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Displaying 241 – 260 of 317

Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator

Bernard Helffer, Thierry Ramond (2000)

Journées équations aux dérivées partielles

We continue the study started by the first author of the semiclassical Kac Operator. This kind of operator has been obtained for example by M. Kac as he was studying a 2D spin lattice by the so-called “transfer operator method”. We are interested here in the thermodynamical limit $Λ (h)$ of the ground state energy of this operator. For Kac’s spin model, $Λ (h)$ is the free energy per spin, and the semiclassical regime corresponds to the mean-field approximation. Under suitable assumptions, which are satisfied...

Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation

Rémi Carles (2003)

Annales de l'I.H.P. Analyse non linéaire

Semiclassical, $t \to \infty$ asymptotics and dispersive effects for Hartree-Fock systems

I. Gasser, R. Illner, P. A. Markowich, C. Schmeiser (1998)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Short waves through thin interfaces and 2-microlocal measures

Luc Miller (1997)

Journées équations aux dérivées partielles

Singular integrals of the time-harmonic relativistic Dirac equation on a piecewise Liapunov surface.

Schneider, Baruch (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation.

Shuji Machihara, Kenji Nakanishi, Tohru Ozawa (2003)

Revista Matemática Iberoamericana

In this paper we study the Cauchy problem for the nonlinear Dirac equation in the Sobolev space Hs. We prove the existence and uniqueness of global solutions for small data in Hs with s > 1...

Smoothing of dispersive waves

Walter A. Strauss (1993)

Journées équations aux dérivées partielles

Solitary waves for Maxwell-Dirac and Coulomb-Dirac models

Simonetta Abenda (1998)

Annales de l'I.H.P. Physique théorique

Solitary waves for Maxwell-Schrödinger equations.

Coclite, Giuseppe Maria, Georgiev, Vladimir (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Solutions faibles du problème de Cauchy pour certaines équations de Dirac non linéaires

Dias, João-Paulo, Figueira, Mário (1989)

Portugaliae mathematica

Solvable nonlinear evolution PDEs in multidimensional space.

Calogero, Francesco, Sommacal, Matteo (2006)

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

Sparse grids for the Schrödinger equation

Michael Griebel, Jan Hamaekers (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a sparse grid/hyperbolic cross discretization for many-particle problems. It involves the tensor product of a one-particle multilevel basis. Subsequent truncation of the associated series expansion then results in a sparse grid discretization. Here, depending on the norms involved, different variants of sparse grid techniques for many-particle spaces can be derived that, in the best case, result in complexities and error estimates which are independent of the number of particles. Furthermore...

Spectral and scattering theory for symbolic potentials of order zero

Andrew Hassell, Richard Melrose, András Vasy (2000/2001)

Séminaire Équations aux dérivées partielles

Spectral Shift Function for the Perturbations of Schrödinger Operators at High Energy

Assel, Rachid, Dimassi, Mouez (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35P20, 35J10, 35Q40.We give a complete pointwise asymptotic expansion for the Spectral Shift Function for Schrödinger operators that are perturbations of the Laplacian on Rn with slowly decaying potentials.

Spherical harmonics and maximal estimates for the Schrödinger equation.

Sjölin, Per (2005)

Annales Academiae Scientiarum Fennicae. Mathematica

Splitting of the Dirac operator in the nonrelativistic limit

Gregory B. White (1990)

Annales de l'I.H.P. Physique théorique

Stability of matter for the Hartree-Fock functional of the relativistic electron-positron field.

Bach, Volker, Barbaroux, Jean-Marie, Helffer, Bernard, Siedentop, Heinz (1998)

Documenta Mathematica

Stability of the Brown-Ravenhall operator.

Hoever, Georg, Siedentop, Heinz (1999)

Mathematical Physics Electronic Journal [electronic only]

Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills Problems

Pierre Raphaël, Igor Rodnianski (2008/2009)

Séminaire Équations aux dérivées partielles

This note summarizes the results obtained in [30]. We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the $𝕊^{2}$ target in all homotopy classes and for the equivariant critical $S O (4)$ Yang-Mills problem. We derive sharp asymptotics on the dynamics at blow up time and prove quantization of the energy focused at the singularity.

Stationary solutions for a Schrödinger-Poisson system in $ℝ^{3}$ .

Benmlih, Khalid (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Currently displaying 241 – 260 of 317

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