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

Quantum pumping and dissipation: from closed to open systems

Current can be pumped through a closed system by changing parameters (or fields) in time. The Kubo formula allows to distinguish between dissipative and non-dissipative contributions to the current. We obtain a Green function expression and an $S$ matrix formula for the associated terms in the generalized conductance matrix: the "geometric magnetism" term that corresponds to adiabatic transport; and the "Fermi golden rule" term which is responsible to the irreversible absorption of energy. We explain the subtle limit of an infinite system, and demonstrate the consistency with the formulas by Landauer and Buttiker, Pretre and Thomas. We also discuss the generalization of the fluctuation-dissipation relation, and the implications of the Onsager reciprocity.Comment: 4 page paper, 1 figure (published version) + 2 page appendi

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

Classical and quantum pumping in closed systems

Pumping of charge (Q) in a closed ring geometry is not quantized even in the strict adiabatic limit. The deviation form exact quantization can be related to the Thouless conductance. We use Kubo formalism as a starting point for the calculation of both the dissipative and the adiabatic contributions to Q. As an application we bring examples for classical dissipative pumping, classical adiabatic pumping, and in particular we make an explicit calculation for quantum pumping in case of the simplest pumping device, which is a 3 site lattice model.Comment: 5 pages, 3 figures. The long published version is cond-mat/0307619. This is the short unpublished versio

Adiabatic response for Lindblad dynamics

We study the adiabatic response of open systems governed by Lindblad evolutions. In such systems, there is an ambiguity in the assignment of observables to fluxes (rates) such as velocities and currents. For the appropriate notion of flux, the formulas for the transport coefficients are simple and explicit and are governed by the parallel transport on the manifold of instantaneous stationary states. Among our results we show that the response coefficients of open systems, whose stationary states are projections, is given by the adiabatic curvature.Comment: 33 pages, 4 figures, accepted versio

Cut-elimination for the modal Grzegorczyk logic via non-well-founded proofs

We present a sequent calculus for the modal Grzegorczyk logic Grz allowing non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs.Comment: WOLLIC'17, 12 pages, 1 appendi

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

Quantum pumping: Coherent Rings versus Open Conductors

We examine adiabatic quantum pumping generated by an oscillating scatterer embedded in a one-dimensional ballistic ring and compare it with pumping caused by the same scatterer connected to external reservoirs. The pumped current for an open conductor, paradoxically, is non-zero even in the limit of vanishing transmission. In contrast, for the ring geometry the pumped current vanishes in the limit of vanishing transmission. We explain this paradoxical result and demonstrate that the physics underlying adiabatic pumping is the same in open and in closed systems.Comment: 4 pages, 2 figure