66 results on '"Anders Karlhede"'
Search Results
2. HYPERKAHLER METRICS AND SUPERSYMMETRY
- Author
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Nigel Hitchin, Anders Karlhede, Ulf Lindström, and Martin Rocek
- Subjects
Duality (mathematics) ,Statistical and Nonlinear Physics ,Context (language use) ,Supersymmetry ,Manifold ,Legendre transformation ,Algebra ,symbols.namesake ,Differential geometry ,symbols ,Mathematical Physics ,Quotient ,Supersymmetry algebra ,Mathematics - Abstract
We describe two constructions of hyperkähler manifolds, one based on a Legendre transform, and one on a sympletic quotient. These constructions arose in the context of supersymmetric nonlinear σ-models, but can be described entirely geometrically. In this general setting, we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry, along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience. © 1987 Springer-Verlag.
- Published
- 2016
3. The equivalence problem
- Author
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Anders Karlhede
- Subjects
Physics ,Lorentz group ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,Differential geometry ,Coordinate system ,Isometry group ,Equivalence (measure theory) ,Covariant derivative - Abstract
The equivalence problem is the problem of deciding whether two metric tensors are related by a coordinate transformation or not. I give a brief historical review of work done on this problem in Stockholm around 1980.
- Published
- 2006
4. Progress towards a solution of the equivalence problem in general relativity.
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Anders Karlhede and Jan E. åman
- Published
- 1979
- Full Text
- View/download PDF
5. Field theory for partially polarized quantum Hall states
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U. Nilsson, Thors Hans Hansson, Anders Karlhede, and Jon Magne Leinaas
- Subjects
Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Sigma model ,Mean field theory ,Spin wave ,Quantum mechanics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Effective field theory ,FOS: Physical sciences ,Quantum Hall effect ,Ground state ,Topological quantum number ,Gauge symmetry - Abstract
We propose a new effective field theory for partially polarized quantum Hall states. The density and polarization for the mean field ground states are determined by couplings to two Chern-Simons gauge fields. In addition there is a $\sigma$-model field, $\mh$, which is necessary both to preserve the Chern-Simons gauge symmetry that determines the correlations in the ground state, and the global SU(2) invariance related to spin rotations. For states with non zero polarization, the low energy dynamics is that of a ferromagnet. In addition to spin waves, the spectrum contains topological solitons, or skyrmions, just as in the fully polarized case. The electric charge of the skyrmions is given by $Q_{el}=\nu P Q_{top}$, where $\nu$ is the filling fraction, $P$ the magnitude of the polarization, and $Q_{top}$ the topological charge. For the special case of full polarization, the theory involves a single scalar field and a single Chern-Simons field in addition to the $\sigma$-model field, $\mh$. We also give a heuristic derivation of the model lagrangians for both full and partial polarization, and show that in a mean field picture, the field $\mh$ is necessary in order to take into account the Berry phases originating from rotations of the electron spins., Comment: RevTex, 9 pages
- Published
- 1999
6. Hartree-Fock theory of Skyrmions in quantum Hall ferromagnets
- Author
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Rene Cote, Anders Karlhede, Allan H. MacDonald, Luis Brey, Herbert Fertig, and Shivaji Lal Sondhi
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Physics ,Zeeman effect ,Condensed Matter - Mesoscale and Nanoscale Physics ,Condensed matter physics ,Skyrmion ,Hartree–Fock method ,FOS: Physical sciences ,02 engineering and technology ,Electron ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,021001 nanoscience & nanotechnology ,Quantum number ,01 natural sciences ,symbols.namesake ,Quantum mechanics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,0103 physical sciences ,Quasiparticle ,symbols ,010306 general physics ,0210 nano-technology ,Fermi gas - Abstract
We report on a study of the charged-skyrmion or spin-texture excitations which occur in quantum Hall ferromagnets near odd Landau level filling factors. Particle-hole symmetry is used to relate the spin-quantum numbers of charged particle and hole excitations and neutral particle-hole pair excitations. Hartree-Fock theory is used to provide quantitative estimates of the energies of these excitations and their dependence on Zeeman coupling strength, Landau level quantum numbers, and the thicknesses of the two-dimensional electron layers. For the case of $\nu$ near three we suggest the possibility of first order phase transitions with increasing Zeeman coupling strength from a many skyrmion state to one with many maximally spin-polarized quasiparticles., Comment: 26 pages, 10 figures
- Published
- 1997
7. Fractional domain walls from on-site softening in dipolar bosons
- Author
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Emma Wikberg, Emil J. Bergholtz, Jonas Larson, and Anders Karlhede
- Subjects
Condensed Matter::Quantum Gases ,Physics ,Quantum Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed matter physics ,FOS: Physical sciences ,Quantum Hall effect ,Atomic and Molecular Physics, and Optics ,Condensed Matter - Strongly Correlated Electrons ,symbols.namesake ,Quantum spin Hall effect ,Quantum Gases (cond-mat.quant-gas) ,Quantum mechanics ,Fractional quantum Hall effect ,symbols ,Coulomb ,Quantum Physics (quant-ph) ,Condensed Matter - Quantum Gases ,Hamiltonian (quantum mechanics) ,Ground state ,Quantum tunnelling ,Boson - Abstract
We study dipolar bosons in a 1D optical lattice and identify a region in parameter space---strong coupling but relatively weak on-site repulsion---hosting a series of stable charge-density-wave (CDW) states whose low-energy excitations, built from "fractional domain walls," have remarkable similarities to those of non-Abelian fractional quantum Hall states. Here, a conventional domain wall between translated CDW's may be split by inserting strings of degenerate, but inequivalent, CDW states. Outside these insulating regions, we find numerous supersolids as well as a superfluid regime. The mentioned phases should be accessible experimentally and, in particular, the fractional domain walls can be created in the ground state using single-site addressing, i.e., by locally changing the chemical potential., 6 pages, 3 figures. Extended discussion. As published
- Published
- 2012
8. Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies
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Edward Rezayi, Shivaji Lal Sondhi, Steven A. Kivelson, and Anders Karlhede
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Physics ,Zeeman effect ,Condensed matter physics ,Filling factor ,Order (ring theory) ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,symbols.namesake ,Quantum mechanics ,Fractional quantum Hall effect ,Quasiparticle ,symbols ,Zeeman energy ,Spin-½ - Abstract
We study the two-dimensional electron gas in a high magnetic field at filling factor \ensuremath{\nu}=1 for an arbitrary ratio of the Zeeman energy g${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$B to the typical interaction energy. We find that the system always has a gap, even when the one-particle gap vanishes, i.e., when g=0. When g is sufficiently large, the quasiparticles are perturbatively related to those in the noninteracting limit; we compute their energies to second order in the Coulomb interaction. For g smaller than a critical value ${\mathit{g}}_{\mathit{c}}$ the quasiparticles change character; in the limit of g\ensuremath{\rightarrow}0, they are skyrmions---spatially unbounded objects with infinite spin. In GaAs heterojunctions, the gap is unambiguously predominantly due to correlation effects; indeed, we tentatively conclude that g is always smaller than ${\mathit{g}}_{\mathit{c}}$, so the relevant quasiparticles are the skyrmions. The generalization to other odd-integer filling factors, and to \ensuremath{\nu}=1/3 and 1/5, is discussed.
