ABSTRACT
Ammonia is a well-known example of a two-state system and must be described in quantum-mechanical terms. In this article, we will explain the tunneling phenomenon that occurs in ammonia molecules from the perspective of trajectory-based quantum dynamics, rather than the usual quantum probability perspective. The tunneling of the nitrogen atom through the potential barrier in ammonia is not merely a probability problem; there are underlying reasons and mechanisms explaining why and how the tunneling in ammonia can happen. Under the framework of quantum Hamilton mechanics, the tunneling motion of the nitrogen atom in ammonia can be described deterministically in terms of the quantum trajectories of the nitrogen atom and the quantum forces applied. The vibrations of the nitrogen atom about its two equilibrium positions are analyzed in terms of its quantum trajectories, which are solved from the Hamilton equations of motion. The vibration periods are then computed by the quantum trajectories and compared with the experimental measurements.
Subject(s)
Ammonia/chemistry , Molecular Dynamics Simulation , Quantum TheoryABSTRACT
Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain extends to the complex space, including the generation of complex trajectory, the definition of the complex probability, and the relation of the complex probability to the quantum probability. The complex treatment proposed in this article applies the optimal quantum guidance law to derive the stochastic differential equation governing a particle's random motion in the complex plane. The probability distribution ρc(t,x,y) of the particle's position over the complex plane z=x+iy is formed by an ensemble of the complex quantum random trajectories, which are solved from the complex stochastic differential equation. Meanwhile, the probability distribution ρc(t,x,y) is verified by the solution of the complex Fokker-Planck equation. It is shown that quantum probability Ψ2 and classical probability can be integrated under the framework of complex probability ρc(t,x,y), such that they can both be derived from ρc(t,x,y) by different statistical ways of collecting spatial points.
ABSTRACT
An important question in healthcare for older patients is whether age-related changes in cortical reorganization can be measured with advancing age. This study investigated the factors behind such age-related changes, using time-frequency analysis of event-related potentials (ERPs). We hypothesized that brain rhythms was affected by age-related changes, which could be reflected in the ERP indices. An oddball task was conducted in two experimental groups, namely young participants (N=15; mean age 23.7±2.8 years) and older participants (N=15; mean age 70.1±7.9 years). Two types of stimuli were used: the target (1 kHz frequency) and standard (2 kHz frequency). We scrutinized three ERP indices: event-related spectral power (ERPSP), inter-trial phase-locking (ITPL), and event-related cross-phase coherence (ERPCOH). Both groups performed equally well for correct response rate. However, the results revealed a statistically significant age difference for inter-trial comparison. Compared with the young, the older participants showed the following age-related changes: (a) power activity decreased; however, an increase was found only in the late (P3, 280-450 ms) theta (4-7 Hz) component over the bilateral frontal and temporo-frontal areas; (b) low phase-locking in the early (N1, 80-140 ms) theta band over the parietal/frontal (right) regions appeared; (c) the functional connections decreased in the alpha (7-13 Hz) and beta (13-30 Hz) bands, but no difference emerged in the theta band between the two groups. These results indicate that age-related changes in task-specific brain activity for a normal aging population can be depicted using the three ERP indices.
