Mathematical Physics
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Paper Uniform Laughlin gap and stability under bounded scalar disorder
Proves the fermionic Laughlin spectral-gap conjecture for the full V1 interaction at filling 1/3 on the round sphere. The unique ground state remains uniformly gapped under sufficiently weak bounded real scalar one-body…
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Paper Sharp finite-matrix Lieb–Thirring inequalities and all equality cases
Proves the sharp one-dimensional Lieb–Thirring inequality for 1/2\lt \gamma\lt 3/2 and arbitrary finite-matrix potentials W ≥ 0 with \int\mathop{\mathrm{tr}}\nolimits (W^{\gamma+1/2})\lt \infty: the optimal…
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Paper Threshold repetition for entangled games
Proves exponential threshold repetition for every finite two-player one-round game: if its entangled value is v < 1, the probability of winning at least a fraction v+\delta of k independent repetitions decays…
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Paper The ionization and generalized ionization conjectures
For the full nonrelativistic Coulomb model with two electron spin states, proves that a molecule with M fixed nuclei of charges at least one and total charge Z strictly binds at most Z+CM electrons. Neutral-atom…
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Paper Classical capacity of generalized amplitude damping
Determines the unassisted classical capacity of every qubit generalized amplitude-damping channel, including all damping and thermal parameters. An explicit one-variable optimization gives the capacity, attained by…
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Paper Parity is not in \mathrm{QAC}^{0}
Resolves Moore's parity conjecture in the measured-output model: constant-depth quantum circuits with arbitrary one-qubit gates, unbounded-arity Toffoli gates and polynomially many total qubits cannot compute parity…
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