We analyze the self-thermalization dynamics of the
M-site Bose-Hubbard model in ring geometry using the single-particle density matrix calculated via the pseudoclassical approach. We show that a weak inter-particle interaction, which has a negligible effect on the thermal state given by the Bose-Einstein distribution, suffices to convert the integrable system of non-interacting bosons into a chaotic system. Next we consider two systems of weakly interacting bosons (i.e., two Bose-Hubbard systems) in different thermal states which are coupled by a point contact. We demonstrate that the chaotic nature of the Bose-Hubbard model ensures irreversible relaxation of both systems to global thermal equilibrium. Finally, substituting the point contact with a lattice of length
L≪M, we numerically calculate the quasi-stationary current of Bose particles across the lattice and show that its magnitude is consistent with the solution of the master equation for the boundary-driven
L-site Bose-Hubbard system.
We investigate quantum phases of the Bose-Bose mixtures in a two dimensional (2D) square lattice under artificial magnetic flux. Our analysis employs the inhomogeneous Dynamical Gutzwiller Mean-Field Theory (DGMFT) to investigate ground state within the two-component Bose-Hubbard model. The results based on various inter-component interactions and magnetic flux. In the case of weak inter-component interaction (wherein the inter-component interactions remain subordinate to intra-component interactions, symbolically expressed as |Uab|≤U), we observe a multitude of captivating quantum phases within the Bose-Bose mixtures. These include the emergence of the jagged density-wave supersolid(SS) phase, the latticed-like density-wave SS phase, and counterflow superfluid (CFSF) phase. Notably, the introduction of artificial magnetic flux expands the range of existence for CFSF phase. In the case of strong inter-component interaction(wherein the inter-component interactions surpass intra-component interactions, symbolically expressed as Uab>U), we delve deeper into the classification of the spatially separated phase, aptly termed the phase separated supersolid (P-SS).