AG Mathematische Physik, Dragan Marković (FAU): Chaos and operator dependent anomalous transport in semiclassical,Bose-Hubbard chains

Dragan Marković (FAU)

Chaos and operator dependent anomalous transport in semiclassical

Bose-Hubbard chains

Abstract:
We investigate anomalous transport and chaotic dynamics in the

semiclassical one-dimensional Bose–Hubbard chain using the Truncated

Wigner Approximation with quantum corrections. At early times, the

system exhibits robust superdiffusion characterized by universal,

quantized exponents governed primarily by the initial state, largely

independent of model parameters or the strength of chaos. This anomalous

regime persists even in long chains and reflects a special scaling

symmetry of the Hamiltonian. At later times, a crossover to normal

diffusion emerges, which is most stable when nonintegrability is strong,

leading to homogeneous states; for weaker nonintegrability, long-lived

oscillations and inhomogeneities survive despite strong chaos. The

coexistence of fast (angle) and slow (action) variables provides a

natural framework to interpret the transport properties through free

energy functionals: while quenched ensembles fail to equilibrate,

annealed ensembles capture the effective late-time behavior. Together,

these results highlight anomalous diffusion as a universal, early-time

phenomenon distinct from prethermalization, smoothly evolving into

conventional hydrodynamic transport at long times.

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Bose-Hubbard chains, Phys. Rev. E 112, 024211; arXiv: 2502.19584

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BH chain, arXiv preprint: 2312.17008