Kubo formula for finite size systems

Abstract

We demonstrate that the proper calculation of the linear response for finite-size systems can only be performed if the coupling to the leads/baths is explicitly taken into consideration. We exemplify this by obtaining a Kubo-type formula for heat transport in a finite-size system coupled to two thermal baths, kept at different temperatures. We show that the proper calculation results in a well-behaved response, without the singular contributions from degenerate states encountered when Kubo formulae for infinite-size systems are inappropriately used for finite-size systems.

4 pages, 1 figure

References in corpus (13)

• Diffusion and ballistic transport in one-dimensional quantum systems
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• Modeling heat transport through completely positive maps
• Transport in open spin chains: A Monte Carlo wave-function approach
• Thermal transport of the XXZ chain in a magnetic field
• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Drude weight in systems with open boundary conditions
• Green-Kubo formula for heat conduction in open systems
• Limited validity of the Kubo formula for thermal conduction in modular quantum systems
• Density dynamics from current auto-correlations at finite time- and length-scales
• Heat conductivity in small quantum systems: Kubo formula in Liouville space
• Equivalence of transport coefficients in bath-induced and dynamical scenarios
• Non-equilibrium BBGKY Hierarchy from the Redfield Equation

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• Diverse fundamental properties in stage-n graphite alkali-intercalation compounds: anode materials of Li+-based batteries
• Reconciling Kubo and Keldysh Approaches to Fermi-Sea-Dependent Nonequilibrium Observables: Application to Spin Hall Current and Spin-Orbit Torque in Spintronics