- Published
- 1993
9. ANYONS IN A MAGNETIC FIELD
- Author
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Anders Karlhede and Erik Westerberg
- Subjects
Closed and exact differential forms ,Physics ,Angular momentum ,Singularity ,Quantum mechanics ,Statistical and Nonlinear Physics ,Perturbation theory (quantum mechanics) ,Function (mathematics) ,Statistical mechanics ,Condensed Matter Physics ,Wave function ,Topological quantum computer - Abstract
We consider N anyons, with statistical parameter ν, in a homogeneous magnetic fieldand discuss exact and perturbative solutions. We show that the energy, E(ν), obeys[Formula: see text] for any bose or fermi state and that the extremal cases correspondto the states where the relative angular momenta of all pairs of particles are negativeand non-negative, respectively. The anyonic continuations of these extremal states aregiven, their energy is linear in ν. We conjecture that the above bounds on [Formula: see text] hold forany ν. This implies that the energy of any many-anyon state decreases monotonicallywith the statistical parameter ν (ν taking any real value). For small enough ν, E=const. [Formula: see text] and the wave function is known. Increasing ν, the wave functionbecomes singular at some bose point. In the following intermediate region (which maybe absent), E(ν) decreases more slowly; the exact form of E(ν) and the wave functionare unknown. Increasing ν further, above some bose point the energy becomes constantand the wave function is again known.
- Published
- 1992
10. Spin chain description of rotating bosons at $\nu=1$
- Author
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Emma Wikberg, Emil J. Bergholtz, and Anders Karlhede
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Statistics and Probability ,Physics ,Condensed Matter::Quantum Gases ,Condensed Matter - Mesoscale and Nanoscale Physics ,Dirac delta function ,Statistical and Nonlinear Physics ,Torus ,Landau quantization ,Fermion ,symbols.namesake ,Condensed Matter - Strongly Correlated Electrons ,Excited state ,Quantum mechanics ,symbols ,Coulomb ,Statistics, Probability and Uncertainty ,Hamiltonian (quantum mechanics) ,Boson - Abstract
We consider bosons at Landau level filling $\nu=1$ on a thin torus. In analogy with previous work on fermions at filling $\nu =1/2$, we map the low-energy sector onto a spin-1/2 chain. While the fermionic system may realize the gapless XY-phase, we show that typically this does not happen for the bosonic system. Instead, both delta function and Coulomb interaction lead to gapped phases in the bosonic system, and in particular we identify a phase corresponding to the non-abelian Moore-Read state. In the spin language, the hamiltonian is dominated by a ferromagnetic next-nearest neighbor interaction, which leads to a description consistent with the non-trivial degeneracies of the ground and excited states of this phase of matter. In addition we comment on the similarities and differences of the two systems mentioned above and fermions at $\nu=5/2$., Comment: Published. 19 pages, 4 figures
- Published
- 2009
11. ON SINGULAR ANYON WAVEFUNCTIONS
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Anders Karlhede, J. Grundberg, Thors Hans Hansson, and J.M. Leinaas
- Subjects
Physics ,Quantum mechanics ,Structure (category theory) ,Anyon ,Flux ,Statistical and Nonlinear Physics ,Condensed Matter Physics ,Mechanical Problem ,Wave function ,Quantum ,Topological quantum computer - Abstract
We show that quantum mechanics allows anyon wavefunctions that are singular as the particles approach each other. An extra real parameter, which determines the nature of this singular behaviour, is necessary to have a well defined quantum mechanical problem. In realistic models, anyons are expected to have an internal structure, corresponding to a smearing of the statistical flux. We study such models and find that, in generic cases, only regular wavefunctions are allowed.
- Published
- 1991
12. Quantum Hall hierarchy wave functions: From conformal correlators to Tao-Thouless states
- Author
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Thors Hans Hansson, Emil J. Bergholtz, Susanne Viefers, Maria Hermanns, and Anders Karlhede
- Subjects
Physics ,Laughlin wavefunction ,Quantum spin Hall effect ,Conformal field theory ,Quantum mechanics ,Conformal anomaly ,Composite fermion ,Fractional quantum Hall effect ,Beta function (physics) ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials - Abstract
Laughlin’s wave functions, which describe the fractional quantum Hall effect at filling factorsν=1/(2k+1), can be obtained as correlation functions in a conformal field theory, and recently, this c ...
- Published
- 2008
13. A Simple View on the Quantum Hall System
- Author
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Emil J. Bergholtz and Anders Karlhede
- Subjects
Physics ,Open quantum system ,Quantum spin Hall effect ,Luttinger liquid ,Simple (abstract algebra) ,Quantum mechanics ,Fractional quantum Hall effect ,Torus ,Landau quantization ,Quantum Hall effect - Abstract
The physics of the quantum Hall system becomes very simple when studied on a thin torus. Remarkably, however, the very rich structure still exists in this limit and there is a continuous route to the bulk system. Here we review recent progress in understanding various features of the quantum Hall system in terms of a simple one-dimensional model corresponding to the thin torus.
