Related papers: An open systems approach to calculating time depen…
The (forced) periodic orbit spectrum is calculated for a chaotic time series (BZ reaction).
With increasing energy the diamagnetic hydrogen atom undergoes a transition from regular to chaotic classical dynamics, and the closed orbits pass through various cascades of bifurcations. Closed orbit theory allows for the semiclassical…
We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the…
The stationary one-dimensional tight-binding Schredinger equation with a weak diagonal long-range correlated disorder in the potential is studied. An algorithm for constructing the discrete binary on-site potential exhibiting a hybrid…
The computation of scientific data can be very time consuming even if they are ultimately determined by a small number of parameters. The principle of compressed sampling suggests that we can achieve a considerable decrease in the…
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively…
The transient-absorption spectrum of a $V$-type three-level system is investigated, when this is periodically excited by a train of equally spaced, $\delta$-like pump pulses as, e.g., from an optical-frequency-comb laser. We show that, even…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
The spectral gap occupies a role of central importance in many open problems in physics. We present an approach for evaluating the spectral gap of a Hamiltonian from a simple ratio of two expectation values, both of which are evaluated…
A key goal of radio and $\gamma-$ray observations of active galactic nuclei is to characterize their time variability in order to elucidate physical processes responsible for the radiation. I describe algorithms for relevant time series…
We present a spectroscopy scheme using transfer matrix and tensor network. With this method, the energy spectrum is obtained from the eigenvalues of the transfer matrix which is estimated by coarse grained tensor network of a lattice model,…
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…
Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of…
We study the spectrum of a one-dimensional Schroedinger operator perturbed by a fast oscillating potential. The oscillation period is a small parameter. The essential spectrum is found in an explicit form. The existence and multiplicity of…
We address the problem of estimating the spherical-harmonic power spectrum of a statistically isotropic scalar signal from noise-contaminated data on a region of the unit sphere. Three different methods of spectral estimation are…
In close binary systems the atmosphere of one or both components can be significantly influenced by irradiation from the companion. Often the irradiated atmosphere is simulated with a single-temperature approximation for the entire…
In quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us…
We developed a measurement system that enables the reconstruction of {\gamma}-ray time spectra in cascade decay schemes. As this system records all the time and energy information of {\gamma}-rays, reconstruction is possible after the…
Two- and multi-dimensional spectroscopy is used in physics and chemistry to obtain structural and dynamical information that would otherwise be invisible by the projection into a one-dimensional data set such as a single emission or…
The superradiant emission properties from an atomic ensemble with cascade level configuration is numerically simulated. The correlated spontaneous emissions (signal then idler fields) are purely stochastic processes which are initiated by…