One of the common techniques for finding resonances in a quantum mechanical system is to confine it in the box of a finite length and then vary its spectrum with respect to the box's length. As the resonance wave function is mainly concentrated in the interaction region, resonance energies are much less influenced by such variation and are visible in the spectrum. Inspired by the rigorous proof of this technique in 1D, we prove it for a general quantum graph and illustrate our results with some examples.

The asymptotic spectra of non-Hermitian block Toeplitz matrices are determined in terms of transfer matrices. This approach also allows one to deal with perturbations. In particular, new results are obtained for perturbations that close the boundary. Moreover, one can detect topological zero modes for chiral Hamiltonians and this gives rise to a new gap condition.

The Bose-Hubbard model effectively describes bosons on a lattice with on-site interactions and nearest-neighbour hopping, serving as a foundational framework for understanding strong particle interactions and the superfluid to Mott-insulator transition. In the physics literature, the mean field theory for this model is known to provide qualitatively accurate results in three or more dimensions. This poster will present a result that establishes the validity of the mean-field approximation for bosonic quantum systems in high dimensions. Unlike the conventional many-body mean-field limit, the high-dimensional mean-field theory exhibits a phase transition and remains compatible with strongly interacting particles.

We introduce a theoretical protocol for entanglement distillation from classically unknown bipartite quantum states. By performing LOCC-based quantum tomography followed by tailored distillation, we achieve entanglement extraction with bounded error. Our method reveals a trade-off between estimation accuracy and distillation rate, enabling practical entanglement processing under limited state knowledge. The proposed LOCC tomography scheme may also be of independent interest.