Quasiprobability distribution of work in the quantum Ising model

Abstract

A complete understanding of the statistics of the work done by quenching a parameter of a quantum many-body system is still lacking in the presence of an initial quantum coherence in the energy basis. In this case, the work can be represented by a class of quasiprobability distributions. Here, we try to clarify the genuinely quantum features of the process by studying the work quasiprobability for an Ising model in a transverse field. We consider both a global and a local quench, by focusing mainly on the thermodynamic limit. We find that, while for a global quench there is a symmetric non-contextual representation with a Gaussian probability distribution of work, for a local quench we can get quantum contextuality as signaled by a negative fourth moment of the work. Furthermore, we examine the critical features related to a quantum phase transition and the role of the initial quantum coherence as useful resource.

15 pages, 4 figures. Comments welcome

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• Quantum advantage in batteries for Sachdev-Ye-Kitaev interactions
• Quantum unital Otto heat engines: using Kirkwood-Dirac quasi-probability for the engine's coherence to stay alive
• Non-positive energy quasidistributions in coherent collision models
• Work fluctuation theorems with initial quantum coherence
• Energy exchange statistics and fluctuation theorem for non-thermal asymptotic states
• Orthogonalization speed-up from quantum coherence after a sudden quench
• Quantum advantage from negativity of a work quasiprobability distribution