Beyond the Lindblad master equation: Heat, work, and energy currents in boundary-driven spin chains

Physical Review. E
Luís H ReisEmmanuel Pereira

Abstract

We consider accurate investigation of the energy current and its components, heat and work, in some boundary-driven quantum spin systems. The expressions for the currents, as well as the associated Lindblad master equation, are obtained via a repeated interaction scheme. We consider small systems in order to analytically compute the steady distribution to study the current in the steady state. Asymmetrical XXZ and quantum Ising models are detailed analyzed. For the XXZ chain we present cases in which different compositions of heat and work currents, obtained via the repeated interaction protocol, lead to the same energy current, which may be obtained via the Lindblad master equation. For the quantum Ising chain, we describe a case of zero energy current and novanishing heat and work currents. Our findings make clear that to talk about heat in these boundary-driven spin quantum systems we must go beyond an investigation involving only the Lindblad master equation.

References

Oct 4, 2003·Physical Review Letters·L-M DuanM D Lukin
Jun 13, 2009·Physical Review Letters·Dragi Karevski, Thierry Platini
Jun 28, 2011·Physical Review Letters·Marko Znidarič
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Nov 7, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Gabriel T LandiDragi Karevski
Nov 5, 2016·Science·Manuel EndresMikhail D Lukin
Nov 15, 2016·Physical Review. E·Lucas SchuabGabriel T Landi
Mar 20, 2018·Physical Review. E·Emmanuel Pereira
Apr 20, 2019·Physical Review. E·Emmanuel Pereira
Nov 9, 2019·Physical Review Letters·Franklin L S RodriguesGabriel T Landi

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