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  • 1.
    Atai, Farrokh
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics.
    Series Solutions of the Non-Stationary Heun Equation2018In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 14, article id 011Article in journal (Refereed)
    Abstract [en]

    We consider the non-stationary Heun equation, also known as quantum Painleve VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the problem to solve this equation into a differential-difference equation which, as we show, can be solved by efficient recursive algorithms. We thus obtain series representations of solutions which provide elliptic generalizations of the Jacobi polynomials. These series reproduce, in a limiting case, a perturbative solution of the Heun equation due to Takemura, but our method is different in that we expand in non-conventional basis functions that allow us to obtain explicit formulas to all orders; in particular, for special parameter values, our series reduce to a single term.

  • 2. Farrokh, Atai
    et al.
    Hallnas, Martin
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Orthogonality of super‐Jack polynomials and a Hilbert space interpretation of deformed Calogero–Moser–Sutherland operators2019In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 51, no 2, p. 353-370Article in journal (Refereed)
    Abstract [en]

    We prove orthogonality and compute explicitly the (quadratic) norms for super-Jack polynomials SP lambda((z1, horizontal ellipsis ,zn),(w1, horizontal ellipsis ,wm);theta) with respect to a natural positive semi-definite, but degenerate, Hermitian product ⟨center dot,center dot⟩n,m,theta '. In case m=0 (or n=0), our product reduces to Macdonald's well-known inner product ⟨center dot,center dot⟩n,theta ', and we recover his corresponding orthogonality results for the Jack polynomials P lambda((z1, horizontal ellipsis ,zn);theta). From our main results, we readily infer that the kernel of ⟨center dot,center dot⟩n,m,theta ' is spanned by the super-Jack polynomials indexed by a partition lambda not containing the mxn rectangle (mn). As an application, we provide a Hilbert space interpretation of the deformed trigonometric Calogero-Moser-Sutherland operators of type A(n-1,m-1).

  • 3.
    Langmann, Edwin
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics.
    Lebowitz, Joel L.
    Mastropietro, Vieri
    Moosavi, Per
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics.
    Time evolution of the Luttinger model with nonuniform temperature profile2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, no 23, article id 235142Article in journal (Refereed)
    Abstract [en]

    We study the time evolution of a one-dimensional interacting fermion system described by the Luttinger model starting from a nonequilibrium state defined by a smooth temperature profile T (x). As a specific example we consider the case when T (x) is equal to T-L (T-R) far to the left (right). Using a series expansion in epsilon = 2(T-R -T-L)/(T-L + T-R), we compute the energy density, the heat current density, and the fermion two-point correlation function for all times t >= 0. For local (delta-function) interactions, the first two are computed to all orders, giving simple exact expressions involving the Schwarzian derivative of the integral of T (x). For nonlocal interactions, breaking scale invariance, we compute the nonequilibrium steady state (NESS) to all orders and the evolution to first order in epsilon. The heat current in the NESS is universal even when conformal invariance is broken by the interactions, and its dependence on T-L,T-R agrees with numerical results for the XXZ spin chain. Moreover, our analytical formulas predict peaks at short times in the transition region between different temperatures and show dispersion effects that, even if nonuniversal, are qualitatively similar to ones observed in numerical simulations for related models, such as spin chains and interacting lattice fermions.

  • 4.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    (3+1)-Dimensional Schwinger Terms and Non-commutative Geometry1994In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 338, p. 241-248Article in journal (Refereed)
  • 5.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    A superversion of quasifree second quantization. I. Charged particles1992In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 3, no 3, p. 1032-1046Article in journal (Refereed)
  • 6.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Bc2(T) of anisotropic systems: some explicit results1990In: Physica B: Physics of Condensed Matter, Vol. 65, p. 1061-1062Article in journal (Refereed)
  • 7.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Cocycles for Boson and Fermion Bogoliubov Transformations1994In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 35, p. 96-112Article in journal (Refereed)
  • 8.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Consistent axial-like gauge fixing on hypertori1994In: Modern Physics Letters A, ISSN 0217-7323, E-ISSN 1793-6632, Vol. 9, p. 2913-2926Article in journal (Refereed)
  • 9.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Descent equations of Yang-Mills anomalies in noncommutative geometry1997In: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, p. 259-279Article in journal (Refereed)
  • 10.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Elementary Derivation of the Chiral Anomaly1996In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 6, p. 45-54Article in journal (Refereed)
  • 11.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Exactly solvable models for 2D correlated fermions2004In: Journal of Physics A: Mathematical and General, Vol. 37, no 2, p. 407-423Article in journal (Refereed)
    Abstract [en]

    I discuss many-body models for correlated fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: two-dimensional (2D) fermions in a constant magnetic field and a particular non-local four-point interaction. It is exactly solvable due to a dynamical symmetry corresponding to the Lie algebra gl∞ ⊕ gl∞. There is an algorithm to construct all energy eigenvalues and eigenfunctions of this model. The latter are, in general, many-body states with spatial correlations. The model also has a non-trivial zero temperature phase diagram. I point out that this QH model can be obtained from a more realistic one using a truncation procedure generalizing a similar one leading to mean field theory. Applying this truncation procedure to other 2D fermion models I obtain various simplified models of increasing complexity which generalize mean field theory by taking into account non-trivial correlations but nevertheless are treatable by exact methods.

