BoseHubbardmallissa

BoseHubbardmallissa is a theoretical extension of the Bose-Hubbard model that describes interacting bosons on a lattice with a network topology inspired by the layout of a shopping mall. The concept is used to explore how lattice geometry affects quantum phase transitions and collective phenomena in bosonic systems.

The formalism retains the standard Bose-Hubbard terms but allows spatial variation in hopping and on-site energy to reflect nonuniform connectivity. The Hamiltonian can be written as H = - sum_<i,j> t_{ij} (a_i^† a_j + h.c.) + sum_i [ U_i/2 n_i(n_i - 1) - μ_i n_i + ε_i n_i ]. Here t_{ij} denotes the boson hopping amplitude between neighboring sites i and j, U_i the on-site interaction strength, μ_i the chemical potential, and ε_i a local potential. In the mallissa geometry, the lattice is interpreted as a graph with variable coordination numbers, including hubs and cul-de-sacs, which produces inhomogeneous local environments.

In such systems, the competition between kinetic energy (t_{ij}) and interaction energy (U_i) gives rise to phases analogous to the superfluid and Mott insulator states found in the original model. The irregular connectivity can give rise to spatially inhomogeneous superfluid regions, Bose-glass-like phases in the presence of disorder, and complex phase boundaries.

Realizations of BoseHubbardmallissa are pursued in theoretical and numerical studies, using quantum Monte Carlo and tensor-network methods, and in experimental platforms such as ultracold atoms in programmable optical lattices, photonic lattices, and circuit-QED arrays tailored to mimic mall-like networks.

See also: Bose-Hubbard model, quantum simulation, optical lattice.