Non-equilibrium quantum transport in presence of a defect: the non-interacting case

Abstract

We study quantum transport after an inhomogeneous quantum quench in a free fermion lattice system in the presence of a localised defect. Using a new rigorous analytical approach for the calculation of large time and distance asymptotics of physical observables, we derive the exact profiles of particle density and current. Our analysis shows that the predictions of a semiclassical approach that has been extensively applied in similar problems match exactly with the correct asymptotics, except for possible finite distance corrections close to the defect. We generalise our formulas to an arbitrary non-interacting particle-conserving defect, expressing them in terms of its scattering properties.

arXiv commentSubmission to SciPost. v2: references added, minor changes v3: improved intro, added comparison with Landauer's theory, added citations, typos corrected v4: added note on more general initial states

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Cited by in corpus (31)

• Speck of Chaos
• Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains
• Time evolution of entanglement negativity across a defect
• Ballistic transport and boundary resistances in inhomogeneous quantum spin chains
• Dynamics of large deviations in the hydrodynamic limit: Non-interacting systems
• Domain wall melting across a defect
• Nonequilibrium phase transition in transport through a driven quantum point contact
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Transport through interacting defects and lack of thermalisation
• Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
• Lack of thermalization for integrability-breaking impurities
• Global Quenches after Localised Perturbations
• Entanglement evolution after a global quench across a conformal defect
• Transport and entanglement across integrable impurities from Generalized Hydrodynamics
• Simulations of the dynamics of quantum impurity problems with matrix product states
• Quench dynamics of noninteracting fermions with a delta impurity
• Exactly solvable models for universal operator growth
• Thermodynamic phases in first detected return times of quantum many-body systems
• Stationary time correlations for fermions after a quench in the presence of an impurity
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• On Landauer--Büttiker formalism from a quantum quench
• The topological Kondo model out of equilibrium
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• Exact asymptotics of long-range quantum correlations in a nonequilibrium steady state
• Coherent charge and spin oscillations induced by local quenches in nanowires with spin-orbit coupling
• Extensive Long-Range Entanglement at Finite Temperatures from a Nonequilibrium Bias
• On the complex behaviour of the density in composite quantum systems
• A hydrodynamic approach to Stark localization
• Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment of the Tonks Girardeau limit
• Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices
• Domain-wall melting and entanglement in free-fermion chains with a band structure