  • 12.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Fermion Current Algebras and Schwinger Terms in 3+1 Dimensions1994In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 162, p. 1-32Article in journal (Refereed)
  • 13.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Fermi-surface harmonics in the theory of the upper critical field1992In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 46, no 14, p. 9104-Article in journal (Refereed)
  • 14.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Finding and solving Calogero-Moser type systems using Yang-Mills gauge theories1999In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 563, p. 506-532Article in journal (Refereed)
  • 15.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Gauge Theories on a Cylinder1992In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 296, p. 117-120Article in journal (Refereed)
  • 16.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Gribov ambiguity and non-trivial vacuum structure of gauge theories on a cylinder1993In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 303, p. 303-307Article in journal (Refereed)
  • 17.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Loop groups, anyons and the Calogero-Sutherland model1999In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 201, p. 1-34Article in journal (Refereed)
  • 18.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Mean field approach to antiferromagnetic domains in the doped Hubbard model1997In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, p. 9439-9451Article in journal (Refereed)
  • 19.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Non-commutative Integration Calculus1995In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 36, p. 3822-3835Article in journal (Refereed)
  • 20.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Novel integrable spin-particle models from gauge theories on a cylinder1998In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 429, p. 336-342Article in journal (Refereed)
  • 21.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    On current superalgebras and super-Schwinger terms1991In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, no 1, p. 69-76Article in journal (Refereed)
  • 22.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    On the upper critical field of anisotropic superconductors1991In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 73, p. 347-356Article in journal (Refereed)
  • 23.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    QCD(1+1) with massless quarks and gauge covariant Sugawara construction1994In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 341, p. 195-204Article in journal (Refereed)
  • 24.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Quantum Gauge Theories and Noncommutative Geometry1996In: Acta Physica Polonica B, ISSN 0587-4254, E-ISSN 1509-5770, Vol. 27, p. 2477-2496Article in journal (Refereed)
  • 25.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Scattering matrix in external field problems1996In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 37, p. 3933-3953Article in journal (Refereed)
  • 26.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Strong coupling gauge theory, quantum spin systems and the spontaneous breaking of chiral symmetry1992In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 297, p. 175-180Article in journal (Refereed)
  • 27.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    SU (N) antiferromagnets and strongly coupled QED: effective field theory for Josephson junctions arrays1993In: Nuclear physics B, Proceedings supplements, ISSN 0920-5632, E-ISSN 1873-3832, Vol. 33, p. 192-208Article in journal (Refereed)
  • 28.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Supersymmetry breaking and the Jaynes-Cummings model1993In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 176, no 5, p. 307-312Article in journal (Refereed)
  • 29.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    The BCS critical temperature in a weak homogeneous magnetic field2019In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403Article in journal (Refereed)
  • 30.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    The critical temperature of superconductors with a cylinder symmetrical Fermi surface1989In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 157, no 3, p. 415-424Article in journal (Refereed)
  • 31.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    The geometric phase and the Schwinger term in some models1992In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 7, no 21, p. 5045-5083Article in journal (Refereed)
  • 32.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    The Luttinger-Schwinger Model1997In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 253, p. 310-331Article in journal (Refereed)
  • 33.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    The Superfluidity and Experimental Properties of Odd-Energy-Gap Superconductors1993In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 26, no 2Article in journal (Refereed)
  • 34.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Theory of the upper critical magnetic field without local approximation1989In: Physica. C, Superconductivity, ISSN 0921-4534, E-ISSN 1873-2143, Vol. 59, p. 561-569Article in journal (Refereed)
  • 35.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Towards a string representation of infrared SU(2) Yang-Mills theory1999In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 463, p. 252-256Article in journal (Refereed)
  • 36.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Ubiquity of superconducting domes in Bardeen-Cooper-Schrieffer theory with finite-range potentials2019In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114Article in journal (Refereed)
    Abstract [en]

    Based on recent progress in mathematical physics, we present a reliable method to analytically solve the linearized BCS gap equation for a large class of finite-range interaction potentials leading to s-wave superconductivity. With this analysis, we demonstrate that the monotonic growth of the superconducting critical temperature Tc with the carrier density, n, predicted by standard BCS theory, is an artifact of the simplifying assumption that the interaction is quasi-local. In contrast, we show that any well-defined non-local potential leads to a "superconducting dome", i.e. a non-monotonic Tc(n) exhibiting a maximum value at finite doping and going to zero for large n. This proves that, contrary to conventional wisdom, the presence of a superconducting dome is not necessarily an indication of competing orders, nor of exotic superconductivity. Our results provide a prototype example and guide towards improving ab-initio predictions of Tc for real materials.

1 - 36 of 36
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