PUBLICATIONS SUPPORTED BY THE EU NETWORK ON PARTIAL DIFFERENTIAL
EQUATIONS AND QUANTUM MECHANICS
- Lieb E.H., Loss M.,
Siedentop H.,
Stability of Relativistic Matter
via Thomas-Fermi Theory.
Helv. Phys. Acta, 69, 974-984, 1996.
- Lieb E.H., Siedentop
H.,
and Solovej J.P.,
Stability and instability
of relativistic electrons in classical electromagnetic fields.
Jour. Stat. Phys. 89, 37-59, 1997.
- Tix C.
(Regensburg),
Strict positivity of a
relativistic Hamiltonian due to Brown and Ravenhall.
Bull. London Math. Soc. 30, 283-290, 1998.
- Helffer, B.,
Semi-classical analysis for the transfer operator: formal WKB constructions in large dimension.
Commun. Math. Phys. 187, 81-113, (1997).
- Erdös L. and
Solovej J.P.,
Semiclassical eigenvalue estimates
for the Pauli operator with strong non-homogeneous
magnetic fields:
I. Non-asymptotic Lieb-Thirring type estimate.
Duke Math Jour, 96, 127-173, 1999.
- Erdös L. and
Solovej J.P.
Semiclassical eigenvalue estimates
for the Pauli operator with strong non-homogeneous
magnetic fields:
II. Leading order asymptotic estimates.
Commun. Math. Phys. 188, 599-656, (1997).
- Helffer, B.,
Splitting in large dimension
and infrared estimates II - Moment
inequalities.
Jour. Math. Phys. 39 , 760-776 (1998).
- Burenkov V.I. and Evans W.D.,
On the evaluation of the norm of
an integral operator associated with the stability of
one-electron atoms.
Proc.Roy.Soc. Edinburgh, 128A, 993-1005 (1998)
- Fournais, S. (Aarhus),
Semiclassics of the quantum current.
Comm. PDE. 23 601-628 (1998).
- De la Breteche, R. (Orsay),
Preuve de la conjecture
de Lieb-Thirring dans le cas des potentiels
quadratiques strictement convexes..
Annales de l'IHP , section Phys. Th.,
70 No 4, 1999, p. 369-380
- Evans W.D. and Lewis, R.T.,
Eigenvalue estimates in
the semi-classical limit for Pauli and Dirac
operators with a magnetic field..
Proc.Roy.Soc.London A455, 183-217 (1999).
- Lieb E.H.,
Siedentop
H.,
and Solovej J.P.,
Stability of relativistic matter
with magnetic fields.
Phys. Rev. Lett.
79,
Issue 10, 1785-1788, 1997.
- Griesemer M. (Regensburg),
Siedentop
H.,
A Minimax Principle for the
Eigenvalues in Spectral Gaps.
J. London Math. Soc.. (2) 60 (1999), no. 2, 490-500.
- Helffer B.,
Siedentop
H.,
Form Perturbations of
the Second Quantized Dirac Field.
Mathematical Physics Electronic Journal,
4(1998).
- Tix
C. (Regensburg),
Lower bound for the
ground state energy of the no-pair
Hamiltonian. Phys. Lett. B, 405 293-296, 1997.
- Tix
C. (Regensburg),
Self-adjointness and spectral properties
of a pseudo-relativistic
Hamiltonian due to Brown and Ravenhall.
Preprint 1997.
- Bach, V., Fröhlich, J., Sigal, I.M., Soffer, A.,
Positive Commutators and
Spectrum of Nonrelativistic QED. To appear in
Commun. Math. Phys.
- Bach, V., Fröhlich, J., Sigal, I.M.,
Quantum Electrodynamics of
Confined Nonrelativistic Particle.
Adv. in Math., 137,299--395, 1998.
- Bach, V., Fröhlich, J., Sigal, I.M.,
Renormalization Group
Analysis of Spectral Problems in Quantum Field Theory.
Adv. in Math.,137, 205--298, 1998.
