Related papers: Spectral method for efficient computation of time-…
Motivated by possible applications of spectral singularities in optics, we develop a semiclassical method of computing spectral singularities. We use this method to examine the spectral singularities of a planar slab gain medium whose gain…
The framework of transition state theory (TST) provides a powerful way for analyzing the dynamics of physical and chemical reactions. While TST has already been successfully used to obtain reaction rates for systems with a single…
While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…
We propose a variant of the Rapidly Exploring Random Tree Star (RRT$^{\star}$) algorithm to synthesize trajectories satisfying a given spatio-temporal specification expressed in a fragment of Signal Temporal Logic (STL) for linear systems.…
We develop a linear response theory to provide a unified description of two recent spectroscopy protocols for probing one-dimensional supersolid states realized in cold-atom systems. Both protocols involve applying a periodic optical…
This article proposes spectral numerical methods to solve the time evolution of convection problems with viscosity strongly depending on temperature at infinite Prandtl number. Although we verify the proposed techniques just for viscosities…
Intracavity frequency-doubled solid-state lasers exhibit intensity fluctuations of their light output, which are cause by nonlinear dynamical processes. Up to now, there are different solutions to this problem, but they reduce the output…
We present a fully quantum mechanical treatment of a single-mode atomic cavity with a pumping mechanism and an output coupling to a continuum of external modes. This system is a schematic description of an atom laser. In the dilute limit…
Attosecond transient absorption spectroscopy has thus far been lacking the capability to simultaneously characterize the intense laser pulses at work within a time-resolved quantum-dynamics experiment. However, precise knowledge of these…
The study of the long time conservation for numerical methods poses interesting and challenging questions from the point of view of geometric integration. In this paper, we analyze the long time energy and magnetic moment conservations of…
Ultra-high intensity femtosecond lasers at focus are now routinely used for relativistic motion of charged particles with peak intensities over 10^18W/cm^2. Such high-field experiments are very sensitive to the value of the peak intensity.…
Ultrafast lasers ($< 500$ fs) have enabled laser-matter interactions at intensities exceeding $10^{18} \rm{Wcm}^{-2}$ with only millijoules of laser energy. However, as pulse durations become shorter, larger spectral bandwidths are…
We perform a first-principles calculation of the quantum-limited laser linewidth, testing the predictions of recently developed theories of the laser linewidth based on fluctuations about the known steady-state laser solutions against…
In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…
A new spectral particle-in-cell (PIC) method for plasma modeling is presented and discussed. In the proposed scheme, the Fourier-Bessel transform is used to translate the Maxwell equations to the quasi-cylindrical spectral domain. In this…
We extend the spectral method for proving limit theorems to random non-uniformly expanding dynamical systems. This yields the CLT and moderate deviations principles (MDP). We show that as the amount of non-uniformity decreases the CLT rates…
The subject of this paper is the design of efficient and stable spectral methods for time-dependent partial differential equations in unit balls. We commence by sketching the desired features of a spectral method, which is defined by a…
Bloch equations for the atomic population and the polarization/coherence and the equation of motion for the photon number in a laser are solved in steady state as a function of the pump rate. Two level atom and two modes of three levels…
Active control of the pump spatial profile is proposed to exercise control over random laser emission. We demonstrate numerically the selection of any desired lasing mode from the emission spectrum. An iterative optimization method is…
Adaptive methods of laser irradiation of plasmas are proposed consisting of deterministic, `on-off' amplitude modulations in time, and intermittently changing speckle-patterns. These laser pulses consist of a series of picosecond time-scale…