PUBLICATIONS SUPPORTED BY THE EU NETWORK ON PARTIAL DIFFERENTIAL EQUATIONS AND QUANTUM MECHANICS

  1. Lieb E.H., Loss M., Siedentop H.,
    Stability of Relativistic Matter via Thomas-Fermi Theory. Helv. Phys. Acta, 69, 974-984, 1996.

  2. 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.

  3. Tix C. (Regensburg),
    Strict positivity of a relativistic Hamiltonian due to Brown and Ravenhall. Bull. London Math. Soc. 30, 283-290, 1998.

  4. Helffer, B.,
    Semi-classical analysis for the transfer operator: formal WKB constructions in large dimension. Commun. Math. Phys. 187, 81-113, (1997).

  5. 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.

  6. 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).

  7. Helffer, B.,
    Splitting in large dimension and infrared estimates II - Moment inequalities. Jour. Math. Phys. 39 , 760-776 (1998).

  8. 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)

  9. Fournais, S. (Aarhus),
    Semiclassics of the quantum current. Comm. PDE. 23 601-628 (1998).

  10. 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

  11. 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).

  12. 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.

  13. 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.

  14. Helffer B., Siedentop H.,
    Form Perturbations of the Second Quantized Dirac Field. Mathematical Physics Electronic Journal, 4(1998).

  15. Tix C. (Regensburg),
    Lower bound for the ground state energy of the no-pair Hamiltonian. Phys. Lett. B, 405 293-296, 1997.

  16. Tix C. (Regensburg),
    Self-adjointness and spectral properties of a pseudo-relativistic Hamiltonian due to Brown and Ravenhall. Preprint 1997.

  17. Bach, V., Fröhlich, J., Sigal, I.M., Soffer, A.,
    Positive Commutators and Spectrum of Nonrelativistic QED. To appear in Commun. Math. Phys.

  18. Bach, V., Fröhlich, J., Sigal, I.M.,
    Quantum Electrodynamics of Confined Nonrelativistic Particle. Adv. in Math., 137,299--395, 1998.

  19. Bach, V., Fröhlich, J., Sigal, I.M.,
    Renormalization Group Analysis of Spectral Problems in Quantum Field Theory. Adv. in Math.,137, 205--298, 1998.

  20. 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

  21. Hardt R., Hoffmann-Ostenhof M., Hoffmann-Ostenhof T., Nadirashvili N.
    Critical Sets of Solutions to Elliptic Equations. J. Diff. Geometry, 52 (1999), 359-373

  22. 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)

  23. Klopp F.
    Precise high energy asymptotics for the integrated density of states of an unbounded random Jacobi matrix Preprint 1997

  24. Helffer, B.
    Remarks on decay of correlations and Witten Laplacians -- Brascamp-Lieb inequalities and semiclassical limit -- Journal of Functional Analysis, 155, 571-586 (1998)

  25. 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.

  26. 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)

  27. Bodineau T (Orsay)
    Phase transition for the Kac model in 2 dimensions Helvetica Physica Acta 1997, 5, 491--517, 1998.

  28. 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)

  29. Hoffmann-Ostenhof T., Michor P. W., Nadirashvili N.
    Bounds on the multiplicity of eigenvalues for fixed membranes Geom.funct.anal. 9,(1999) 1169-1188

  30. 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

  31. 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.

  32. Griesemer M., Lutgen J. (Regensburg)
    Accumulation of Discrete Eigenvalues of the Radial Dirac Operator , J. Funct. Anal. 162 (1999), no. 1, 120--134.

  33. Balinsky A.A., Evans W.D.
    Stability of one-electron molecules in the Brown-Ravenhall model, Commun. Math. Phys. 202, 481-500(1999)

  34. 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)

  35. 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.

  36. 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.

  37. 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

  38. Jecko Th.
    Estimations de Born-Oppenheimer de la resolvante pour une molecule diatomique Comm. Math. Phys. 195, 585-612 (1998).

  39. 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).

  40. Weidl, T
    Another Look at Cwikel's inequality Preprint 1998

  41. 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)

  42. 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)

  43. 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)

  44. A. Laptev and T. Weidl
    Sharp Lieb-Thirring Inequalities in High Dimensions Acta Mathematica 184 (2000) 87-111

  45. D. Hundertmark, A. Laptev and T. Weidl
    New bounds on the Lieb-Thirring constants Inventiones mathematicae 140 3 (2000) 693-704

  46. T. Bodineau and B. Helffer.
    Log-Sobolev inequality for unbounded spins systems. Journal of Functional Analysis 166,1, 1999

  47. 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

  48. Helffer B., Martinez A.
    Phase Transition in the Semiclassical Regime Rev. in Math. Phys., Vol. 12 (11), p. 1429, (2000)

  49. M.J. Esteban, E. Sere.
    Solutions of the Dirac-Fock Equations for Atoms and Molecules. Comm. Math. Phys. 203, p. 499-530 (1999)

  50. Dolbeault J., Esteban Maria J., Sere E.
    Variational characterization for eigenvalues of Dirac operators Cal. Var. 10 321-347, (2000)

  51. 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).

