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Noncommuting conserved quantities in quantum many-body thermalization

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In statistical mechanics, a small system exchanges conserved quantities—heat, particles, electric charge, etc.—with a bath. The small system may thermalize to the canonical ensemble, the grand canonical ensemble, etc. The conserved quantities are represented by operators usually assumed to commute with each other. But noncommutation distinguishes quantum physics from classical. What if the operators fail to commute? I will argue, using quantum-information-theoretic thermodynamics, that the small system thermalizes to near a “non-Abelian thermal state.” I will present a protocol for realizing this state experimentally, supported with numerical simulations of a spin chain. The protocol is suited to ultracold atoms, trapped ions, quantum dots, and more. This work introduces a nonclassical phenomenon—noncommutation of conserved quantities—into a decades-old thermodynamics problem.


1) NYH , Beverland, and Kalev, Phys. Rev. E 101 , 042117 (2020)

2) NYH , Faist, Oppenheim, and Winter, Nat. Comms. 7, 12051 (2016)

3) NYH , J. Phys. A 51 , 094001 (2018)

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This talk is part of the Cavendish Quantum Information Seminar Series series.

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