- Hoffmann-Ostenhof M., Hoffmann-Ostenhof T.,
Nadirashvili N.
On the Nodal Line Conjecture.
Advances in differential equations and mathematical
physics (Atlanta, GA, 1997), 33--48,
Contemp. Math. 217, Amer. Math.Soc., Providence,
RI,
1998
- Hardt R., Hoffmann-Ostenhof M., Hoffmann-Ostenhof T.,
Nadirashvili N.
Critical Sets of
Solutions to Elliptic Equations.
J. Diff. Geometry, 52 (1999), 359-373
- Balinsky A.A., Evans W.D.
On the virial theorem for the
relativistic operator of Brown and Ravenhall, and the
absence of embedded eigenvalues.
Letters in Mathematical Physics 44: 233-248 (1998)
- Klopp F.
Precise high energy asymptotics for the
integrated density of states of an unbounded random Jacobi
matrix
Preprint 1997
- Helffer, B.
Remarks on decay of correlations and Witten Laplacians -- Brascamp-Lieb inequalities and semiclassical limit --
Journal of Functional Analysis,
155,
571-586 (1998)
- Helffer, B.
Remarks on decay of
correlations and Witten Laplacians II -- Analysis of the dependence on the interaction --
Rev. in Math. Phys. Vol. 11, No. 3 (1999), p. 321-336.
- Helffer, B.
Remarks on decay of correlations and Witten Laplacians III --Applications to logarithmic Sobolev inequalities--
Ann. Inst. Henri Poincar\'e (Section Probabilit\'e statistiques
35, No 4, 483-508 (1999)
- Bodineau T (Orsay)
Phase transition for the Kac model in 2 dimensions
Helvetica Physica Acta 1997, 5, 491--517, 1998.
- Hoffmann-Ostenhof M., Hoffmann-Ostenhof T., Nadirashvili N.
On the multiplicity of eigenvalues of the Laplacian on surfaces
Ann. Global Ana. Geom. 17, 42-48, (1999)
- Hoffmann-Ostenhof T., Michor P. W., Nadirashvili N.
Bounds on the multiplicity of eigenvalues for fixed membranes
Geom.funct.anal. 9,(1999) 1169-1188
- Bach, V.,
Barbaroux, J.-M., Helffer, B., Siedentop, H.
On the stability of the Relativistic Electron-Positron Field
, Communications in Mathematical Physics 201 Issue 2 (1999) pp 445--460
- Johnsen, J. (Orsay)
On the spectral properties of
Witten-Laplacians, their range projections
and Brascamp--Lieb's inequality
Integral Equations and Operator Theory
36 (2000) 288-324.
- Griesemer M., Lutgen J. (Regensburg)
Accumulation of Discrete
Eigenvalues of the Radial Dirac Operator , J. Funct. Anal. 162 (1999), no. 1,
120--134.
- Balinsky A.A., Evans W.D.
Stability of one-electron
molecules in the Brown-Ravenhall model,
Commun. Math. Phys. 202, 481-500(1999)
- Helffer B., Hoffmann-Ostenhof M., Hoffmann-Ostenhof T., Owen M. P.
Nodal sets for the groundstate of the Schrödinger operator with zero
magnetic field in a non simply connected domain
Commun. Math. Phys., 202, 629-649 (1999)
- J. Sjöstrand, W.-M. Wang
Supersymmetric Measures and Maximum Principles in the Complex Domain:
Exponential Decay of Green's Functions Ann. Sci. École Norm.
Sup., 32, 347--414, 1999.
- J. Sjöstrand, W.-M. Wang
Exponential decay of averaged
Green functions for random Schr\"odinger operators, a
direct approach Ann. Sci. École Norm. Sup.,
32, 415--431, 1999.
- Bach, V., Jecko T., Sjöstrand J.
Correlation Asymptotics of Classical Lattice Spin Systems with Nonconvex Hamilton
Function at Low Temperature To appear in Annales H. Poincare
- Jecko Th.
