Results 1 - 10 of 9307
Results 1 - 10 of 9307. Search took: 0.027 seconds
|Sort by: date | relevance|
[en] We derive a semiclassical secular equation which applies for quantized (compact) billiards of any shape. Our approach is based on the fact that the billiard boundary defines two dual problems: the 'inside problem' of the bounded dynamics, and the 'outside problem' which can be looked upon as a scattering from a boundary as an obstacle. This duality exists both on the classical and quantum mechanical levels, and is therfore very useful in deriving a semiclassical quantization rule. We obtain a semiclassical secular equation which is based on classical input from a finite number of classical periodic orbits. We compare our results to secular equations which were recently derived by other means, and provide some numerical data which illustrates our method when applied to the quantization of the Sinai billiard. (author)
[en] A unified presentation of the most common semi-classical approximations to non-relativistic quantum mechanics is given: the Wigner representation, the WKB-Maslov method and Bohr like quantization along closed classical paths
[fr]On donne une presentation unifiee des approximations semi-classiques les plus communes de la mecanique quantique non relativiste: la representation de Wigner, la methode W.K.B.-Maslov et la quantification de Bohr le long des chemins classiques fermes
[en] In multidimensional barrier tunneling, there exist different semiclassical mechanisms, i.e., the well-established instanton mechanism and the recently discovered mechanism utilizing complexified stable-unstable manifolds as the guide of tunneling paths. We demonstrate that the transition between the two mechanisms can be observed as a remarkable change in the spectrum of tunneled particles and propose a practical method to evaluate the tunneling rates of the two mechanisms.
[en] In this paper, we investigate quantum ergodicity in negatively curved manifolds. We consider the symbols depending on a semiclassical parameter h with support shrinking down to a point as . The rate of shrinking is a power of . This extends the asymptotic equidistribution of quantum ergodic eigenfunctions to a logarithmical scale. (paper)
[en] Using the semiclassical picture proposed by Arndt and Roper for Δ33 resonance, in this work we show that the other resonances as well as dibaryons can be described by this approach. (author)
[en] The open binding quarks in hadron is obtained from non-perturbative calculations of the hadronic field correlations in the frame of the SU(N) gauge field theory. Differences are displayed mainly in the calculation of the partition function but as it turns out disappear from the expressions for the correlators
[en] Highlights: • The fluctuations in the escape probability manifest a good agreement with the diffracted distributions. • Coherent backscattering leads to prominent interference between electrons. • There is a good correspondence between the distribution of classical trajectories and the time-reversed path. We use a semiclassical approximation to study the escape of electrons through a circular mesostructure with the diffractive effect at the entrance lead taken into consideration. We find that the fluctuating shapes of the escape probability manifests a good agreement with the diffracted distributions of the incident angles for different transverse modes, and show that several classical trajectories with certain lengths have prominent contributions on the escape probability. In addition, we define the coherence factor to investigate the interference between electrons for different transverse modes and we find that it is the coherent backscattering that is responsible for the prominent interference. Moreover, we find there is a good correspondence between the distribution of classical trajectories and the time-reversed path.
[en] Traditionally quantum mechanics is viewed as having made a sharp break from classical mechanics, and the concepts and methods of these two theories are viewed as incommensurable with one another. A closer examination of the history of quantum mechanics, however, reveals that there is a strong sense in which quantum mechanics was built on the backbone of classical mechanics. As a result, there is a considerable structural continuity between these two theories, despite their important differences. These structural continuities provide a ground for semiclassical methods in which classical structures, such as trajectories, are used to investigate and model quantum phenomena. After briefly tracing the history of semiclassical approaches, I show how current research in semiclassical mechanics is revealing new bridges across the quantum-classical divide.