  52. E. Paturel
    Solutions of the Dirac-Fock equations without projector. Ann. H. Poincare vol 1 (2000), p. 1123-1157.

  53. Jacob Schach Møller
    Two-body short-range systems in a time-periodic electric field Duke Math. Jour. Vol. 105 (2000), p. 767-803

  54. Jonathan D. Butler
    Semi-Classical Counting Function with Application to Quantum Current to appear in Asymptotic Analysis

  55. 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.

  56. S. Fournais
    Semiclassics of the Quantum Current in a strong constant magnetic field Preprint 1999

  57. S. Fournais
    The Nodal Surface Of The Second Eigenfunction Of The Laplacian In RD Can Be Closed Preprint 1999

  58. A. Balinsky and W. D. Evans,
    On the stability of relativistic one-electron molecules. J. Phys. A 32 (11), L129--L132 (1999)

  59. M. Moser, A. Prets and W. L. Spitzer
    Time Evolution of Spin Waves. Phys. Rev. Lett.83, 3542 (1999)

  60. Isabelle Catto, Claude Le Bris, Pierre-Louis Lions
    On some periodic Hartree-type models for crystals Preprint 1999

  61. Georg Hoever, Heinz Siedentop
    Stability of the Brown-Ravenhall Operator Math. Phys. Electronic Journ. Vol 5, No. 6 (1999)

  62. 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)

  63. 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

  64. L. Erdos, J.P. Solovej
    The kernel of Dirac operators on $\S^3$ and $\R^3$ to appear in Rev. Math. Phys

  65. 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.

  66. A. A. Balinsky and W. D. Evans
    On the zero modes of Pauli operators J. Funct. Analysis 179, pp 120-135 (2001)

  67. Jacob Schach Møller
    The low-temperature limit of transfer operators in fixed dimension To appear in Annales Henri Poincare

  68. Maria Hoffmann-Ostenhof, Thomas Hoffmann-Ostenhof, Thomas Østergaard Sørensen
    Electron Wavefunctions and Densities for Atoms. Annales H. Poincare, 2 (2001) 77-100

  69. 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

  70. 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

  71. S. Fournais
    The magnetisation of large atoms in strong magnetic fields Preprint 2000

  72. E.H. Lieb and J.P. Solovej
    Ground State Energy of the One-Component Charged Bose Gas Commun. Math. Phys., 217>, 127-163 (2001)

  73. 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

  74. J. Sjöstrand
    Complete asymptotics for correlations of Laplace integrals in the semi-classical limit. Mémoires de la SMF No 83 (2000)

  75. 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

  76. 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

  77. Now obsolete

  78. 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

  79. 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.

  80. 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.

  81. Elliott H. Lieb and Heinz Siedentop
    Renormalization of the Regularized Relativistic Electron-Positron Field Commun. Math. Phys. 213, 673-683, 2000

  82. Maria J. Esteban, Eric Sere
    Nonrelativistic limit of the Dirac-Fock equations To appear in Ann. H. Poincare

  83. M.Dimassi, G.D.Raikov
    Spectral asymptotics for quantum Hamiltonians in strong magnetic fields Preprint 2001

  84. M. Dimassi and J.-C. guillot
    The quantum electrodynamics of relativistic bound states with cutoffs.I. Preprint 2001

  85. L. Amour, R. Brummelhuis, J. Nourrigat
    Resonances of the Dirac Hamiltonian in the non relativistic limit Preprint 2001

  86. L. Amour, P. Kerdelhue, J. Nourrigat
    Calcul pseudodiff\'erentiel en grande dimension Asymptotic Analysis, Vol. 26, No 2, May 2001, p. 135-162.

