The Generalized Fibonacci Oscillator as an Open Quantum System

TL;DR

This paper studies an open quantum system with a Hamiltonian spectrum based on a generalized Fibonacci sequence, analyzing its dynamics, stationary state, and convergence properties, especially at low temperatures.

Contribution

It introduces a model with a Fibonacci spectrum Hamiltonian coupled to a Boson reservoir and explicitly computes the stationary state and spectral gap, highlighting quantum features at low temperatures.

Findings

Unique and faithful stationary state derived

Exponential convergence to the stationary state established

Explicit spectral gap computed at low temperatures

Abstract

We consider an open quantum system with Hamiltonian $H_S$ whose spectrum is given by a generalized Fibonacci sequence weakly coupled to a Boson reservoir in equilibrium at inverse temperature $\beta$. We find the generator of the reduced system evolution and explicitly compute the stationary state of the system, that turns out to be unique and faithful, in terms of parameters of the model. If the system Hamiltonian is generic we show that convergence towards the invariant state is exponentially fast and compute explicitly the spectral gap for low temperatures, when quantum features of the system are more significant, under an additional assumption on the spectrum of $H_S$.