992 research outputs found
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 the energy shift determines the outgoing state.Comment: 11 pages, 1 figur
The Hidden Structural Rules of the Discontinuous Lambek Calculus
The sequent calculus sL for the Lambek calculus L (lambek 58) has no
structural rules. Interestingly, sL is equivalent to a multimodal calculus mL,
which consists of the nonassociative Lambek calculus with the structural rule
of associativity. This paper proves that the sequent calculus or hypersequent
calculus hD of the discontinuous Lambek calculus (Morrill and Valent\'in),
which like sL has no structural rules, is also equivalent to an omega-sorted
multimodal calculus mD. More concretely, we present a faithful embedding
translation between mD and hD in such a way that it can be said that hD absorbs
the structural rules of mD.Comment: Submitted to Lambek Festschrift volum
Avron [A] Blumberg to Mr. and Mrs. J.H. Meredith (28 September 1962)
https://egrove.olemiss.edu/mercorr_pro/1265/thumbnail.jp
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
On the spectrum and Lyapunov exponent of limit periodic Schrodinger operators
We exhibit a dense set of limit periodic potentials for which the
corresponding one-dimensional Schr\"odinger operator has a positive Lyapunov
exponent for all energies and a spectrum of zero Lebesgue measure. No example
with those properties was previously known, even in the larger class of ergodic
potentials. We also conclude that the generic limit periodic potential has a
spectrum of zero Lebesgue measure.Comment: 12 pages. To appear in Communications in Mathematical Physic
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
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