arXiv subjects

Florian Lorenz

Publications and source records attributed to Florian Lorenz.

3 recordsLinked to original sources

arXiv2026

Norm of resonance states in quantum scattering and electromagnetic systems

Resonance states spatially diverge and are thus not square integrable. Instead, their norm is defined by the biorthogonal scalar product of left and right states. We replace the corresponding volume integral by a convenient boundary integral in piecewise homogeneous systems and apply this procedure to diverse physical settings. For a quantum particle in any number of dimensions we treat hard-wall and piecewise constant potentials. For electromagnetic systems with piecewise homogeneous material properties, we consider three-dimensional and effectively two-dimensional cavities of arbitrary shape. As examples, we treat the spherical scatterer and the circular disk.

quant-ph↗

arXiv2025

Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization

For chaotic scattering systems we investigate the left-right Husimi representation, which combines left and right resonance states. We demonstrate that the left-right Husimi representation is invariant in the semiclassical limit under the corresponding closed classical dynamics, which we call quantum invariance. Furthermore, we show that it factorizes into a classical multifractal structure times universal quantum fluctuations. Numerical results for a dielectric cavity, the three-disk scattering system, and quantum maps confirm both the quantum invariance and the factorization.

nlin.CD↗

arXiv2025

Semiclassical Limit of Resonance States in Chaotic Scattering

Resonance states in quantum chaotic scattering systems have a multifractal structure that depends on their decay rate. We show how classical dynamics describes this structure for all decay rates in the semiclassical limit. This result for chaotic scattering systems corresponds to the well-established quantum ergodicity for closed chaotic systems. Specifically, we generalize Ulam's matrix approximation of the Perron-Frobenius operator, giving rise to conditionally invariant measures of various decay rates. There are many matrix approximations leading to the same decay rate and we conjecture a criterion for selecting the one relevant for resonance states. Numerically, we demonstrate that resonance states in the semiclassical limit converge to the selected measure. Example systems are a dielectric cavity, the three-disk scattering system, and open quantum maps.

nlin.CD↗