We present a wide array of quantum measures on numerical solutions of 1D Bose-and FermiHubbard Hamiltonians for finite-size systems with open boundary conditions. Finite size effects are highly relevant to ultracold quantum gases in optical lattices, where an external trap creates smaller effective regions in the form of the celebrated "wedding cake" structure and the local density approximation is often not applicable. Specifically, for the Bose-Hubbard Hamiltonian we calculate number, quantum depletion, local von-Neumann entropy, generalized entanglement or Q-measure, fidelity, and fidelity susceptibility; for the Fermi-Hubbard Hamiltonian we also calculate the pairing correlations, magnetization, charge-density correlations, and antiferromagnetic structure factor. Our numerical method is imaginary time propagation via time-evolving block decimation. As part of our study we provide a careful comparison of canonical vs. grand canonical ensembles and Gutzwiller vs. entangled simulations. The most striking effect of finite size occurs for bosons: we observe a strong blurring of the tips of the Mott lobes accompanied by higher depletion, and show how the location of the first Mott lobe tip approaches the thermodynamic value as a function of system size.

Introduction Bortezomib (BTZ) is a selective and reversible proteasome inhibitor and first line treatment for multiple myeloma (MM). One of the side effects is BTZ-induced peripheral neuropathy (BIPN). Until now there is no biomarker which can predict this side effect and its severity. Neurofilament light chain (NfL) is a neuron specific cytoskeletal protein, of which higher levels can be detected in peripheral blood in case of axon damage. In this study, we aimed to evaluate the relationship between NfL serum levels and characteristics of BIPN. Methods We performed a first interim analysis of a monocentric, non-randomized, observational clinical trial including 70 patients (DRKS00025422) diagnosed with MM in the inclusion period of June 2021 until March 2022. Two groups of patients—one with ongoing BTZ treatment at the time of recruiting, and one with BTZ treatment in the past—were compared to controls. NfL in serum was analyzed via the ELLA™ device. Results Both patients with previous and ongoing BTZ treatment had higher serum NfL levels than controls, and patients with ongoing BTZ treatment had higher NfL levels than patients with BTZ treatment in the past. Serum NfL levels correlated with electrophysiological measures of axonal damage in the group with ongoing BTZ treatment. Conclusion Elevated NfL levels indicate acute axonal damage under BTZ in MM patients.

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