Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics

Abstract

Motivated by the search for a quantum analogue of the macroscopic fluctuation theory, we study quantum spin chains dissipatively coupled to quantum noise. The dynamical processes are encoded in quantum stochastic differential equations. They induce dissipative friction on the spin chain currents. We show that, as the friction becomes stronger, the noise induced dissipative effects localize the spin chain states on a slow mode manifold, and we determine the effective stochastic quantum dynamics of these slow modes. We illustrate this approach by studying the quantum stochastic Heisenberg spin chain.

Revised version. Main text: 19 pages, Appendices+References: 10 pages

References in corpus (5)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Progressive field-state collapse and quantum non-demolition photon counting
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Fluctuating hydrodynamics, current fluctuations and hyperuniformity in boundary-driven open quantum chains
• Diffusion and signatures of localization in stochastic conformal field theory

Cited by in corpus (53)

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• Diffusion in generalized hydrodynamics and quasiparticle scattering
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• Open Quantum Symmetric Simple Exclusion Process
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• Generalised hydrodynamics with dephasing noise
• Monitored Open Fermion Dynamics: Exploring the Interplay of Measurement, Decoherence, and Free Hamiltonian Evolution
• The Page Curve for Fermionic Gaussian States
• Integrability of $1D$ Lindbladians from operator-space fragmentation
• Enhanced entanglement negativity in boundary driven monitored fermionic chains
• Yang-Baxter integrable Lindblad equations
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• Equilibrium Fluctuations in Maximally Noisy Extended Quantum Systems
• Symmetry-resolved Page curves
• Noisy Coupled Qubits: Operator Spreading and the Fredrickson-Andersen Model
• Noisy Spins and the Richardson-Gaudin Model
• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Exact description of quantum stochastic models as quantum resistors
• Generic transport formula for a system driven by Markovian reservoirs
• Particle-hole pairs and density-density correlations in the Lieb-Liniger model
• Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• Exact description of transport and non-reciprocity in monitored quantum devices
• Diffusion from Convection
• Can the Macroscopic Fluctuation Theory be Quantized?
• Density and current statistics in boundary-driven monitored fermionic chains
• Free Bosons with a Localized Source
• Interplay between transport and quantum coherences in free fermionic systems
• Ballistic-to-diffusive transition in spin chains with broken integrability
• Designs via Free Probability
• Measurement-induced phase transition in a single-body tight-binding model
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Corrections to diffusion in interacting quantum systems
• Entanglement asymmetry dynamics in random quantum circuits
• Universal out-of-equilibrium dynamics of 1D critical quantum systems perturbed by noise coupled to energy
• Emergence of jumps in quantum trajectories via homogeneization
• Spacetime picture for entanglement generation in noisy fermion chains
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• Exact density profile in a tight-binding chain with dephasing noise
• Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• Stochastic analysis & discrete quantum systems
• $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
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• Entanglement dynamics from universal low-lying modes
• Dynamics in the presence of local symmetry-breaking impurities
• Domain-wall melting in all-to-all QSSEP from random-matrix theory
• Volume-law entanglement entropy of typical pure quantum states
• Inhomogeneous quenches and GHD in the $\nu =1$ QSSEP model
• Feynman checkers: lattice quantum field theory with real time
• Equations driven by fast-oscillating functions of an Itô diffusion process