On Killing tensors and constants of motion

We revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles on a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, we demonstrate that besides the two non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, found by Rüdiger, non-trivial quasi-conserved quantities are in one-to-one correspondence with non-trivial mixed-symmetry Killing tensors. We prove that no such stationary and axisymmetric mixed-symmetry Killing tensor exists on the Kerr geometry. We discuss the implications for the motion of spinning particles on Kerr spacetime where the quasi-constants of motion are shown not to be in complete involution.

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Killing tensors on tori

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2017.02.010 ◽

2017 ◽

Vol 117 ◽

pp. 1-6

Author(s):

Konstantin Heil ◽

Andrei Moroianu ◽

Uwe Semmelmann

Keyword(s):

Killing Tensors

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Studies in perturbation theory. XIV. Treatment of constants of motion, degeneracies and symmetry properties by means of multidimensional partitioning

International Journal of Quantum Chemistry ◽

10.1002/qua.560050878 ◽

2009 ◽

Vol 5 (S5) ◽

pp. 685-705 ◽

Cited By ~ 49

Author(s):

P.-O. Löwdin ◽

O. Goscinski

Keyword(s):

Perturbation Theory ◽

Symmetry Properties ◽

Constants Of Motion

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Signature of Generalized Gibbs Ensemble Deviation from Equilibrium: Negative Absorption Induced by a Local Quench

Entropy ◽

10.3390/e23020220 ◽

2021 ◽

Vol 23 (2) ◽

pp. 220

Author(s):

Lorenzo Rossi ◽

Fabrizio Dolcini ◽

Fabio Cavaliere ◽

Niccolò Traverso Ziani ◽

Maura Sassetti ◽

...

Keyword(s):

Optical Gain ◽

Electron System ◽

Bound State ◽

Stimulated Emission ◽

Optical Measurements ◽

Gibbs Ensemble ◽

Attractive Potential ◽

Dimensional Electron System ◽

Constants Of Motion ◽

Generalized Gibbs Ensemble

When a parameter quench is performed in an isolated quantum system with a complete set of constants of motion, its out of equilibrium dynamics is considered to be well captured by the Generalized Gibbs Ensemble (GGE), characterized by a set {λα} of coefficients related to the constants of motion. We determine the most elementary GGE deviation from the equilibrium distribution that leads to detectable effects. By quenching a suitable local attractive potential in a one-dimensional electron system, the resulting GGE differs from equilibrium by only one single λα, corresponding to the emergence of an only partially occupied bound state lying below a fully occupied continuum of states. The effect is shown to induce optical gain, i.e., a negative peak in the absorption spectrum, indicating the stimulated emission of radiation, enabling one to identify GGE signatures in fermionic systems through optical measurements. We discuss the implementation in realistic setups.

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