## Publication List

J. Asch, O. Bourget,  A. Joye, Chirality induced Interface Currents in the Chalker Coddington Model,
arXiv:1708.02120 [math-ph] (2017)

Joachim Asch, Olivier Bourget, Victor Cortes, Claudio Fernandez, Lower bounds for sojourn time in a simple shape resonance model
Proceedings of the conference Spectral Theory and Mathematical Physics, Santiago 2014 (2015)

Joachim Asch, Olivier Bourget, Victor Cortes, Claudio Fernandez,  Energy-time uncertainty principle and lower bounds on sojourn time
to appear in Ann. Henri Poincaré,  link (2016)

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 de�localization 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. Cort\'es, P. Duclos, C. Fern\'andez  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,  It\^o's lemma without non-anticipatory conditions.
Prob. Th. Re. Fields {\bf 88} (1991), 17--46.

J. Asch,  {\"U}ber den semiklassischen limes der Berryschen
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 It\^o's lemma. Proc. Jpn.
Acad. {\bf 63} (1987), no. A 8.

J. Asch,
Diploma Thesis, Berlin, 1985.