Related papers: Coupled Oscillators and Dielectric Function

In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the…

The dissipative Hofstadter model describes the quantum mechanics of a charged particle in two dimensions subject to a periodic potential, uniform magnetic field, and dissipative force. Its phase diagram exhibits an SL(2,Z) duality symmetry…

Classical electrodynamics uses a dielectric constant to describe the polarization response of electromechanical systems to changes in an electric field. We generalize that description to include a wide variety of responses to changes in the…

Flexoelectricity is characterised by the coupling of the gradient of the deformation and the electrical polarization in a dielectric material. A novel micromorphic approach is presented to accommodate the resulting higher-order gradient…

The dielectric response and structural properties of finite-temperature electron liquids are central to accurately describing the physical behavior of electronic systems. This study presents a robust analytical model for the static…

We report a thorough dielectric characterization of the alpha relaxation of glass forming glycerol with varying additions of LiCl. Nine salt concentrations from 0.1 - 20 mol% are investigated in a frequency range of 20 Hz - 3 GHz and…

It is shown that the classical damped harmonic oscillator belongs to the family of fourth-order Pais-Uhlenbeck oscillators. It follows that the solutions to the damped harmonic oscillator equation make the Pais-Uhlenbeck action stationary.…

Inspired by the natural piezoelectric effect, we introduce hybrid-wave electromechanical meta-atoms and meta-molecules that consist of coupled electrical and mechanical oscillators with similar resonance frequencies. We propose an…

We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncom- mutative space where the noncommutativity is induced by a shift of the dynamical variables with generators of SL(2;R) in a unitary irreducible…

We show that the dissipation term in the Hamiltonian for a couple of classical damped-amplified oscillators manifests itself as a geometric phase and is actually responsible for the appearance of the zero point energy in the quantum…

The polarization function of electrons with the tilted Dirac cone found in organic conductors is studied using the tilted Weyl equation. The dynamical property is explored based on the analytical treatment of the particle-hole excitation.…

The Seebeck coefficient plays a fundamental role in identifying the efficiency of a thermoelectric device. Its theoretical evaluation for atomistic models is routinely based on Density Functional Theory calculations combined with the…

General formalism of quantum field theory and addition theorem for Bessel functions are applied to derive formula for Casimir-Polder energy of interaction between a polarizable particle and a dilute dielectric ball. The equivalence of…

We present a first-principles calculation of the electronic properties of crystalline silicon and gallium arsenide in a uniform electric field. Polarized Wannier-like functions which are confined in a finite region are obtained by…

We have shown that in some region where the Euler integral of the first kind diverges, the Euler formula defines a generalized function. The connected of this generalized function with the Dirac delta function is found.

Some aspects of adelic generalized functions, as linear continuous functionals on the space of Schwartz-Bruhat functions, are considered. The importance of adelic generalized functions in adelic quantum mechanics is demonstrated. In…

In this paper an approach is outlined. With this approach some explicit algorithms can be applied to solve the initial value problem of $n-$dimensional damped oscillators. This approach is based upon following structure: for any…

The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of Morera theorem, because distributional Cauchy-Riemann…

Background: The isotropic harmonic oscillator supplemented by a strong spin-orbit interaction has been the cornerstone of nuclear structure since its inception more than seven decades ago. In this paper we introduce---or rather…

Electron pairs have an illustrious history in chemistry, from powerful concepts to understanding structural stability and reactive changes, to the promise of serving as building blocks of quantitative descriptions of the electronic…