- Published
- 2008
14. On Polyakov's spin factors
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J. Grundberg, Anders Karlhede, and Thors Hans Hansson
- Subjects
Physics ,Nuclear and High Energy Physics ,Wilson loop ,High Energy Physics::Lattice ,Angular velocity ,Gauge (firearms) ,Connection (mathematics) ,Thomas precession ,Quantum mechanics ,Path integral formulation ,Condensed Matter::Strongly Correlated Electrons ,Mathematical physics ,Sign (mathematics) ,Spin-½ - Abstract
We discuss the connection between the description of spin using Grassmann variables and that using Polyakov's spin factor. The spin factor can be interpreted as a geometrical phase and expressed as a Wilson loop with the angular velocity of Thomas precession as gauge potential. We show that the non-covariant spin factor has a sign ambiguity, and is thus not suitable for use in path integrals.
- Published
- 1990
15. Quantum Hall system in Tao-Thouless limit
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Anders Karlhede and Emil J. Bergholtz
- Subjects
Physics ,Condensed matter physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,FOS: Physical sciences ,Landau quantization ,Quantum Hall effect ,Condensed Matter Physics ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Electronic, Optical and Magnetic Materials ,Particle in a one-dimensional lattice ,Quantum spin Hall effect ,Quantum mechanics ,Composite fermion ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Spin Hall effect ,Quantum spin liquid ,Lattice model (physics) - Abstract
We consider spin-polarized electrons in a single Landau level on a torus. The quantum Hall problem is mapped onto a one-dimensional lattice model with lattice constant $2\pi/L_1$, where $L_1$ is a circumference of the torus (in units of the magnetic length). In the Tao-Thouless limit, $L_1\to 0$, the interacting many-electron problem is exactly diagonalized at any rational filling factor $\nu=p/q\le 1$. For odd $q$, the ground state has the same qualitative properties as a bulk ($L_1 \to \infty$) quantum Hall hierarchy state and the lowest energy quasiparticle exitations have the same fractional charges as in the bulk. These states are the $L_1 \to 0$ limits of the Laughlin/Jain wave functions for filling fractions where these exist. We argue that the exact solutions generically, for odd $q$, are continuously connected to the two-dimensional bulk quantum Hall hierarchy states, {\it ie} that there is no phase transition as $L_1 \to \infty$ for filling factors where such states can be observed. For even denominator fractions, a phase transition occurs as $L_1$ increases. For $\nu=1/2$ this leads to the system being mapped onto a Luttinger liquid of neutral particles at small but finite $L_1$, this then develops continuously into the composite fermion wave function that is believed to describe the bulk $\nu=1/2$ system. The analysis generalizes to non-abelian quantum Hall states., Comment: 25 pages, 9 figures
- Published
- 2007
16. Quantum Hall wave functions on the torus
- Author
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Anders Karlhede, Maria Hermanns, Emil J. Bergholtz, Juha Suorsa, and Thors Hans Hansson
- Subjects
Physics ,Quantum geometry ,Condensed Matter - Mesoscale and Nanoscale Physics ,FOS: Physical sciences ,Torus ,First quantization ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials ,Open quantum system ,Quantum spin Hall effect ,Quantum mechanics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Quantum field theory ,Wave function ,Mathematical physics - Abstract
We present explicit expressions for a large set of hierarchy wave functions on the torus. Included are the Laughlin states, the states in the positive Jain series, and recently observed states at e.g. $\nu = 4/11$. The techniques we use constitute a nontrivial extension of the conformal field theory methods developed earlier to construct the corresponding wave functions in disc geometry.
- Published
- 2007
17. Microscopic theory of the quantum Hall hierarchy
- Author
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Emil J. Bergholtz, Maria Hermanns, Anders Karlhede, and Thors Hans Hansson
- Subjects
Physics ,Hierarchy (mathematics) ,Condensed Matter - Mesoscale and Nanoscale Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,General Physics and Astronomy ,FOS: Physical sciences ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Open quantum system ,Theoretical physics ,Condensed Matter - Strongly Correlated Electrons ,Quantum spin Hall effect ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Limit (mathematics) ,Statistical physics ,Microscopic theory ,Adiabatic process ,Wave function - Abstract
We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan {\it et. al.}, and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states., Comment: 4 pages, 2 figures. Published
- Published
- 2007
18. The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
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Anders Karlhede, Emma Wikberg, J. Kailasvuori, Emil J. Bergholtz, and Thors Hans Hansson
- Subjects
Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed Matter - Mesoscale and Nanoscale Physics ,FOS: Physical sciences ,Torus ,Pfaffian ,Quantum Hall effect ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials ,Condensed Matter::Soft Condensed Matter ,Condensed Matter - Strongly Correlated Electrons ,Quantum mechanics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Degeneracy (mathematics) - Abstract
We analyze the Moore-Read Pfaffian state on a thin torus. The known six-fold degeneracy is realized by two inequivalent crystalline states with a four- and two-fold degeneracy respectively. The fundamental quasihole and quasiparticle excitations are domain walls between these vacua, and simple counting arguments give a Hilbert space of dimension $2^{n-1}$ for $2n-k$ holes and $k$ particles at fixed positions and assign each a charge $\pm e/4$. This generalizes the known properties of the hole excitations in the Pfaffian state as deduced using conformal field theory techniques. Numerical calculations using a model hamiltonian and a small number of particles supports the presence of a stable phase with degenerate vacua and quarter charged domain walls also away from the thin torus limit. A spin chain hamiltonian encodes the degenerate vacua and the various domain walls., 4 pages, 1 figure. Published, minor changes
- Published
- 2006
19. One-Dimensional Theory of the Quantum Hall System
- Author
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Emil J. Bergholtz and Anders Karlhede
- Subjects
Statistics and Probability ,Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed Matter - Mesoscale and Nanoscale Physics ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Torus ,State (functional analysis) ,Landau quantization ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Dipole ,Condensed Matter - Strongly Correlated Electrons ,Luttinger liquid ,Quantum mechanics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Statistics, Probability and Uncertainty ,Wave function ,Ground state - Abstract
