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Prof J Martin Speight

Professor of Mathematics
Pure Mathematics

Contact details

Room: 9.11
Tel: +44 (0)113 3435169
Email: J.M.Speight @ leeds.ac.uk

Keywords

Topological solitons
Moduli spaces
Mathematical physics
Differential geometry
Superconductivity

Research interests

There are many systems of partial differential equations of interest in theoretical physics which possess soliton solutions (stable, smooth, localized lumps of energy). Often the space of static soliton solutions forms a smooth manifold, called the moduli space, which can be equipped with a natural Riemannian metric. This is true, for example, of the Yang-Mills-Higgs, abelian Higgs and nonlinear sigma models, whose solitons are called respectively monopoles, vortices and lumps. Following a conjecture of N.S. Manton, it is believed that slow soliton dynamics in such systems is well approximated by geodesic motion in the corresponding moduli space. This leads one to study the Riemannian geometry of soliton moduli spaces and exploit this geometry to understand slow soliton dynamics. My own research concentrates on solitons in 2+1 dimensions, in particular, the completeness, volume and curvature properties of moduli spaces of vortices and lumps.

Useful links

Research homepage

Publications

Adam C, Speight JM, Wereszczynski A Volume of a vortex and the Bradlow bound Physical Review D, 95, 2017
DOI:10.1103/PhysRevD.95.116007
View abstract

Gillard M, Harland D, Kirk E, Maybee B, Speight M A point particle model of lightly bound skyrmions Nuclear Physics B, 917, 286-316, 2017
DOI:10.1016/j.nuclphysb.2017.01.027
View abstract

Babaev E, Carlström J, Silaev M, Speight JM Type-1.5 superconductivity in multicomponent systems Physica C: Superconductivity and its Applications, 533, 20-35, 2017
DOI:10.1016/j.physc.2016.08.003
View abstract

Adam C; Naya C; Speight JM; Vazquez R; Sanchez-Guillen J; Wereszczynski A A unified approach to nuclei: The BPS Skyrme ModelNuclear and Particle Physics Proceedings, 1480-1486 2016
DOI:10.1016/j.nuclphysbps.2015.09.239
View abstract

Alqahtani LS, Speight JM Ricci magnetic geodesic motion of vortices and lumps Journal of Geometry and Physics, 98, 556-574, 2015
DOI:10.1016/j.geomphys.2015.07.008
View abstract

Speight JM Near BPS Skyrmions and restricted harmonic maps Journal of Geometry and Physics, 92, 30-45, 2015
DOI:10.1016/j.geomphys.2015.02.001
View abstract

Gillard M, Harland D, Speight M Skyrmions with low binding energies Nuclear Physics B, 895, 272-287, 2015
DOI:10.1016/j.nuclphysb.2015.04.005
View abstract

Speight JM Solitons on tori and soliton crystals Communications in Mathematical Physics, 332, 355-377, 2014
DOI:10.1007/s00220-014-2104-z
View abstract

Babaev E, Carlström J, Garaud J, Silaev M, Speight JM Type-1.5 superconductivity in multiband systems: Magnetic response, broken symmetries and microscopic theory - A brief overview Physica C: Superconductivity and its Applications, 479, 2-14, 2012
DOI:10.1016/j.physc.2012.01.002
View abstract

Speight JM Long range vortex interactions and type 1.5 superconductivity AIP Conference Proceedings, 1389, 660-663, 2011
DOI:10.1063/1.3636817
View abstract

Harland D, Speight M, Sutcliffe P Hopf solitons and elastic rods Physical Review D - Particles, Fields, Gravitation and Cosmology, 83, 2011
DOI:10.1103/PhysRevD.83.065008
View abstract

Speight JM The volume of the space of holomorphic maps from S-2 to CPk J GEOM PHYS, 61, 77-84, 2011
DOI:10.1016/j.geomphys.2010.09.005

Speight JM Compactons and semi-compactons in the extreme baby Skyrme model J PHYS A-MATH THEOR, 43, 2010
DOI:10.1088/1751-8113/43/40/405201

Speight JM Supercurrent coupling in the Faddeev-Skyrme model J GEOM PHYS, 60, 599-610, 2010
DOI:10.1016/j.geomphys.2009.12.007

