Related papers: Large Petermann factor in chaotic cavities with ma…
Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…
Fix a space dimension $d\ge 2$, parameters $\alpha > -1$ and $\beta \ge 1$, and let $\gamma_{d,\alpha, \beta}$ be the probability measure of an isotropic random vector in $\mathbb{R}^d$ with density proportional to \begin{align*}…
In gravitational scattering the quantum particle probes the Fourier-transforms of a metric. I evaluate the Fourier-transforms of Schwarzschild metrics in standard, harmonic and other coordinate systems in linear and $G^2-$approximations. In…
The $M$-dimensional unitary matrix $S(E)$, which describes scattering of waves, is a strongly fluctuating function of the energy for complex systems such as ballistic cavities, whose geometry induces chaotic ray dynamics. Its statistical…
Radiation from a chaotic cavity filled with gain medium is considered. A set of coupled equations describing the photon density and the population of gain medium is proposed and solved. The spectral distribution and fluctuations of the…
Atoms, propagating across a detuned standing laser wave, can be scattered in a chaotic way even in the absence of spontaneous emission and any modulation of the laser field. Spontaneous emission masks the effect in some degree, but the…
In the framework of a random matrix description of chaotic quantum scattering the positions of $S-$matrix poles are given by complex eigenvalues $Z_i$ of an effective non-Hermitian random-matrix Hamiltonian. We put forward a conjecture on…
We semiclassically derive the leading off-diagonal correction to the spectral form factor of quantum systems with a chaotic classical counterpart. To this end we present a phase space generalization of a recent approach for uniformly…
We present a method based on the scattering $\mathbb{T}$ operator, and conservation of net real and reactive power, to provide physical bounds on any electromagnetic design objective that can be framed as a net radiative emission,…
Chaotic pattern dynamics in many experimental systems show structured time averages. We suggest that simple universal boundary effects underly this phenomenon and exemplify them with the Kuramoto-Sivashinsky equation in a finite domain. As…
A set of zero-range scatterers along its axis lifts the integrability of a harmonic waveguide. Effective solution of the Schr\"odinger equation for this model is possible due to the separable nature of the scatterers and millions of…
The distortion-rate performance of certain randomly-designed scalar quantizers is determined. The central results are the mean-squared error distortion and output entropy for quantizing a uniform random variable with thresholds drawn…
A system plus environment conservative model is used to characterize the nonlinear dynamics when the time averaged energy for the system particle starts to decay. The system particle dynamics is regular for low values of the $N$ environment…
The analysis of diffusive energy spreading in quantized chaotic driven systems, leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation a driven chaotic system exhibits stochastic-like diffusion…
We consider the zero frequency fluctuations of charge inside a mesoscopic conductor in the large capacitance limit. In analogy to current counting statistics we derive the characteristic function of charge fluctuations in terms of the…
This paper discusses the leading-order correction induced by cosmological perturbations on the average expansion rate of an expanding spacetime, containing one or many perfect fluids. The calculation is carried out up to the second order in…
We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a…
An original experimental method for determining the empirical probability distribution function (PDF) of the quality factor (Q) of a mode-stirred reverberation chamber is presented. Spectral averaging of S-parameters across a relatively…
Ensemble filters implement sequential Bayesian estimation by representing the probability distribution by an ensemble mean and covariance. Unbiased square root ensemble filters use deterministic algorithms to produce an analysis (posterior)…
Spatio-temporal instabilities are widespread phenomena resulting from complexity and nonlinearity. In broad-area edge-emitting semiconductor lasers, the nonlinear interactions of multiple spatial modes with the active medium can result in…