| 1. |
- Andersson, Fredrik, et al.
(författare)
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Spin coefficients as Lanczos scalars : Underlying spinor relations
- 2000
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Ingår i: Journal of Mathematical Physics. - 0022-2488 .- 1089-7658. ; 41:5, s. 2990-3001
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Tidskriftsartikel (refereegranskat)abstract
- It has been conjectured by Lopez-Bonilla and co-workers that there is some linear relationship between the NP spin coefficients and the Lanczos scalars, and examples have been given for a number of different classes of space-times. We show that in each of those examples a Lanczos potential can be defined in a very simple way directly from the spinor dyad. Although some of these examples seem to have no deeper geometric meaning, we emphasize that there are structural links between Lanczos potential and spin coefficients which we highlight in some other examples. In particular we show that the direct identification of Lanczos potentials with spin coefficients is possible for some important classes of space-times while the direct identification of Lanczos potentials with the properly weighted spin coefficients is also possible for several important classes of space-times. In both of these cases we obtain the necessary and sufficient conditions on the spin coefficients for such identifications to be possible, which enables us to test space-times directly. (C) 2000 American Institute of Physics. [S0022-2488(00)03104-2].
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| 2. |
- Aghapour, Sajad, et al.
(författare)
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The zilch electromagnetic conservation law revisited
- 2020
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 61:12
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that the zilch conservation law arises as the Noether current corresponding to a variational symmetry of a duality-symmetric Maxwell Lagrangian. The action of the corresponding symmetry generator on the duality-symmetric Lagrangian, while non-vanishing, is a total divergence as required by the Noether theory. The variational nature of the zilch conservation law was previously known only for some of the components of the zilch tensor, notably the optical chirality. By contrast, our analysis is fully covariant and is, therefore, valid for all components of the zilch tensor. The analysis is presented here for both the real and complex versions of duality-symmetric Maxwell Lagrangians.
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| 3. |
- Akemann, G., et al.
(författare)
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The elliptic Ginibre ensemble : A unifying approach to local and global statistics for higher dimensions
- 2023
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 64:2
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Tidskriftsartikel (refereegranskat)abstract
- The elliptic Ginibre ensemble of complex non-Hermitian random matrices allows us to interpolate between the rotationally invariant Ginibre ensemble and the Gaussian unitary ensemble of Hermitian random matrices. It corresponds to a two-dimensional one-component Coulomb gas in a quadrupolar field at inverse temperature beta = 2. Furthermore, it represents a determinantal point process in the complex plane with the corresponding kernel of planar Hermite polynomials. Our main tool is a saddle point analysis of a single contour integral representation of this kernel. We provide a unifying approach to rigorously derive several known and new results of local and global spectral statistics, including in higher dimensions. First, we prove the global statistics in the elliptic Ginibre ensemble first derived by Forrester and Jancovici [Int. J. Mod. Phys. A 11, 941 (1996)]. The limiting kernel receives its main contribution from the boundary of the limiting elliptic droplet of support. In the Hermitian limit, there is a known correspondence between non-interacting fermions in a trap in d real dimensions R-d and the d-dimensional harmonic oscillator. We present a rigorous proof for the local d-dimensional bulk (sine) and edge (Airy) kernel first defined by Dean et al. [Europhys. Lett. 112, 60001 (2015)], complementing the recent results by Deleporte and Lambert [arXiv:2109.02121 (2021)]. Using the same relation to the d-dimensional harmonic oscillator in d complex dimensions C-d, we provide new local bulk and edge statistics at weak and strong non-Hermiticity, where the former interpolates between correlations in d real and d complex dimensions. For C-d with d = 1, this corresponds to non-interacting fermions in a rotating trap.
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| 4. |
- Aksteiner, S., et al.
(författare)
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Symmetries of linearized gravity from adjoint operators
- 2019
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 60:8
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Tidskriftsartikel (refereegranskat)abstract
- Based on operator identities and their formal adjoints, we derive two symmetry operators for the linearized Einstein operator on vacuum backgrounds of Petrov type D and, in particular, the Kerr spacetime. One of them is of differential order four and coincides with a result of Cohen and Kegeles. The other one is a new operator of differential order six. The corresponding operator identities are based on the Teukolsky equation and the Teukolsky-Starobinsky identities, respectively. The method applies to other field equations as well, which is illustrated with the Maxwell equation. The resulting symmetry operators are connected to Hertz and Debye potentials as well as to the separability of the Teukolsky equation for both Maxwell and linearized gravity.
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| 5. |
- Albeverio, S., et al.
