Related papers: The Dance of the Sheared Eigenfunctions
We develop a nonequilibrium mode-coupling theory for uniformly sheared systems starting from microscopic, thermostatted SLLOD equations of motion. Our theory aims at describing stationary-state properties including rheological ones of…
We consider a two-parameter non hermitean quantum-mechanical hamiltonian that is invariant under the combined effects of parity and time reversal transformation. Numerical investigation shows that for some values of the potential parameters…
Recently, Chatterjee has introduced a new coefficient of correlation which has several natural properties. In particular, the coefficient attains its maximal value if and only if one variable is a measurable function of the other variable.…
Deterministic and stochastic coupled oscillators with inertia are studied on the rectangular lattice under the shear-velocity boundary condition. Our coupled oscillator model exhibits various nontrivial phenomena and there are various…
Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the…
Within the framework of the recently proposed formalism using non-hermitean Hamiltonians constrained merely by their PT invariance we describe a new exactly solvable family of the harmonic-oscillator-like potentials with non-equidistant…
We describe analytical and numerical results on the statistical properties of complex eigenvalues and the corresponding non-orthogonal eigenvectors for non-Hermitian random matrices modeling one-channel quantum-chaotic scattering in systems…
In this paper we show how the quantum mechanics of the inverted harmonic oscillator can be mapped to the quantum mechanics of a particle in a super-critical inverse square potential. We demonstrate this by relating both of these systems to…
We analyze transition potentials $(V(r) \stackrel{r\sim 0}{\rightarrow} {\alpha r^{-2}})$ in non-relativistic quantum mechanics using the techniques of supersymmetry. For the range $-1/4 < \alpha < 3/4$, the eigenvalue problem becomes…
In this paper, the squared eigenfunction symmetries for the BTL and CTL hierarchies are explicitly constructed with the suitable modification of the ones for the TL hierarchy, by considering the BTL and CTL constraints. Also the connections…
A quasi-product on the normed space is defined. In addition, the notions of the eigenvectors of a linear operator can be extended for the nonlinear operator. Based on the quasi-product and the generalized eigenvectors, the spectral theorems…
We study spectral properties of a non-Hermitian Hamiltonian describing a quantum particle propagating in a random imaginary scalar potential. Cast in the form of an effective field theory, we obtain an analytical expression for the ensemble…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
We tried to determine the range of validity of a recently proposed modification of the Hellmann potential that leads to analytical eigenvalues and eigenfunctions. We discuss the difficulties that we found in the analysis of the main…
We consider two families of extensions of the oscillator in a $d$-dimensional constant-curvature space and analyze them in a deformed supersymmetric framework, wherein the starting oscillator is known to exhibit a deformed shape invariance…
We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories…
We report the complete statistical treatment of a system of particles interacting via Newtonian forces in continuous boundary-driven flow, far from equilibrium. By numerically time-stepping the force-balance equations of a model fluid we…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
The presence of long-ranged correlations in a fluid undergoing uniform shear flow is investigated. An exact relation between the density autocorrelation function and the density-mometum correlation function implies that the former must…
Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schr\"odinger equation provide bases of representations of the $q$-deformed Heisenberg-Weyl algebra. When the parameter $q$ is a…