We consider the lowest Landau level on a torus as a function of its circumference $L_1$. When $L_1\to 0$, the ground state at general rational filling fraction is a crystal with a gap--a Tao-Thouless state. For filling fractions $\nu=p/(2pm+1)$, these states are the limits of Laughlin's or Jain's wave functions describing the gapped quantum Hall states when $L_1\to \infty$. For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral dipoles, or rather to a Luttinger liquid modification thereof, at $L_1\sim5$ magnetic lengths. This state is a version of the Rezayi-Read state, and develops continuously into the state that is believed to describe the observed metallic phase as $L_1\to \infty$. Furthermore, the effective Landau level structure that emerges within the lowest Landau level follows from the magnetic symmetries., Comment: 4 pages, 1 figure
- Published
- 2005
20. Properties of the doped spin-32Mott insulator near half filling
- Author
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Anders Karlhede, Stellan Östlund, and T. H. Hansson
- Subjects
Condensed Matter::Quantum Gases ,Physics ,Hubbard model ,Condensed matter physics ,Mott insulator ,Unitary transformation ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials ,Fock space ,Mott transition ,Bogoliubov transformation ,Mean field theory ,Quantum mechanics ,Condensed Matter::Strongly Correlated Electrons ,Ground state - Abstract
We develop an exact generalized Bogoliubov transformation for the spin 3/2 Hubbard model with large anti-Hunds rule coupling near half filling. Since our transformation is unitary, we can thereafter employ standard approximate mean field theory methods in the full Hilbert space to analyze the doped Mott insulator, in contrast to a conventional approach based on truncated Hilbert spaces complemented with hard core constraints. The ground state at exactly half filling is an insulating (Mott) singlet, and according to our analysis a non-Fermi liquid order parameter $ \Delta $ usually associated with extended s-wave superconductivity, will appear self-consistently as soon as a finite density $ n $ holes are introduced. The non-Fermi liquid behavior is a consequence of the nonlinear nature of the unitary transformation mapping the Mott singlet state to a Fock vacuum which introduces anomalous terms such as $\Delta n$ in the effective Lagrangian. Our analysis uses an approach that generalizes readily to multi-band Hubbard models and could provide a mechanism whereby a non-Fermi liquid order parameter proportional to density is developed in Mott insulators with locally entangled ground states. For more complicated systems, such an order parameter could coexist naturally with a variety of other order parameters.
- Published
- 2005
21. Half-Filled Lowest Landau Level on a Thin Torus
- Author
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Anders Karlhede and Emil J. Bergholtz
- Subjects
Condensed Matter::Quantum Gases ,Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Condensed matter physics ,FOS: Physical sciences ,General Physics and Astronomy ,Torus ,Landau quantization ,Fermion ,Luttinger liquid ,Excited state ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Composite fermion ,Fermi gas ,Ground state - Abstract
We solve a model that describes an interacting electron gas in the half-filled lowest Landau level on a thin torus, with radius of the order of the magnetic length. The low energy sector consists of non-interacting, one-dimensional, neutral fermions. The ground state, which is homogeneous, is the Fermi sea obtained by filling the negative energy states and the excited states are gapless neutral excitations out of this one-dimensional sea. Although the limit considered is extreme, the solution has a striking resemblance to the composite fermion description of the bulk $\nu=1/2$ state--the ground state is homogeneous and the excitations are neutral and gapless. This suggests a one-dimensional Luttinger liquid description, with possible observable effects in transport experiments, of the bulk state where it develops continuously from the state on a thin torus as the radius increases., Comment: 4 pages, 1 figure
- Published
- 2005
22. Phase space topology of a switching current detector
- Author
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Anders Karlhede, Jochen Walter, Hans Hansson, Erik A. Tholén, Joachim Sjöstrand, and David B. Haviland
- Subjects
Josephson effect ,Physics ,Condensed Matter - Superconductivity ,Detector ,FOS: Physical sciences ,Topology (electrical circuits) ,Condensed Matter Physics ,Topology ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Capacitance ,Electronic, Optical and Magnetic Materials ,Superconductivity (cond-mat.supr-con) ,Quantum state ,Phase space ,Qubit ,Condensed Matter::Superconductivity ,Voltage - Abstract
We examine in theory and by numerical simulation, the dynamic process of switching from a zero voltage to a finite voltage state in a Josephson junction circuit. The theoretical model describes small capacitance Josephson junctions which are overdamped at high frequencies, and can be applied to detection of the quantum state of a qubit circuit. We show that the speed and fidelity of the readout are strongly influenced by the topology of the phase space attractors. The readout will be close to optimal when choosing the circuit parameters so as to avoid having an unstable limiting cycle which separates the two basins of attraction., Comment: 4 pages, 5 figures
- Published
- 2005
- Full Text
- View/download PDF
23. Erratum: Charge and current in the quantum Hall matrix model [Phys. Rev. B68, 035327 (2003)]
- Author
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Thors Hans Hansson, J. Kailasvuori, and Anders Karlhede
- Subjects
Physics ,Quantum spin Hall effect ,Condensed matter physics ,Quantum mechanics ,Density matrix renormalization group ,Fractional quantum Hall effect ,Charge (physics) ,Current (fluid) ,Quantum Hall effect ,Condensed Matter Physics ,Matrix model ,Electronic, Optical and Magnetic Materials - Published
- 2004
24. Noise and quantum measurements in a circular Josephson array qubit
- Author
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Joachim Sjöstrand and Anders Karlhede
- Subjects
Physics ,Josephson effect ,Flux qubit ,Charge qubit ,Quantum Physics ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Condensed Matter Physics ,Electronic, Optical and Magnetic Materials ,Phase qubit ,Quantum error correction ,Quantum mechanics ,Qubit ,Superconducting quantum computing ,Quantum dissipation - Abstract
We study the decoherence and the quantum measurement of charge in a qubit consisting of a circular array of Josephson junctions. The two-level system we consider couples the two charge states through a higher-order tunneling process thus making it possible to achieve a long relaxation time. Using the spin-boson Hamiltonian, we estimate decoherence due to ohmic as well as 1/f noise. We simulate the quantum-mechanical measurement process by studying the density matrix of the qubit and a capacitively coupled single-electron transistor that measures the charge.
