Tensor-simple spectrum of unitary flows

TL;DR

This paper introduces a class of unitary flows with the property that tensor products over any countable subset have simple spectrum, a generic feature for measure-preserving flows, expanding understanding of spectral simplicity in dynamical systems.

Contribution

It constructs specific unitary flows whose tensor products over countable sets always have simple spectrum, revealing new generic spectral properties in measure-preserving dynamics.

Findings

Tensor products of these flows have simple spectrum for any countable subset.

The property is generic among flows preserving sigma-finite measures.

Provides a new class of flows with predictable spectral behavior.

Abstract

Unitary flows $T_t$ of dynamic origin are proposed such that for every countable subset $Q\subset (0,+\infty)$ the tensor product $\bigotimes_{q\in Q} T_q $ has simple spectrum. This property is generic for flows preserving the sigma-finite measure.