for the time dependence of the macoscopic magnetisation M(t) of a sample under the influence of an external field H(t) where γ =μ / Ih is the gyromagnetic ratio of the nuclei under consideration with magnetic moment μ and spin I, i, j, and k are the usual triad of unit vectors along the Cartesian axes. The external field has the form H(t) = H0k + H1(t), where H0 is strong and constant while H1 ...

A general theory of thermal magnetic fluctuations near the surface of conductive and/or magnetically permeable slabs is developed; such fluctuations are the magnetic analog of Johnson voltage noise. Starting with the fluctuation-dissipation theorem and Maxwell’s equations, a closed-form expression for the magnetic noise spectral density is derived. Quantum decoherence, as induced by thermal mag...

Magnetic Resonance Imaging (MRI) techniques have been used to determine the spin-lattice, T1, and the spin-spin, T2, relaxation times in three phantoms with compositions simulating the T1 and T2 values of human tissues. Some methods of analysis were used in order to obtain the relaxation time maps. It has been shown that reliable results can be also obtained by using approximating methods of in...

Graphene quantum dots are attractive candidates for solid-state quantum bits. In fact, the predicted weak spin-orbit and hyperfine interaction promise spin qubits with long coherence times. Graphene quantum dots have been extensively investigated with respect to their excitation spectrum, spin-filling sequence and electron-hole crossover. However, their relaxation dynamics remain largely unexpl...

In this paper we measure the two-body relaxation time from the angular deflection of test particles launched in a rigid configuration of field particles. We find that centrally concentrated configurations have relaxation times that can be shorter than those of the corresponding homogeneous distributions by an order of magnitude or more. For homogeneous distributions we confirm that the relaxati...

The use of hyperpolarized agents in magnetic resonance, such as (13)C-labelled compounds, enables powerful new imaging and detection modalities that stem from a 10,000-fold boost in signal. A major challenge for the future of the hyperpolarization technique is the inherently short spin-relaxation times, typically <60 s for (13)C liquid-state compounds, which limit the time that the signal remai...

We review some results obtained in a recent series of papers on thermal relaxation in classical and quantum dissipative systems. We consider models where a small system S , with a finite number of degrees of freedom, interacts with a large environment R in thermal equilibrium at positive temperature T . The zeroth law of thermodynamics postulates that, independently of its initial configuration...

This paper presents a model for option pricing in markets that experience financial crashes. The stochastic differential equation (SDE) of stock price dynamics is coupled to a post-crash market index. The resultant SDE is shown to have stock price and time dependent volatility. The partial differential equation (PDE) for call prices is derived using risk-neutral pricing. European call prices ar...

We focus on the slow relaxations observed in the conductance of disordered insulators at low temperature (especially granular aluminum films). They manifest themselves as a temporal logarithmic decrease of the conductance after a quench from high temperatures and the concomitant appearance of a field effect anomaly centered on the gate voltage maintained. We are first interested in ageing effec...