Thermodynamics of Permutation-Invariant Quantum Many-Body Systems: A Group-Theoretical Framework

• URL: http://arxiv.org/abs/2206.12639v2
• Date: Wed, 12 Jul 2023 09:47:58 GMT
• Title: Thermodynamics of Permutation-Invariant Quantum Many-Body Systems: A Group-Theoretical Framework
• Authors: Benjamin Yadin, Benjamin Morris, Kay Brandner
• Abstract summary: Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation. Coherence-induced many-body effects such as superradiance can arise even in systems whose constituents are not fundamentally indistinguishable.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle permutations. Coherence-induced many-body effects such as superradiance, however, can arise even in systems whose constituents are not fundamentally indistinguishable as long as all relevant dynamical observables are permutation-invariant. Such systems are not confined to symmetric or anti-symmetric states and therefore require a different theoretical approach. Focusing on non-interacting systems, here we combine tools from representation theory and thermodynamically consistent master equations to develop such a framework. We characterise the structure and properties of the steady states emerging in permutation-invariant ensembles of arbitrary multi-level systems that are collectively weakly coupled to a thermal environment. As an application of our general theory, we further explore how these states can in principle be used to enhance the performance of quantum thermal machines. Our group-theoretical framework thereby makes it possible to analyse various limiting cases that would not be accessible otherwise. In addition, it allows us to show that the properties of multi-level ensembles differ qualitatively from those of spin ensembles, which have been investigated earlier using the standard Clebsch-Gordan theory. Our results have a large scope for future generalisations and pave the way for systematic investigations of collective effects arising from permutation-invariance in quantum thermodynamics.

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