Static and dynamic collective behavior of disordered systems

• Applicant: Professor Dr. Thomas Nattermann, since 9/2010
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2001 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5298540

• Final Report Year: 2013

Final Report Abstract

Within this project, the focus has been shifted towards fluctuation induced interactions in systems with collective long-ranged fluctautions. Fluctuation induced quantum forces between macroscopic objects of arbitrary shape, orientation and material composition have been studied. From a marriage of path integral quantization and scattering theory, a novel approach has been developed that yields a general formula for these interactions in terms of the scattering matrices of the individual objects. This formula has been applied successfully both analytically and numerically to obtain a plethora of new results for Casimir and van der Waals interactions that were inaccessibly before and are of utmost importance to recent experiments and presumably future applications in nanomechanical systems. In a separate line of research, the competition between quenched disorder and extended defect planes on the structural properties of (vortex) line lattices was studied by functional renormalization group. A defect plane was shown to be a relevant if it is oriented parallel to the lines as well as one of the main axis of the lattice. There has been a report in MIT news on the progress made on the computation and understanding of Casimir force within this project. [http://web.mit.edu/newsoffice/2010/casimir-0511.html]

Publications

• String Picture of a Frustrated Quantum Magnet and Dimer Model, Phys. Rev. Lett. 94, 110604 (2005)
  Y. Jiang, T. Emig
  
• Casimir interaction between a plate and a cylinder, Phys. Rev. Lett. 96, 080403 (2006)
  T. Emig, R. L. Jaffe, M. Kardar, A. Scardicchio
  
• Casimir force driven ratchets, Phys. Rev. Lett. 98,160801 (2007)
  T. Emig
  
• Casimir forces between arbitrary compact objects, Phys. Rev. Lett. 99, 170403 (2007)
  T. Emig, N. Graham, R. L. Jaffe, M. Kardar
  
• Fluctuation induced quantum interactions between compact objects and a plane mirror, J. Stat. Mech., P04007 (2008)
  T. Emig
  
• Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders, Phys. Rev. A 77, 030101(R) (2008)
  S. J. Rahi, A. W. Rodriguez, T. Emig, R. L. Jaffe, S. G. Johnson, M. Kardar
  
• Orientation dependence of Casimir forces, Phys. Rev. A 79, 054901 (2009)
  T. Emig, N. Graham, R. L. Jaffe, M. Kardar
  
• Scattering Theory Approach to Electrodynamic Casimir Forces, Phys. Rev. D 80, 085021 (2009)
  S. J. Rahi, T. Emig, N. Graham, R. L. Jaffe, M. Kardar
  
• Constraints on stable equilibria with fluctuation-induced forces, Phys. Rev. Lett. 105, 070404 (2010)
  S. J. Rahi, M. Kardar, T. Emig
  
• Analytical results on Casimir forces for conductors with edges and tips, PNAS 108, 6867 (2011)
  M. F. Maghrebi, S. J.Rahi, T. Emig, N. Graham, R. L. Jaffe, M. Kardar