Work

Quantum systems with jump-discontinous mass. I

Year: 2026

Type: article

Abstract: We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by the boundary conditions at the points of mass discontinuity. For a family of scale-free boundary conditions, we analyse the associated spectral problem. We find that the eigenfunctions exhibit a highly sensitive and erratic dependence on the energy. Notably, the system supports infinitely many distinct semiclassical limits, each labelled by a point on a spectral curve embedded in the two-torus. These results demonstrate a rich interplay between discontinuous coefficients, boundary data, and spectral asymptotics.

Source: Nonlinearity

DOI: 10.1088/1361-6544/ae4afb

Authors: Fabio Deelan Cunden, Giovanni Gramegna, Marilena Ligabò

Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Bari, University of Bari Aldo Moro

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Istituto Nazionale di Fisica Nucleare, Ministero dell'Università e della Ricerca, Gruppo Nazionale per la Fisica Matematica