Author

Jacob Shapiro

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Preprint Aug 2026

The $\mathbb{Z}_2$-Index of a Pair of Pure States and the Topology of Interacting 1D Superconductors

We define a relative $\mathbb{Z}_2$-index $\mathcal{N}(\omega_1,\omega_2)$ for locally-comparable, parity-invariant pure states on a unital $C^*$-algebra. We prove that the index is well-defined, multiplicative, invariant under parity-preserving automorphisms, and locally constant in the norm topology. For the one-dime...

Anna Mazhar, Jacob Shapiro · 0 citations

Preprint Aug 2026

Instantons in a Double-Well are Poisson Distributed

We give a rigorous realization of the dilute instanton picture for a semiclassical Schr\"odinger operator with a symmetric double-well potential on $\mathbb{R}^n$. Using a localized Feynman--Kac representation, we decompose the heat-kernel trace according to the number of passages made by a Brownian bridge between shri...

Jacob Shapiro · 0 citations