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We develop the statistical mechanics of the Hopfield model in a transverse field to investigate how quantum fluctuations affect the macroscopic behavior of neural networks. When the number of embedded patterns is finite, the Trotter…
We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces with curved and flat initial conditions. We introduce a control parameter p as the…
The fluctuations are termed mesoscopic, when their typical size is essentially larger then the average distance between the nearest neighbors, while being much smaller than the overall system size. Since the features of mesoscopic…
By combining very low temperature scanning tunneling microscopy and spectroscopy on a TiN film we have observed a non uniform state comprising of superconducting (S) and normal (N) areas. The local density of states displays a spatial…
We study S-matrix correlations for random matrix ensembles with a Hamiltonian which is the sum of a given deterministic part and of a random matrix with a Gaussian probability distribution. Using Efetov's supersymmetry formalism, we show…
We study the effect of single biased tracer particle in a bath of other particles performing the random average process (RAP) on an infinite line. We focus on the large time behavior of the mean and the fluctuations of the positions of the…
We study mesoscopic fluctuations of the conductance through a quantum dot at the wings of the Coulomb blokade peaks. At low temperatures, the main mechanism of conduction is the elastic cotunneling. The conductance strongly fluctuates with…
The fluctuations and the distribution of the conductance peak spacings of a quantum dot in the Coulomb-blockade regime are studied and compared with the predictions of random matrix theory (RMT). The experimental data were obtained in…
The standard semiclassical calculation of transmission correlation functions for chaotic systems is severely influenced by unitarity problems. We show that unitarity alone imposes a set of relationships between cross sections correlation…
The probability distribution of the reflection coefficient for light reflected from a one-dimensional random amplifying medium with {\it cross-correlated} spatial disorder in the real and the imaginary parts of the refractive index is…
A general theory of thermal magnetic fluctuations near conductive materials is developed; such fluctuations are the magnetic analog of Johnson noise. For realistic experiments in quantum computing and magnetic resonance force microscopy,…
We theoretically study propagating correlation fronts in non-interacting fermions on a one-dimensional lattice starting from an alternating state, where the fermions occupy every other site. We find that, in the long-time asymptotic regime,…
The analytical probability distribution of finite systems obeying Bose-Einstein statistics in one, two, and three dimensions are investigated by using a canonical ensemble approach. Starting from the canonical partition function of the…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
All the available data for the dispersion and linewidth of the single-particle spectra above the superconducting gap and the pseudogap in metallic cuprates for any doping has universal features. The linewidth is linear in energy below a…
Wishart random matrices are often used to model multivariate systems in physics, finance, biology and wireless communication. Extreme value statistics, such as those of the smallest eigenvalue, can be used to test the accuracy of the model.…
These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…
These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the…
The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data…
Let $N(L)$ be the number of eigenvalues, in an interval of length $L$, of a matrix chosen at random from the Gaussian Orthogonal, Unitary or Symplectic ensembles of ${\cal N}$ by ${\cal N}$ matrices, in the limit ${\cal…