Chris Hooley

Developing and evaluating animations for teaching quantum mechanics concepts

In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantum mechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantum mechanics concepts. They focus on known areas of student difficulty and misconceptions by including animated step-by-step explanations of key points. The animations are freely available, with additional resources available to instructors. We have investigated their educational effectiveness both in terms of student attitude and performance. Questionnaires showed that students are on the whole very positive about the animations and make substantial use of them. A diagnostic survey administered to level 2 and 3 students showed that level 2 students significantly outperformed level 3 students on topics which they had investigated using the animations.

Single-Atom Density of States of an Optical Lattice

We consider a single atom in an optical lattice, subject to a harmonic trapping potential. The problem is treated in the tight-binding approximation, with an extra parameter kappa denoting the strength of the harmonic trap. It is shown that the kappa-->0 limit of this problem is singular, in the sense that the density of states for a very shallow trap (kappa-->0) is qualitatively different from that of a translationally invariant lattice (kappa=0). The physics of this difference is discussed, and densities of states and wave functions are exhibited and explained.

Perturbative expansion of the magnetization in the out-of-equilibrium Kondo model

This paper is concerned with the out-of-equilibrium two-lead Kondo model, considered as a model of a quantum dot in the Kondo regime. We revisit the perturbative expansion of the dot’s magnetization, and conclude that, even at order 0 in the Kondo interactions, the magnetization is not given by the usual equilibrium result. We use the Schwinger-Keldysh method to derive a Dyson equation describing the steady state induced by the voltage between the two leads, and thus present the correct procedure for calculating perturbative expansions of steady-state properties of the system.

Is the Quantum Dot at Large Bias a Weak-Coupling Problem?

We examine the two-lead Kondo model for a dc-biased quantum dot in the Coulomb blockade regime. From perturbative calculations of the magnetic susceptibility, we show that the problem retains its strong-coupling nature, even at bias voltages larger than the equilibrium Kondo temperature. We give a speculative discussion of the nature of the renormalization group flows and the strong-coupling state that emerges at large voltage bias.

Spin dynamics from majorana fermions.

Using the Majorana fermion representation of spin-1/2 local moments, we show how the dynamic spin correlation and susceptibility are obtained directly from the one-particle Majorana propagator. We illustrate our method by applying it to the spin dynamics of a nonequilibrium quantum dot, computing the voltage-dependent spin relaxation rate and showing that, at weak coupling, the fluctuation-dissipation relation for the spin of a quantum dot is voltage dependent. We confirm the voltage-dependent Curie susceptibility recently found by Parcollet and Hooley [Phys. Rev. B 66, 085315 (2002)]].

A new multimedia resource for teaching quantum mechanics concepts

We describe a collection of interactive animations and visualizations for teaching quantum mechanics. The animations can be used at all levels of the undergraduate curriculum. Each animation includes a step-by-step exploration that explains the key points. The animations and instructor resources are freely available. By using a diagnostic survey, we report substantial learning gains for students who have worked with the animations.

Pomeranchuk instability : Symmetry-breaking and experimental signatures

We discuss the emergence of symmetry-breaking via the Pomeranchuk instability from interactions that respect the underlying point-group symmetry. We use a variational mean-field theory to consider a 2D continuum and a square lattice. We describe two experimental signatures: a symmetry-breaking pattern of Friedel oscillations around an impurity; and a structural transition.

Non-Fermi-liquid behavior and anomalous suppression of Landau damping in layered metals close to ferromagnetism

We analyze the low-energy physics of nearly ferromagnetic metals in two spatial dimensions using the functional renormalization group technique. We find a new low-energy fixed point, at which the fermionic (electronlike) excitations are non-Fermi-liquid (z_{f}=13/10) and the magnetic fluctuations exhibit an anomalous Landau damping whose rate vanishes as Γ_{q}∼|q|^{3/5} in the low-|q| limit. We discuss this renormalization of the Landau-damping exponent, which is the major novel prediction of our work, and highlight the possible link between that renormalization and neutron-scattering data on UGe_{2} and related compounds. Implications of our analysis for YFe_{2}Al_{10} are also discussed.

Unbinding of Giant Vortices in States of Competing Order

We consider a two-dimensional system with two order parameters, one with O(2) symmetry and one with O(M), near a point in parameter space where they couple to become a single O(2+M) order. While the O(2) sector supports vortex excitations, these vortices must somehow disappear as the high symmetry point is approached. We develop a variational argument which shows that the size of the vortex cores diverges as 1/√Δ and the Berezinskii-Kosterlitz-Thouless transition temperature of the O(2) order vanishes as 1/ln(1/Δ), where Δ denotes the distance from the high-symmetry point. Our physical picture is confirmed by a renormalization group analysis which gives further logarithmic corrections, and demonstrates full symmetry restoration within the cores.

Thermal versus quantum fluctuations of optical-lattice fermions

We show that, for fermionic atoms in a one-dimensional optical lattice, the fraction of atoms in doubly occupied sites is a highly nonmonotonic function of temperature. We demonstrate that this property persists even in the presence of realistic harmonic confinement, and that it leads to a suppression of entropy at intermediate temperaturesthatoffersaroutetoadiabaticcooling.Ourinterpretationofthesuppressionisthatsuchintermediate temperatures are simultaneously too high for quantum coherence and too low for significant thermal excitation of double occupancy thus offering a clear indicator of the onset of quantum fluctuations.