arXiv subjects

Derek Harland

Publications and source records attributed to Derek Harland.

At least 37 records · Page 2Linked to original sources

arXiv2018

Rolling Skyrmions and the Nuclear Spin-Orbit Force

We compute the nuclear spin-orbit coupling from the Skyrme model. Previous attempts to do this were based on the product ansatz, and as such were limited to a system of two well-separated nuclei. Our calculation utilises a new method, and is applicable to the phenomenologically important situation of a single nucleon orbiting a large nucleus. We find that, to second order in perturbation theory, the coefficient of the spin-orbit coupling induced by pion field interactions has the wrong sign, but as the strength of the pion-nucleon interactions increases the correct sign is recovered non-perturbatively.

hep-th↗

arXiv2016

The Skyrme model and chiral perturbation theory

A lagrangian which describes interactions between a soliton and a background field is derived for sigma models whose target is a symmetric space. The background field modifies the usual moduli space approximation to soliton dynamics in two ways: by introducing a potential energy, and by inducing a Kaluza-Klein metric on the moduli space. In the particular case of the Skyrme model, this lagrangian is quantised and shown to agree with the leading pion-nucleon term in the chiral effective lagrangian, which is widely used in theoretical nuclear physics. Thus chiral perturbation theory could be considered a low energy limit of the Skyrme model.

hep-th↗

arXiv2016

A point particle model of lightly bound skyrmions

A simple model of the dynamics of lightly bound skyrmions is developed in which skyrmions are replaced by point particles, each carrying an internal orientation. The model accounts well for the static energy minimizers of baryon number $1\leq B\leq 8$ obtained by numerical simulation of the full field theory. For $9\leq B\leq 23$, a large number of static solutions of the point particle model are found, all closely resembling size $B$ subsets of a face centred cubic lattice, with the particle orientations dictated by a simple colouring rule. Rigid body quantization of these solutions is performed, and the spin and isospin of the corresponding ground states extracted. As part of the quantization scheme, an algorithm to compute the symmetry group of an oriented point cloud, and to determine its corresponding Finkelstein-Rubinstein constraints, is devised.

hep-th↗

arXiv2016

Deformations of nearly Kähler instantons

We formulate the deformation theory for instantons on nearly Kähler six-manifolds using spinors and Dirac operators. Using this framework we identify the space of deformations of an irreducible instanton with semisimple structure group with the kernel of an elliptic operator, and prove that abelian instantons are rigid. As an application, we show that the canonical connection on three of the four homogeneous nearly Kähler six-manifolds G/H is a rigid instanton with structure group H. In contrast, these connections admit large spaces of deformations when regarded as instantons on the tangent bundle with structure group SU(3).

math.DG↗

arXiv2015

On the charge density and asymptotic tail of a monopole

We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose expansion in powers of 1/r agrees with that of the conventional asymptotic magnetic field to all orders. We also show that the asymptotic field can be easily calculated from the spectral curve. Explicit examples are given for known monopole solutions.

hep-th↗

arXiv2015

Skyrmions with low binding energies

Nuclear binding energies are investigated in two variants of the Skyrme model: the first replaces the usual Skyrme term with a term that is sixth order in derivatives, and the second includes a potential that is quartic in the pion fields. Solitons in the first model are shown to deviate significantly from ansätze previously assumed in the literature. The binding energies obtained in both models are lower than those obtained from the standard Skyrme model, and those obtained in the second model are close to the experimental values.

hep-th↗

arXiv2015

Magnetic bags in hyperbolic space

A magnetic bag is an abelian approximation to a large number of coincident SU(2) BPS monopoles. In this paper we consider magnetic bags in hyperbolic space and derive their Nahm transform from the large charge limit of the discrete Nahm equation for hyperbolic monopoles. An advantage of studying magnetic bags in hyperbolic space, rather than Euclidean space, is that a range of exact charge N hyperbolic monopoles can be constructed, for arbitrarily large values of N, and compared with the magnetic bag approximation. We show that a particular magnetic bag (the magnetic disc) provides a good description of the axially symmetric N-monopole. However, an abelian magnetic bag is not a good approximation to a roughly spherical N-monopole that has more than N zeros of the Higgs field. We introduce an extension of the magnetic bag that does provide a good approximation to such monopoles and involves a spherical non-abelian interior for the bag, in addition to the conventional abelian exterior.

hep-th↗

arXiv2013

Topological energy bounds for the Skyrme and Faddeev models with massive pions

A topological lower bound on the Skyrme energy which depends explicity on the pion mass is derived. This bound coincides with the previously best known bound when the pion mass vanishes, and improves on it whenever the pion mass is non-zero. The new bound can in particular circumstances be saturated. New energy bounds are also derived for the Skyrme model on a compact manifold, for the Faddeev-Skyrme model with a potential term, and for the Aratyn-Ferreira-Zimerman and Nicole models.

