Related Experiment Videos
Nodal domain distribution for a nonintegrable two-dimensional anharmonic oscillator
1Kyoto Koka Women's College, 38 Kadono-cho Nishikyogoku, Ukyo-ku, 615-0882 Kyoto, Japan.
Abstract:
We investigate the transition from integrable to chaotic dynamics in the quantum mechanical wave functions from the point of view of the nodal structure by employing a two-dimensional quartic oscillator. We find that the number of nodal domains is drastically reduced as the dynamics of the system changes from integrable to nonintegrable, and then gradually increases as the system becomes chaotic. The number of nodal intersections with the classical boundary as a function of the level number shows a characteristic dependence on the dynamics of the system, too. We also calculate the area distribution of nodal domains and study the emergence of the power law behavior with the Fisher exponent in the chaotic limit.
Related Concept Videos
Nodal Analysis
Consider, for instance, a simple circuit composed of three nodes and three resistors, as shown in...
Damped Oscillations
Although friction and other non-conservative...
Nodal Analysis with Voltage Sources
Consider a circuit that contains four resistors and two voltage sources, as shown in Figure 1. One of these voltage sources is connected between a...
RLC Circuit as a Damped Oscillator
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Oscillations about an Equilibrium Position
Electric Field of a Non Uniformly Charged Sphere
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...