TY  - JOUR
A1  - Zass, Alexander
T1  - A Gibbs point process of diffusions: Existence and uniqueness
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471951
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 13
EP  - 22
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Azzali, Sara
A1  - Wahl, Charlotte
T1  - Two-cocycle twists and Atiyah-Patodi-Singer index theory
JF  - Mathematical Proceedings of the Cambridge Philosophical Society
N2  - We construct eta- and rho-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah-Patodi-Singer index theorem in this setting, as well as its higher generalisation. Applications concern the classification of positive scalar curvature metrics on closed spin manifolds. We also investigate the properties of these twisted invariants for the signature operator and the relation to the higher invariants.
Y1  - 2019
U6  - https://doi.org/10.1017/S0305004118000427
SN  - 0305-0041
SN  - 1469-8064
VL  - 167
IS  - 3
SP  - 437
EP  - 487
PB  - Cambridge Univ. Press
CY  - New York
ER  - 
TY  - JOUR
A1  - Ludewig, Matthias
A1  - Rosenberger, Elke
T1  - Asymptotic eigenfunctions for Schrödinger operators on a vector bundle
JF  - Reviews in mathematical physics
N2  - In the limit (h) over bar -> 0, we analyze a class of Schrödinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V .id(epsilon) acting on sections of a vector bundle epsilon over a Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has a non-degenerate minimum at some point p is an element of M. We construct quasimodes of WKB-type near p for eigenfunctions associated with the low-lying eigenvalues of H-(h) over bar. These are obtained from eigenfunctions of the associated harmonic oscillator H-p,H-(h) over bar at p, acting on smooth functions on the tangent space.
KW  - Semi-classical analysis
KW  - WKB approximation
KW  - Schrödinger operators
KW  - semi-classical limit
Y1  - 2020
U6  - https://doi.org/10.1142/S0129055X20500208
SN  - 0129-055X
SN  - 1793-6659
VL  - 32
IS  - 7
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - THES
A1  - Mahmoudi, Mahdi Hedayat
T1  - New applications of the edge calculus
Y1  - 
ER  - 
TY  - JOUR
A1  - Flad, Heinz-Jürgen
A1  - Flad-Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Ellipticity of the quantum mechanical Hamiltonians
BT  - corner singularity of the helium atom
JF  - Journal of pseudo-differential operators and applications
N2  - In paper (Flad and Harutyunyan in Discrete Contin Dyn Syst 420-429, 2011) is shown that the Hamiltonian of the helium atom in the Born-Oppenheimer approximation, in the case if two particles coincide, is an edge-degenerate operator, which is elliptic in the corresponding edge calculus. The aim of this paper is an analogous investigation in the case if all three particles coincide. More precisely, we show that the Hamiltonian in the mentioned case is a corner-degenerate operator, which is elliptic as an operator in the corner analysis.
Y1  - 2018
U6  - https://doi.org/10.1007/s11868-017-0201-4
SN  - 1662-9981
SN  - 1662-999X
VL  - 9
IS  - 3
SP  - 451
EP  - 467
PB  - Springer
CY  - Basel
ER  -