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arXiv:1909.12402 · Physical review. B./Physical review. B

Landauer transport as a quasisteady state on finite chains under unitary quantum dynamics

J. P. Santos Pires, Bruno Amorim, João M. Viana Parente Lopes

Published Mar 31, 2020• 10 citations
arXivHTMLPDF

Abstract

In this paper, we study the emergence of a Landauer transport regime from the quantum-mechanical dynamics of free electrons in a disordered tight-binding chain, which is coupled to finite leads with open boundaries. Both partitioned and partition-free initial conditions are analyzed and seen to give rise, for large enough leads, to the same spatially uniform quasisteady-state current, which agrees with the Landauer value. The quasisteady-state regime is preceded by a transient regime, which lasts for a time proportional to the length of the disordered sample, and followed by recursions, after a time that is proportional to the lead size. These theoretical predictions may be of interest to future experiments on transport of fermionic ultracold atoms across optical lattices. We also observe finite-size current oscillations, superimposed on the quasisteady state, whose behavior depends crucially on the conditions initially imposed on the system. Finally, we show how a time-resolved Kubo formula is able to reproduce this Landauer transport regime, as the leads grow bigger.

DOI
10.1103/physrevb.101.104203

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In this paper, we study the emergence of a Landauer transport regime from the quantum-mechanical dynamics of free electrons in a disordered tight-binding chain, which is coupled to finite leads with open boundaries. Both partitioned and partition-free initial conditions are analyzed and seen to give rise, for large enough leads, to the same spatially uniform quasisteady-state current, which agrees with the Landauer value. The quasisteady-state regime is preceded by a transient regime, which lasts for a time proportional to the length of the disordered sample, and followed by recursions, after a time that is proportional to the lead size. These theoretical predictions may be of interest to future experiments on transport of fermionic ultracold atoms across optical lattices. We also observe finite-size current oscillations, superimposed on the quasisteady state, whose behavior depends crucially on the conditions initially imposed on the system. Finally, we show how a time-resolved Kubo formula is able to reproduce this Landauer transport regime, as the leads grow bigger.
Using the microcanonical picture of transport---a framework ideally suited to describe the dynamics of closed quantum systems such as ultracold atom experiments---we show that the exact dynamics of noninteracting fermions and bosons exhibits very different transport properties when the system is set out of equilibrium by removing the particles from half of the lattice. We find that fermions rapidly develop a finite quasisteady-state current reminiscent of electronic transport in nanoscale systems. This result is robust---it occurs with or without a harmonic confining potential and at zero or finite temperature. The zero-temperature bosonic current instead exhibits strong oscillatory behavior that decays into a steady-state of zero current only in the thermodynamic limit. These differences appear most strikingly in the different particle number fluctuations on half of the lattice as a consequence of the spin statistics. These predictions can be readily verified experimentally.
We construct a non-equilibrium steady state and calculate the corresponding current for a mesoscopic Fermi system in the partition-free setting. To this end we study a small sample coupled to a finite number of semi-infinite leads. Initially, the whole system of quasi-free fermions is in a grand canonical equilibrium state. At t = 0 we turn on a potential bias on the leads and let the system evolve. We study how the charge current behaves in time and how it stabilizes itself around a steady state value, which is given by a Landauer-type formula.
Reduced transport and localization in isolated quantum systems are typically attributed to spatially-extended disorder, but may also emerge from the influence of a few controllable defects. We show here how a single defect profoundly reshapes wave-function spreading on a finite and periodic tight-binding lattice. Adapting the defect technique from classical random-walk studies, we obtain exact time-resolved site-occupation probabilities and several observables of interest. Even a single defect induces remarkable nonlinear effects, including non-monotonic suppression of transport, enhanced localization at distant sites, and strong sensitivity to the initial particle position at long times. These results demonstrate that minimal perturbations can generate nontrivial long-time transport signatures, giving rise to a microscopic defect-driven mechanism of quantum localization. Although the main results presented pertain to a single isolated defect, we show that the developed formalism may naturally extend to multiple as well as to a wider class of defects.
We construct a non-equilibrium steady state and calculate the corresponding current for a mesoscopic Fermi system in the partition-free setting. To this end we study a small sample coupled to a finite number of semi-infinite leads. Initially, the whole system of quasi-free fermions is in a grand-canonical equilibrium state. At t = 0 we turn on a potential bias on the leads and let the system evolve. We study how the charge current behaves in time and how it stabilizes itself around a steady-state value, which is given by a Landauer-type formula.
An intriguing regime of universal charge transport at high entropy density has been proposed for periodically driven interacting one-dimensional systems with Bloch bands separated by a large single-particle band gap. For weak interactions, a simple picture based on well-defined Floquet quasiparticles suggests that the system should host a quasisteady state current that depends only on the populations of the system's Floquet-Bloch bands and their associated quasienergy winding numbers. Here we show that such topological transport persists into the strongly interacting regime where the single-particle lifetime becomes shorter than the drive period. Analytically, we show that the value of the current is insensitive to interaction-induced band renormalizations and lifetime broadening when certain conditions are met by the system's nonequilibrium distribution function. We show that these conditions correspond to a quasisteady state. We support these predictions through numerical simulation of a system of strongly interacting fermions in a periodically modulated chain of Sachdev-Ye-Kitaev dots. Our paper establishes universal transport at high entropy density as a robust far from equilibrium topological phenomenon, which can be readily realized with cold atoms in optical lattices. Published by the American Physical Society 2024
We investigate the static and dynamical behavior of one-dimensional interacting fermions in disordered Hubbard chains contacted to semi-infinite leads. The chains are described via the repulsive Anderson-Hubbard Hamiltonian, using static and time-dependent lattice density-functional theory. The dynamical behavior of our quantum transport system is studied using an integration scheme available in the literature, which we modify via the recursive Lanczos method to increase its efficiency. To quantify the degree of localization due to disorder and interactions, we adapt the definition of the inverse participation ratio to obtain an indicator which is suitable for quantum transport geometries and can be obtained within density-functional theory. Lattice density-functional theories are reviewed and, for contacted chains, we analyze the merits and limits of the coherent-potential approximation in describing the spectral properties, with interactions included via lattice density-functional theory. Our approach appears to be able to capture complex features due to the competition between disorder and interactions. Specifically, we find a dynamical enhancement of delocalization in the presence of a finite bias and an increase of the steady-state current induced by interparticle interactions. This behavior is corroborated by results for the time-dependent densities and for the inverse participation ratio. Using short isolated chains with interaction and disorder, a brief comparative analysis between time-dependent density-functional theory and exact results is then given, followed by general concluding remarks.