Estimations de Born-Oppenheimer de
la resolvante pour une molecule diatomique
Comm. Math. Phys. 195, 585-612 (1998).
- Jecko Th.
Classical limit of elastic scattering operator for diatomic molecules in Born-Oppenheimer
approximation
Annales de l'Institut Poincare, Physique theorique,
69, 83-131 (1998).
- Weidl, T
Another Look at Cwikel's
inequality
Preprint 1998
- P. Balodis Matesanz, J.P.Solovej,
On the asymptotic exactness of Thomas-Fermi
theory in the thermodynamic limit Annales H. Poincare,
1, 281-306 (2000)
- M. Griesemer, C. Tix
Instability of a Pseudo-Relativistic
Model of Matter with Self- Generated Magnetic Field, J. Math. Phys.
40(4) 1780--1791 (1999)
- Bach,
V., Barbaroux, J.-M., Helffer, B., Siedentop, H.
Stability of Matter for the Hartree-Fock Functional of the
Relativistic Electron-Positron Field , Documenta
Mathematica 3, 358-364 (1998)
- A. Laptev and T. Weidl
Sharp Lieb-Thirring Inequalities in High
Dimensions Acta Mathematica 184 (2000) 87-111
- D. Hundertmark, A. Laptev and T. Weidl
New bounds on the Lieb-Thirring
constants Inventiones mathematicae 140 3 (2000) 693-704
- T. Bodineau and B. Helffer.
Log-Sobolev inequality for unbounded spins systems.
Journal of Functional Analysis 166,1, 1999
- Marcel Griesemer, Roger T. Lewis, Heinz Siedentop
A Minimax Principle for Eigenvalues in
Spectral Gaps: Dirac Operators with Coulomb Potentials DOCUMENTA
MATHEMATICA, 4 (1999), 275-283
- Helffer B., Martinez A.
Phase Transition in the
Semiclassical Regime
Rev. in Math. Phys., Vol. 12 (11), p. 1429,
(2000)
- M.J. Esteban, E. Sere.
Solutions of the Dirac-Fock
Equations for Atoms and Molecules.
Comm. Math. Phys.
203, p. 499-530 (1999)
- Dolbeault J., Esteban Maria J., Sere E.
Variational characterization for
eigenvalues of Dirac operators Cal. Var. 10
321-347, (2000)
- Dolbeault J., Esteban Maria J., Sere E.
On the eigenvalues of operators with
gaps. Application to Dirac operators
J. Func. Anal.174 208-226, (2000).
- E. Paturel
Solutions of
the Dirac-Fock equations without projector.
Ann. H. Poincare vol 1 (2000), p. 1123-1157.
- Jacob Schach Møller
Two-body short-range systems in a
time-periodic electric field Duke Math. Jour.
Vol. 105 (2000), p. 767-803
- Jonathan D. Butler
Semi-Classical Counting Function with
Application to Quantum Current to appear in Asymptotic
Analysis
- Bach,
V., Fröhlich, J., Sigal, I.M.
Spectral Analysis for Systems of Atoms and
Molecules coupled to the Quantized Radiation Field To appear in
Commun. Math. Phys.
- S. Fournais
Semiclassics of the Quantum Current in a
strong constant magnetic field Preprint 1999
- S. Fournais
The Nodal
Surface Of The Second Eigenfunction Of The Laplacian In
RD Can Be Closed
Preprint 1999
- A. Balinsky and W. D. Evans,
On the stability of relativistic
one-electron molecules. J. Phys. A 32 (11),
L129--L132 (1999)
- M. Moser, A. Prets and W. L. Spitzer
Time Evolution of Spin Waves.
