Twisted Pseudodifferential Calculus And Application To The Quantum Evolution Of Molecules
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| Author | : Andr Martinez |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 96 |
| Release | : 2009-06-05 |
| Genre | : Mathematics |
| ISBN | : 082184296X |
The authors construct an abstract pseudodifferential calculus with operator-valued symbol, suitable for the treatment of Coulomb-type interactions, and they apply it to the study of the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case of the electronic Hamiltonian admitting a local gap in its spectrum. In particular, they show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, they study the propagation of certain wave packets up to long time values of Ehrenfest order.
| Author | : André Martinez |
| Publisher | : American Mathematical Society(RI) |
| Total Pages | : 96 |
| Release | : 2014-09-11 |
| Genre | : MATHEMATICS |
| ISBN | : 9781470405502 |
| Author | : Drew Armstrong |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 176 |
| Release | : 2009-10-08 |
| Genre | : Mathematics |
| ISBN | : 0821844903 |
This memoir is a refinement of the author's PhD thesis -- written at Cornell University (2006). It is primarily a desription of new research but also includes a substantial amount of background material. At the heart of the memoir the author introduces and studies a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and each positive integer $k$. When $k=1$, his definition coincides with the generalized noncrossing partitions introduced by Brady and Watt in $K(\pi, 1)$'s for Artin groups of finite type and Bessis in The dual braid monoid. When $W$ is the symmetric group, the author obtains the poset of classical $k$-divisible noncrossing partitions, first studied by Edelman in Chain enumeration and non-crossing partitions.
| Author | : Cdric Villani |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 154 |
| Release | : 2009-10-08 |
| Genre | : Mathematics |
| ISBN | : 0821844989 |
This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, taking the general form ${\frac{\partial f}{\partial t}}+ L f =0$. The question is whether and how one can overcome the degeneracy by exploiting commutators.
| Author | : Nan-Kuo Ho |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 113 |
| Release | : 2009-10-08 |
| Genre | : Mathematics |
| ISBN | : 0821844911 |
In ``The Yang-Mills equations over Riemann surfaces'', Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. In ``Yang-Mills Connections on Nonorientable Surfaces'', the authors study Yang-Mills functional on the space of connections on a principal $G_{\mathbb{R}}$-bundle over a closed, connected, nonorientable surface, where $G_{\mathbb{R}}$ is any compact connected Lie group. In this monograph, the authors generalize the discussion in ``The Yang-Mills equations over Riemann surfaces'' and ``Yang-Mills Connections on Nonorientable Surfaces''. They obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups $SO(n)$ and $Sp(n)$.
| Author | : Thomas Lam |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 103 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821846582 |
The authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian ${\rm Gr}$ associated with $SL(n,\mathbb{C})$.Their main results are: Pieri rules for the Schubert bases of $H^*({\rm Gr})$ and $H_*({\rm Gr})$, which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. A new combinatorial definition for $k$-Schur functions, which represent the Schubert basis of $H_*({\rm Gr})$. A combinatorial interpretation of the pairing $H^*({\rm Gr})\times H_*({\rm Gr}) \rightarrow\mathbb Z$ induced by the cap product.
| Author | : Alfonso Castro |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 87 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821847260 |
The authors provide a complete classification of the radial solutions to a class of reaction diffusion equations arising in the study of thermal structures such as plasmas with thermal equilibrium or no flux at the boundary. In particular, their study includes rapidly growing nonlinearities, that is, those where an exponent exceeds the critical exponent. They describe the corresponding bifurcation diagrams and determine existence and uniqueness of ground states, which play a central role in characterizing those diagrams. They also provide information on the stability-unstability of the radial steady states.
| Author | : Ping-Shun Chan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 185 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821848224 |
"Volume 204, number 957 (first of 5 numbers)."
| Author | : Mark Behrens |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 167 |
| Release | : 2010-02-22 |
| Genre | : Mathematics |
| ISBN | : 082184539X |
The authors apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type $U(1,n-1)$. These cohomology theories of topological automorphic forms ($\mathit{TAF}$) are related to Shimura varieties in the same way that $\mathit{TMF}$ is related to the moduli space of elliptic curves.
| Author | : Alvaro Pelayo |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 96 |
| Release | : 2010-02-22 |
| Genre | : Mathematics |
| ISBN | : 0821847139 |
In this paper the author classifies symplectic actions of $2$-tori on compact connected symplectic $4$-manifolds, up to equivariant symplectomorphisms. This extends results of Atiyah, Guillemin-Sternberg, Delzant and Benoist. The classification is in terms of a collection of invariants of the topology of the manifold, of the torus action and of the symplectic form. The author constructs explicit models of such symplectic manifolds with torus actions, defined in terms of these invariants.
