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We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge gap dominates the neutral gap. We verify these conditions under a triad of symmetries (translation-invariance, charge and dipole conservation) that are present, e.g., in periodic fractional quantum Hall systems. Thus, this gap domination, previously observed numerically, is a universal feature imposed by symmetry. A second relation yields a new induction-on-particle-number method for deriving spectral gaps. The results cover both bosons and fermions.more » « lessFree, publicly-accessible full text available July 24, 2026
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In Phase II of the Project 8 neutrino mass experiment, electrons from the decays of tritium or 83mKr are detected via their ≈26 GHz cyclotron radiation while contained within a circular waveguide. The signal from a given electron is characterized as a brief chirp, lasting ≲10 ms and changing in frequency by ≲1 MHz∕ms. To detect these signals, the Project 8 collaboration developed a Data Acquisition (DAQ) system tailored to the signal properties. The DAQ is responsible for simultaneously selecting up to three 100MHz-wide frequency windows to study, detect, and trigger on likely signals from different electron kinetic energies, and for writing the relevant data to disk. We describe the Phase II DAQ system in detail and address how the system was used for data-taking operations.more » « lessFree, publicly-accessible full text available January 1, 2027
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