dorsal/arxiv
View SchemaQuantum Dynamics of a Particle with a Spin-dependent Velocity
| Authors | Claude Aslangul |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406057 |
| URL | https://arxiv.org/abs/quant-ph/0406057 |
| DOI | 10.1088/0305-4470/38/1/001 |
Abstract
We study the dynamics of a particle in continuous time and space, the displacement of which is governed by an internal degree of freedom (spin). In one definite limit, the so-called quantum random walk is recovered but, although quite simple, the model possesses a rich variety of dynamics and goes far beyond this problem. Generally speaking, our framework can describe the motion of an electron in a magnetic sea near the Fermi level when linearisation of the dispersion law is possible, coupled to a transverse magnetic field. Quite unexpected behaviours are obtained. In particular, we find that when the initial wave packet is fully localized in space, the $J_{z}$ angular momentum component is frozen; this is an interesting example of an observable which, although it is not a constant of motion, has a constant expectation value. For a non-completely localized wave packet, the effect still occurs although less pronounced, and the spin keeps for ever memory of its initial state. Generally speaking, as time goes on, the spatial density profile looks rather complex, as a consequence of the competition between drift and precession, and displays various shapes according to the ratio between the Larmor period and the characteristic time of flight. The density profile gradually changes from a multimodal quickly moving distribution when the scatttering rate is small, to a unimodal standing but flattening distribution in the opposite cas case.
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"abstract": "We study the dynamics of a particle in continuous time and space, the\ndisplacement of which is governed by an internal degree of freedom (spin). In\none definite limit, the so-called quantum random walk is recovered but,\nalthough quite simple, the model possesses a rich variety of dynamics and goes\nfar beyond this problem. Generally speaking, our framework can describe the\nmotion of an electron in a magnetic sea near the Fermi level when linearisation\nof the dispersion law is possible, coupled to a transverse magnetic field.\nQuite unexpected behaviours are obtained. In particular, we find that when the\ninitial wave packet is fully localized in space, the $J_{z}$ angular momentum\ncomponent is frozen; this is an interesting example of an observable which,\nalthough it is not a constant of motion, has a constant expectation value. For\na non-completely localized wave packet, the effect still occurs although less\npronounced, and the spin keeps for ever memory of its initial state. Generally\nspeaking, as time goes on, the spatial density profile looks rather complex, as\na consequence of the competition between drift and precession, and displays\nvarious shapes according to the ratio between the Larmor period and the\ncharacteristic time of flight. The density profile gradually changes from a\nmultimodal quickly moving distribution when the scatttering rate is small, to a\nunimodal standing but flattening distribution in the opposite cas case.",
"arxiv_id": "quant-ph/0406057",
"authors": [
"Claude Aslangul"
],
"categories": [
"quant-ph",
"cond-mat.other"
],
"doi": "10.1088/0305-4470/38/1/001",
"title": "Quantum Dynamics of a Particle with a Spin-dependent Velocity",
"url": "https://arxiv.org/abs/quant-ph/0406057"
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