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The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and…
We consider elastic reflection and transmission of electrons by a disordered system characterized by a $2N\!\times\!2N$ scattering matrix $S$. Expressing $S$ in terms of the $N$ radial parameters and of the four $N\!\times\!N$ unitary…
The variation with energy of the total cross section for elastic electron scattering from atoms of several elements is caused primarily by shape resonances corresponding to the formation of temporary negative ions. It is shown that such…
The capability to probe the dispersion of elementary spin, charge, orbital, and lattice excitations has positioned resonant inelastic x-ray scattering (RIXS) at the forefront of photon science. Here we develop the scattering theory for RIXS…
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We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
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We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the…
Superconducting junctions are essential building blocks for quantum hardware, and their fundamental behaviour remains a highly active research field. The behaviour of generic junctions is conveniently described by Beenakker's determinant…
A complex interplay of single-neuron properties and the recurrent network structure shapes the activity of cortical neurons. The single-neuron activity statistics differ in general from the respective population statistics, including…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
The transfer matrix of scattering theory in one dimension can be expressed in terms of the time-evolution operator for an effective non-unitary quantum system. In particular, it admits a Dyson series expansion which turns out to facilitate…
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We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small…
We develop novel methods to compute auto-correlation functions, or power spectral densities, for chaotic dynamical systems generated by an inverse method whose starting point is an invariant distribution and a two-form. In general, the…
We define auto- and cross-correlation functions capable to capture dynamical characteristics induced by local phase space structures in a general dynamical system. These correlation functions are calculated in the Standard Map for a range…
We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic…
We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula for correlation functions of boundary CFT…
The current literature is rather vague regarding how to calculate the exact numerical value of the resonant ion scattering cross-section that should be used for a specific bandpass of finite width. Such a value was needed in order to…