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This study establishes rigorous conditions guaranteeing thermalization in complex many-body bosonic systems using Gaussian quantum cellular automata with continuous degrees of freedom. By removing strict upper bounds on particle density and leveraging an advanced version of the Riemann-Lebesgue lemma, researchers have expanded the theoretical framework for understanding long-time dynamics in these models without relying on simplified approximations.

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Quantum Systems Reliably Reach Equilibrium under Specific Conditions

Quantum ZeitgeistJune 10, 20265 min read

Thermalization, the process by which quantum systems reach equilibrium, has historically relied on simplified models. Now, conditions guaranteeing this process have been established for more complex many-body bosonic systems using Gaussian quantum cellular automata and continuous degrees of freedom. This work generalizes previous thermalization results, moving beyond compact descriptions to address systems with locally normal states and finite particle density.

Scientists Roman Geiko and Jake Gerenraich at UCLA, in collaboration with University of California, have detailed conditions guaranteeing thermalization within many-body bosonic lattice systems evolving under translation-invariant Gaussian quantum cellular automata. Geiko and colleagues define two separate sets of conditions ensuring any locally normal state with uniformly bounded particle density will evolve towards the infinite temperature state over time. The study builds upon a quantum many-body generalisation of the classic Riemann-Lebesgue lemma, providing a bound on expectation values of local Weyl operators and advancing understanding of long-time dynamics in these complex systems. The upper bound on…

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