Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates

Abstract

We consider a family of chaotic Bose-Hubbard Hamiltonians (BHH) parameterized by the coupling strength $k$ between neighboring sites. As $k$ increases the eigenstates undergo changes, reflected in the structure of the Local Density of States. We analyze these changes, both numerically and analytically, using perturbative and semiclassical methods. Although our focus is on the quantum trimer, the presented methodology is applicable for the analysis of longer lattices as well.

4 pages, 4 figures

References in corpus (18)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Cold bosonic atoms in optical lattices
• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates
• Discrete breathers in nonlinear lattices: Experimental detection in a Josephson array
• Observation of breathers in Josephson ladders
• Geometric approach to Hamiltonian dynamics and statistical mechanics
• Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States
• Quantum Chaos in the Bose-Hubbard model
• Collective modes, chaotic behavior and self-trapping in the dynamics of three coupled Bose-Einstein condensates
• Quantum Dynamics of Three Coupled Atomic Bose-Einstein Condensates
• Chaos and energy spreading for time-Dependent Hamiltonians, and the various Regimes in the theory of Quantum Dissipation
• Self-trapping mechanisms in the dynamics of three coupled Bose-Einstein condensates
• Parametric dependent Hamiltonians, wavefunctions, random-matrix-theory, and quantal-classical correspondence
• Unification of perturbation theory, RMT and semiclassical considerations in the study of parametrically-dependent eigenstates
• Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions
• Wavepacket Dynamics, Quantum Reversibility and Random Matrix Theory
• The twilight zone in the parametric evolution of eigenstates: beyond perturbation theory and semiclassics

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• Interacting bosons in a triple well: Preface of many-body quantum chaos
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• Ground-state Properties of Small-Size Nonlinear Dynamical Lattices
• Counting statistics in multiple path geometries and the fluctuations of the integrated current in a quantum stirring device
• Applications of fidelity measures to complex quantum systems
• How to seed ergodic dynamics of interacting bosons under conditions of many-body quantum chaos
• Quasistatic transfer protocols for atomtronic superfluid circuits
• Controlled quantum stirring of Bose-Einstein condensates
• Quantum irreversibility of quasistatic protocols for finite-size quantized systems
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• Chaos, Metastability and Ergodicity in Bose-Hubbard Superfluid Circuits
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