Chaos in the three-site Bose-Hubbard model: Classical versus quantum

Nakerst, Goran; Haque, Masudul

doi:10.1103/physreve.107.024210

Cited by 12 publications

(1 citation statement)

References 117 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Bose-Hubbard model is an example of a cold-atom system which is nonintegrable and exhibits quantum chaos [13][14][15][16][17][18][19]. A convenient property of this model is also that it has a classical limit [20,21], facilitating the comparisons of classical and quantum dynamics.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic formalism and anomalous transport in 1D semiclassical Bose-Hubbard chain

Marković,

Čubrović

2024

Preprint

View full text Add to dashboard Cite

We analyze the time-dependent free energy functionals of the semiclassical one-dimensional Bose-Hubbard chain. We first review the weakly chaotic dynamics and the consequent early-time anomalous diffusion in the system. The anomalous diffusion is robust, appears with strictly quantized coefficients, and persists even for very long chains (more than hundred sites), crossing over to normal diffusion at late times. We identify fast (angle) and slow (action) variables and thus consider annealed and quenched partition functions, corresponding to fixing the actions and integrating over the actions, respectively. We observe the leading quantum effects in the annealed free energy, whereas the quenched energy is undefined in the thermodynamic limit, signaling the absence of thermodynamic equilibrium in the quenched regime. But already the leading correction away from the quenched regime reproduces the annealed partition function exactly. This encapsulates the fact that in both slow- and fast-chaos regime both the anomalous and the normal diffusion can be seen (though at different times).

show abstract

Section: Introductionmentioning

confidence: 99%

Thermodynamic formalism and anomalous transport in 1D semiclassical Bose-Hubbard chain

Marković,

Čubrović

2024

Preprint

View full text Add to dashboard Cite

show abstract

Operator growth and Krylov complexity in Bose-Hubbard model

Bhattacharyya,

Ghosh,

Nandi

2023

J. High Energ. Phys.

View full text Add to dashboard Cite

We study Krylov complexity of a one-dimensional Bosonic system, the celebrated Bose-Hubbard Model. The Bose-Hubbard Hamiltonian consists of interacting bosons on a lattice, describing ultra-cold atoms. Apart from showing superfluid-Mott insulator phase transition, the model also exhibits both chaotic and integrable (mixed) dynamics depending on the value of the interaction parameter. We focus on the three-site Bose Hubbard Model (with different particle numbers), which is known to be highly mixed. We use the Lanczos algorithm to find the Lanczos coefficients and the Krylov basis. The orthonormal Krylov basis captures the operator growth for a system with a given Hamiltonian. However, the Lanczos algorithm needs to be modified for our case due to the instabilities instilled by the piling up of computational errors. Next, we compute the Krylov complexity and its early and late-time behaviour. Our results capture the chaotic and integrable nature of the system. Our paper takes the first step to use the Lanczos algorithm non-perturbatively for a discrete quartic bosonic Hamiltonian without depending on the auto-correlation method.

show abstract

Quantum information scrambling in two-dimensional Bose–Hubbard lattices

Tripathy,

Touil,

Gardas

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

It is a well-understood fact that the transport of excitations throughout a lattice is intimately governed by the underlying structures. Hence, it is only natural to recognize that the dispersion of information also has to depend on the lattice geometry. In the present work, we demonstrate that two-dimensional lattices described by the Bose–Hubbard model exhibit information scrambling for systems as little as two hexagons. However, we also find that the out-of-time-ordered correlator (OTOC) shows the exponential decay characteristic for quantum chaos only for a judicious choice of local observables. More generally, the OTOC is better described by Gaussian-exponential convolutions, which alludes to the close similarity of information scrambling and decoherence theory.

show abstract

Chaos in the three-site Bose-Hubbard model: Classical versus quantum

Cited by 12 publications

References 117 publications

Thermodynamic formalism and anomalous transport in 1D semiclassical Bose-Hubbard chain

Thermodynamic formalism and anomalous transport in 1D semiclassical Bose-Hubbard chain

Operator growth and Krylov complexity in Bose-Hubbard model

Quantum information scrambling in two-dimensional Bose–Hubbard lattices

Contact Info

Product

Resources

About