The Connes-Kasparov conjecture for almost connected groups and for linear p-adic groups

Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C^*-algebra of G is an isomorphism. The same is shown for the groups of k-rational points of any linear algebraic group over a local field k of characteristic zero. Dedicated to the memory of Peter Slodowy     

Temperature effects for vibrational relaxation of hydrogen adsorbed on Si(100): a stochastic multiconfigurational time-dependent Hartree (MCTDH) study

Using a previously developed system–bath model Hamiltonian for the vibrational relaxation of H atoms adsorbed on a Si(100) surface (Andrianov and Saalfrank in J Chem Phys 124:034710, 2006), temperature effects on the relaxation of excited adsorbate vibrations are studied non-perturbatively. In particular, the Si–Si–H bending mode, for which relaxation times in the order of picoseconds have been predicted theoretically, is considered. Also, the excitation by infrared laser pulses is explicitly modelled. To do so, a combined system–bath Schrödinger equation is considered, in which an anharmonic system describing the vibrating H atom is coupled non-linearly to a set of harmonic oscillators which represent the phonon bath of the solid. For the time evolution, the multiconfigurational time-dependent Hartree (MCTDH) method is used together with a stochastic approach to sample thermal initial conditions. In contrast to perturbative approaches (Golden Rule), it is found that the bending mode relaxes the slower, the hotter the surface is. Possible reasons for this “puzzle”, which also seems at variance with measurements for H:Si(100), are discussed.     

Dixmier's trace for boundary value problems

Let X be a smooth manifold with boundary of dimension n > 1. The operators of order −n and type zero in Boutet de Monvel's calculus form a subset of Dixmier's trace ideal for the Hilbert space of L ² sections in vector bundles E over X, F over ∂X. We show that, on these operators, Dixmier's trace can be computed in terms of the same expressions that determine the noncommutative residue. In particular it is independent of the averaging procedure. However, the noncommutative residue and Dixmier's trace are not multiples of each other unless the boundary is empty. As a corollary we show how to compute Dixmier's trace for parametrices or inverses of classical elliptic boundary value problems of the form Pu=f; Tu=0 with an elliptic differential operator P of order n in the interior and a trace operator T. In this particular situation, Dixmier's trace and the noncommutative residue do coincide up to a factor. Received: Received: 13 January 1998     

The Baum-Connes Conjecture via Localization of Categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This interpretation is ideal for studying functorial properties and gives analogues of the Baum-Connes assembly map for all equivariant homology theories.     

Magnetic torque behavior and rotational hysteresis of amorphous uniaxial Sm-Co alloy films

Amorphous films of Sm_100–x Co _x with 70x90 were made by vapor deposition on flat glass substrates at 300 K with a magnetic field parallel to the film plane, as described in a preceding paper; the field induces a uniaxial anisotropyK _u of the order 10⁶ erg cm^–3 with the easy axis,x, in the film plane. The film plane (xy plane) is the easy plane with a planar anisotropyK _p of the order 10⁷ erg cm^–3, i.e. the film normal,z, is the hard axis. For such films, torque curvesT(H, ) (: angle betweenH and an axis normal to the axis of rotation) are calculated, and are measured in fieldsH 30 kOe for the three axes of rotation,x, y, andz. The results are evaluated to give the spontaneous magnetization, M, the anisotropies,K _u ,K _p , the rotational hysteresis losses,W _Rx (H),W _Ry (H),W _Rz (H), and the rotational hysteresis integrals,R _x ,R _y ,R _z .     

Magnetic behavior of amorphous Sm-Co alloy films

Amorphous films of Sm_100–x Co _x with 70x90 were made by vapor deposition on flat glass substrates kept at 300 K. The films crystallize above 700 K. The film plane is the easy plane with the planar anisotropy of the order of 10⁷ erg cm^–3, indicating a local anisotropy of the order 10⁸ erg cm^–3. With regard to local anisotropy and magnetization, the films appear to correspond to the random anisotropy concept of amorphous magnets. Films evaporated in a magnetic field parallel to the film plane have an induced uniaxial anisotropy of the order of 10⁶ erg cm^–3. Hysteresis loops in fields parallel to the easy axis are perfectly rectangular with coercive fieldsH _c in the range 30 Oe<H _c<3000 Oe, depending on composition, temperature and heat treatment. The magnetization reverses by a thermally activated domain nucleation and growth process having a narrow distribution of time constants. Aging at temperatures below the crystallization temperature reduces the anisotropies andH _c.     

The adaptive hierarchical expansion of the kinetic energy operator

The hierarchical expansion of the kinetic energy (HEKE) operator in curvilinear coordinates presented recently (Strobusch and Scheurer, J. Chem. Phys. 2011a, 135, 124102; Strobusch and Scheurer, J. Chem. Phys. 2011b, 135, 144101) relies on a many‐body expansion of the metric tensor. It is shown how this expansion can be adapted to a specific system. An analytic formula is derived, which yields an estimate of the impact of a certain expansion term on the spectrum. In combination with the hierarchical structure of the many‐body expansion and interpolation techniques, the memory consumption and evaluation time of the HEKE operator as well as the computational costs for subsequent vibrational self‐consistent field and vibrational configuration interaction calculations are reduced significantly, which is demonstrated by studies on two small test systems H₂O₂ and formaldehyde (H₂CO). © 2013 Wiley Periodicals, Inc.     

Coherent control and time-dependent density functional theory: towards creation of wave packets by ultrashort laser pulses

Explicitly time-dependent density functional theory (TDDFT) is a formally exact theory, which can treat very large systems. However, in practice it is used almost exclusively in the adiabatic approximation and with standard ground state functionals. Therefore, if combined with coherent control theory, it is not clear which control tasks can be achieved reliably, and how this depends on the functionals. In this paper, we continue earlier work in order to establish rules that answer these questions. Specifically, we look at the creation of wave packets by ultrashort laser pulses that contain several excited states. We find that (i) adiabatic TDDFT only works if the system is not driven too far from the ground state, (ii) the permanent dipole moments involved should not differ too much, and (iii) these results are independent of the functional used. Additionally, we find an artifact that produces fluence-dependent excitation energies.