8,146 research outputs found
Scattering of magnetic edge states
We consider a charged particle following the boundary of a two-dimensional
domain because a homogeneous magnetic field is applied. We develop the basic
scattering theory for the corresponding quantum mechanical edge states. The
scattering phase attains a limit for large magnetic fields which we interpret
in terms of classical trajectories.Comment: 34 pages, 2 figure
The heat kernel expansion for the electromagnetic field in a cavity
We derive the first six coefficients of the heat kernel expansion for the
electromagnetic field in a cavity by relating it to the expansion for the
Laplace operator acting on forms. As an application we verify that the
electromagnetic Casimir energy is finite.Comment: 12 page
A general resonance theory based on Mourre's inequality
We study the perturbation of bound states embedded in the continuous spectrum
which are unstable by the Fermi Golden Rule. The approach to resonance theory
based on spectral deformation is extended to a more general class of quantum
systems characterized by Mourre's inequality and smoothness of the resolvent.
Within the framework of perturbation theory it is still possible to give a
definite meaning to the notion of complex resonance energies and of
corresponding metastable states. The main result is a quasi-exponential decay
estimate up to a controlled error of higher order in perturbation theory.Comment: 17 page
Comparison of quantization of charge transport in periodic and open pumps
We compare the charges transported in two systems, a spatially periodic and
an open quantum pump, both depending periodically and adiabatically on time.
The charge transported in a cycle was computed by Thouless, respectively by
Buttiker et al. in the two cases. We show that the results agree in the limit
where the two physical situations become the same, i.e., that of a large open
pump.Comment: 7 page
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
Dynamics of a classical Hall system driven by a time-dependent Aharonov--Bohm flux
We study the dynamics of a classical particle moving in a punctured plane
under the influence of a strong homogeneous magnetic field, an electrical
background, and driven by a time-dependent singular flux tube through the hole.
We exhibit a striking classical (de)localization effect: in the far past the
trajectories are spirals around a bound center; the particle moves inward
towards the flux tube loosing kinetic energy. After hitting the puncture it
becomes ``conducting'': the motion is a cycloid around a center whose drift is
outgoing, orthogonal to the electric field, diffusive, and without energy loss
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