Publication List
J. Asch, M. Mouneime, Examples for stable quantum currents,
arXiv:1908.11689[math-ph](2019)
J. Asch, O.Bourget, A. Joye, On stable quantum currents ,
J. Math. Phys. 61, 092104 (2020); doi: 10.1063/5.0005737
J. Asch, A. Joye, Lower Bounds on the Localisation Length of Balanced Random Quantum Walks,arXiv:1812.05842
Letters in Mathematical Physics, 109(9), 2133-2155 (2019)
J. Asch, O. Bourget, A. Joye, Chirality induced Interface Currents in the Chalker Coddington Model,
arXiv:1708.02120, J. Spectr. Theory 9 (2019), 1405-1429
Joachim Asch, Olivier Bourget, Victor Cortes, Claudio Fernandez, Lower
bounds for sojourn time in a simple shape resonance model
in: Mantoiu M. et al Spectral Theory and Mathematical Physics. Operator Theory: Advances and Applications, vol 254. (2016)
Joachim Asch, Olivier Bourget, Victor Cortes, Claudio Fernandez, Energy-time uncertainty
principle and lower bounds on sojourn time
Ann. Henri Poincaré, Volume 17, Issue 9, pp 2513-2527 (2016) link
J. Asch, O. Bourget, A. Joye, Spectral
Stability of
Unitary Network Models,
Reviews in Mathematical Physics No.27, Issue No. 7 (2015)
J. Asch, O. Bourget, C. Meresse, Stability of the electron
cyclotron resonance
Comm. Math. Phys. 341(2), 607-623 (2016), link
J. Asch, O. Bourget, V.H. Cortés, C. Fernández, Remarks on
Sojourn Time Estimates for Periodic Time-dependent Quantum Systems
Operator Theory: Advances and Applications, Vol. 224, 1-10, Springer
Basel, 2012
J. Asch, O. Bourget, A. Joye, Dynamical Localization of the
Chalker-Coddington Model far from Transition
J. of Stat. Phys: Volume 147, Issue 1 (2012), Page 194-205
J. Asch, T. Kalvoda, P. Stovicek, Resonant
cyclotron
acceleration of particles by a time periodic singular flux tube
SIAM J. Appl. Math. Vol. 71, No. 3, (2011) pp. 829–853
J. Asch, C. Meresse, A constant of quantum motion in
two dimensions in crossed magnetic and electric fields
J. Phys. A: Math. Theor. 43 (2010) 474002.
J. Asch, O. Bourget, A. Joye, Localization
Properties of the
Chalker-Coddington Model
Ann. Henri Poincare 11 (2010), 1341–1373
J. Asch, P. Stovicek, Dynamics of a classical Hall
system driven by a
time-dependent Aharonov-Bohm flux,
Journal of Mathematical Physics 48, 052901 (2007)
Abstract:
We study the
dynamics of a classical particle moving in a punctured plane under the
influence of a homogeneous magnetic field, an electric background, and
driven by a time-dependent singular flux tube through the
hole. We exhibit a striking delocalization effect: when the electric
background is absent we prove that a linearly time-dependent flux tube
opposite to the homogeneous flux eventually leads to the usual
classical Hall motion: the particle follows a cycloid whose center is
drifting orthogonal to the electric field; if the fluxes are additive,
the drifting center eventually gets pinned by the flux tube whereas the
kinetic energy is growing with the additional flux.
J. Asch, P. Stovicek, On the Dynamics
Created by a
time-dependent Aharonov-Bohm Flux,
Reports on Mathematical Physics, Vol. 59, (2007)
J. Asch and A. Joye (eds.), Mathematical Physics of
Quantum Mechanics.
Springer, Lecture Notes in Physics, Vol. 690, (2006).
J. Asch, I. Hradecky, P. Stovicek, Propagators
weakly
associated to a family of Hamiltonians and the adiabatic theorem for
the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux
.
Journal of Mathematical Physics 46, 053303 (2005)
Abstract:
We study the
dynamics of a quantum particle moving in a plane under the influence of
a constant magnetic field and driven by a slowly time-dependent
singular flux tube through a puncture. The known adiabatic results do
not cover these models as the Hamiltonian has time
dependent domain. We give a meaning to the propagator and
prove
an adiabatic theorem. To this end we introduce and develop the new
notion of a propagator weakly associated to a time-dependent
Hamiltonian.
J. Asch, P. Briet, M. A. Astaburuaga, V. Cortés,
P. Duclos, C. Fernández Sojourn time for
rank one
perturbations.
