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arXiv:1804.02805 · Fundamental theories of physics

The Role of Quantum Work Statistics in Many-Body Physics

John Goold, Francesco Plastina, Andrea Gambassi, Alessandro Silva

Published Jan 1, 2018• 9 citations
arXivHTMLPDF
DOI
10.1007/978-3-319-99046-0_13

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The Role of Quantum Work Statistics in Many-Body Physics

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In this contribution, we aim to illustrate how quantum work statistics can be used as a tool in order to gain insight on the universal features of non-equilibrium many-body systems. Focusing on the two-point measurement approach to work, we first outline the formalism and show how the related irreversible entropy production may be defined for a unitary process. We then explore the physics of sudden quenches from the point of view of work statistics and show how the characteristic function of work can be expressed as the partition function of a corresponding classical statistical physics problem in a film geometry. Connections to the concept of fidelity susceptibility are explored along with the corresponding universal critical scaling. We also review how large deviation theory applied to quantum work statistics gives further insight to universal properties. The quantum-to-classical mapping turns out to have close connections with the historical problem of orthogonality catastrophe: we therefore discuss how this relationship may be exploited in order to experimentally extract quantum work statistics in many-body systems.

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In this contribution, we aim to illustrate how quantum work statistics can be used as a tool in order to gain insight on the universal features of non-equilibrium many-body systems. Focusing on the two-point measurement approach to work, we first outline the formalism and show how the related irreversible entropy production may be defined for a unitary process. We then explore the physics of sudden quenches from the point of view of work statistics and show how the characteristic function of work can be expressed as the partition function of a corresponding classical statistical physics problem in a film geometry. Connections to the concept of fidelity susceptibility are explored along with the corresponding universal critical scaling. We also review how large deviation theory applied to quantum work statistics gives further insight to universal properties. The quantum-to-classical mapping turns out to have close connections with the historical problem of orthogonality catastrophe: we therefore discuss how this relationship may be exploited in order to experimentally extract quantum work statistics in many-body systems.
Statistical mechanics relies on the maximization of entropy in a system at thermal equilibrium. However, an isolated quantum many-body system initialized in a pure state remains pure during Schrödinger evolution, and in this sense it has static, zero entropy. We experimentally studied the emergence of statistical mechanics in a quantum state and observed the fundamental role of quantum entanglement in facilitating this emergence. Microscopy of an evolving quantum system indicates that the full quantum state remains pure, whereas thermalization occurs on a local scale. We directly measured entanglement entropy, which assumes the role of the thermal entropy in thermalization. The entanglement creates local entropy that validates the use of statistical physics for local observables. Our measurements are consistent with the eigenstate thermalization hypothesis.
Entanglement entropy is a measure of quantum correlations between separate parts of a many‐body system, which plays an important role in many areas of physics. Here we review recent work in which a relation between this quantity and the Full Counting Statistics description of electron transport was established for noninteracting fermion systems. Using this relation, which is of a completely general character, we discuss how the entanglement entropy can be directly measured by detecting current fluctuations in a driven quantum system such as quantum point contact.