hep-th↗

arXiv2013

Collapse and Revival and Cat States with an N Spin System

We discuss collapse and revival of Rabi oscillations in a system comprising a qubit and a "big spin" (made of N qubits, or spin-1/2 particles). We demonstrate a regime of behaviour analogous to conventional collapse and revival for a qubit-field system, employing spin coherent states for the initial state of the big spin. These dynamics can be used to create a "Schrodinger cat" state of the big spin. Even for relatively small values of N, states with significant potential for quantum metrology applications can result, giving sensitivity approaching the Heisenberg limit.

quant-ph↗

arXiv2013

Isospinning hopfions

The problem of constructing internally rotating solitons of fixed angular frequency $ω$ in the Faddeev-Skyrme model is reformulated as a variational problem for an energy-like functional, called pseudoenergy, which depends parametrically on $ω$. This problem is solved numerically using a gradient descent method, without imposing any spatial symmetries on the solitons, and the dependence of the solitons' energy on $ω$, and on their conserved total isospin $J$, studied. It is found that, generically, the shape of a soliton is independent of $ω$, and that its size grows monotonically with $ω$. A simple elastic rod model of time-dependent hopfions is developed which, despite having only one free parameter, accounts well for most of the numerical results.

hep-th↗

arXiv2013

Towards a complete, continuous, Wigner function for an ensemble of spins or qubits

We present a new quasi-probability distribution function for ensembles of spin-half particles or qubits that has many properties in common with Wigner's original function for systems of continuous variables. We show that this function provides clear and intuitive graphical representation of a wide variety of states, including Fock states, spin-coherent states, squeezed states, superpositions and statistical mixtures. Unlike previous attempts to represent ensembles of spins/qubits, this distribution is capable of simultaneously representing several angular momentum shells.

quant-ph↗

arXiv2012

Magnetic Domains

Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n. We interpret these ideas using string theory and present some partial proofs of this conjecture. We then extend the notion of bags and their Nahm transform to higher gauge theories and arbitrary domains. Bags in four dimensions conjecturally describe the large n limit of n self-dual strings. We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space. We also formulate our Nahm equations using strong homotopy Lie algebras.

hep-th↗

arXiv2012

Yang-Mills fields in flux compactifications on homogeneous manifolds with SU(4)-structure

The SU(4)-instanton equations are natural BPS equations for instantons on 8-manifolds. We study these equations on nearly Kaehler and Calabi-Yau torsion manifolds of the form M x G/H, with G/H a coset space and M a product of a torus with Euclidean space. By imposing G-invariance the instanton equations reduce to interesting equations on M; for example, equations used by Kapustin and Witten in the geometric Langlands program arise in this way. We carry out reductions in a number of examples, and where possible present simple solutions.

hep-th↗

arXiv2012

Helical buckling of Skyrme-Faddeev solitons

Solitons in the Skyrme-Faddeev model on R^2xS^1 are shown to undergo buckling transitions as the circumference of the S^1 is varied. These results support a recent conjecture that solitons in this field theory are well-described by a much simpler model of elastic rods.

hep-th↗

arXiv2011

Instantons and Killing spinors

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.

hep-th↗

arXiv2011

The large N limit of the Nahm transform

We consider the large N limit of the Nahm transform, which relates charge N monopoles to solutions to the Nahm equation involving NxN matrices. In the large N limit the former approaches a magnetic bag, and the latter approaches a solution of the Nahm equation based on the Lie algebra of area-preserving vector fields on the 2-sphere. We show that the Nahm transform simplifies drastically in this limit.

hep-th↗

arXiv2010

Hopf solitons and elastic rods

Hopf solitons in the Skyrme-Faddeev model are string-like topological solitons classified by the integer-valued Hopf charge. In this paper we introduce an approximate description of Hopf solitons in terms of elastic rods. The general form of the elastic rod energy is derived from the field theory energy and is found to be an extension of the classical Kirchhoff rod energy. Using a minimal extension of the Kirchhoff energy, it is shown that a simple elastic rod model can reproduce many of the qualitative features of Hopf solitons in the Skyrme-Faddeev model. Features that are captured by the model include the buckling of the charge three solution, the formation of links at charges five and six, and the minimal energy trefoil knot at charge seven.

hep-th↗

arXiv2010

Yang-Mills flows on nearly Kaehler manifolds and G_2-instantons

We consider Lie(G)-valued G-invariant connections on bundles over spaces G/H, RxG/H and R^2xG/H, where G/H is a compact nearly Kaehler six-dimensional homogeneous space, and the manifolds RxG/H and R^2xG/H carry G_2- and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on RxG/H is reduced to Newtonian mechanics of a particle moving in a plane with a quartic potential. For particular values of the torsion, we find explicit particle trajectories, which obey first-order gradient or hamiltonian flow equations. In two cases, these solutions correspond to anti-self-dual instantons associated with one of two G_2-structures on RxG/H. It is shown that both G_2-instanton equations can be obtained from a single Spin(7)-instanton equation on R^2xG/H.

hep-th↗