In Schwarzschild spacetime, a weak gravitational field splits Landau levels by an amount proportional to GMm times the square root of the magnetic field, with explicit Yukawa, power-law, and relativistic corrections derived.
Quantum states of neutrons in the gravitational field and limits for non-Newtonian interaction in the range between 1 micron and 10 microns
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abstract
Quantum states in the Earth's gravitational field can be observed, when ultra-cold neutrons fall under gravity. In an experiment at the Institut Laue-Langevin in Grenoble, neutrons are reflected and trapped in a gravitational cavity above a horizontal mirror. The population of the ground state and the lowest states follows, step by step, the quantum mechanical prediction. An efficient neutron absorber removes the higher, unwanted states. The quantum states probe Newtonian gravity on the micrometer scale and we place limits for gravity-like forces in the range between 1 micron and 10 microns.
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2019 1verdicts
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Landau levels in a gravitational field: The Schwarzschild spacetime case
In Schwarzschild spacetime, a weak gravitational field splits Landau levels by an amount proportional to GMm times the square root of the magnetic field, with explicit Yukawa, power-law, and relativistic corrections derived.