Spektralabschätzungen in der mathematischen Physik und deren Anwendungen auf mathematische Modelle der Quantenmechnik und der Nanoelektronik

• Applicant: Professor Dr. Timo Weidl
• Subject Area: Mathematics
• Term: from 2004 to 2009
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5437028

• Final Report Year: 2009

Final Report Abstract

No abstract available

Publications

• Polya's Conjecture in the Presence of a Constant Magnetic Field. Preprint. JEMS
  R.L. Frank, M. Loss, T. Weidl
  
• Two-dimensional Berezin-Li-Yau inequalities with a correction term. Preprint. Comm. Math. Phys.
  H. Kovarik, S. Vugalter, T. Weidl
  
• Quantative estimates on the enhances binding for the Pauli-Fierz operator. J. Math. Phys. 46 (2005), no. 12, 122103, 11 pp.
  J.-M. Barbaroux, H. Linde, S. Vugalter
  
• Spectrum of the magnetic Schrödinger operator in a waveguide with combined boundary conditions, Ann. Henri Poincaré 6 (2005) 327-342
  D. Borisov, T. Ekholm, H. Kovarík
  
• Stability of the magnetic Schrödinger operator in a waveguide, Comm. PDE 4-6 (2005) 539-565
  T. Ekholm, H. Kovarík
  
• Lieb-Thirring inequalities for higher order differential operators. Math. Nachr. (2006)
  C. Föster, J. Österson
  
• Stability of atoms in the Brown-Ravenhall model. Ann. Henri Poincaré 7 (2006), no. 4, 661-687
  S. Morozov, S. Vugalter
  
• Trapped modes for an elastic strip with perturbation of the material properties. Quaterly Journal of Mechanics and Applied Mathematics 2006 59(3), 399-418
  C. Förster, T. Weidl
  
• Nonstandard Cwikel type estimates. 337-357, Contemp. Math., 445, Amer. Math. Soc, Providence, RI, 2007
  T. Weidl
  
• Spectral estimates for two-dimensional Schrödinger operators with applications to quantum layers. Comm. Math. Phys. 275 (2007), no. 3, 827-838
  H. Kovarík, S. Vugalter and T. Weidl
  
• A Hardy inequality in twisted waveguides. Arch. Ration. Mech. Anal 188 (2008), no. 2, 245-264
  T. Ekholm, H. Kovarík, D. Krejcirík
  
• Eigenvalue Bounds for Perturbations of Schrödinger Operators and Jacobi Matrices With Regular Ground States. Comm. Math. Phys. 278 (2008), no. 1, 199-208
  R.L. Frank, B. Simon, T. Weidl
  
• Estimates on trapped modes in deformed quantum layers. J. Math. Anal. Appl. 345 (2008), no. 1, 566-572
  H. Kovarík, S. Vugalter
  
• Improved Berezin-Li-Yau inequalities with a remainder term. Amer. Math. Soc. Transl. 225(2) (2008) 253-263
  T. Weidl
  
• The ground state energy of the translation invariant Pauli-Fierz model. Proc. Amer. Math. Soc. 136 (2008), no. 3, 1057-1064
  J.-M. Barbaroux, Th. Chen, V. Vougalter, S. Vugalter
  
• Trapped modes for the elastic plate with a perturbation of Young's modulus. Comrn. Partial Differential Equations 33 (2008), no. 7-9, 1339-1367
  C. Förster