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 paper, 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 the reservoir to the system such that the dynamics of the system are divided into intervals in which it is described 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 with the same system parameters.

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• Exceptional points
• Non-Markovian processes