Larmor precession and barrier tunneling time of a neutral spinning particle

Z, Li; Liang, J.-Q.; Kobe, Donald H.

doi:10.1103/physreva.64.042112

Cited by 22 publications

(16 citation statements)

References 16 publications

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“…This Larmor time has been shown to equal the dwell time for both relativistic and nonrelativistic particles [19,20,25].…”

Section: ͑15͒mentioning

confidence: 93%

“…This effect has recently been explained as arising from the saturation of stored energy or number of particles under the barrier [11][12][13]. With some exceptions [14][15][16][17][18][19][20][21][22][23], most discussions of quantum tunneling time have been based on the nonrelativistic Schrödinger equation even when apparent "faster than c" effects are considered. In particular there has been no discussion of the relation between the various tunneling times for relativistic particles.…”

Section: Introductionmentioning

confidence: 99%

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Relation between quantum tunneling times for relativistic particles

2004

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A general relation between the phase time (group delay) and the dwell time is derived for relativistic tunneling particles described by the Dirac equation. It is shown that the phase time equals the dwell time plus a self-interference delay which is a relativistic generalization of previous results.Then the Hermitian conjugate of Eq.(1) is multiplied from the right by ‫ץ‬ / ‫ץ‬E, yieldingEquation (3) is then left-multiplied by † and added to Eq.(4), resulting in the expression *

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“…This Larmor time has been shown to equal the dwell time for both relativistic and nonrelativistic particles [19,20,25].…”

Section: ͑15͒mentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Relation between quantum tunneling times for relativistic particles

2004

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“…The equality is proven for the double Dirac δ-barrier in Appendix D and actually holds true for more general cases. 23,25,26,44 Note that in our calculation, we only consider slowmoving particle, like neutron or Ag atom (for the numerical examples presented here, the particle is taken as "neutral electron" with (v/c) ≤ 0.6% for simplicity), so the relevant Hamiltonian is the nonrelativistic Schrödinger-Pauli HamiltonianĤ = (p 2 /2m) + V (x) −μ · Bχ(x). In the Schrödinger picture, d Ŝ /dt = (1/i ) [Ŝ,Ĥ] = μ×B χ(x), so Ŝ stops running when particle leaves the nonzero magnetic region.…”

Section: The Double Dirac δ-Barrier Limitmentioning

confidence: 99%

Resonant tunneling dynamics and the related tunneling time

Xiao

Huang

2015

Int. J. Mod. Phys. B

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In close analogy with optical Fabry-Pérot (FP) interferometer, we rederive the transmission and reflection coefficients of tunneling through a rectangular double barrier (RDB). Based on the same analogy, we also get an analytic finesse formula for its filtering capability of matter waves, and with this formula, we reproduce the RDB transmission rate in exactly the same form as that of FP interferometer. Compared with the numerical results obtained from the original finesse definition, we find the formula works well. Next, we turn to the elusive time issue in tunneling, and show that the "generalized Hartman effect" can be regarded as an artifact of the opaque limit βl → ∞. In the thin barrier approximation, phase (or dwell) time does depend on the free inter-barrier distance d asymptotically. Further, the analysis of transmission rate in the neighborhood of resonance shows that, phase (or dwell) time could be a good estimate of the resonance lifetime. The numerical results from the uncertainty principle support this statement. This fact can be viewed as a support to the idea that, phase (or dwell) time is a measure of lifetime of energy stored beneath the barrier. To confirm this result, we shrink RDB to a double Dirac δ-barrier. The landscape of the phase (or dwell) time in k and d axes fits excellently well with the lifetime estimates near the resonance. As a supplementary check, we also apply phase (or dwell) time formula to the rectangular well, where no obstacle exists to the propagation of particle. However, due to the self-interference induced by the common cavity-like structure, phase (or dwell) time calculation leads to a counterintuitive "slowing down" effect, which can be explained appropriately by the lifetime assumptions.

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“…Janosfalvi et al [16] described the numerous phenomenological equations used in the study of the behavior of single-domain magnetic nano-particles. Li et al [17] investigated the Larmor precession of a neutral spinning particle in a magnetic field confined to the region of a one-dimensional rectangular barrier. Guo et al [18] proposed an experimental method to detect the Larmor precession of a single spin with a spin-polarized tunneling current.…”

Section: Introductionmentioning

confidence: 99%

Precessional angular velocity and field strength in the complex octonion space

Weng

2020

Preprint

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The paper aims to apply the octonions to explore the precessional angular velocities of several particles in the electromagnetic and gravitational fields. Some scholars utilize the octonions to research the electromagnetic and gravitational fields. One formula can be derived from the octonion torque, calculating the precessional angular velocity generated by the gyroscopic torque. When the octonion force is equal to zero, it is able to deduce the force equilibrium equation and precession equilibrium equation and so forth. From the force equilibrium equation, one can infer the angular velocity of revolution for the particles. Meanwhile, from the precession equilibrium equation, it is capable of ascertaining the precessional angular velocity induced by the torque derivative, including the angular velocity of Larmor precession. Especially, some ingredients of torque derivative are in direct proportion to the field strengths. The study reveals that the precessional angular velocity induced by the torque derivative is independent of that generated by the torque. The precessional angular velocity, induced by the torque derivative, is relevant to the torque derivative and the spatial dimension of precessional velocity. It will be of great benefit to understanding further the precessional angular velocity of the spin angular momentum.

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Larmor precession and barrier tunneling time of a neutral spinning particle

Cited by 22 publications

References 16 publications

Relation between quantum tunneling times for relativistic particles

Relation between quantum tunneling times for relativistic particles

Resonant tunneling dynamics and the related tunneling time

Precessional angular velocity and field strength in the complex octonion space

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