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Search Results: 1 - 10 of 585787 matches for " P. A. Horvathy "
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Fermat Principle for spinning light
C. Duval,Z. Horvathy,P. A. Horvathy
Physics , 2005, DOI: 10.1103/PhysRevD.74.021701
Abstract: Mimicking the description of spinning particles in General Relativity, the Fermat Principle is extended to spinning photons. Linearization of the resulting Papapetrou-Souriau type equations yields the semiclassical model used recently to derive the ``Optical Hall Effect'' (alias the ``Optical Magnus Effect'') for polarized light.
The Maslov correction in the semiclassical Feynman integral
P. A. Horvathy
Physics , 2007, DOI: 10.2478/s11534-010-0055-3
Abstract: The Maslov correction to the wave function is to the jump of $-\pi/2$ in the phase when the system passes through a caustic point. This phenomenon is related to the second variation and to the geometry of paths, as conveniently explained in Feynman's path integral framework. The results can be extended to any system using the semiclassical approximation. The 1-dimensional harmonic oscillator is used to illustrate the different derivations reviewed here.
Anomalous Hall Effect in non-commutative mechanics
P. A. Horvathy
Physics , 2006, DOI: 10.1016/j.physleta.2006.07.033
Abstract: The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole in momentum space as found recently in some ferromagnetic semiconductors while observing the anomalous Hall effect, we get a transverse shift, similar to that in the optical Hall effect.
The non-commutative Landau problem
P. A. Horvathy
Physics , 2002, DOI: 10.1006/aphy.2002.6271
Abstract: The Landau problem is discussed in two similar but still different non-commutative frameworks. The ``standard'' one, where the coupling to the gauge field is achieved using Poisson brackets, yields all Landau levels. The ``exotic'' approach, where the coupling to the gauge field is achieved using the symplectic structure, only yields lowest-Landau level states, as advocated by Peierls and used in the description of the ground states of the Fractional Quantum Hall Effect. The same reduced model also describes vortex dynamics in a superfluid ${}^4$He film. Remarkably, the spectrum depends crucially on the quantization scheme. The system is symmetric w. r. t. area-preserving diffeomorphisms.
Celestial mechanics, from high-school to Newton's Principia
P. A. Horvathy
Physics , 2003,
Abstract: A high-school exercise is used to get an insight into planetary motion.
Exotic galilean symmetry and non-commutative mechanics in mathematical & in condensed matter physics
P. A. Horvathy
Physics , 2006,
Abstract: The ``exotic'' particle model with non-commuting position coordinates, associated with the two-parameter central extension of the planar Galilei group, can be used to derive the ground states of the Fractional Quantum Hall Effect. The relation to other NC models is discussed. Anomalous coupling is presented. Similar equations arise for a semiclassical Bloch electron, used to explain the anomalous/spin/optical Hall effects.
Mathisson' spinning electron: noncommutative mechanics & exotic Galilean symmetry, 66 years ago
P. A. Horvathy
Physics , 2003,
Abstract: The acceleration-dependent system with noncommuting coordinates, proposed by Lukierski, Stichel and Zakrzewski [Ann. Phys. 260, 224 (1997)] is derived as the non-relativistic limit of Mathisson's classical electron [Acta Physica Polonica 6, 218 (1937)], further discussed by Weyssenhoff and Raabe [Acta Physica Polonica 9, 7 (1947)]. The two-parameter centrally extended Galilean symmetry of the model is recoved using elementary methods. The relation to Schr\"odinger's Zitternde Elektron is indicated.
Non-commutative mechanics, in mathematical & in condensed matter physics
P. A. Horvathy
Physics , 2006,
Abstract: Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ``exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.
Nonrelativistic conformal structures
P. A. Horvathy
Physics , 2003,
Abstract: The ``Kaluza-Klein-type'' geometric structure appropriate to study the central extension of the Galilei group and non-relativistic physics is reviewed.
The laws of planetary motion, derived from those of a harmonic oscillator (following Arnold)
P. A. Horvathy
Physics , 2014,
Abstract: Kepler's laws are deduced from those valid for a harmonic oscillator, following the approach of Bohlin, Levi-Civita and Arnold.
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