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Register a new userThe Relativistic Stern-Gerlach Force
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Added by
Christoph Tschalaer
Publication date
2013
fields
Physics
and research's language is
English
Authors
C. Tschalaer
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The relativistic Lagrangian for a spinning particle in an electromagnetic field is derived from the known Lagrangian in the particles rest frame. The resulting relativistic Stern-Gerlach and Thomas precession forces on the particle are then derived from the Lagrangian in the laboratory frame. In particular, the longitudinal component of this combined Stern-Gerlach-Thomas force does not contain a term proportional to gamma-squared as was claimed in a previous derivation [1].
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The claim in ref.1 [M. Conte et al: Stern-Gerlach Force on a Precessing Magnetic Moment, Proceedings of PAC07 (http://cern.ch/AccelConf/p07/PAPER/THPAS105.pdf)] that the Stern-Gerlach force on a charged particle with a magnetic moment causes a change in longitudinal momentum proportional to gamma-squared when it traverses a specially configured localized electromagnetic field, contradicts the prediction based on the established interaction Lagrangian. It is shown that extending the calculation in ref. 1 to include the entire spin motion eliminates the gamma-squared term and thus the inconsistency.
We design a Stern-Gerlach apparatus that separates quasispin components on the lattice, without the use of external fields. The effect is engineered using intrinsic parameters, such as hopping amplitudes and on-site potentials. A theoretical description of the apparatus relying on a generalized Foldy-Wouthuysen transformation beyond Dirac points is given. Our results are verified numerically by means of wavepacket evolution, including an analysis of Zitterbewegung on the lattice. The necessary tools for microwave realizations, such as complex hopping amplitudes and chiral effects, are simulated.
We describe an interactive computer program that simulates Stern-Gerlach measurements on spin-1/2 and spin-1 particles. The user can design and run experiments involving successive spin measurements, illustrating incompatible observables, interference, and time evolution. The program can be used by students at a variety of levels, from non-science majors in a general interest course to physics majors in an upper-level quantum mechanics course. We give suggested homework exercises using the program at various levels.
The full story of the Stern-Gerlach experiment and its reception, interpretation and final understanding has many unexpected surprises. Here, we review the history and the context of the proposal, the experiment, and the subsequent story of the aftermath. We also discuss the story of the possible Stern-Gerlach experiment for free electrons etc. Finally, we comment on the remarkable career of Otto Stern.
We present a unique matter-wave interferometer whose phase scales with the cube of the time the atom spends in the interferometer. Our scheme is based on a full-loop Stern-Gerlach interferometer incorporating four magnetic field gradient pulses to create a state-dependent force. In contrast to typical atom interferometers which make use of laser light for the splitting and recombination of the wave packets, this realization uses no light and can therefore serve as a high-precision surface probe at very close distances.
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