Moment of inertia of superconductors

Hirsch, J. E.

doi:10.1016/j.physleta.2018.09.031

Cited by 9 publications

(13 citation statements)

References 31 publications

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“…In a similar manner, using deformations of Poisson brackets and corresponding Poisson maps, one can also study various generalizations of the motion of the Chaplygin sphere [5,36] and other nonholonomic systems [6,9,11,34,35] in a magnetic field. As a development of the problems considered here, we also point out the possibility of introducing inhomogeneous and nonstationary magnetic fields [23,26,37]. The first possibility is closely related to the Levitron theory and will allow the sphere, for example, to jump without additional mechanical actions.…”

Section: Resultsmentioning

confidence: 99%

“…In a number of instruments utilizing a contact less suspension system a rotor spins at high speed in a suspension magnetic field. The design of such instruments is feasible only if the properties of bodies rotating in a magnetic field are known [23,26,37]. We could enrich this theory by taking into account various nonholonomic effects modelling friction.…”

Section: Resultsmentioning

confidence: 99%

“…The resulting magnetic moment will depend on the shape of the body and is called the "London moment". A modern discussion of the dynamical understanding of the Meissner effect and the London moment may be found in [23], where the reader can also find references on experimental verifications of this effect for a variety of superconductors.…”

Section: Chaplygin Sphere and Barnett-london Effectmentioning

confidence: 99%

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On the Chaplygin Sphere in a Magnetic Field

Borisov

Tsiganov

2019

Regul. Chaot. Dyn.

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We consider the possibility of using Dirac's ideas of the deformation of Poisson brackets in nonholonomic mechanics. As an example, we analyze the composition of external forces that do no work and reaction forces of nonintegrable constraints in the model of a nonholonomic Chaplygin sphere on a plane. We prove that, when a solenoidal field is applied, the general mechanical energy, the invariant measure and the conformally Hamiltonian representation of the equations of motion are preserved. In addition, we consider the case of motion of the nonholonomic Chaplygin sphere in a constant magnetic field taking dielectric and ferromagnetic (superconducting) properties of the sphere into account. As a by-product we also obtain two new integrable cases of the Hamiltonian rigid body dynamics in a constant magnetic field taking the magnetization by rotation effect into account.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Chaplygin Sphere and Barnett-london Effectmentioning

confidence: 99%

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On the Chaplygin Sphere in a Magnetic Field

Borisov

Tsiganov

2019

Regul. Chaot. Dyn.

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“…Using these concepts together with the essential fact that the normal state charge carriers are holes we are able to completely describe the physics that takes place when either magnetization or angular momentum [26,27] changes in superconductors, in a way that satisfies the conservation laws, explains the physical processes by which momentum is transferred between different components of the system, and respects the fact that the processes are reversible under ideal conditions. We cannot say the same thing about ferromagnets.…”

Section: Discussionmentioning

confidence: 99%

Spinning Superconductors and Ferromagnets

Hirsch

2018

Acta Phys. Pol. A

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When a magnetic field is applied to a ferromagnetic body it starts to spin (Einstein-de Haas effect). This demonstrates the intimate connection between the electron's magnetic moment µB e {2mec, associated with its spin angular momentum S {2, and ferromagnetism. When a magnetic field is applied to a superconducting body it also starts to spin (gyromagnetic effect), and when a normal metal in a magnetic field becomes superconducting and expels the magnetic field (Meissner effect) the body also starts to spin. Yet according to the conventional theory of superconductivity the electron's spin only role is to label states, and the electron's magnetic moment plays no role in superconductivity. Instead, within the unconventional theory of hole superconductivity, the electron's spin and associated magnetic moment play a fundamental role in superconductivity. Just like in ferromagnets the magnetization of superconductors is predicted to result from an aggregation of magnetic moments with angular momenta {2. This gives rise to a "Spin Meissner effect", the existence of a spin current in the ground state of superconductors. The theory explains how a superconducting body starts spinning when it expels magnetic fields, which we argue is not explained by the conventional theory, it provides a dynamical explanation for the Meissner effect, which we argue the conventional theory cannot do, and it explains how supercurrents stop without dissipation, which we argue the conventional theory fails to explain. Essential elements of the theory of hole superconductivity are that superconductivity is driven by lowering of kinetic energy, which we have also proposed is true for ferromagnets], that the normal state charge carriers in superconducting materials are holes, and that the spin-orbit interaction plays a key role in superconductivity. The theory is proposed to apply to all superconductors.

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“…Для ферромагнетиков этот вопрос начал рассматриваться только недавно и пока остается нерешенным, а для сверхпроводников пока даже не признается, что такой вопрос существует и на него нужно ответить, см. обсуждение в работах [18,19,23,39]. Классическое описание динамики намагниченности микроскопических объектов включает феноменологические уравнения Ландау-Лифшица-Гильберта, см.…”

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Influence of Bartnett-London and Einstein-de Haas effects on the motion of the nonholonomic sphere of Routh

Borisov¹,

Tsiganov²

2019

Vestn. Udmurt. Univ. Mat. Mekh. Komp’yut. Nauki

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Рассматривается качение неуравновешенного динамически симметричного шара по плоскости без проскальзывания в присутствии внешнего магнитного поля. Предполагается, что шар может полностью или частично состоять из диэлектрического, ферромагнитного или сверхпроводящего материалов. Согласно существующей феноменологической теории в этом случае при изучении динами шара требуется учитывать момент силы Лоренца, момент Барнетта-Лондона и момент Эйнштейна-де Гааза. В рамках данной математической модели нами получены условия существования интегралов движения, которые позволяют свести интегрирование уравнений движения к квадратуре аналогичной квадратуре Лагранжа для тяжелого твердого тела.

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Moment of inertia of superconductors

Cited by 9 publications

References 31 publications

On the Chaplygin Sphere in a Magnetic Field

On the Chaplygin Sphere in a Magnetic Field

Spinning Superconductors and Ferromagnets

Influence of Bartnett-London and Einstein-de Haas effects on the motion of the nonholonomic sphere of Routh

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