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Quantum mechanics is one of the most successful physical theories. This course presents the mathematical formalism (functional analysis and spectral theory) that underlies quantum mechanics. It is sim
Related publications (30)
Please note that this is not a complete list of this person’s publications. It includes only semantically relevant works. For a full list, please refer to Infoscience.
We generalize the existing finite-size criteria for spectral gaps offrustration-free spin systems to D>2 dimensions. We obtain a local gapthreshold of 3/n, independent of D, for nearest-neighbor interactions. The 1/n scaling persists for arbitrary finite-r ...
The AKLT spin chain is the prototypical example of a frustration-free quantum spin system with a spectral gap above its ground state. Affleck, Kennedy, Lieb, and Tasaki also conjectured that the two-dimensional version of their model on the hexagonal latti ...
The Lyapunov exponent characterizes the asymptotic behavior of long matrix products. Recognizing scenarios where the Lyapunov exponent is strictly positive is a fundamental challenge that is relevant in many applications. In this work we establish a novel ...