Coherence, Transport, and Chaos in 1D Bose-Hubbard Model: Disorder vs. Stark Potential

Quantum coherence and phase transitions are studied in a finite one-dimensional Bose--Hubbard model using exact diagonalization under thermal fluctuations, a Stark potential, and disorder. The condensate fraction, superfluid fraction, visibility, number fluctuations, and the $\ell_1$-norm of coherence are computed to characterize the Mott insulator--superfluid transition. Although finite-size effects prevent a sharp transition, ground-state properties reveal signatures of quantum criticality. Thermal fluctuations can enhance coherence via tunneling, a Stark potential promotes localization, and disorder suppresses global superfluidity while preserving local coherence. These results highlight how disorder, tilt, and temperature reshape coherence and offer insights for quantum simulation and strongly correlated phases. For systems up to six sites with unit filling, a spectral analysis is also performed through the metric mean gap ratio (MGR). However, limited statistics due to the small system size and computational constraints prevent a complete characterization of quantum chaos, yielding only approximate signatures.