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This content will become publicly available on March 18, 2026

Title: Integrals of products of Bessel functions: a perspective from the physics of Bloch electrons
Abstract Integrals of products of Bessel functions exhibit an intriguing feature: they may vanish identically, not due to an orthogonality property, but rather when certain conditions on the parameters specifying the integrand are satisfied. We provide a physical interpretation of this feature in the context of both single-particle and many-body properties of electrons on a lattice (“Bloch electrons“), namely, in terms of their density of states and umklapp scattering rate. (In an umklapp event, the change in the momentum of two colliding electrons is equal to a reciprocal lattice vector, which gives rise to a finite resistivity due to electron-electron interaction.) In this context, the vanishing of an integral follows simply from the condition that either the density of states vanishes due to the electron energy lying outside the band in which free propagation of electron waves is allowed, or that an umklapp process is kinematically forbidden due to the Fermi surface being smaller than a critical value.  more » « less
Award ID(s):
2224000
PAR ID:
10648019
Author(s) / Creator(s):
;
Publisher / Repository:
IOPscience
Date Published:
Journal Name:
Physica Scripta
Volume:
100
Issue:
4
ISSN:
0031-8949
Page Range / eLocation ID:
045229
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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