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arXiv:cond-mat/0106646

Landau diamagnetism revisited

Sushanta Dattagupta, Arun M. Jayannavar, Narendra Kumar

Published Jun 29, 2001• 5 citations
arXivHTMLPDF

Abstract

The problem of diamagnetism, solved by Landau, continues to pose fascinating issues which have relevance even today. These issues relate to inherent quantum nature of the problem, the role of boundary and dissipation, the meaning of thermodynamic limits, and above all, the quantum-classical crossover occasioned by environment-induced decoherence. The Landau Diamagnetism provides a unique paradigm for discussing these issues, the significance of which are far-reaching. Our central result is a remarkable one as it connects the mean orbital magnetic moment, a thermodynamic property, with the electrical resistivity, which characterizes transport properties of materials.

DOI
10.48550/arxiv.cond-mat/0106646

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The problem of diamagnetism, solved by Landau, continues to pose fascinating issues which have relevance even today. These issues relate to inherent quantum nature of the problem, the role of boundary and dissipation, the meaning of thermodynamic limits, and above all, the quantum-classical crossover occasioned by environment-induced decoherence. The Landau Diamagnetism provides a unique paradigm for discussing these issues, the significance of which are far-reaching. Our central result is a remarkable one as it connects the mean orbital magnetic moment, a thermodynamic property, with the electrical resistivity, which characterizes transport properties of materials.
1. In a recent paper Landau has shown that, when electrons are moving freely in a magnetic field, they exhibit, in addition to the paramagnetic effect of their spin, a diamagnetic effect due to their motion. This result is rather unexpected, since it is quite contrary to the classical case. There it might appear as though the circles described by the electrons must produce a magnetic moment, but the error was long ago pointed out by Bohr. The motion of the electrons must be confined to some region by means of a boundary wall, and the electrons near the wall describe a succession of circular arcs, repeatedly bouncing on the wall, and slowly creeping round it in the direction opposite to that of the uninterrupted circles; when the moment of these electrons is taken into account, it exactly cancels out that due to the free circles. In Landau's work it is of course necessary to consider the boundary, but he shows how allowance is to be made for it by an appropriate process. The complete justification is rather subtle, and so it may be worth considering a special case, admitting of exact solution, which takes the boundary into account, and so makes it possible to follow more closely the analogy between the classical and quantum problems. With regard to the general case with a boundary wall of any type, we shall only observe that the different results arise, because in the wave problem ψ must vanish at the bounding “potential wall,” and so will be small near it; this upsets the balance of the electric current near the wall, and yields the magnetic moment.
Abstract This paper provides a simple derivation of the decoherence rate for a diamagnetic nanoparticle in the presence of fluctuations of the magnetic field in a thermal environment. Diamagnetic levitation is one of the key techniques for trapping, cooling, and creating a macroscopic quantum spatial superposition in many experiments. It is widely applied in many theoretical and experimental endeavours to test fundamental physics in matter-wave interferometers. To estimate the decoherence rate originating from magnetic-field fluctuations, we use the fluctuation-dissipation theorem. We show that our resulting decoherence rate expression is analogous to that of a dielectric material interacting with the electric field component of the background field; however, it is often relatively suppressed due to the material properties.
Reviewing macroscopic quantum phenomena and quantum dissipation, from the phenomenology of magnetism and superconductivity to the presentation of alternative models for quantum dissipation, this book develops the basic material necessary to understand the quantum dynamics of macroscopic variables. Macroscopic quantum phenomena are presented through several examples in magnetism and superconductivity, developed from general phenomenological approaches to each area. Dissipation naturally plays an important role in these phenomena, and therefore semi-empirical models for quantum dissipation are introduced and applied to the study of a few important quantum mechanical effects. The book also discusses the relevance of macroscopic quantum phenomena to the control of meso- or nanoscopic devices, particularly those with potential applications in quantum computation or quantum information. It is ideal for graduate students and researchers.
This book provides an overview of how diverse issues of Magnetism have implications for other areas of physics. Attention will be drawn to different aspects of many-body physics, which first appeared in Magnetism but have had deep impact in different branches of physics. Each of these aspects will be illustrated schematically and in terms of physical examples, chosen from multicritical phenomena, quantum phase transition, spin glasses, relaxation, phase ordering and quantum dissipation. A unique feature of this book is a unified and coherent discussion of magnetic phenomena, presented in a luc
The thermodynamical properties of a system of two coupled harmonic oscillators in the presence of a uniform magnetic field B are investigated. Using an unitary transformation, we show that the system can be diagonalized in a simple way and then obtain the energy spectrum solutions. These are then used to determine the thermodynamical potential in terms of different physical parameters like the coupling parameter α. This allows us to give a generalization of significant work already published and obtain different results, which can be used to discuss the magnetism of the system. Different limiting cases, in terms of α and B, are discussed. In fact, quantum corrections to the Landau diamagnetism and orbital paramagnetism are found.