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GEOMETRY AND SPECTRUM IN 2D MAGNETIC WELLS
"... Abstract. This paper is devoted to the classical mechanics and spectral analysis of a pure magnetic Hamiltonian in R 2. It is established that both the dynamics and the semiclassical spectral theory can be treated through a Birkhoff normal form and reduced to the study of a family of one dimensional ..."
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Abstract. This paper is devoted to the classical mechanics and spectral analysis of a pure magnetic Hamiltonian in R 2. It is established that both the dynamics and the semiclassical spectral theory can be treated through a Birkhoff normal form and reduced to the study of a family of one dimensional Hamiltonians. As a corollary, recent results by HelfferKordyukov are extended to higher energies. 1.
Singular BohrSommerfeld conditions for 1D Toeplitz operators: hyperbolic case
, 2013
"... In this article, we state the BohrSommerfeld conditions around a singular value of hyperbolic type of the principal symbol of a selfadjoint semiclassical Toeplitz operator on a compact connected Kähler surface. These conditions allow the description of the spectrum of the operator in a fixed size n ..."
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In this article, we state the BohrSommerfeld conditions around a singular value of hyperbolic type of the principal symbol of a selfadjoint semiclassical Toeplitz operator on a compact connected Kähler surface. These conditions allow the description of the spectrum of the operator in a fixed size neighbourhood of the singularity. We provide numerical computations for three examples, each associated to a different topology. 1
Hamiltonians Spectrum in Fermi Resonance via The BirkhoffGustavson Normal Form
, 2009
"... Abstract We investigate in this paper the theorem of Birkhoff normal form near an equilibrium point in infinite dimension and discuss the dynamical consequences for Schrödinger Hamiltonians. We calculate also the spectrum in Fermi resonance by using the Bargmann transform. Mathematics Subject Class ..."
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Abstract We investigate in this paper the theorem of Birkhoff normal form near an equilibrium point in infinite dimension and discuss the dynamical consequences for Schrödinger Hamiltonians. We calculate also the spectrum in Fermi resonance by using the Bargmann transform. Mathematics Subject Classification: 58K50, 81S10, 81Q10
Symplectic inverse spectral theory for pseudodifferential operators
, 2008
"... We prove, under some generic assumptions, that the semiclassical spectrum modulo O( � 2) of a one dimensional pseudodifferential operator completely determines the symplectic geometry of the underlying classical system. In particular, the spectrum determines the hamiltonian dynamics of the principal ..."
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We prove, under some generic assumptions, that the semiclassical spectrum modulo O( � 2) of a one dimensional pseudodifferential operator completely determines the symplectic geometry of the underlying classical system. In particular, the spectrum determines the hamiltonian dynamics of the principal symbol. 1
Little Magnetic Book  Geometry and Bound States of the Magnetic Schrödinger Operator
, 2013
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QUANTUM REVIVALS IN TWO DEGREES OF FREEDOM INTEGRABLE SYSTEMS: THE TORUS CASE
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Symplectic inverse spectral theory for pseudodifferential operators Vu ̃ Ngo.c San
, 2008
"... We prove, under some generic assumptions, that the semiclassical spectrum modulo O(~2) of a one dimensional pseudodifferential operator completely determines the symplectic geometry of the underlying classical system. In particular, the spectrum determines the hamiltonian dynamics of the principal ..."
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We prove, under some generic assumptions, that the semiclassical spectrum modulo O(~2) of a one dimensional pseudodifferential operator completely determines the symplectic geometry of the underlying classical system. In particular, the spectrum determines the hamiltonian dynamics of the principal symbol. 1