Related papers: A Note on Approximating the Symplectic Spectrum
Within the framework of likelihood-based statistical tests for high energy physics measurements, we derive generalized expressions for estimating the statistical significance of discovery using the asymptotic approximations of Wilks and…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite…
This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are…
Complex Gaussian basis sets are optimized to accurately represent continuum radial wavefunctions over the whole space. First, attention is put on the technical ability of the optimization method to get more flexible series of Gaussian…
This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
We investigate the use of extended phase-space symplectic integration for simulating two different classes of electron dynamics. The first one, with one and a half degrees of freedom, comes from plasma physics and describes the classical…
We address quantum systems isospectral to the harmonic oscillator, as those found within the framework of supersymmetric quantum mechanics, as potential resources for continuous variable quantum information. These deformed oscillator…
A class of non-linear eigenvalue problems defined in the form of operator polynomials is investigated. The problems are related to wave equations which appear in a relativistic quantum field theory. Spectral asymptotics for this class are…
A class of non-selfadjoint, $\PT$-symmetric operators is identified similar to a self-adjoint one, thus entailing the reality of the spectrum. The similarity transformation is explicitly constructed through the method of the quantum normal…
This work studies finite sample approximations of the exact and entropic regularized Wasserstein distances between centered Gaussian processes and, more generally, covariance operators of functional random processes. We first show that…
We present a new technique, based on semivariogram methodology, for obtaining point estimates for use in prior modeling for solving Bayesian inverse problems. This method requires a connection between Gaussian processes with covariance…
A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…
We study an abstract family of asymptotically degenerating variational problems. Those are natural generalisations of families of problems emerging upon application of a rescaled Floquet-Bloch-Gelfand transform to resolvent problems for…
We study operators obtained by coupling an $n \times n$ random matrix from one of the Gaussian ensembles to the discrete Laplacian. We find the joint distribution of the eigenvalues and resonances of such operators. This is one of the…
We study the third quantized formulation of the massive inflaton quantum cosmology for the Friedmann-Robertson-Walker universe. The Hamiltonian is equivalent to an infinite number of coupled oscillators whose couplings and frequencies are…
Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of positive-definite matrices (here called covariance…
We propose to quantify the complexity of non-equilibrium steady state density operators, as well as of long-lived Liouvillian decay modes, in terms of level spacing distribution of their spectra. Based on extensive numerical studies in a…
Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…