Krusch S, Speight JM Exact moduli space metrics for hyperbolic vortex polygons J MATH PHYS, 51, 2010
DOI:10.1063/1.3277189

Speight JM A pure Skyrme instanton PHYS LETT B, 659, 429-433, 2008
DOI:10.1016/j.physletb.2007.10.040

Speight JM Magnetic bubble refraction and quasibreathers in inhomogeneous antiferromagnetsTHEOR MATH PHYS+, 1043-1055 2007
View abstract

Speight JM, Svensson M On the strong coupling limit of the Faddeev-Hopf model COMMUN MATH PHYS, 272, 751-773, 2007
DOI:10.1007/s00220-007-0240-4

Speight JM Sigma models on curved space and bubble refraction in doped antiferromagnets NONLINEARITY, 19, 1565-1579, 2006
DOI:10.1088/0951-7715/19/7/006

Speight JM, Zolotaryuk Y Kinks in dipole chains NONLINEARITY, 19, 1365-1382, 2006
DOI:10.1088/0951-7715/19/6/008

Krusch S, Speight JM Fermionic quantization of Hopf solitons Communications in Mathematical Physics, 264, 391-410, 2006
DOI:10.1007/s00220-005-1469-4

Auckly D, Speight JM Fermionic quantization and configuration spaces for the Skyrme and Faddeev-Hopf Models Communications in Mathematical Physics, 263, 173-216, 2006
DOI:10.1007/s00220-005-1496-1

Speight JM Slow equivariant lump dynamics on the two-sphere Nonlinearity, 19, 441-452, 2006
DOI:10.1088/0951-7715/19/2/011

Babaev E, Speight JM Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors Physical Review B (Condensed Matter and Materials Physics), 72, 1-4, 2005
DOI:10.1103/PhysRevB.72.180502

Speight JM Homotopy classification of multiply based textures None, 72, 79-82, 2005

Romao NM, Speight JM Slow Schrodinger dynamics of gauged vortices NONLINEARITY, 17, 1337-1355, 2004
DOI:10.1088/0951-7715/17/4/010

Haskins M, Speight JM The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps J MATH PHYS, 44, 3470-3494, 2003
DOI:10.1063/1.1586480

Speight JM The L-2 geometry of spaces of harmonic maps S-2 ->S-2 and RP2 ->RP2 J GEOM PHYS, 47, 343-368, 2003

Manton N, Speight JM Asymptotic interactions of critically coupled vortices Communications in Mathematical Physics, 236, 535-555, 2003
DOI:10.1007/s00220-003-0842-4

Speight JM The L^2 geometry of spaces of harmonic maps $S^2 \to S^2$ and $RP^2 \to RP^2$ Journal of Geometry and Physics, 47, 343-368, 2002
DOI:10.1016/S0393-0440(02)00227-9

Haskins M, Speight JM Breather initial profiles in chains of weakly coupled anharmonic oscillators PHYS LETT A, 299, 549-557, 2002

Speight JM, Sutcliffe PM Discrete breathers in anisotropic ferromagnetic spin chains J PHYS A-MATH GEN, 34, 10839-10858, 2001

Speight JM The deformed conifold as a geometry on the space of unit charge CP1 lumps PHYS LETT B, 511, 295-301, 2001

Speight JM Instability of breathers in the topological discrete sine-Gordon system NONLINEARITY, 14, 843-848, 2001

Speight JM A quantum Peierls-Nabarro barrier Journal of Physics A: Mathematical and General, 33, 4741-4754, 2000

Speight JM Topological discrete kinks Nonlinearity, 12, 1373-1387, 1999

Speight JM Breathers in the weakly coupled topological discrete sine-Gordon system Nonlinearity, 11, 1651-1671, 1998

Speight JM Lump dynamics in the CP1model on the torus Communications in Mathematical Physics, 194, 513-539, 1998

Speight JM A discreteφ4system without a Peierls-Nabarro barrier Nonlinearity, 10, 1615-1625, 1997

Speight JM, Svensson M Some global minimizers of a symplectic Dirichlet energy vol, 62, 737-745,
View abstract

