相关论文: Analysis of Superoscillatory Wave Functions
Fluctuation dynamics of an experimentally measured observable offer a primary signal for nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean have actively been studied recently, constraints for…
When the universe is treated as a quantum system, it is described by a wave function. This wave function is a function not only of the matter fields, but also of spacetime. The no-boundary proposal is the idea that the wave function should…
In this paper we study the eigenvalues of the angular spheroidal wave equation and its generalization, the Coulomb spheroidal wave equation. An associated differential system and a formula for the connection coefficients between the various…
Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering…
Silicon microdisks are optical resonators that can exhibit surprising nonlinear behavior. We present a new analysis of the dynamics of these resonators, elucidating the mathematical origin of spontaneous oscillations and deriving…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
We define the quadratic algebra su(2)_{\alpha} which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can…
The object of this laboratory work: to explore dependence mass point oscillatory motion parameters in the following cases: - without resistance (free oscillations); - the resistance force is proportional to the velocity vector; - the…
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…
This work deals with the measurability of Fourier integral operators (FIOs) with random phase and amplitude functions. The key ingredient is the proof that FIOs depend continuously on their phase and amplitude functions, taken from suitable…
We discuss theoretically the properties of an electromechanical oscillating system whose operation is based upon the cyclic conservative conversion between gravitational potential, kinetic, and magnetic energies. The system consists of a…
In this study, we estimate parameters in stochastic oscillatory systems by developing a novel cost function. This function incorporates power spectral density, analytic signal, and position crossings, each weighted to capture distinct…
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple…
A numerical method to build an orthonormal basis of properly symmetrized hyperspherical harmonic functions is developed. As a part of it, refined algorithms for calculating the transformation coefficients between hyperspherical harmonics…
Gutzwiller projection allows a construction of an assortment of variational wave functions for strongly correlated systems. For quantum spin S=1/2 models, Gutzwiller-projected wave functions have resonating-valence-bond structure and may…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
Sylvester showed that the partition function can be written as a sum of the polynomial term and quasiperiodic components called the Sylvester waves. Recently an explicit expression of the Sylvester wave as a finite sum over the Bernoulli…
In contrast to wave functions in nonrelativistic quantum mechanics interpreted as probability amplitudes, wave functions in relativistic quantum mechanics have generalized meanings such as charge-density amplitudes, energy-density…
A short review of the history and the contemporary numerical calculations of the operation of an electronic device for generation of electric oscillations by negative differential conductivity of a supercooled below the critical temperature…
We collect some peculiarities of higher-order fractional Laplacians $(-\Delta)^s$, $s>1$, with special attention to the range $s\in(1,2)$, which show their oscillatory nature. These include the failure of the polarization and…