Exceptional points of arbitrary high orders induced by non-Markovian dynamics

TL;DR

This paper demonstrates that non-Markovian dynamics can induce exceptional points of arbitrarily high order, surpassing the limitations imposed by the system's degrees of freedom, through specific energy return mechanisms.

Contribution

It challenges the common belief that exceptional point order is limited by system degrees of freedom, showing non-Markovian effects can create higher-order exceptional points.

Findings

Non-Markovian effects enable higher-order exceptional points.

Energy return from reservoir causes polynomial-exponential dynamics.

Observation time selection reveals arbitrarily high-order exceptional points.

Abstract

Exceptional points are singularities in the spectrum of non-Hermitian systems in which several eigenvectors are linearly dependent and their eigenvalues are equal to each other. Usually it is assumed that the order of the exceptional point is limited by the number of degrees of freedom of a non-Hermitian system. In this letter, we refute this common opinion and show that non-Markovian effects can lead to dynamics characteristic of systems with exceptional points of higher orders than the number of degrees of freedom in the system. This takes place when the energy returns from reservoir to the system such that the dynamics of the system are divided into intervals in which it describes by the product of the exponential and a polynomial function of ever-increasing order. We demonstrate that by choosing the observation time, it is possible to observe exceptional points of arbitrary high orders.