either channel individually through a combination of Floquet engineering and (optical) environment modulation. We find that disorder, typically viewed as detrimental, here proves protective, generating isolated electron-free clusters that localize polarization and prolong coherence lifetimes. These findings establish a microscopic framework for manipulating decoherence pathways and suggests engineered disorder as a new design principle for realizing long-lived quantum memories and sensors.

quant-pharXiv:2511.07785Nov 12, 2025

Transport in strongly disordered classical spin chains

Vadim Oganesyan, Arijeet Pal, David A. Huse

Bulletin of the American Physical SocietyMar 10, 20080 citations

Transport in dimerized and frustrated spin systems

Fabian Heidrich‐Meisner, A. Honecker, D. C. Cabra +1 more

arXiv:cond-mat/0406362Journal of Magnetism and Magnetic MaterialsJan 16, 200413 citations

Disorder-Induced Anomalous Diffusion in a 3D Spin Network

Andrew Stasiuk, Garrett Heller, Lance Berkey +2 more

Emergent hydrodynamics (EHD) bridges short-time unitarity with late-time thermodynamics, universal transport phenomena characterize the manner and speed of transport and thermalization. Typical non-integrable systems with few conserved local quantities are expected to be diffusive. In contrast, strongly disordered systems which admit phases such as many-body localization, are predicted to inhibit thermalization and thus slow dynamical transport. Disordered systems represent a uniquely poised platform to probe the quantum-to-classical transition and the emergence of irreversible thermodynamics from the underlying unitary structure. Here, we study a strongly disordered nuclear spin ensemble, using local measurements enabled by the disordered-state technique. We observe an apparent phase transition into a sub-diffusive regime, which we model as a random walk on the emergent fractal structure of a percolating network in the dipolar spin ensemble. Our novel theoretical model provides a framework for characterizing the emergence of thermalization in closed quantum systems, even in the presence of strong disorder.Emergent hydrodynamics (EHD) bridges short-time unitarity with late-time thermodynamics, universal transport phenomena characterize the manner and speed of transport and thermalization. Typical non-integrable systems with few conserved local quantities are expected to be diffusive. In contrast, strongly disordered systems which admit phases such as many-body localization, are predicted to inhibit thermalization and thus slow dynamical transport. Disordered systems represent a uniquely poised platform to probe the quantum-to-classical transition and the emergence of irreversible thermodynamics from the underlying unitary structure. Here, we study a strongly disordered nuclear spin ensemble, using local measurements enabled by the disordered-state technique. We observe an apparent phase transition into a sub-diffusive regime, which we model as a random walk on the emergent fractal structure of a percolating network in the dipolar spin ensemble. Our novel theoretical model provides a framework for characterizing the emergence of thermalization in closed quantum systems, even in the presence of strong disorder.

arXiv:2510.09549Oct 10, 20250 citations

e^{-\sqrt{R_{p}t}}e^{-R_{d}t}

, that is robust across broad parameter regimes. We trace its microscopic origins to two interdependent decoherence channels: long-range interactions mediated by the electron network and spin transport within the nuclear network exhibiting anomalous, sub-diffusive dynamics. We demonstrate the capacity to control--and even eliminate--either channel individually through a combination of Floquet engineering and (optical) environment modulation. We find that disorder, typically viewed as detrimental, here proves protective, generating isolated electron-free clusters that localize polarization and prolong coherence lifetimes. These findings establish a microscopic framework for manipulating decoherence pathways and suggests engineered disorder as a new design principle for realizing long-lived quantum memories and sensors.