Phantom relaxation in non-Hermitian systemsBensa, Jaš (Avtor) Žnidarič, Marko (Mentor) pseudospectrumrandom quantum circuitsnon-Hermiticitynon-normal matrixMarkov chaintransfer matrixentanglementoperator correlationsOftentimes, intuition gained from simple systems is used to predict the behavior of more complex scenarios. For example, if we iterate a vector with a Hermitian matrix its norm (or inner product with another vector) is expected to evolve exponentially in time with the exponent equal to the largest eigenvalue of the matrix. Believing that this holds in non-Hermitian systems is wrong. In infinite systems and for general vectors, it is not the spectrum of the matrix that predicts how the iterated quantity will behave, but rather the spectrum of the slightly perturbed matrix, i.e., the pseudospectrum. In this thesis, we will explore quantities iterated with non-Hermitian matrices. In the majority of the examples that we will delve into, these quantities show a two-stage relaxation. In the first stage, the exponential behavior is determined by the largest pseudoeigenvalue of the iterated matrix. Interestingly, this stage persists up to times that scale with the system size, meaning that in infinite systems it is the only kind of behavior. The second stage is given by the largest eigenvalue, as one expects in Hermitian systems. Some physical examples that can be evolved using this setting are purity and out-of-time-ordered correlations in random quantum circuits and certain biased random walks. The setting we will explore is quite general and thus it might be applied in a wide variety of physical fields. Whenever one encounters iterations with a non-Hermitian transfer matrix, one can refer to the work presented here and hopefully predict the results of the iteration.20242024-09-28 08:15:05Doktorsko delo/naloga162859VisID: 144594COBISS_ID: 209938179sl