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

We extend a theory of first order hbar corrections to Gutzwiller's trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform…

We describe a method of analysis which allows for reconstructing the nonlinear disturbance of a high Q harmonic oscillator. When the oscillator is driven with two or more frequencies, the nonlinearity causes intermodulation of the drives,…

For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…

The sparse approximation of high-frequency Helmholtz-type integral operators has many important physical applications such as problems in wave propagation and wave scattering. The discrete system matrices are huge and densely populated;…

The computational cost of quantum algorithms for physics and chemistry is closely linked to the spectrum of the Hamiltonian, a property that manifests in the necessary rescaling of its eigenvalues. The typical approach of using the 1-norm…

We measured the resonance spectra of two stadium-shaped dielectric microwave resonators and tested a semiclassical trace formula for chaotic dielectric resonators proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)]. We found good…

We show that spectral problems for periodic operators on lattices with embedded defects of lower dimensions can be solved with the help of matrix-valued integral continued fractions. While these continued fractions are usual in the…

Gutzwiller's trace formula for the semiclassical density of states in a chaotic system diverges near bifurcations of periodic orbits, where it must be replaced with uniform approximations. It is well known that, when applying these…

We measure elastomechanical spectra for a family of thin shells. We show that these spectra can be described by a "semiclassical" trace formula comprising periodic orbits on geodesics, with the periods of these orbits consistent with those…

In the present article, we investigate the properties of motion in Hamiltonian systems of two and three degrees of freedom, using the distribution of the values of two new dynamical parameters. The distribution functions of the new…

An algorithm for detecting unstable periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-6175] which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.…

The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely…

Many PDEs involving fractional Laplacian are naturally set in unbounded domains with underlying solutions decay very slowly, subject to certain power laws. Their numerical solutions are under-explored. This paper aims at developing accurate…

We propose an efficient numerical method for a non-selfadjoint Steklov eigenvalue problem. The Lagrange finite element is used for discretization. The convergence is proved using the spectral perturbation theory for compact operators. The…

A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of…

Symplectic integrators that preserve the geometric structure of Hamiltonian flows and do not exhibit secular growth in energy errors are suitable for the long-term integration of N-body Hamiltonian systems in the solar system. However, the…

Reconstructive spectrometers are a promising emerging class of devices that combine complex light scattering with inference to enable compact, high-resolution spectrometry. Thus far, the physical determinants of these devices' performance…

We extend the application of the concept of structural invariance to bounded time independent systems. This concept, previously introduced by two of us to argue that the connection between random matrix theory and quantum systems with a…

The problem of computing spectra of operators is arguably one of the most investigated areas of computational mathematics. However, the problem of computing spectra of general bounded infinite matrices has only recently been solved. We…

The existence of periodic orbit bunches is proven for the diamagnetic Kepler problem. Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters.…