Jian Jing

Quantum speed limit for a relativistic electron in the noncommutative phase space

The influence of the noncommutativity on the average speed of a relativistic electron interacting with a uniform magnetic field within the minimum evolution time is investigated. We find that it is possible for the wave packet of the electron to travel faster than the speed of light in vacuum because of the noncommutativity. It suggests that due to the noncommutativity, Lorentz invariance is violated in the relativistic quantum mechanics region.

Quantum Speed Limit for Relativistic Spin-0 and Spin-1 Bosons on Commutative and Noncommutative Planes

Quantum speed limits of relativistic charged spin-0 and spin-1 bosons in the background of a homogeneous magnetic field are studied on both commutative and noncommutative planes. We show that, on the commutative plane, the average speeds of wave packets along the radial direction during the interval in which a quantum state is evolving from an initial state to the orthogonal final one can not exceed the speed of light, regardless of the intensities of the magnetic field. However, due to the noncommutativity, the average speeds of the wave packets on noncommutative plane will exceed the speed of light in vacuum provided the intensity of the magnetic field is strong enough. It is a clear signature of violating Lorentz invariance in the relativistic quantum mechanics region.

CHERN–SIMONS MECHANICS IN NONCOMMUTATIVE PHASE SPACE

Chern–Simons mechanics in noncommutative phase space is studied from both classical and quantum aspects in this paper. We find that there are two parameters in the full theory which lead to two different reduced theories when they take certain values. We analyze these two reduced models also from two aspects and find that the classical aspect of the full theory has a continuous limit when both of these parameters take their certain values. However, the quantum aspect of the full theory does not have the similar limit. The spectra of the full theory will be infinite when these parameters take these values. We propose artificial regularization schemes to get rid of these infinity and resort to Diracs theories to verify our scheme.

Fractional Zero-Point Angular Momenta in Noncommutative Quantum Mechanics

Abstract The charged particle confined by a harmonic potential in a noncommutative planar phase space interacting with a homogeneous dynamical magnetic field and Aharonov-Bohm potentials is studied. We find that the canonical orbital angular momenta of the reduced models, which are obtained by setting the mass and a dimensionless parameter to zero, take fractional values. These fractional angular momenta are not only determined by the flux inside the thin long solenoid but also affected by the noncommutativities of phase space.