Time-Energy coherent states and adiabatic scattering

Coherent states in the time-energy plane provide a natural basis to study adiabatic scattering. We relate the (diagonal) matrix elements of the scattering matrix in this basis with the frozen on-shell scattering data. We describe an exactly solvable model, and show that the error in the frozen data cannot be estimated by the Wigner time delay alone. We introduce the notion of energy shift, a conjugate of Wigner time delay, and show that for incoming state $\rho(H_0)$ the energy shift determines the outgoing state.Comment: 11 pages, 1 figur

Transport and Dissipation in Quantum Pumps

This paper is about adiabatic transport in quantum pumps. The notion of ``energy shift'', a self-adjoint operator dual to the Wigner time delay, plays a role in our approach: It determines the current, the dissipation, the noise and the entropy currents in quantum pumps. We discuss the geometric and topological content of adiabatic transport and show that the mechanism of Thouless and Niu for quantized transport via Chern numbers cannot be realized in quantum pumps where Chern numbers necessarily vanish.Comment: 31 pages, 10 figure

Smooth adiabatic evolutions with leaky power tails

Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. Adiabatic evolutions without a gap condition do not seem to have this feature in general. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by considering the Friedrichs model.Comment: Final form, to appear in J. Phys. A; 11 pages, no figure

Distilling entanglement from cascades with partial "Which Path" ambiguity

We develop a framework to calculate the density matrix of a pair of photons emitted in a decay cascade with partial "which path" ambiguity. We describe an appropriate entanglement distillation scheme which works also for certain random cascades. The qualitative features of the distilled entanglement are presented in a two dimensional "phase diagram". The theory is applied to the quantum tomography of the decay cascade of a biexciton in a semiconductor quantum dot. Agreement with experiment is obtained

One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by Impurities

A one-dimensional discrete Stark Hamiltonian with a continuous electric field is constructed by extension theory methods. In absence of the impurities the model is proved to be exactly solvable, the spectrum is shown to be simple, continuous, filling the real axis; the eigenfunctions, the resolvent and the spectral measure are constructed explicitly. For this (unperturbed) system the resonance spectrum is shown to be empty. The model considering impurity in a single node is also constructed using the operator extension theory methods. The spectral analysis is performed and the dispersion equation for the resolvent singularities is obtained. The resonance spectrum is shown to contain infinite discrete set of resonances. One-to-one correspondence of the constructed Hamiltonian to some Lee-Friedrichs model is established.Comment: 20 pages, Latex, no figure

Quantum Transport in Molecular Rings and Chains

We study charge transport driven by deformations in molecular rings and chains. Level crossings and the associated Longuet-Higgins phase play a central role in this theory. In molecular rings a vanishing cycle of shears pinching a gap closure leads, generically, to diverging charge transport around the ring. We call such behavior homeopathic. In an infinite chain such a cycle leads to integral charge transport which is independent of the strength of deformation. In the Jahn-Teller model of a planar molecular ring there is a distinguished cycle in the space of uniform shears which keeps the molecule in its manifold of ground states and pinches level crossing. The charge transport in this cycle gives information on the derivative of the hopping amplitudes.Comment: Final version. 26 pages, 8 fig

A geometric theory of swimming: Purcell's swimmer and its symmetrized cousin

We develop a qualitative geometric approach to swimming at low Reynolds number which avoids solving differential equations and uses instead landscape figures of two notions of curvatures: The swimming curvature and the curvature derived from dissipation. This approach gives complete information for swimmers that swim on a line without rotations and gives the main qualitative features for general swimmers that can also rotate. We illustrate this approach for a symmetric version of Purcell's swimmer which we solve by elementary analytical means within slender body theory. We then apply the theory to derive the basic qualitative properties of Purcell's swimmer.Comment: 24 pages, 12 figure