Babaev E, Jäykkä J, Speight M Magnetic field delocalization and flux inversion in fractional vortices in two-component superconductors Phys. Rev. Lett, 103, 237002,
DOI:10.1103/PhysRevLett.103.237002
View abstract

Babaev E, Carlstrom J, Speight M Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors Phys.Rev.Lett., 105, 067003,
DOI:10.1103/PhysRevLett.105.067003
View abstract

Carlstrom J, Babaev E, Speight M Type-1.5 superconductivity in multiband systems: the effects of interband couplings Phys. Rev. B, 83, 174509,
DOI:10.1103/PhysRevB.83.174509
View abstract

Jäykkä J, Speight M Easy plane baby skyrmions Phys.Rev.D, 82, 125030,
DOI:10.1103/PhysRevD.82.125030
View abstract

Harland D, Speight M, Sutcliffe P Hopf solitons and elastic rods Phys.Rev.D, 83, 065008,
DOI:10.1103/PhysRevD.83.065008
View abstract

Speight JM The ground state energy of a charged particle on a Riemann surface.
View abstract

Jäykkä J, Speight M, Sutcliffe P Broken Baby Skyrmions Proc. R. Soc. A, 468, 1085-1104,
DOI:10.1098/rspa.2011.0543
View abstract

Speight JM, Jäykkä J Supercurrent coupling destabilizes knot solitons Phys. Rev. D, 84, 125035,
DOI:10.1103/PhysRevD.84.125035
View abstract

Auckly D, Kapitanski L, Speight M Geometry and analysis in non-linear sigma models St. Petersburg Mathematical Journal, 18, 1-31,
View abstract

Speight JM Static intervortex forces Phys.Rev. D, 55, 3830-3835,
DOI:10.1103/PhysRevD.55.3830
View abstract

Speight JM Lump dynamics in the CP^1 model on the torus Commun.Math.Phys., 194, 513-539,
DOI:10.1007/s002200050367
View abstract

Sadun LA, Speight JM Geodesic incompleteness in the CP^1 model on a compact Riemann surface Lett.Math.Phys., 43, 329-334,
View abstract

Speight JM Low energy dynamics of a CP^1 lump on the sphere J.Math.Phys., 36, 796,
DOI:10.1063/1.531157
View abstract

Speight JM The kink Casimir energy in a lattice sine-Gordon model Phys.Rev. D, 49, 6914-6919,
DOI:10.1103/PhysRevD.49.6914
View abstract

Speight JM, Strachan IAB Gravity thaws the frozen moduli of the CP^1 lump Phys.Lett. B, 457, 17-22,
DOI:10.1016/S0370-2693(99)00526-2
View abstract

Haskins M, Speight JM Breather initial profiles in chains of weakly coupled anharmonic oscillators Phys. Lett. A., 299, 549-557,
DOI:10.1016/S0375-9601(02)00670-9
View abstract

Speight JM, Ward RS Kink dynamics in a novel discrete sine-Gordon system Nonlinearity, 7, 475-484,
DOI:10.1088/0951-7715/7/2/009
View abstract

Babaev E, Carlstrom J, Garaud J, Silaev M, Speight JM Type-1.5 superconductivity in multiband systems: magnetic response, broken symmetries and microscopic theory. A brief overview Physica C, 479, 2-14,
DOI:10.1016/j.physc.2012.01.002
View abstract

Krusch S, Speight JM Quantum lump dynamics on the two-sphere Commun. Math. Phys, 322, 95-126,
DOI:10.1007/s00220-013-1730-1
View abstract

Garaud J, Carlstrom J, Babaev E, Speight M Chiral CP^2 skyrmions in three-band superconductors Phys. Rev. B, 87, 014507,
DOI:10.1103/PhysRevB.87.014507
View abstract

Harland D, Jäykkä J, Shnir Y, Speight M Isospinning hopfions J. Phys. A: Math. Theor., 46, 225402,
DOI:10.1088/1751-8113/46/22/225402
View abstract

Adam C, Naya C, Sanchez-Guillen J, Speight JM, Wereszczynski A Thermodynamics of the BPS Skyrme model Phys. Rev. D, 90, 045003,
DOI:10.1103/PhysRevD.90.045003
View abstract

Speight JM The adiabatic limit of wave map flow on a two torus.
View abstract