相关论文: On resonant energy sets for Hamiltonian systems wi…
We show that quantum optical systems preserving the total number of excitations admit a simple classification of possible resonant transitions (including effective), which can be classified by analizying the free Hamiltonian and the…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
The resonator is one of the main building blocks of a plethora of photonic and microwave devices from nanolasers to compact biosensors and magnetic resonance scanners. The symmetry of the resonators is tightly related to their mode…
We introduce two-parameter classes of exactly-solvable novel systems whose Hamiltonian operators could be represented by tridiagonal symmetric matrices in some orthogonal bases. The associated wavefunction is written as point-wise…
Massive planets form within the lifetime of protoplanetary disks and undergo orbital migration due to planet-disk interactions. When the first planet reaches the inner edge of the disk its migration stops and the second planet is locked in…
Rotobreathers in the chain of coupled linearly elastic rotators are analyzed. Each rotator is a particle connected by a massless elastic rod with a frictionless pivot; it has two degrees of freedom, length and angle of rotation. The rods of…
Oscillatory reconnection is a specific type of time-dependent reconnection which involves periodic changes in the magnetic topology of a null point. The mechanism has been reported for a variety of magnetic field strengths and…
We perform a rigorous mathematical analysis of the bending modes of a linear triatomic molecule that exhibits the Renner-Teller effect. Assuming the potentials are smooth, we prove that the wave functions and energy levels have asymptotic…
In this work we present the results of a study of spectral statistics for a classically integrable system, namely the rectangle billiard. We show that the spectral statistics are indeed Poissonian in the semiclassical limit for almost all…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
We study a one-dimensional system composed of three charged bosons confined in an external harmonic potential. More precisely, we investigate the ground-state correlation properties of the system, paying particular attention to the…
The results of an extensive numerical study of the periodic orbits of planar, elliptic restricted three-body planetary systems consisting of a star, an inner massive planet and an outer mass-less body in the external 1:2 mean-motion…
We present a comprehensive study of a one-dimensional two-orbital model at and below quarter-filling that realizes a number of unconventional phases. In particular, we find an excitonic density wave in which excitons quasi-condense with…
In this work, we try to shed some light to the nature of orbits in a three-dimensional potential of a perturbed harmonic oscillator with eight possible channels of escape, which was chosen as an interesting example of open three-dimensional…
We show the existence of drifting orbits for certain perturbations of non-convex Hamiltonian systems with several degrees of freedom. These orbits remain in the vicinity of resonant surfaces where the action variables can undergo changes…
Many physical, chemical and biological processes rely on intrinsic oscillations to employ resonance responses to external stimuli of certain frequency. Such resonance phenomena in biological systems are typically explained by one of two…
We consider a damped impact oscillator subject to the action of a biharmonic force. The conditions for the existence and stability of almost periodic resonance solutions are investigated.
The variance of the number of levels in an energy interval around a level with large quantum numbers (semiclassical quantization) is studied for a particle in a rectangular box. Sampling involves changing the ratio of the rectangle's sides…
A novel method for the calculation of eigenfrequencies of non-uniformly filled spherical cavity resonators is developed. The impact of the system symmetry on the electromagnetic field distribution as well as on its degrees of freedom (the…
The low-energy scattering properties of two aligned identical bosonic and identical fermionic dipoles are analyzed. Generalized scattering lengths are determined as functions of the dipole moment and the scattering energy. Near resonance,…