相关论文: Classical Mobius-Ring Resonators Exhibit Fermion-B…
We study the vibrational motion of membrane resonators upon strong drive in the strongly nonlinear regime. By imaging the vibrational state of rectangular siliconnitride membrane resonators and by analyzing the frequency response using…
For a quantum system of N identical, harmonically interacting particles in a one-dimensional harmonic trap we calculate for the bosonic and fermionic ground state the corresponding 1-particle reduced density operator $\rho_1$ analytically.…
The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic…
Complete description of the classical and quantum dynamics of a particle in an anisotropic, rotating, harmonic trap is given. The problem is studied in three dimensions and no restrictions on the geometry are imposed. In the generic case,…
We study the evolution of an oscillator interacting via the most general bilinear coupling (with time-independent coefficients) with an ``environment'' consisting of a set of other harmonic oscillators. We are mainly interested in a…
We consider a quantum space with rotationally invariant noncommutative algebra of coordinates and momenta. The algebra contains tensors of noncommutativity constructed involving additional coordinates and momenta. In the rotationally…
We investigate the dynamics of a microelectromechanical (MEMS) self-sustained oscillator supporting multiple resonating and interacting modes. In particular, the interaction of the first four flexural modes along with the first torsional…
We obtain results describing the behavior of the action of rotation generators on polynomials over a commutative ring. We also explore harmonic polynomials in a purely algebraic setting.
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
We study a parametrically modulated oscillator that has two stable states of vibrations at half the modulation frequency $\omega_F$. Fluctuations of the oscillator lead to interstate switching. A comparatively weak additional field can…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
Linear mechanical systems with time-modulated parameters can harbor oscillations with amplitudes that grow or decay exponentially with time due to the phenomenon of parametric resonance. While the resonance properties of individual…
A two interacting rotors Hamiltonian is alternatively treated semi-classically and by a Dyson boson expansion method. The linearized equations of motion lead to dispersion equation for the wobbling frequency. One defined a ground band with…
We investigate the occurrence of vibrational resonance in both classical and quantum mechanical Morse oscillators driven by a biharmonic force. The biharmonic force consists of two forces of widely different frequencies \omega and \Omega…
The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it…
The frequency dependence of the interlayer conductivity of a layered Fermi liquid in a magnetic field which is tilted away from the normal to the layers is considered. For both quasi-one- and quasi-two-dimensional systems resonances occur…
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
Mechanical resonators that possess coupled modes with harmonic frequency relations have recently sparked interest due to their suitability for controllable energy transfer and non-Hermitian dynamics. Here, we show coupling between high…
We study the localization of particles rotating in a two-dimensional harmonic potential by solving their rotational spectrum using many-particle quantum mechanics and comparing the result to that obtained with quantizing the rigid rotation…
This book chapter describes the dynamics of a modulated oscillator for resonant and nonresonant modulation. Two types of resonant modulation are considered: additive, with frequency close to the oscillator eigenfrequency, and parametric,…