DFT-inspired methods for quantum thermodynamics

Marcela Herrera,Roberto M Serra,Irene D’Amico

doi:10.1038/s41598-017-04478-y

Marcela Herrera, Roberto M Serra + Show 1 more

Open Access

https://doi.org/10.1038/s41598-017-04478-y

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Abstract

In the framework of quantum thermodynamics, we propose a method to quantitatively describe thermodynamic quantities for out-of-equilibrium interacting many-body systems. The method is articulated in various approximation protocols which allow to achieve increasing levels of accuracy, it is relatively simple to implement even for medium and large number of interactive particles, and uses tools and concepts from density functional theory. We test the method on the driven Hubbard dimer at half filling, and compare exact and approximate results. We show that the proposed method reproduces the average quantum work to high accuracy: for a very large region of parameter space (which cuts across all dynamical regimes) estimates are within 10% of the exact results.

Highlights

In the framework of quantum thermodynamics, we propose a method to quantitatively describe thermodynamic quantities for out-of-equilibrium interacting many-body systems
Because of its non-trivial dynamics, this model is ideal as a test bed for assessing the accuracy of approximations in reproducing quantities related to quantum fluctuations and quantum thermodynamics
We have proposed a new method which uses some tools and concepts from density functional theory to study the non-equilibrium thermodynamics of driven quantum many-body systems, and illustrated it by the calculation of the average extractable work in a driven protocol

Summary

Introduction

In the framework of quantum thermodynamics, we propose a method to quantitatively describe thermodynamic quantities for out-of-equilibrium interacting many-body systems. A Ramsey-like interferometry experimental protocol has been proposed in refs 41 and 42 to explore the statistics of energy fluctuations and work in quantum systems This protocol has been so far implemented for single spin systems[20, 22] while its application to a quantum many-body system implies, considerable experimental (and theoretical) difficulties. We propose a new method to accurately describe some thermodynamics quantities (such as the mean work) in out-of-equilibrium quantum systems which can be applied to small, medium and large interacting many-body systems In addition this method could be used to make the Ramsey-like interferometry experimental protocol accessible when consider many-body interacting systems. We consider the time-dependent one-dimensional Hubbard Hamiltonian[55] described by

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