Related papers: Adiabatic Limits, Vanishing Theorems and the Nonco…
We use adiabatic limits to study foliated manifolds. The Bott connection naturally shows up as the adiabatic limit of Levi-Civita connections. As an application, we then construct certain natural elliptic operators associated to the…
We present a simpler proof for the existence of adiabatic limits. Moreover, we added a new section where the adiabatic process is reversed and in some nondegenerate cases we deform the adiabatic limits to genuine irreducible solutions of…
We extend the adiabatic limit formula for eta-invariants by Bismut-Cheeger and Dai to Seifert fibrations. Our formula contains a new contribution from the singular fibres that takes the form of a generalised Dedekind sum. As an application,…
Linear response theory for open (infinite) systems leads to an expression for the current response which contains surface terms in addition to the usual bulk Kubo term. We show that this surface term vanishes identically if the correct…
We review recent results concerning the exponential behaviour of transition probabilities across a gap in the adiabatic limit of the time-dependent Schr\"odinger equation. They range from an exponential estimate in quite general situations…
A sharp definition of what "adiabatic" means is given; it is then shown that the time-dependent expectation value of a quantum-mechanical observable in the adiabatic limit can be expressed -- in many cases -- by means of the appropriate…
Quillen's local index theorem is used to study the charge transport coefficients (adiabatic curvature) associated to the ground state of a Schr\"odinger operator for a charged (spinless) particle on a closed, multiply connected surface. The…
We discuss asymptotic behavior of the eigenvalue distribution of the differential form Laplacian on a Riemannian foliated manifold when the metric on the ambient manifold is blown up in directions normal to the leaves (in the adiabatic…
We show that in a quantum adiabatic evolution, even though the adiabatic approximation is valid, the total phase of the final state indicated by the adiabatic theorem may evidently differ from the actual total phase. This invalidates the…
We study adiabatic limits of Ricci-flat Kahler metrics on a Calabi-Yau manifold which is the total space of a holomorphic fibration when the volume of the fibers goes to zero. By establishing some new a priori estimates for the relevant…
We consider a smooth fibration equipped with a flat complex vector bundle and a hypersurface cutting the fibration into two pieces. Our main result is a gluing formula relating the Bismut-Lott analytic torsion form of the whole fibration to…
We discuss a one-dimensional version of the Landau-Pekar equations, which are a system of coupled differential equations with two different time scales. We derive an approximation on the slow time scale in the spirit of a non-linear…
We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the…
A new simple proof of the adiabatic theorem is given in the finite dimensional case for nondegenerate as well as degenerate states. The explicitly integrable two level system is considered as an example. It is demonstrated that the error…
We study co-associative fibrations of G_{2}-manifolds. We propose that the adiabatic limit of this structure should be given locally by a maximal submanifold in a space of indefinite signature and set up global versions of the…
The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter $\epsilon$. Under suitable assumptions the solution of the…
The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations…
The viscous inhomogeneities of a relativistic plasma determine a further class of entropic modes whose amplitude must be sufficiently small since curvature perturbations are observed to be predominantly adiabatic and Gaussian over large…
We study the problem of conformal deformation of Riemannian structure to constant scalar curvature with zero mean curvature on the boundary. We prove compactness for the full set of solutions when the boundary is umbilic and the dimension…
The analysis of gravitational wave data may require greater accuracy than is afforded by the adiabatic approximation to the trajectory of and field produced by a particle moving in curved spacetime. Higher accuracy is available with a…