相关论文: On the Isochronous analytic motions and the quantu…

In this paper, the quantum spectrum of isochronous potentials is investigated. Given that the frequency of the classical motion in such potentials is energy-independent, it is natural to expect their quantum spectra to be equispaced.…

Isochrone potentials, as defined by Michel H\'enon in the fifties, are spherically symmetric potentials within which a particle orbits with a radial period that is independent of its angular momentum. Isochrone potentials encompass the…

In many physical problems it is not possible to find an exact solution. However, when some parameter in the problem is small, one can obtain an approximate solution by expanding in this parameter. This is the basis of perturbative methods,…

We revisit in this note the H\'enon's isochrone problem. By using the standard Abel inversion technique for one-dimensional motion, we recover in a simple way the H\'enon's parabolae and get all isochrone central potentials under mild…

We are interested at first in the study of the monotonicity for the period function of the conservative equation \ $(1)\quad \ddot x + g(x) = 0.$\quad Some refinements of known criteria are brought. Moreover, we give necessary and…

We study the existence of centers of planar autonomous system of the form $$(S) \quad \dot x=y,\qquad \dot y = -h(x) - g(x)y - f(x)y^2.$$ We are interested in the period function $T$ around a center 0. A sufficient condition for the…

We introduce the relativistic version of the well-known Henon's isochrone spherical models: static spherically symmetrical spacetimes in which all bounded trajectories are isochrone in Henon's sense, i.e., their radial periods do not depend…

We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions---subsets of the phase space filled…

Revisiting and extending an old idea of Michel H\'enon, we geometrically and algebraically characterize the whole set of isochrone potentials. Such potentials are fundamental in potential theory. They appear in spherically symmetrical…

The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…

We extend topological string methods in order to perform WKB approximations for quantum mechanical problems with higher order potentials efficiently. This requires techniques for the evaluation of the relevant quantum periods for Riemann…

Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been…

We explore the possibility of modifying the Lewis-Riesenfeld method of invariants developed originally to find exact solutions for time-dependent quantum mechanical systems for the situation in which an exact invariant can be constructed,…

It has been recently realized that, in the case of polynomial potentials, the exact WKB method can be reformulated in terms of a system of TBA equations. In this paper we study this method in various examples. We develop a graphical…

We apply the effective potential analytic continuation (EPAC) method to one-dimensional asymmetric potential systems to obtain the real time quantum correlation functions at various temperatures. Comparing the EPAC results with the exact…

A method, recently devised to obtain analytical approximations to certain classes of integrals, is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of…

For a single degree of freedom confined mechanical system with given energy, we know that the motion is always periodic and action-angle variables are convenient choice as conjugate phase-space variables. We construct action-angle coherent…

An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the dynamics may change and the phenomenon of resonance can appear. In this context,…

In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…

In this paper we give a streamlined derivation of the exact quantization condition (EQC) on the quantum periods of the Schr\"odinger problem in one dimension with a general polynomial potential, based on Wronskian relations. We further…