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Displaying 81 – 98 of 98

Strichartz and smoothing estimates for Schrödinger operators with large magnetic potentials in $ℝ^{3}$

M. Burak Erdoğan, Michael Goldberg, Wilhelm Schlag (2008)

Journal of the European Mathematical Society

We present a novel approach for bounding the resolvent of $H = - Δ + i (A \cdot \nabla + \nabla \cdot A) + V = : - Δ + L 1$ for large energies. It is shown here that there exist a large integer $m$ and a large number $λ_{0}$ so that relative to the usual weighted $L^{2}$ -norm, $∥ {(L {(- Δ + (λ + i 0))}^{- 1})}^{m} ∥ < \frac{1}{2} 2$ for all $λ > λ_{0}$ . This requires suitable decay and smoothness conditions on $A, V$ . The estimate (2) is trivial when $A = 0$ , but difficult for large $A$ since the gradient term exactly cancels the natural decay of the free resolvent. To obtain (2), we introduce a conical decomposition of the resolvent and then sum over...

Strichartz inequalities for Lipschitz metrics on manifolds and nonlinear Schrödinger equation on domains

Ramona Anton (2008)

Bulletin de la Société Mathématique de France

We prove wellposedness of the Cauchy problem for the nonlinear Schrödinger equation for any defocusing power nonlinearity on a domain of the plane with Dirichlet boundary conditions. The main argument is based on a generalized Strichartz inequality on manifolds with Lipschitz metric.

Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrödinger operators

Alexander Fedotov, Frédéric Klopp (2005)

Annales scientifiques de l'École Normale Supérieure

Structure fractals and para-quaternionic geometry

Julian Ławrynowicz, Massimo Vaccaro (2011)

Annales UMCS, Mathematica

It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions p = 2, 4 and 8, respectively, but the procedure fails for p = 16 in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are n = 27. Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of...

Study of the behavior of quantum dynamics as $ℏ \to 0$

Jaume Haro (2004)

Rendiconti del Seminario Matematico della Università di Padova

Super-geometric quantization.

Vaisman, I. (1995)

Acta Mathematica Universitatis Comenianae. New Series

Supersymmetric extension of non-Hermitian $s u (2)$ Hamiltonian and supercoherent states.

Cherbal, Omar, Drir, Mahrez, Maamache, Mustapha, Trifonov, Dimitar A. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Supersymmetric quantum mechanics and Painlevé IV equation.

Bermúdez, David, C., David J.Fernández (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Supersymmetrical separation of variables in two-dimensional quantum mechanics.

Ioffe, Mikhail V. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Supersymmetry and Ghosts in Quantum Mechanics

Robert, Didier (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 81Q60, 35Q40.A standard supersymmetric quantum system is defined by a Hamiltonian [^H] = ½([^Q]*[^Q] +[^Q][^Q]*), where the super-charge [^Q] satisfies [^Q]2 = 0, [^Q] commutes with [^H]. So we have [^H] ≥ 0 and the quantum spectrum of [^H] is non negative. On the other hand Pais-Ulhenbeck proposed in 1950 a model in quantum-field theory where the d'Alembert operator [¯] = [(∂2)/( ∂t2)] − Δx is replaced by fourth order operator [¯]([¯] + m2), in order to...

Supersymmetry transformations for delta potentials.

Fernández C., David J., Gadella, Manuel, Nieto, Luis Miguel (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Sur l'approximation de Born-Oppenheimer des opérateurs d'onde

A. Martinez (1994/1995)

Séminaire Équations aux dérivées partielles (Polytechnique)

Sur le caractère bien posé des équations de Schrödinger non linéaires

Patrick Gérard (2005/2006)

Séminaire Équations aux dérivées partielles

Sur le spectre semi-classique d’un système intégrable de dimension 1 autour d’une singularité hyperbolique

Olivier Lablée (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Dans cette article on décrit le spectre semi-classique d’un opérateur de Schrödinger sur $ℝ$ avec un potentiel type double puits. La description qu’on donne est celle du spectre autour du maximum local du potentiel. Dans la classification des singularités de l’application moment d’un système intégrable, le double puits représente le cas des singularités non-dégénérées de type hyperbolique.

Sur le spectre semi-classique d’un système intégrable de dimension 1 autour d’une singularité hyperbolique

Olivier Lablée (2007/2008)

Séminaire de théorie spectrale et géométrie

Dans cet article on décrit le spectre semi-classique d’un opérateur de Schrödinger sur $ℝ$ avec un potentiel type double puits. La description qu’on donne est celle du spectre autour du maximum local du potentiel. Dans la classification des singularités de l’application moment d’un système intégrable, le double puits représente le cas des singularités non-dégénérées de type hyperbolique.

Sur les mesures de Wigner.

Pierre-Louis Lions, Thierry Paul (1993)

Revista Matemática Iberoamericana

We study the properties of the Wigner transform for arbitrary functions in L2 or for hermitian kernels like the so-called density matrices. And we introduce some limits of these transforms for sequences of functions in L2, limits that correspond to the semi-classical limit in Quantum Mechanics. The measures we obtain in this way, that we call Wigner measures, have various mathematical properties that we establish. In particular, we prove they satisfy, in linear situations (Schrödinger equations)...

Symmetries, variational principles, and quantum dynamics.

Manjavidze, J., Sissakian, A. (2004)

Discrete Dynamics in Nature and Society

Symmetry operators of a Hartree-type equation with quadratic potential.

Lisok, A.L., Trifonov, A.Yu., Shapovalov, A.V. (2005)

Sibirskij Matematicheskij Zhurnal

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