- Published
- 2004
25. Charge and current in the quantum Hall matrix model
- Author
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Anders Karlhede, J. Kailasvuori, and Thors Hans Hansson
- Subjects
Physics ,Condensed Matter - Strongly Correlated Electrons ,Open quantum system ,Strongly Correlated Electrons (cond-mat.str-el) ,Quantum spin Hall effect ,Quantum process ,Quantum mechanics ,Composite fermion ,Fractional quantum Hall effect ,FOS: Physical sciences ,Quantum simulator ,Landau quantization ,Quantum Hall effect - Abstract
We extend the quantum Hall matrix model to include couplings to external electric and magnetic fields. The associated current suffers from matrix ordering ambiguities even at the classical level. We calculate the linear response at low momenta -- this is unambigously defined. In particular, we obtain the correct fractional quantum Hall conductivity, and the expected density modulations in response to a weak and slowly varying magnetic field. These results show that the classical quantum Hall matrix models describe important aspects of the dynamics of electrons in the lowest Landau level. In the quantum theory the ordering ambiguities are more severe; we discuss possible strategies, but we have not been able to construct a good density operator, satisfying the pertinent lowest Landau level commutator algebra., 12 pages, no figures; a logical error below the proposed density operator (46) in version 1 is corrected, and the claim that this density operator satisfy the magnetic algebra (2) is withdrawn. Some formulations have been changed and a few misprints corrected
- Published
- 2003
26. Sample and hold strategy for quantum measurements of Josephson charge qubits
- Author
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Peter Ågren, V. Schollmann, Thors Hans Hansson, David B. Haviland, and Anders Karlhede
- Subjects
Phase qubit ,Physics ,Flux qubit ,Charge qubit ,Condensed matter physics ,Quantum error correction ,Condensed Matter::Superconductivity ,Qubit ,Quantum mechanics ,Superconducting tunnel junction ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Superconducting quantum computing ,Trapped ion quantum computer - Abstract
We present a design for a charge qubit, and an associated quantum sample and hold measurement scheme. Using arrays of superconducting. islands, connected by tunable tunnel junctions, we can sample ...
- Published
- 2001
27. Landau levels for anyons
- Author
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Anders Karlhede, Erik Westerberg, Thors Hans Hansson, and J. Grundberg
- Subjects
Physics ,Quantum mechanics ,Quantum electrodynamics ,Anyon ,Champ magnetique ,Landau quantization ,Topological quantum computer ,Magnetic field - Published
- 1991
28. Dynamics of the Compact, Ferromagnetic \nu=1 Edge
- Author
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K. Lejnell, Shivaji Lal Sondhi, and Anders Karlhede
- Subjects
Physics ,Gapless playback ,Ferromagnetism ,Condensed matter physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Filling factor ,Spin wave ,Quasiparticle ,Condensed Matter::Strongly Correlated Electrons ,Charge density wave ,Instability - Abstract
We consider the edge dynamics of a compact, fully spin polarized state at filling factor $\nu=1$. We show that there are two sets of collective excitations localized near the edge: the much studied, gapless, edge magnetoplasmon but also an additional edge spin wave that splits off below the bulk spin wave continuum. We show that both of these excitations can soften at finite wave-vectors as the potential confining the system is softened, thereby leading to edge reconstruction by spin texture or charge density wave formation. We note that a commonly employed model of the edge confining potential is non-generic in that it systematically underestimates the texturing instability., Comment: 13 pages, 7 figures, Revtex
- Published
- 1999
29. SU(N) Quantum Hall Skyrmions
- Author
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Daniel P. Arovas, Anders Karlhede, and D. Lilliehöök
- Subjects
Physics ,Condensed matter physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Skyrmion ,FOS: Physical sciences ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Isospin ,Quantum mechanics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Quasiparticle ,Symmetry breaking ,Degeneracy (mathematics) ,Spin (physics) - Abstract
We have investigated skyrmions in N-component quantum Hall systems. We find that SU(N) skyrmions are the lowest energy charged excitations for filling factors ��= 1,2,...,N-1 for small enough symmetry breaking terms. N>2 skyrmions can be realized in Si QH systems based on the (110) or (111) interfaces of Si, or perhaps in Si (100) systems, where the spin and valley isospin together provide an SU(4)-symmetry, or in multilayer QH systems. We also present Hartree-Fock results for a phenomenological easy-axis SU(2)-breaking model appropriate to valley degeneracy., 5 pages, 2 figures
- Published
- 1998
- Full Text
- View/download PDF
30. Effective Action Studies of Quantum Hall Spin Textures
- Author
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K. Lejnell, Anders Karlhede, and Shivaji Lal Sondhi
- Subjects
Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Skyrmion ,Degrees of freedom (physics and chemistry) ,FOS: Physical sciences ,Charge (physics) ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Electric charge ,Quantum spin Hall effect ,Quantum mechanics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Effective action ,Spin-½ - Abstract
We report on analytic and numerical studies of spin textures in quantum Hall systems using a long-wavelength effective action for the magnetic degrees of freedom derived previously. The majority of our results concern skyrmions or solitons of this action. We have constructed approximate analytic solutions for skyrmions of arbitrary topological and electric charge and derived expressions for their energies and charge and spin radii. We describe a combined shooting/relaxational technique for numerical determination of the skyrmion profiles and present results that compare favorably with the analytic treatment as well as with Hartree-Fock studies of these objects. In addition, we describe a treatment of textures at the edges of quantum Hall systems within this approach and provide details not reported previously., Comment: 13 pages, 10 figures
- Published
- 1998
- Full Text
- View/download PDF
31. Quantum Hall Skyrmions with Higher Topological Charge
- Author
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D. Lilliehöök, Shivaji Lal Sondhi, Anders Karlhede, and K. Lejnell
- Subjects
