Related papers: Optimal Fluctuations and Tail States of non-Hermit…
A statistical field theory is developed to explore the density of states and spatial profile of `tail states' at the edge of the spectral support of a general class of disordered non-Hermitian operators. These states, which are identified…
Non-Hermitean operators may appear during the calculation of a partition function in various models of statistical mechanics. The tail eigen-states, having anomalously small real part of energy $Re(\eps)$, became naturally important in this…
We discuss the distribution of the largest eigenvalue of a random N x N Hermitian matrix. Utilising results from the quantum gravity and string theory literature it is seen that the orthogonal polynomials approach, first introduced by…
At long times, a fractional Brownian particle in a confining external potential reaches a non-equilibrium (non-Boltzmann) steady state. Here we consider scale-invariant power-law potentials $V(x)\sim |x|^m$, where $m>0$, and employ the…
Besides perturbation theory (which clearly requires the knowledge of the exact unperturbed solution), variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum…
The optimal fluctuation approach is applied to study the most distant (non-universal) tails of the free-energy distribution function P(F) for an elastic string (of a large but finite length L) interacting with a quenched random potential. A…
We propose the new method for finding the non-Gaussian tails of probability distribution function (PDF) for solutions of a stochastic differential equation, such as convection equation for a passive scalar, random driven Navier-Stokes…
We establish the one-to one bilateral interrelations between an asymptotic behavior for the tail of distributions for random variables and its great moments evaluation. Our results generalize the famous Richter's ones.
Besides perturbation theory, which requires, of course, the knowledge of the exact unperturbed solution, variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in…
The search of topological states in non-Hermitian systems has gained a strong momentum over the last two years climbing to the level of an emergent research front. In this Perspective we give an overview with a focus in connecting this…
We propose a novel non-Hermitian adiabatic quantum optimization algorithm. One of the new ideas is to use a non-Hermitian auxiliary "initial'' Hamiltonian that provides an effective level repulsion for the main Hamiltonian. This effect…
We describe a diagrammatic technique for non-Hermitian fermionic systems that is applicable in the steady state, and which allows addressing correlations effects by systematic expansion. Applying this method to exceptional points or rings,…
We consider the quantum tunneling phenomenon in a well-behaved triple-well potential. As required by the semiclassical approximation we take into account the quadratic fluctuations over the instanton which represents as usual the localised…
We provide a necessary and sufficient condition for the ratio of two jointly alpha-Frechet random variables to be regularly varying. This condition is based on the spectral representation of the joint distribution and is easy to check in…
We consider the quantum dynamics of a particle on a lattice for large times. Assuming translation invariance, and either discrete or continuous time parameter, the distribution of the ballistically scaled position $Q(t)/t$ converges weakly…
We demonstrate that quantum fluctuations can cause, under certain conditions, the dynamical instability of pure states that can result in their evolution into mixed states. It is shown that the degree and type of such an instability are…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…
We develop an instanton approach to the non-equilibrium dynamics in one-dimensional random environments. The long time behavior is controlled by rare fluctuations of the disorder potential and, accordingly, by the tail of the distribution…
By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.
The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation…