We formulate a semiclassical theory for systems with spin-orbit interactions. Using spin coherent states, we start from the path integral in an extended phase space, formulate the classical dynamics of the coupled orbital and spin degrees of freedom, and calculate the ingredients of Gutzwiller's trace formula for the density of states. For a two-dimensional quantum dot with a spin-orbit interaction of Rashba type, we obtain satisfactory agreement with fully quantum-mechanical calculations. The mode-conversion problem, which arose in an earlier semiclassical approach, has hereby been overcome.
We discuss the semiclassical approaches for describing systems with spin-orbit interactions by Flynn (1991, 1992), Frisk and Guhr (1993), and by Keppeler (1998, 1999). We use these methods to derive trace formulae for several two-and three-dimensional model systems, and exhibit their successes and limitations. We discuss, in particular, also the mode conversion problem that arises in the strong-coupling limit.v3, in print for J. Phys. A 35, 6009 (2002) Awhere T ppo is the period of the primitive orbit and M po the stability matrix of the periodic orbit.Examples of amplitude factors for systems with continuous symmetries or for integrable systems may be found in the literature quoted in the introduction. The po sum in (4) does not converge in most cases; it must in general be understood as a an asymptotic series that is only semiconvergent. However, much practical use can be made of trace formulae if one does not attempt to obtain an exact energy spectrum (given by the poles of the
Abstract. In this work, we address the problem of human pose estimation in still images by proposing a holistic model for learning the appearance of the human body from image patches. These patches, which are randomly chosen, are used for extracting features and training a regression forest. During training, a mapping between image features and human poses, defined by joint offsets, is learned; while during prediction, the body joints are estimated with an efficient mode-seeking algorithm. In comparison to other holistic approaches, we can recover body poses from occlusion or noisy data. We demonstrate the power of our method in two publicly available datasets and propose a third one. Finally, we achieve state-of-the-art results in comparison to other approaches.
We summarize recent developments of the semiclassical description of shell effects in finite fermion systems with explicit inclusion of spin degrees of freedom, in particluar in the presence of spin-orbit interactions. We present a new approach that makes use of spin coherent states and a correspondingly enlarged classical phase space. Taking suitable limits, we can recover some of the earlier approaches. Applications to some model systems are presented.
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