Phys. Rev. Lett.83, 3542 (1999)
- Isabelle Catto, Claude Le Bris, Pierre-Louis Lions
On some periodic Hartree-type models for
crystals Preprint 1999
- Georg Hoever, Heinz Siedentop
Stability of the Brown-Ravenhall
Operator
Math. Phys. Electronic Journ. Vol 5, No. 6 (1999)
- Bernhard Baumgartner, Jan Philip Solovej, and Jakob
Yngvason
Atoms in strong magnetic fields:The high field limit at
fixed nuclear charge
Commun. Math. Phys.,212,703-724 (2000)
- A. A. Balinsky, W. D. Evans, Roger T. Lewis
Semi-classical asymptotics for
the counting functions and Riesz means of Pauli and Dirac
operators with large magnetic fields Preprint 1999
- L. Erdos, J.P. Solovej
The kernel of Dirac operators on
$\S^3$ and $\R^3$ to appear in Rev. Math. Phys
- Isabelle Catto, Claude Le Bris and Pierre-Louis
Lions
On the thermodynamic
limit for Hartree-Fock type models To appear in
Ann. I. H. Poincar\'e, Anal.Non Lin.
- A. A. Balinsky and W. D. Evans
On the zero modes of Pauli
operators J. Funct. Analysis 179, pp 120-135 (2001)
- Jacob Schach Møller
The low-temperature limit of
transfer operators in fixed dimension To appear in
Annales Henri Poincare
- Maria Hoffmann-Ostenhof, Thomas Hoffmann-Ostenhof,
Thomas Østergaard Sørensen
Electron Wavefunctions and
Densities for Atoms. Annales H. Poincare, 2
(2001) 77-100
- Dirk Hundertmark, Norbert Röhrl, Heinz Siedentop
The Sharp Bound on the
Stability of the Relativistic Electron-Positron Field in
Hartree-Fock Approximation Communications in Mathematical
Physics Volume 211 Issue 3 (2000) pp 629-642
- S. Fournais
On
the semiclassical asymptotics of the current and magnetisation
of a non-interacting electron gas at zero temperature in a
strong constant magnetic field. Preprint 2000
- S. Fournais
The magnetisation of large atoms in
strong magnetic fields Preprint 2000
- E.H. Lieb and J.P. Solovej
Ground State Energy of the
One-Component Charged Bose Gas
Commun. Math. Phys., 217>, 127-163 (2001)
- J. Dolbeault, M.J. Esteban, E. Sere,
M. Vanbreugel
Minimization
methods for the one-particle Dirac equation,
Phys. Rev. Letters. vol 85 (19) (2000), p. 4020-4023
- J. Sjöstrand
Complete asymptotics for correlations of Laplace integrals
in the semi-classical limit. Mémoires
de la SMF No 83 (2000)
- T. Bodineau and B. Helffer.
Correlations, spectral gap and
LogSobolev inequalities for unbounded spins systems
Proc. of the UAB conf. March 16-20 1999 Diff. Eq. and
Math. Physics, p. 27-42
- B. Helffer, M. Hoffmann-Ostenhof,
T. Hoffmann-Ostenhof and M. Owen
Nodal sets, multiplicity and
superconductivity in non simply connected domains
In Connectivity and Superconductivity
Springer Lecture Notes in Physics m62,
J. Berger and J. Rubinstein (Editors)
p. 63-86
- Now obsolete
- A.A. Balinsky, W.D. Evans and Roger T. Lewis
Sobolev, Hardy and CLR
inequalities associated with Pauli operators in
R3 J. Phys. A: Math. Gen. 34 (2001) L19-L23
- A.A. Balinsky and W.D. Evans
On the zero modes of Weyl-Dirac
operators and their multiplicity To appear in
Bull. Lond. Math. Soc.
- A.A. Balinsky, W.D. Evans and Roger T. Lewis
On the number of negative
eigenvalues of Schr\"{o}dinger operators with an Aharonov-Bohm
magnetic field To appear in Proc.Roy.Soc.Lond.
