Related papers: The rolling sphere and the quantum spin
In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…
The Larmor precession of a relativistic neutral spin-1/2 particle in a uniform constant magnetic field confined to the region of a one-dimensional arbitrary potential barrier is investigated. The spin precession serves as a clock to measure…
The phase diagram of spins 1/2 embedded in a magnetic field mutually interacting antiferromagnetically is determined. Contrary to the ferromagnetic case where a second order quantum phase transition occurs, a first order transition is…
A well known description of superradiance from pointlike collections of many atoms involves the dissipative motion of a large spin. The pertinent ``superradiance master equation'' allows for a formally exact solution which we subject to a…
There are several physical situations in which the `tangling' of a loop is relevant: the game of cat's cradle is a simple example, but a more important application involves the stirring of a fluid by rods. Here we discuss how elementary…
The spin density matrix for spin-3/2 hole systems can be decomposed into a sequence of multipoles which has important higher-order contributions beyond the ones known for electron systems [R. Winkler, Phys. Rev. B \textbf{70}, 125301…
(Talk presented at the 7th Marcel Grossmann Meeting on General Relativity, Stanford, CA, July 24-30, 1994) We study the semi-classical limit of the solution of the Dirac equation in a background electromagnetic/gravitational plane wave. We…
Magnetization of a spin1/2 set is determined by means of their individual wave function. The theoretical treatment based on the fundamental axioms of quantum mechanics and solving explicitly Schr\"odinger equation gives the evolution of…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
Quantum spin liquids are long-range entangled phases whose magnetic correlations are determined by strong quantum fluctuations. While an overarching principle specifying the precise microscopic coupling scenarios for which quantum…
Exploiting quantum properties to outperform classical ways of information-processing is an outstanding goal of modern physics. A promising route is quantum simulation, which aims at implementing relevant and computationally hard problems in…
Extra dimensions are introduced: 3 in Classical Mechanics and 6 in Relativistic Mechanics, which represent orientations, resulting from rotations, of a particle, described by quaternions, and leading to a 7-dimensional, respectively…
The paper studies the problem of prescribing positive cross curvature on the three-dimensional sphere. We produce several existence results and an example of non-uniqueness, disproving a conjecture of Hamilton's.
An experiment to test for relativistic frame dragging effects with quantum interferometry is proposed. The idea that the classical trajectories of the interferometer surround a spherical mass source whose angular momentum is perpendicular…
Quantum annealing leverages the properties of interacting quantum spin systems to solve computational problems, typically optimisation problems. Current hardware now has capabilities that can be used to solve condensed matter physics…
We consider the possibility of detecting spin precession in a magnetic field by nonequilibrium transport processes. We find that time reversal symmetry imposes strong constraints on the problem. Suppose the tunneling occurs directly between…
Quantum entanglement occurs not just in discrete systems such as spins, but also in the spatial wave functions of systems with more than one degree of freedom. It is easy to introduce students to entangled wave functions at an early stage,…
We compute the analytic torsion of a cone over a sphere of dimension 1, 2, and 3, and we conjecture a general formula for the cone over an odd dimensional sphere.
We consider a disk-shaped thin elastic sheet bonded to a compliant sphere. (Our sheet can slip along the sphere; the bonding controls only its normal displacement.) If the bonding is stiff (but not too stiff), the geometry of the sphere…
We consider a charged particle following the boundary of a two-dimensional domain because a homogeneous magnetic field is applied. We develop the basic scattering theory for the corresponding quantum mechanical edge states. The scattering…