Nico Hahn's research while affiliated with University of Duisburg-Essen and other places

Publications (6)

Preprint
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Topological invariance is a powerful concept in different branches of physics as they are particularly robust under perturbations. We generalize the ideas of computing the statistics of winding numbers for a specific parametric model of the chiral Gaussian Unitary Ensemble to other chiral random matrix ensembles. Especially, we address the two chir...
Article
The winding number is a concept in complex analysis which has, in the presence of chiral symmetry, a physics interpretation as the topological index belonging to gapped phases of fermions. We study statistical properties of this topological quantity. To this end, we set up a random matrix model for a chiral unitary system with a parametric dependen...
Preprint
The winding number is a concept in complex analysis which has, in the presence of chiral symmetry, a physics interpretation as the topological index belonging to gapped phases of fermions. We study statistical properties of this topological quantity. To this end, we set up a random matrix model for a chiral unitary system with a parametric dependen...
Article
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition probabilities. In this context we also find that the transition probability of two random uniformly distributed stat...
Preprint
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition probabilities. In this context we also find that the transition probability of two random uniformly distributed stat...

Citations

... If disorder comes into play, the winding number can become random and a statistical analysis is called for. We refer the reader to Ref. 9 for further discussion of the physics aspects. Here, we consider simple schematic models of chiral systems with a parametric dependence. ...
... Quite naturally, research on pure state statistical mechanics has started to focus on nonequilibrium phenomena. For instance, it has been shown that typicality arguments remain useful even out of equilibrium ("dynamical typicality" [28][29][30]) and can be used to derive master equations [31][32][33][34]. Moreover, random matrix theory has been used to predict the time evolution of expectation values of observables [35][36][37][38] and general results on the time-scales of thermalization have been found [39][40][41][42][43][44][45]. ...
... While Floquet RUC have given access to the study of non-trivial spectral properties in extended many-body systems -like the onset of RMT behaviour [6,25,[27][28][29], spectral Lyapunov exponents [26], and novel scaling forms and limits [23,25] -translational-invariant (TI) RUC give rise, via the socalled space-time duality, to non-Hermitian dual transfer matrix (DTM) (Fig. 1 red) with complex eigenvalues, the dual spectrum. The study of many-body quantum system using space-time duality began in the study of the kicked Ising model at the self-dual point [8,[30][31][32][33] and concurrently in the transfer matrix approach in Floquet RUC [6, 25,26]. Subsequently, numerous works have investigated the non-unitary "dynamics" in the space direction [34][35][36][37][38]. ...