- Elliott H. Lieb and Heinz Siedentop
Renormalization of the Regularized
Relativistic Electron-Positron Field
Commun. Math. Phys. 213, 673-683,
2000
- Maria J. Esteban, Eric Sere
Nonrelativistic limit of the
Dirac-Fock equations To appear in Ann. H. Poincare
- M.Dimassi, G.D.Raikov
Spectral asymptotics for quantum
Hamiltonians in strong magnetic fields Preprint 2001
- M. Dimassi and J.-C. guillot
The quantum electrodynamics of
relativistic bound states with cutoffs.I. Preprint 2001
- L. Amour, R. Brummelhuis, J. Nourrigat
Resonances of the Dirac Hamiltonian
in the non relativistic limit Preprint 2001
- L. Amour, P. Kerdelhue, J. Nourrigat
Calcul
pseudodiff\'erentiel en grande dimension Asymptotic
Analysis, Vol. 26, No 2, May 2001, p. 135-162.
- C. Royer
Formes
quadratiques et calcul pseudo-diff\'erentiel en grande
dimension Prepublication 00-05 of the University of Reims
(2000)
- J. Butler,
Semi-classical asymptotics of the
spectral functions of pseudo-differential operators, to
appear in Communications in PDE
- J. Butler,
Global h-Fourier integral
operators with complex-valued phase functions, to appear in
the Bulletin of the London Mathematical Society
- B. Helffer (d'apres Helffer-Morame, Lu-Pan,
Helffer-Pan)
Bouteilles
magnetiques et supraconductivite Seminaire Equations
aux derivees partielles de l'Ecole Polytechnique
- J. Derezinski, C. Gérard
Asymptotic Completeness in Quantum
Field Theory: massive Pauli-Fierz Hamiltonians
Rev. Math. Phys. 11 (4) (1999) p 383-450
- C. Gérard, V.Georgescu
On the Virial Theorem in Quantum
Mechanics Comm. Math. Phys. 208 (1999) p
275-281.
- J. Derezinski, C. Gérard
Spectral and scattering theory of
spatially cut-off P(\varphi)2 Hamiltonians
Comm. Math. Phys. 213 (2000), no. 1, p 39-125
- C. Gérard
On
the existence of ground states for massless Pauli-Fierz
Hamiltonians Ann. Henri Poincare 1 (2000),
no. 3, p 443-45
- Iantchenko, Alexei; Siedentop, Heinz
Asymptotic behavior of the
one-particle density matrix of atoms at distances Z-1
from the nucleus Math. Z. 236 (2001), no. 4,
787-796
- Benguria, Rafael; Siedentop, Heinz; Stockmeyer,
Edgardo
Dissociation of
homonuclear relativistic molecular ions Ann. Henri
Poincaré 2(2001), no. 1, 27-40
- Brummelhuis, Raymond; Röhrl, Norbert; Siedentop,
Heinz
Stability of the relativistic electron-positron
field of atoms in Hartree-Fock approximation: heavy
elements. Doc. Math. 6 (2001), 1-8
- A. Laptev, T. Weidl
Recent results on Lieb-Thirring inequalities,
Proceedings Journees EDP 5-9 juin 2000 (2000) XX-1 --
XX-14
- P. Exner, T. Weidl
Lieb-Thirring
Inequalities on Trapped Modes in Quantum Wires, to appear in
Proceedings ICMP London 2000.
