相关论文: On resumming periodic orbits in the spectra of int…

We address the problems in applying cycle expansions to bound chaotic systems, caused by e.g. intermittency and incompleteness of the symbolic dynamics. We discuss zeta functions associated with weighted evolution operators and in…

Traditional resolvent analysis is a powerful framework for identifying the most amplified input-output structures in fluid flows from a stationary base state. Extending this resolvent analysis to periodic base flows poses computational…

In semiclassical theories for chaotic systems such as Gutzwiller's periodic orbit theory the energy eigenvalues and resonances are obtained as poles of a non-convergent series g(w)=sum_n A_n exp(i s_n w). We present a general method for the…

We prove convergence of the spectral element method for piecewise polynomial collocation applied to periodic boundary value problems for functional differential equations. In particular, we prove that the numerical collocation solution…

In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even…

We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…

This note is devoted to inverse spectral problems for canonical Hamiltonian systems on the half-line. An approach to inverse spectral problems based on the use of truncated Toeplitz operators has been especially effective in the case when…

This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called…

By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for…

We develop a practical approach to semidefinite programming (SDP) that includes the von Neumann entropy, or an appropriate variant, as a regularization term. In particular we solve the dual of the regularized program, demonstrating how a…

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…

Semiclassical spectra weighted with products of diagonal matrix elements of operators A_{alpha}, i.e., g_{alpha alpha'}(E) = sum_n <n|A_{alpha}|n><n|A_{alpha'}|n>/(E-E_n) are obtained by harmonic inversion of a cross-correlation signal…

We consider the semiclassical limit of the spectral form factor $K(\tau)$ of fully chaotic dynamics. Starting from the Gutzwiller type double sum over classical periodic orbits we set out to recover the universal behavior predicted by…

This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…

In exactly solvable quantum-mechanical systems, ladder and intertwining operators play a central role because, if they are found, the energy spectra can be obtained algebraically. In this paper, we propose the spectral intertwining relation…

Despite the huge spread and economical importance of configurable software systems, there is unsatisfactory support in utilizing the full potential of these systems with respect to finding performance-optimal configurations. Prior work on…

The generalization of the Gutzwiller approximation to inhomogeneous systems is considered, with extra spin-and-site-dependent fugacity factors included. It is found that the inclusion of fugacity factors reconciles the seemingly…

Well-conditioned spectral collocation and spectral methods have recently been proposed to solve differential equations. In this paper, we revisit the well-conditioned spectral collocation methods proposed in [T.~A. Driscoll, {\it J. Comput.…

This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the…

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…