Related papers: Ramanujan's oscillator
We investigate parametric resonance in oscillator networks subjected to periodically time-varying oscillations in the edge strengths. Such models are inspired by the well-known parametric resonance phenomena for single oscillators, as well…
The purpose of this article is to describe the singularities of one-dimensional oscillatory integrals, whose phases have a certain singularity, in the form of an asymptotic expansion. In the case of the Laplace integral, an analogous result…
In this paper, we study high-dimensional nonlinear quantum harmonic oscillator equation. We show the equation admits many time quasi-periodic solutions by establishing an abstract infinite dimensional KAM theorem with multiple normal…
We present analytical and numerical results on the joint dynamics of two coupled Duffing oscillators with nonlinearity of opposite signs (hardening and softening). In particular, we focus on the existence and stability of synchronized…
In this paper, we consider estimates for the two-dimensional oscillatory integrals. The phase function of the oscillatory integrals is the linear perturbation of a function having $D$ type singularities. We consider estimates for the…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…
Two harmonic oscillators interacting through the exchange of a quantum field leads to non-zero entanglement between the two, which is absent for classical interaction. In this work, we determine the entanglement between two such harmonic…
Resonance, defined as the oscillation of a system when the temporal frequency of an external stimulus matches a natural frequency of the system, is important in both fundamental physics and applied disciplines. However, the spatial…
The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models.…
We study the dynamics of coupled phase oscillators on a two-dimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phase-locking, we find localized spatiotemporal patterns…
A 3-dimensional non-commutative oscillator with no mass term but with a certain momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The latter corresponds to a Dirac…
We discuss hybrid systems in which a mechanical oscillator is coupled to another (microscopic) quantum system, such as trapped atoms or ions, solid-state spin qubits, or superconducting devices. We summarize and compare different coupling…
The frequency of a classical periodic system can be obtained using action variables without solving the dynamical equations. We demonstrate the construction of two equivalent forms of the action variable for a one dimensional relativistic…
The study of Ramanujan-type congruences for functions specific to additive number theory has a long and rich history. Motivated by recent connections between divisor sums and overpartitions via congruences in arithmetic progressions, we…
A nonlinear model of the scalar field with a coupling between the field and its gradient is developed. It is shown, that such model is suitable for the description of phase transition accompanied by formation of spatial inhomogeneous…
This paper addresses the behavior of large systems of heterogeneous, globally coupled oscillators each of which is described by the generic Landau-Stuart equation, which incorporates both phase and amplitude dynamics of individual…
This paper revisits the resonant behavior of a harmonically-forced Duffing oscillator with a specific attention to phase resonance and to its relation with amplitude resonance. To this end, the different families of resonances, namely…
We review some basic elements on k-fermions, which are objects interpolating between bosons and fermions. In particular, we define k-fermionic coherent states and study some of their properties. The decomposition of a Q-uon into a boson and…
Quantum control of engineered mechanical oscillators can be achieved by coupling the oscillator to an auxiliary degree of freedom, provided that the coherent rate of energy exchange exceeds the decoherence rate of each of the two…
The energy spectrum and wave functions for Kane oscillator describing the spectra of electrons, light hole and spin-orbit-splitting bands in a quantum dots with harmonic lateral confinement is found.