Physics ,Condensed Matter::Quantum Gases ,Charge conservation ,Condensed matter physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Filling factor ,Skyrmion ,FOS: Physical sciences ,Charge (physics) ,02 engineering and technology ,Quantum Hall effect ,021001 nanoscience & nanotechnology ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,01 natural sciences ,Quantum mechanics ,0103 physical sciences ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Zeeman energy ,010306 general physics ,0210 nano-technology ,Topological quantum number ,Spin-½ - Abstract
We have investigated quantum Hall skyrmions at filling factor \nu=1 carrying more than one unit of topological, and hence electric, charge. Using a combination of analytic and numerical methods we find the counterintuitive result that when the Zeeman energy is tuned to values much smaller than the interaction energy (g \mu_B B/(e^2/\epsilon\ell) < 9*10^{-5}),the creation energy of a charge two skyrmion becomes less than twice the creation energy of a charge one skyrmion, i.e. skyrmions bind in pairs. The doubly charged skyrmions are stable to further accretion of charge and exhibit a 10% larger spin per unit charge than charge one skyrmions which would, in principle, signal this pairing., Comment: 4 pages, 3 figures. Submitted to Phys. Rev. B, Rapid Communications
- Published
- 1997
- Full Text
- View/download PDF
32. Nonlinear sigma model for partially polarized quantum Hall states
- Author
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Anders Karlhede, Jon Magne Leinaas, and Thors Hans Hansson
- Subjects
Physics ,High Energy Physics::Theory ,Mean field theory ,Field (physics) ,Sigma model ,Quantum spin Hall effect ,Quantum electrodynamics ,Quantum mechanics ,Charge (physics) ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Quantum number ,Spin-½ - Abstract
We consider a two-component quantum Hall system within a Landau-Ginzburg theory with two Chern-Simons gauge fields. From this theory we derive a sigma model covariantly coupled to one Chern-Simons field and find mean field solutions that could describe partially polarized quantum Hall states. The quasiparticles in the original model, which have quantized charge and spin, are described in the covariant sigma model by topological excitations, with the correct quantum numbers. They have finite energy due to the presence of the Chern-Simons field, and closely resemble the skyrmions in the usual non-linear sigma model. For the fully polarized states the spin is no longer quantized, but determined by Coulomb and Zeeman interactions.
- Published
- 1996
33. Textured Edges in Quantum Hall Systems
- Author
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Steven A. Kivelson, Anders Karlhede, K. Lejnell, and Shivaji Lal Sondhi
- Subjects
Physics ,Zeeman effect ,Condensed matter physics ,Spin polarization ,Condensed Matter (cond-mat) ,General Physics and Astronomy ,FOS: Physical sciences ,Condensed Matter ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,symbols.namesake ,Ferromagnetism ,Quantum spin Hall effect ,Spin Hall effect ,symbols ,Condensed Matter::Strongly Correlated Electrons ,Spin-½ - Abstract
We have investigated the formation of spin textures at the edges of quantum Hall systems for several ferromagnetic filling factors. The textures are driven by the same physics that leads to ``skyrmions'' in the bulk. For hard confinement and large Zeeman energies, the edges are narrow and spin polarized. Away from this limit and for $\nu=1/3$, $1/5$ and $1$, we find that they widen by developing spin textures. In contrast, for $\nu=3$, the edge remains spin polarized, even as it reconstructs. We comment on the mode structure of the reconstructed edges and on possible experimental signatures., Comment: 4 pages (2 columns), Revtex 3.0, 3 figures, better estimate for polarized instability gives narrower range of Zeeman energies for textures (still all physical values), slightly different numbers (changed finite size convention), to appear in PRL
- Published
- 1996
34. Topological field theory for p-wave superconductors
- Author
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Masatoshi Sato, Thors Hans Hansson, and Anders Karlhede
- Subjects
High Energy Physics - Theory ,Superconductivity ,Physics ,Topological quantum field theory ,Condensed matter physics ,Condensed Matter - Superconductivity ,FOS: Physical sciences ,General Physics and Astronomy ,Pfaffian ,Torus ,Quantum Hall effect ,Superconductivity (cond-mat.supr-con) ,Theoretical physics ,MAJORANA ,High Energy Physics - Theory (hep-th) ,Condensed Matter::Superconductivity ,Ground state ,Gauge symmetry - Abstract
We propose a topological field theory for a spin-less two-dimensional chiral superconductor that contains fundamental Majorana fields. Due to a fermionic gauge symmetry, the Majorana modes survive as dynamical degrees of freedom only at magnetic vortex cores, and on edges. We argue that these modes have the topological properties pertinent to a p-wave superconductor including the non-abelian braiding statistics, and support this claim by calculating the ground state degeneracy on a torus. We also briefly discuss the connection to the Moore-Read Pfaffian quantum Hall state, and extensions to the spinful case and to three-dimensonal topological superconductors., Comment: 6 pages, Some explanatory text added, and the discussion of degeneracy on the torus reformulated
- Published
- 2012
35. Exclusion statistics for quantum Hall states in the Tao–Thouless limit
- Author
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Mikael Kardell and Anders Karlhede
- Subjects
Statistics and Probability ,Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed Matter - Mesoscale and Nanoscale Physics ,Filling factor ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Torus ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Condensed Matter - Strongly Correlated Electrons ,Low energy ,Quantum mechanics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Limit (mathematics) ,Statistics, Probability and Uncertainty ,Abelian group - Abstract
We consider spin-polarized abelian quantum Hall states in the Tao-Thouless limit, {\it ie} on a thin torus. For any filling factor $\nu=p/q$ a well-defined sector of low-energy states is identified and the exclusion statistics of the excitations is determined. We study numerically, at and near $\nu=1/3$ and $2/5$, how the low energy states develop as one moves away from the TT-limit towards the physical regime. We find that the lowest energy states in the physical regime develop from states in the low energy sector but that the exclusion statistics is modified.
