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  • 1.
    Arnlind, Joakim
    et al.
    Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden .
    Bordemann, Martin
    Laboratoire de MIA, 4 rue des Frères Lumière, Univ. deHaute-Alsace, 68093, Mulhouse, France .
    Hoppe, Jens
    Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden .
    Lee, Choonkyu
    Department of Physics and Center for Theoretical Physics, Seoul National University, 151-747, Seoul, South Korea .
    Goldfish Geodesics and Hamiltonian Reduction of Matrix Dynamics2008Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 84, s. 89-98Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We describe the Hamiltonian reduction of a time-dependent real-symmetric N×N matrix system to free vector dynamics, and also provide a geodesic interpretation of Ruijsenaars–Schneider systems. The simplest of the latter, the goldfish equation, is found to represent a flat-space geodesic in curvilinear coordinates.

  • 2.
    Arnlind, Joakim
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Choe, Jaigyoung
    Korea Institute Adv Study, South Korea.
    Hoppe, Jens
    Royal Institute Technology, Sweden.
    Noncommutative Minimal Surfaces2016Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 106, nr 8, s. 1109-1129Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass representation.

  • 3.
    Arnlind, Joakim
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Holm, Christoffer
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
    A noncommutative catenoid2018Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 108, nr 7, s. 1601-1622Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated. A noncommutative analogue of the fact that the catenoid is a minimal surface is studied by constructing a Laplace operator from the connection and showing that the embedding coordinates are harmonic. Furthermore, an integral is defined and the total curvature is computed. Finally, classes of left and right modules are introduced together with constant curvature connections, and bimodule compatibility conditions are discussed in detail.

  • 4.
    Arnlind, Joakim
    et al.
    Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden.
    Hoppe, Jens
    Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden.
    Eigenvalue-Dynamics off the Calogero–Moser System2004Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 68, s. 121-129Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    By finding N(N− 1)/2 suitable conserved quantities, free motions of real symmetric N×N matrices X(t), with arbitrary initial conditions, are reduced to nonlinear equations involving only the eigenvalues of X – in contrast to the rational Calogero-Moser system, for which [X(0),Xd(0)] has to be purely imaginary, of rank one.

  • 5.
    Arnlind, Joakim
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Huisken, Gerhard
    University of Tubingen, Germany.
    Pseudo-Riemannian Geometry in Terms of Multi-Linear Brackets2014Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 104, nr 12, s. 1507-1521Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)Kahler geometry.

  • 6.
    Arnlind, Joakim
    et al.
    Mathematical Physics, Royal Institute of Technology, SE-106 91, Stockholm, Sweden .
    Mickelsson, Jouko
    Mathematical Physics, Royal Institute of Technology, SE-106 91, Stockholm, Sweden .
    Trace Extensions, Determinant Bundles, and Gauge Group Cocycles2002Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 62, nr 2, s. 101-110Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study the geometry of determinant line bundles associated with Dirac operators on compact odd-dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated nonmultiplicative renormalized determinants.

  • 7.
    Enblom, Alexandra
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Estimates for Eigenvalues of Schrodinger Operators with Complex-Valued Potentials2016Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 106, nr 2, s. 197-220Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    New estimates for eigenvalues of non-self-adjoint multi-dimensional Schrodinger operators are obtained in terms of L (p) -norms of the potentials. The results cover and improve those known previously, in particular, due to Frank (Bull Lond Math Soc 43(4):745-750, 2011), Safronov (Proc Am Math Soc 138(6):2107-2112, 2010), Laptev and Safronov (Commun Math Phys 292(1):29-54, 2009). We mention the estimations of the eigenvalues situated in the strip around the real axis (in particular, the essential spectrum). The method applied for this case involves the unitary group generated by the Laplacian. The results are extended to the more general case of polyharmonic operators. Schrodinger operators with slowly decaying potentials and belonging to weak Lebesgues classes are also considered.

  • 8.
    Maz´ya, Vladimir G.
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Shubin, Mikhail
    Can one see the fundamental frequency of a drum?2005Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 74, nr 2, s. 135-151Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We establish two-sided estimates for the fundamental frequency (the lowest eigenvalue) of the Laplacian in an open set Ω⊂ℝn with the Dirichlet boundary condition. This is done in terms of the interior capacitary radius of Ω which is defined as the maximal possible radius of a ball B with a negligible intersection with the complement of Ω. Here negligibility of F ⊂ B means that cap(F)≤γ cap (B), where cap a means the Wiener (harmonic) capacity and γ is arbitrarily fixed with the sole restriction 0 < γ < 1. We provide explicit values of constants in the two-sided estimates. © Springer 2005.

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