(författare)
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S-matrix, resonances, and wave functions for transport through billiards with leads
- 1996
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 37:10, s. 4888-4903
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Tidskriftsartikel (refereegranskat)abstract
- For a simple model describing the S-matrices of open resonators the statistical properties of the resonances are investigated, as well as the wave functions inside the resonator
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| 6. |
- Alcock-Zeilinger, Judith, et al.
(författare)
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Wigner 6 j symbols for SU(N) : Symbols with at least two quark-lines
- 2023
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 64:2
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Tidskriftsartikel (refereegranskat)abstract
- We study a class of SU(N) Wigner 6j symbols involving two fundamental representations and derive explicit formulas for all 6j symbols in this class. Our formulas express the 6j symbols in terms of the dimensions of the involved representations, and they are thereby functions of N. We view these explicit formulas as a first step toward efficiently decomposing SU(N) color structures in terms of group invariants.
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| 7. |
- Alho, Artur, et al.
(författare)
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Global dynamics and inflationary center manifold and slow-roll approximants
- 2015
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Ingår i: Journal of Mathematical Physics. - : American Institute of Physics (AIP). - 0022-2488 .- 1089-7658. ; 56:1
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Tidskriftsartikel (refereegranskat)abstract
- We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lemaître-Robertson-Walker cosmology to illustrate a number of techniques and tools, which can be applied to a wide range of scalar field potentials and problems in, e.g., modified gravity. We present a global and regular dynamical systems description that yields a global understanding of the solution space, including asymptotic features. We introduce dynamical systems techniques such as center manifold expansions and use Padé approximants to obtain improved approximations for the “attractor solution” at early times. We also show that future asymptotic behavior is associated with a limit cycle, which shows that manifest self-similarity is asymptotically broken toward the future and gives approximate expressions for this behavior. We then combine these results to obtain global approximations for the attractor solution, which, e.g., might be used in the context of global measures. In addition, we elucidate the connection between slow-roll based approximations and the attractor solution, and compare these approximations with the center manifold based approximants.
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| 8. |
- Alhulaimi, Bassemah, et al.
(författare)
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Anisotropic Einstein-aether cosmological models
- 2013
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Ingår i: Journal of Mathematical Physics. - Melville, USA : American Institute of Physics (AIP). - 0022-2488 .- 1089-7658. ; 54:4
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Tidskriftsartikel (refereegranskat)abstract
- We investigate a class of spatially anisotropic cosmological models in Einstein-aether theory with a scalar field in which the self-interaction potential depends on the timelike aether vector field through the expansion and shear scalars. We derive the evolution equations in terms of expansion-normalized variables, which reduce to a dynamical system. We study the local stability of the equilibrium points of the dynamical system corresponding to physically realistic solutions, and find that there are always ranges of values of the parameters of the models for which there exists an inflationary attractor. © 2013 AIP Publishing LLC.
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| 9. |
- Alpan, Gökalp, et al.
(författare)
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Hermitian and non-Hermitian perturbations of chiral Gaussian beta-ensembles
- 2022
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Ingår i: Journal of Mathematical Physics. - : American Institute of Physics (AIP). - 0022-2488 .- 1089-7658. ; 63:4
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Tidskriftsartikel (refereegranskat)abstract
- We compute the joint eigenvalue distribution for the rank one Hermitian and non-Hermitian perturbations of chiral Gaussian beta-ensembles (beta > 0) of random matrices.
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| 10. |
- Andersson, Erik
(författare)
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On the M-function and Borg-Marchenko theorems for vector-valued Sturm-Liouville equations
- 2003
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488. ; 44:12, s. 6077-6100
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Tidskriftsartikel (refereegranskat)abstract
- We will consider a vector-valued Sturm-Liouville equation of the form R[U]:=-(PU')(')+QU=lambdaWU, xis an element of[0,b), with P-1, W, Qis an element ofL(loc)(1)([0,b))(mxm) being Hermitian and under some additional conditions on P-1 and W. We give an elementary deduction of the leading order term asymptotics for the Titchmarsh-Weyl M-function corresponding to this equation. In the special case of P=W=I, Qis an element ofL(1)([0,infinity))(mxm) and the Neumann boundary conditions at 0, we will also prove that M=(1/root-lambda) (I+R) (I-R)(-1), where R=lim(n-->infinity) R-n=Sigma(n=1)(infinity)Q(n), for recursively defined sequences {R-n} and {Q(n)}. If Qis an element ofL(loc)(1)([0,b))(mxm), 0
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