  87. C. Royer
    Formes quadratiques et calcul pseudo-diff\'erentiel en grande dimension Prepublication 00-05 of the University of Reims (2000)

  88. J. Butler,
    Semi-classical asymptotics of the spectral functions of pseudo-differential operators, to appear in Communications in PDE

  89. J. Butler,
    Global h-Fourier integral operators with complex-valued phase functions, to appear in the Bulletin of the London Mathematical Society

  90. B. Helffer (d'apres Helffer-Morame, Lu-Pan, Helffer-Pan)
    Bouteilles magnetiques et supraconductivite Seminaire Equations aux derivees partielles de l'Ecole Polytechnique

  91. J. Derezinski, C. Gérard
    Asymptotic Completeness in Quantum Field Theory: massive Pauli-Fierz Hamiltonians Rev. Math. Phys. 11 (4) (1999) p 383-450

  92. C. Gérard, V.Georgescu
    On the Virial Theorem in Quantum Mechanics Comm. Math. Phys. 208 (1999) p 275-281.

  93. 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

  94. C. Gérard
    On the existence of ground states for massless Pauli-Fierz Hamiltonians Ann. Henri Poincare 1 (2000), no. 3, p 443-45

  95. 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

  96. Benguria, Rafael; Siedentop, Heinz; Stockmeyer, Edgardo
    Dissociation of homonuclear relativistic molecular ions Ann. Henri Poincaré 2(2001), no. 1, 27-40

  97. 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

  98. A. Laptev, T. Weidl
    Recent results on Lieb-Thirring inequalities, Proceedings Journees EDP 5-9 juin 2000 (2000) XX-1 -- XX-14

  99. P. Exner, T. Weidl
    Lieb-Thirring Inequalities on Trapped Modes in Quantum Wires, to appear in Proceedings ICMP London 2000.

  100. W.M. Wang
    Supersymmetry and density of states of the magnetic Schrödinger operator with a random potential revisited, Commun. PDE(1999)

  101. W.M. Wang
    Supersymmetry, Witten complex and asymptotics for directional Lyapunov exponents in Zd, Ann. Henri Poincare (2001)

  102. W.M. Wang
    Fonction de correelation pour des mesures complexes et principe du maximum, s\eminaire EDP Ecole polytechnique (1999)

  103. 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)

  104. W.M. Wang
    Mean-field bounds on Lyapunov exponents in Zd at the critical energy, Prob. Theo. Rel. Fields (2001)

  105. W.M. Wang
    Localization and universality of Poisson statistics for the multi-dimensional Anderson model at weak disorder, Invent. Math. (2001)

  106. W.M. Wang
    Mean field upper and lower bounds on Lyapunov exponents, Amer. J. Math (2001)

  107. 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)

  108. 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

  109. 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

  110. M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and A. Laptev
    A geometrical version of Hardy's inequality, to appear in Jour. Funct. Analysis

  111. Christian Hainzl, Robert Seiringer
    General decomposition of radial functions on R^n and refined conditions for positive definiteness Preprint

  112. Zied Ammari
    Asymptotic completeness for a renormalized non-relativistic Hamiltonian in quantum field theory: the Nelson model. Preprint

  113. Bernard Helffer and Abderemane Morame
    Magnetic bottles in connection with superconductivity Preprint

  114. Christian Gerard
    On the scattering theory of massless Nelson models Preprint

  115. B. Helffer, T. Ramond
    Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator Preprint

  116. B. Helffer, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, N. Nadirashvili
    Spectral Theory for the Dihedral Group Preprint

  117. Helffer B., Pan X.-B.
    Upper Critical Field And Location Of Surface Nucleation Of Superconductivity Preprint

  118. Brummelhuis R., Siedentop, H., Stockmeyer, E.
    The Ground State Energy of Relativistic One-Electron Atoms According to Jansen and Hess Preprint

  119. Bach V., Klopp F., Zenk H.
    Mathematical Analysis of the Photoelectric Effect Preprint

  120. Jacob Schach Møller
    Low-temperature localization for continuous spin-systems Preprint

  121. D.Elton.
    The local structure of zero mode producing magnetic potentials. Commun. Math. Phys. 229 Issue 1 (2002) pp 121-139

  122. D.Elton.
    Fredholm properties of elliptic operators on Rn. Preprint

  123. K.M.Schmidt
    A short proof for Bargmann-type inequalities. Preprint

  124. A.Sobolev and L.Parnovsky.
    On the Bethe-Sommerfeld conjecture for the polyharmonic operator. Duke Math. J. 107, pp 209-238 (2001)

  125. A.Sobolev and L.Parnovsky.
    Lattice points, perturbation theory and periodic polyharmonic operator. Ann. H. Poincare, 2 pp 573- 581 (2001)

  126. A.Sobolev and L.Parnovsky
    On the Bethe-Sommerfeld conjecture. Proceedings of Journees Equations aux Derivees Partielles, Nantes, (2000).

  127. A.Sobolev and E.Shargorodsky.
    Quasi-conformal mappings and periodic spectral problems in dimension two. Preprint

  128. A.Sobolev and J.Walthoe.
    Absolute continuity for periodic wave guides. Preprint

  129. 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