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E. Díaz-Bautista et al.
Fig. 3 (a, b) Probability density ρ α (x) in Eq. (18a) for |α| = 6 and some values of the parameter
ζ . For ϕ = (2m + 1)π/2, m = 0, 1, . . . , ρ α (x) is centered in the position x 0 (horizontal red
lines). (σ ξ ) α (σ p ) α as function of α. As |α| increases, the HUR tends to 1/2. In these cases, we set
B 0 = 1/2, k = ω B = 1 and δ = 0
4 Conclusions
In this work, we have supplied a semi-classical description of the effects of
anisotropy on the dynamics of the Dirac particles in a magnetic field. Describing the
background field in Landau gauge, we construct the coherent states that depend on
anisotropy through ζ = v xx /v yy . According to these states, when the anisotropy is
aligned to the p x -axis (ζ < 1), the distance between the turning points x of the semiclassical oscillatory motion of electrons and the equilibrium position x 0 = 2k/ω B
is less than when the anisotropy is aligned to the p y -axis (ζ > 1), for which the
points x move away from x 0 . For the first case, the NLCSs in (19a) could better
describe such situation because they tend to oscillate close to the equilibrium point
x 0 (Fig. 4), while the NLCSs (17a) and (18a) could be used to describe the second
one (Figs. 2 and 3).
We consider that the results obtained in this work can be useful to describe
phenomena on 2DDMs by using the coherent states formulation, which has been
E. Díaz-Bautista et al.
Fig. 3 (a, b) Probability density ρ α (x) in Eq. (18a) for |α| = 6 and some values of the parameter
ζ . For ϕ = (2m + 1)π/2, m = 0, 1, . . . , ρ α (x) is centered in the position x 0 (horizontal red
lines). (σ ξ ) α (σ p ) α as function of α. As |α| increases, the HUR tends to 1/2. In these cases, we set
B 0 = 1/2, k = ω B = 1 and δ = 0
4 Conclusions
In this work, we have supplied a semi-classical description of the effects of
anisotropy on the dynamics of the Dirac particles in a magnetic field. Describing the
background field in Landau gauge, we construct the coherent states that depend on
anisotropy through ζ = v xx /v yy . According to these states, when the anisotropy is
aligned to the p x -axis (ζ < 1), the distance between the turning points x of the semiclassical oscillatory motion of electrons and the equilibrium position x 0 = 2k/ω B
is less than when the anisotropy is aligned to the p y -axis (ζ > 1), for which the
points x move away from x 0 . For the first case, the NLCSs in (19a) could better
describe such situation because they tend to oscillate close to the equilibrium point
x 0 (Fig. 4), while the NLCSs (17a) and (18a) could be used to describe the second
one (Figs. 2 and 3).
We consider that the results obtained in this work can be useful to describe
phenomena on 2DDMs by using the coherent states formulation, which has been