- W.M. Wang
Supersymmetry and density of
states of the magnetic Schrödinger operator with a random
potential revisited, Commun. PDE(1999)
- W.M. Wang
Supersymmetry, Witten complex and
asymptotics for directional Lyapunov exponents in
Zd, Ann. Henri Poincare (2001)
- W.M. Wang
Fonction de correelation pour des
mesures complexes et principe du maximum, s\eminaire
EDP Ecole polytechnique (1999)
- W.M. Wang
Supersymmetry, Witten complex and
asymptotics for directional Lyapunov exponents in Zd,
Proceedings of Colloque Equations aux Derivees Partielles,
St. Jean de Monts, (1999)
- W.M. Wang
Mean-field bounds on Lyapunov
exponents in Zd at the critical energy,
Prob. Theo. Rel. Fields (2001)
- W.M. Wang
Localization and universality of
Poisson statistics for the multi-dimensional Anderson model at
weak disorder, Invent. Math. (2001)
- W.M. Wang
Mean field upper and lower bounds
on Lyapunov exponents, Amer. J. Math (2001)
- I. Catto, C. Le Bris, P.L. Lions
Recent
mathematical results on the quantum modeling of crystals,
Proceeding of the Minisymposia ``Mathematics applied to
Quantum Chemistry: Theoretical, computational and experimental
aspects'' at ICIAM 99, Edinburgh, Juillet 1999. In:
Mathematical Models and Methods for Ab Initio Quantum
Chemistry, M. Defrancesci & C. Le Bris Ed., Lecture Notes in
Chemistry Vol. 74, Springer-Verlag, (2001)
- I. Catto, C. Le Bris, P.L. Lions
On the
thermodynamic limit for Hartree-Fock type models, to appear in
Annales de l'Institut Henri Poincare -- Analyse Non
Lineaire
- I. Catto, C. Le Bris, P.L. Lions
On some
periodic Hartree-type models for crystals, to appear in
Annales de l'Institut Henri Poincare -- Analyse Non
Lineaire
- M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and
A. Laptev
A geometrical version of Hardy's inequality,
to appear in Jour. Funct. Analysis
- Christian Hainzl, Robert Seiringer
General decomposition of radial
functions on R^n and refined conditions for positive
definiteness Preprint
- Zied Ammari
Asymptotic completeness for a
renormalized non-relativistic Hamiltonian in quantum field
theory: the Nelson model. Preprint
- Bernard Helffer and Abderemane Morame
Magnetic bottles in connection
with superconductivity Preprint
- Christian Gerard
On the scattering theory of massless
Nelson models Preprint
- B. Helffer, T. Ramond
Semiclassical expansion for the
thermodynamic limit of the ground state energy of Kac's
operator Preprint
- B. Helffer, M. Hoffmann-Ostenhof,
T. Hoffmann-Ostenhof, N. Nadirashvili
Spectral Theory for the Dihedral
Group Preprint
- Helffer B., Pan X.-B.
Upper Critical Field And Location
Of Surface Nucleation Of Superconductivity Preprint
- Brummelhuis R., Siedentop, H., Stockmeyer, E.
The Ground State Energy of
Relativistic One-Electron Atoms According to Jansen and Hess
Preprint
- Bach V., Klopp F., Zenk H.
Mathematical Analysis of the
Photoelectric Effect Preprint
- Jacob Schach Møller
Low-temperature localization for
continuous spin-systems Preprint
- D.Elton.
The
local structure of zero mode producing magnetic
potentials. Commun. Math. Phys. 229 Issue 1
(2002) pp 121-139
- D.Elton.
Fredholm properties of elliptic
operators on
Rn. Preprint
- K.M.Schmidt
A short proof for Bargmann-type
inequalities.
Preprint
- A.Sobolev and L.Parnovsky.
On the
Bethe-Sommerfeld conjecture for the polyharmonic
operator. Duke Math. J. 107, pp 209-238 (2001)
- A.Sobolev and L.Parnovsky.
Lattice points,
perturbation theory and periodic polyharmonic operator.
Ann. H. Poincare, 2 pp 573- 581 (2001)
- A.Sobolev and L.Parnovsky
On the
Bethe-Sommerfeld conjecture. Proceedings of Journees
Equations aux Derivees Partielles, Nantes, (2000).
- A.Sobolev and E.Shargorodsky.
Quasi-conformal
mappings and periodic spectral problems in dimension two. Preprint
- A.Sobolev and J.Walthoe.
Absolute continuity
for periodic wave guides. Preprint
- S. Fournais, M. Hoffmann-Ostenhof,
T. Hoffmann-Ostenhof, T. Østergaard
Sørensen
The
electron density is smooth away from the nuclei.
Commun. Math. Phys., 228 Issue 3 (2002) pp
401-415