Title: Quantum to classical crossover in many-body chaos in a glass

Abstract: Chaotic quantum systems with Lyapunov exponent λ_L obey an upper bound λ_L≤2πk_B T/ℏ at temperature T, implying a divergence of the bound in the classical limit ℏ→0. Following this trend, does a quantum system necessarily become ‘more chaotic’ when quantum fluctuations are reduced? I will explore this question by computing λ_L (ℏ,T) in the quantum spherical p-spin glass model, where ℏ can be continuously varied. We find that quantum fluctuations, in general, make paramagnetic phase less chaotic and the spin glass phase more chaotic. We show that the approach to the classical limit could be non-trivial, with non-monotonic dependence of λ_L on ℏ close to the dynamical glass transition temperature T_d. Our results in the classical limit (ℏ→0) naturally describe chaos in super-cooled liquid in structural glasses. We find a crossover from strong to weak chaos substantially above T_d concomitant the onset of two-step glassy relaxation. We further show that λ_L~ T^α, with the exponent α varying between 2 and 1 from quantum to classical limit, at low temperatures in the spin glass phase. Our results reveal intricate interplay between quantum fluctuations, glassy dynamics, replica symmetry breaking and chaos.

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