- Published
- 2011
36. Anyons on Higher Genus Surfaces - a Constructive Approach
- Author
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Erik Westerberg, Thors Hans Hansson, and Anders Karlhede
- Subjects
Physics ,Surface (mathematics) ,Nuclear and High Energy Physics ,Braid group ,Condensed Matter (cond-mat) ,Structure (category theory) ,General Physics and Astronomy ,FOS: Physical sciences ,Astronomy and Astrophysics ,Condensed Matter ,Space (mathematics) ,Constructive ,Topological quantum computer ,Theoretical physics ,Genus (mathematics) ,Embedding - Abstract
We reconsider the problem of anyons on higher genus surfaces by embedding them in three dimensional space. From a concrete realization based on three dimensional flux tubes bound to charges moving on the surface, we explicitly derive all the representations of the spinning braid group. The component structure of the wave functions arises from winding the flux tubes around the handles. We also argue that the anyons in our construction must fulfil the generalized spin-statistics relation., Comment: 8 pages, LaTex, 2 figures available on request (wes@vana.physto.se), USITP-93-11
- Published
- 1993
- Full Text
- View/download PDF
37. Quantum Hall Circle
- Author
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Emil J. Bergholtz and Anders Karlhede
- Subjects
Statistics and Probability ,Physics ,Range (particle radiation) ,Condensed Matter - Mesoscale and Nanoscale Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,Landau quantization ,Electron ,Quantum Hall effect ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Kinetic energy ,Circumference ,Wigner crystal ,Condensed Matter - Strongly Correlated Electrons ,Quantum mechanics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,Cylinder ,Statistics, Probability and Uncertainty - Abstract
We consider spin-polarized electrons in a single Landau level on a cylinder as the circumference of the cylinder goes to infinity. This gives a model of interacting electrons on a circle where the momenta of the particles are restricted and there is no kinetic energy. Quantum Hall states are exact ground states for appropriate short range interactions, and there is a gap to excitations. These states develop adiabatically from this one-dimensional quantum Hall circle to the bulk quantum Hall states and further on into the Tao-Thouless states as the circumference goes to zero. For low filling fractions a gapless state is formed which we suggest is connected to the Wigner crystal expected in the bulk., Comment: 12 pages, published
- Published
- 2009
38. A review of the geometrical equivalence of metrics in general relativity
- Author
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Anders Karlhede
- Subjects
Physics ,Algebra ,General Relativity and Quantum Cosmology ,Mathematics of general relativity ,Theory of relativity ,Physics and Astronomy (miscellaneous) ,General relativity ,Schwarzschild metric ,Four-force ,Petrov classification ,Isometry group ,Equivalence (measure theory) - Abstract
We review the solution to the equivalence problem in general relativity given by Cartan and Brans and present a practically useful method to obtain a coordinate-invariant description of a geometry. The method, which can be seen as a generalized Petrov classification, automatically gives the dimensions of the isometry group and its isotropy subgroup. Finally, we illustrate the method using the Schwarzschild solution as a very simple example.
- Published
- 1980
39. Spontaneous symmetry breaking in Kaluza-Klein theories
- Author
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Anders Karlhede and T.N. Tomaras
- Subjects
Physics ,Nuclear and High Energy Physics ,Introduction to gauge theory ,Gauge boson ,Spontaneous symmetry breaking ,High Energy Physics::Phenomenology ,Vacuum state ,High Energy Physics::Theory ,General Relativity and Quantum Cosmology ,Theoretical physics ,Higgs field ,Supersymmetric gauge theory ,Quantum mechanics ,Gauge symmetry ,Vacuum expectation value - Abstract
We study the bosonic spectrum of Kaluza-Klein theories by considering the symmetries of the vacuum. We find that the introduction of external gauge fields with non-vanishing vacuum expectation values affects the massless vectors and may break isometries of the internal space making the corresponding gauge vectors massive.
- Published
- 1983
40. On the ultraviolet properties of twisted supersymmetric non-linear σ-models
- Author
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Ulf Lindström, G. Theodoridis, Anders Karlhede, and J. Grundberg
- Subjects
Physics ,Nuclear and High Energy Physics ,High Energy Physics::Phenomenology ,Structure (category theory) ,medicine.disease_cause ,Space (mathematics) ,Nonlinear system ,Theoretical physics ,Chiral superfield ,Quantum mechanics ,Product (mathematics) ,medicine ,Perturbation theory ,Divergence (statistics) ,Ultraviolet - Abstract
We discuss D = 2 supersymmetric non-linear σ-models involving chiral and twisted chiral superfields. We prove that N = 4 models with local product structure in the target space are ultraviolet finite to all orders in perturbation theory. This result is checked in an explicit three-loop calculation and the relevance of our results to N = 2 models is discussed; we expect that they possess a four-loop divergence.
- Published
- 1987
41. Inequivalent metrics with equal spin coefficients
- Author
-
Anders Karlhede and Jan E. Åman
- Subjects
Physics ,Tensor contraction ,Weyl tensor ,Riemann curvature tensor ,Physics and Astronomy (miscellaneous) ,Tensor field ,Covariant derivative ,symbols.namesake ,Quantum mechanics ,symbols ,Curvature form ,Second covariant derivative ,Tensor density ,Mathematical physics - Abstract
The spin coefficients, the curvature tensor, and the first covariant derivative of the curvature tensor are shown to be insufficient for a complete description of a gravitational field. The inadequacy of the description becomes evident when a set of (unphysical) inequivalent metrics is constructed which cannot be distinguished by only examining these entities. The inequivalence manifests itself in the second covariant derivative.
- Published
- 1982
42. Finding space-time geometries without using a metric
- Author
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Anders Karlhede and Ulf Lindström
- Subjects
Weyl tensor ,Tensor contraction ,Physics ,Riemann curvature tensor ,Christoffel symbols ,Physics and Astronomy (miscellaneous) ,Einstein tensor ,symbols.namesake ,Theoretical physics ,Differential geometry ,Linearized gravity ,Quantum mechanics ,symbols ,Ricci decomposition ,ComputingMethodologies_COMPUTERGRAPHICS - Abstract
A new method for obtaining solutions to Einstein's field equations is presented. It is based on the description of a geometry in terms of the curvature tensor and a number of its covariant derivatives. These entities are used instead of the metric. Physical requirements, such as symmetries, are easily imposed in this picture. An example, including the Schwarzschild geometry, is discussed in detail, but no attempts to find new solutions are made.
