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

Abstract

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.

Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity

“…First, the critical speed, which the particle can not overcome during its evolution in gravitational field, can be more than the speed of light. The same observation has been made from analysis of MPTD particle in specific metrics [49][50][51][52][53]. Second, the longitudinal acceleration grows up to infinity in the ultrarelativistic limit.…”

“…Using this expression, (67) reads (three-dimensional geometry is defined now by ; in this case we can not use (51) and (52) to estimate the acceleration)…”

Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space

“…Such a model was originally proposed to address the infinity problem in quantum field theory [1,2] and was shown later that similar property can also appear in both string theory embedded in a background magnetic field [3] and quantum gravity [4]. It has been shown that the rotational symmetry can be broken [5,6], and consequently the energy levels of hydrogen atom [7] and Rydberg atoms [8] and topological phase effects [9][10][11] as well as the quantum speed of relativistic charged particles [12][13][14][15] and fluid [16] can receive interesting corrections. Algebra (1) can be accomplished by a replacement → + /(2ℏ).…”

Probing noncommutativities of phase space by using persistent charged current and its asymmetry

“…Nevertheless, noncommutative property can also appear in a real quantum system [6,7]. Because the noncommutative extension is fundamental, all the ordinary quantum physics are deformed with corrections parametrized by the constant θ μν , for instance, the breaking of rotational symmetry [8,9], distortion of energy levels of the atoms [10][11][12], corrections on the spin-orbital interactions [13][14][15][16][17][18][19][20], and the quantum speed of relativistic charged particles [21][22][23][24][25] and fluid dynamics [26,27]. Most importantly, the spatial component of the noncommutative parameter (θ μν ), θ ij , behaves like a permanent magnetic dipole moment and gives a contribution ϵ ijk θ ij B k to the energy of system.…”