Journal of Mathematical Physics 47, 033501 (2006)
J. Asch, R. Benguria, and P. Stovicek, Asymptotics of solutions of the
equation $h^3(h''+h')=1$.
Asymptotic Analysis,
41(1), 23--40 (2005)
Abstract:
We derive the
complete asymptotic series, as t → +∞, for a general
solution h(t) of the nonlinear differential equation h^3 (h'' + h' )
= 1. The equation originates from a physical model related to the Hall
effect.
J.Asch, F. Bentosela, P. Duclos, G. Nenciu,
On the Dynamics of Crystal Electrons, high
Momentum Regime.
Journ. Math. Anal. Appl.\ {\bf 256} (2001) , 99--114.
Abstract : We study the quantum dynamics generated by
$H^{SW}=-{d^2\over dx^2}+V-x$ with $V$ a real periodic
function
of weak regularity. We prove that the continuous spectrum of $H^{SW}$
is never empty, and furthermore that for $V$ small enough there are no
bound states.
J. Asch, Contributions à la
théorie
mathématique de la dynamique des electrons.
Habilitation, Toulon, (1999).
J. Asch and A. Knauf, Quantum Transport on KAM
Tori.
Comm. Math. Phys.\ {\bf 205} (1999), 113--128.
Abstract: Although quantum tunneling between phase space tori occurs,
it is suppressed in the semiclassical limit $\hbar\searrow 0$ for the
Schr\"{o}dinger equation of a particle in $\bR^d$ under the influence
of a smooth periodic potential. In particular this implies that the
distribution of quantum group velocities near energy $E$ converges to
the distribution of the classical asymptotic velocities near $E$, up to
a term of the order $\cO(1/\sqrt{E}.
J. Asch, P. Duclos and P. Exner, Stability of driven systems with growing gaps, Quantum rings and Wannier
ladders.
J. Stat. Phys. {\bf 92} (1998),
1053--1069.
Abstract: We consider a quantum particle in a periodic structure
submitted to a constant external electromotive force. We prove that the
particle is localized for a class of physical reasonable models which
involve singular point interactions.
J. Asch and A. Knauf, Motion in periodic
potenials.
Nonlinearity {\bf 11} (1998), 175--200.
Abstract: We consider motion in a periodic potential in a classical,
quantum, and semiclassical context. Various results on the distribution
of asymptotic velocities are proven.
J. Asch, P. Duclos, and P. Exner, Stark-Wannier Hamiltonians
with
pure point spectrum.
in
M.\ Demuth , B.-W.\ Schultze, eds., Birkh\"auser Verlag,
1997.
J. Asch and P. Briet, Lower
bounds on the width of Stark--Wannier
type resonances.
Commun.
Math. Phys. {\bf 179} (1996), 725--735.
Abstract: We prove that the Schr\"odinger operator
$-d^2/dx^2+Fx+W(x)$ on $L^2({\bf R})$ with $W$ bounded and
analytic in a strip has no resonances in a region ${\hbox{\rm Im }}
E\ge-\exp{(-C/F)}$
J. Asch,
H. Over, and R. Seiler, Magnetic
bloch analysis and
Bochner laplacians.
Journal of
Geometry and Physics {\bf 13} (1994),
275--288.
Abstract:
Hamiltonians for a
particle on a manifold in a magnetic field are constructed as Bochner
Laplacians. We show for the case of a torus and a given magnetic field
that they are in one to one correspondence with the constituents in the
Bloch decomposition of the unique Hamiltonian on the universal covering.
J. Asch and P. Duclos, An
elementary model of dynamical
tunneling. in
W.F. Ames, J.V. Herod, E.M. Harrell II (eds.), Academic
Press,
1993.
J. Asch and J.Potthoff, Itô's
lemma without non-anticipatory
conditions.
Prob. Th.
Re. Fields {\bf 88} (1991), 17--46.
J. Asch, Über den
semiklassischen limes der Berryschen phase.
Dissertation for Dr. rer. nat. , Berlin,
1990.
J. Asch, On the classical limit
of Berry's phase, integrable
systems.
Comm. Math. Phys. {\bf 127} (1990), 637 ff.
J. Asch, On the classical limit
of the quantum phase, one
degree of freedom.
TU
Berlin, 1989.
J. Asch and J. Potthoff, A
generalization of Itô's lemma.
Proc.
Jpn.
Acad. {\bf 63} (1987), no. A 8.
J. Asch, Über die
Prädissoziation von diatomischen Molekülen.
Diploma Thesis, Berlin, 1985.