- Published
- 1983
43. Hyperkähler manifolds and nonlinear supermultiplets
- Author
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U. Lindström, Martin Rocek, and Anders Karlhede
- Subjects
High Energy Physics::Theory ,Theoretical physics ,Nonlinear system ,Supermultiplet ,Quantum electrodynamics ,High Energy Physics::Phenomenology ,Complex system ,Statistical and Nonlinear Physics ,Superspace ,Multiplet ,Mathematical Physics ,Mathematics - Abstract
We present a new construction of hyperkahler metrics that derives from the 3-dimensionalN=4 nonlinear supermultiplet. Further, we give a detailed description of the nonlinear multiplet inN=2 and 4 superspace.
- Published
- 1987
44. N=1 superspace components of extended supergravity
- Author
-
Ulf Lindström, Sylvester James Gates, Martin Rocek, and Anders Karlhede
- Subjects
Physics ,Particle physics ,Physics and Astronomy (miscellaneous) ,Supergravity ,High Energy Physics::Phenomenology ,Superspace ,Action (physics) ,Moduli ,General Relativity and Quantum Cosmology ,High Energy Physics::Theory ,Metric space ,Theoretical physics ,Order (group theory) ,Higher-dimensional supergravity ,Gauge theory - Abstract
The authors give the constraints for N=2 supergravity in terms of N=1 supergravity and matter fields. They solve the constraints to second order in the matter fields, keeping full nonlinearity in the N=1 supergravity fields, and give the action to the same order. This is sufficient for one-loop background superfield calculations.
- Published
- 1984
45. Spin, statistics and linked loops
- Author
-
Anders Karlhede, Thors Hans Hansson, J. Grundberg, and Ulf Lindström
- Subjects
Physics ,High Energy Physics::Theory ,Nuclear and High Energy Physics ,Introduction to gauge theory ,Quantum gauge theory ,Hamiltonian lattice gauge theory ,Supersymmetric gauge theory ,High Energy Physics::Lattice ,Lattice gauge theory ,Statistics ,Spin–statistics theorem ,Gauge fixing ,Gauge symmetry - Abstract
We show that Polyakov's loop formulation of fermion-boson transmutation in (2+1)-dimensional gauge theories with a Chern-Simons term, is consistent with other calculations based on adiabatic transport. We give an independent derivation of the statistics of particles coupled to a gauge field with a pure Chern-Simons action and explicitly demonstrate the spin statistics theorem for spin half using the method of loops. We also make several comments on Polyakov's derivation of spin factors and propagators in the context of the general theory of twisted ribbons.
- Published
- 1989
46. Topological quantum field theory and N=2 conformal supergravity
- Author
-
Anders Karlhede and Martin Rocek
- Subjects
Physics ,Nuclear and High Energy Physics ,Topological quantum field theory ,Conformal field theory ,Supergravity ,Chern–Simons theory ,Topological string theory ,Symmetry protected topological order ,General Relativity and Quantum Cosmology ,High Energy Physics::Theory ,Killing spinor ,Quantum electrodynamics ,Higher-dimensional supergravity ,Mathematical physics - Abstract
We show how the BRST symmetry of Witten's topological field theory arises as a Killing spinor in N=2 conformal supergravity. We extend the model to include the twisted N=2 scalar multiplet, thus including commuting and anticommuting spinors.
- Published
- 1988
47. On a coordinate-invariant description of Riemannian manifolds
- Author
-
Anders Karlhede
- Subjects
Physics ,Tensor contraction ,Weyl tensor ,Riemann curvature tensor ,Christoffel symbols ,Pure mathematics ,Curvature of Riemannian manifolds ,Physics and Astronomy (miscellaneous) ,symbols.namesake ,symbols ,Ricci decomposition ,Mathematics::Differential Geometry ,Ricci curvature ,Scalar curvature - Abstract
A coordinate-invariant description of a Riemannian manifold is known to be furnished by the curvature tensor and a finite number of its covariant derivatives relative to a field of orthogonal frames. These tensors are closer to measurements than the metrical tensor is. The present article discusses this description's usefulness in general relativity and the redundancy among the curvature tensor and its derivatives.
- Published
- 1980
48. On determining the isometry group of a riemannian space
- Author
-
Anders Karlhede and Malcolm MacCallum
- Subjects
Physics ,symbols.namesake ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,Riemannian submersion ,symbols ,Canonical coordinates ,Isothermal coordinates ,Information geometry ,Fundamental theorem of Riemannian geometry ,Riemannian geometry ,Isometry group ,Exponential map (Riemannian geometry) - Abstract
We present an extension of the recently discussed algorithm [1, 2] for deciding the equivalence problem for Riemannian metrics. The extension determines the structure constants of the isometry group and enables us to obtain some information about its orbits, including the form of the Killing vectors in canonical coordinates.
- Published
- 1982
49. Supersymmetric vector-vector duality
- Author
-
P. van Nieuwenhuizen, Anders Karlhede, Ulf Lindström, and Martin Rocek
- Subjects
Physics ,Physics and Astronomy (miscellaneous) ,Quantum electrodynamics ,Seiberg duality ,Duality (optimization) ,Vector field ,Gauge (firearms) ,Mathematical physics - Abstract
The authors give the supersymmetric generalisation of the duality between topologically massive and self-dual vector fields in three dimensions. In particular, this shows that the topologically massive theory with two interacting sets of gauge vectors admits couplings to matter.
- Published
- 1987
50. Nonlinear σ-models and their gauging in and out of superspace
- Author
-
Anders Karlhede, Martin Rocek, Ulf Lindström, and Chris Hull
- Subjects
Physics ,Nuclear and High Energy Physics ,Sigma model ,High Energy Physics::Phenomenology ,Supersymmetry ,Kähler manifold ,Gauge (firearms) ,Superspace ,Action (physics) ,High Energy Physics::Theory ,Quantum electrodynamics ,Mathematics::Differential Geometry ,Symmetry breaking ,Quantum field theory ,Mathematical physics - Abstract
We analyze and generalize bosonic nonlinear σ-models and their N = 1,2 supersymmetric extensions in (4 spacetime-dimensional) N = 1 superspace. We give a general construction of nonminimal kinetic terms for gauge fields and of N = 1,2 gauging of isometries on Kahler and hyper-Kahler manifolds. In particular, we study the gauging of noncompact groups. We derive the complete component action and supertrace formula. For N = 2 models, the supertrace always vanishes.
- Published
- 1986
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