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We present here a simplified version of recent results obtained with B. Helffer and M. Klein. They are concerned with the exponentally small eigenvalues of the Witten Laplacian on $0$ -forms. We show how the Witten complex structure is better taken into account by working with singular values. This provides a convenient framework to derive accurate approximations of the first eigenvalues of $Δ_{f, h}^{(0)}$ and solves efficiently the question of weakly resonant wells.

Quantization of a dimensionally reduced Seiberg-Witten moduli space.

Dey, Rukmini (2004)

Mathematical Physics Electronic Journal [electronic only]

Quantum Barnes function as the partition function of the resolved conifold.

Koshkin, Sergiy (2008)

International Journal of Mathematics and Mathematical Sciences

Quantum Equivalent Magnetic Fields that Are Not Classically Equivalent

Carolyn Gordon, William Kirwin, Dorothee Schueth, David Webb (2010)

Annales de l’institut Fourier

We construct pairs of compact Kähler-Einstein manifolds $(M_{i}, g_{i}, ω_{i}) (i = 1, 2)$ of complex dimension $n$ with the following properties: The canonical line bundle $L_{i} = ⋀^{n} T^{*} M_{i}$ has Chern class $[ω_{i} / 2 π]$ , and for each positive integer $k$ the tensor powers $L_{1}^{\otimes k}$ and $L_{2}^{\otimes k}$ are isospectral for the bundle Laplacian associated with the canonical connection, while $M_{1}$ and $M_{2}$ – and hence $T^{*} M_{1}$ and $T^{*} M_{2}$ – are not homeomorphic. In the context of geometric quantization, we interpret these examples as magnetic fields which are quantum equivalent but not classically equivalent....

Quantum gravity: unification of principles and interactions, and promises of spectral geometry.

Booss-Bavnbek, Bernhelm, Esposito, Giampiero, Lesch, Matthias (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Quantum isometries and group dual subgroups

Teodor Banica, Jyotishman Bhowmick, Kenny De Commer (2012)

Annales mathématiques Blaise Pascal

We study the discrete groups $Λ$ whose duals embed into a given compact quantum group, $\hat{Λ} \subset G$ . In the matrix case $G \subset U_{n}^{+}$ the embedding condition is equivalent to having a quotient map $Γ_{U} \to Λ$ , where $F = {Γ_{U} ∣ U \in U_{n}}$ is a certain family of groups associated to $G$ . We develop here a number of techniques for computing $F$ , partly inspired from Bichon’s classification of group dual subgroups $\hat{Λ} \subset S_{n}^{+}$ . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot have non-abelian...

Quantum isometry group for spectral triples with real structure.

Goswami, Debashish (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Quantum vacuum polarization at the Black-Hole horizon

Alain Bachelot (1997)

Annales de l'I.H.P. Physique théorique

Quasilinear waves and trapping: Kerr-de Sitter space

Peter Hintz, András Vasy (2014)

Journées Équations aux dérivées partielles

In these notes, we will describe recent work on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr-de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non-elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks with the normally...

Quaternionic contact structures in dimension $7$

David Duchemin (2006)

Annales de l’institut Fourier

The conformal infinity of a quaternionic-Kähler metric on a $4 n$ -manifold with boundary is a codimension $3$ distribution on the boundary called quaternionic contact. In dimensions $4 n - 1$ greater than $7$ , a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension $7$ , we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionic-Kähler metric. This allows us to find the quaternionic-contact structures...

Currently displaying 1 – 18 of 18

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Displaying 1 – 18 of 18

$Q$ -curvature, spectral invariants, and representation theory.

Quantification d'une variété symplectique

Quantification et analyse pseudo-différentielle

Quantification et approximations semi-classiques

Quantification relativiste

Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach.