In this work, I present measurements of persistent currents in normal metal rings performed with cantilever torsional magnetometry. With this technique, the typical persistent current (the component that varies randomly from ring to ring) was measured with high sensitivity. I report measured magnitudes as low as 1 pA, over two orders of magnitude smaller than that observed in previous studies. These measurements extend the range of temperature and magnetic field over which the typical current has been observed. The wide magnetic field range allowed us to study the effect of magnetic field penetrating the ring. It also enabled the recording of many independent measurements of the current magnitude in a single sample. These independent measurements are necessary to characterize the persistent current magnitude because it is a random quantity. From these measurements of the persistent current, I also characterize the parametric dependence of the typical current on sample orientation and number of rings. In addition to presenting the experimental results, I thoroughly review the theory of the typical persistent current in the diffusive regime. I begin with the simplest model and build up to the case appropriate for the samples studied in our experiments. I also present in detail the experimental apparatus used to measure the persistent currents.

Persistent Currents in Normal Metal Rings (Yale PhD thesis)

This paper reports the work on the development and analysis of a model for quantum rings in which persistent currents are induced by Aharonov–Bohm (AB) or other similar effects. The model is based on a centric and annual potential profile. The time-independent Schrodinger equation including an external magnetic field and an AB flux is analytically solved. The outputs, namely energy dispersion and wavefunctions, are analyzed in detail. It is shown that the rotation quantum number m is limited to small numbers, especially in weak confinement, and a conceptual proposal is put forward for acquiring the flux and eventually estimating the persistent currents in a Zeeman spectroscopy. The wavefunctions and electron distributions are numerically studied and compared to one-dimensional (1D) quantum well. It is predicated that the model and its solutions, eigen energy structure and analytic wavefunctions, would be a powerful tool for studying various electric and optical properties of quantum rings.

Analytic Aharonov-Bohm rings — Currents readout from Zeeman spectrum

We present theoretical studies of temperature dependent diamagnetic-paramagnetic transitions in thin quantum rings. Our studies show that the magnetic susceptibility of metal/semiconductor rings can exhibit multiple sign flips at intermediate and high temperatures depending on the number of conduction electrons in the ring ($N$) and whether or not spin effects are included. When the temperature is increased from absolute zero, the susceptibility begins to flip sign above a characteristic temperature that scales inversely with the number of electrons according to ${N}^{\ensuremath{-}1}$ or ${N}^{\ensuremath{-}1/2}$, depending on the presence of spin effects and the value of $N\phantom{\rule{0.16em}{0ex}}\mathrm{mod}\phantom{\rule{0.16em}{0ex}}4$. Analytical results are derived for the susceptibility in the low and high temperature limits, explicitly showing the spin effects on the ring Curie constant.

Temperature-dependent diamagnetic-paramagnetic transitions in metal/semiconductor quantum rings

Objective. Modelling is an important way to study the working mechanism of brain. While the characterization and understanding of brain are still inadequate. This study tried to build a model of brain from the perspective of thermodynamics at system level, which brought a new thinking to brain modelling. 
Approach. Regarding brain regions as systems, voxels as particles, and intensity of signals as energy of particles, the thermodynamic model of brain was built based on canonical ensemble theory. Two pairs of activated regions and two pairs of inactivated brain regions were selected for comparison in this study, and the analysis on thermodynamic properties based on the model proposed were performed. In addition, the thermodynamic properties were also extracted as input features for the detection of Alzheimer's disease. 
Main results. The experiment results verified the assumption that the brain also follows the thermodynamic laws. It demonstrated the feasibility and rationality of brain thermodynamic modelling method proposed, indicating that thermodynamic parameters could be applied to describe the state of neural system. Meanwhile, the brain thermodynamic model achieved much better accuracy in detection of Alzheimer's disease, suggesting the potential application of thermodynamic model in auxiliary diagnosis. 
Significance. (1) Instead of applying some thermodynamic parameters to analyze neural system, a brain model at system level was proposed from perspective of thermodynamics for the first time in this study. (2) The study discovered that the neural system also follows the laws of thermodynamics, which leads to increased internal energy, increased free energy and decreased entropy when system is activated. (3) The detection of neural disease was demonstrated to be benefit from thermodynamic model, implying the immense potential of thermodynamics in auxiliary diagnosis.

Modelling brain based on canonical ensemble with functional MRI: A thermodynamic exploration on neural system

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Man-Kit Yip

Papers

Persistent current of one-dimensional perfect rings under the canonical ensemble.