Variational theory of elastic manifolds with correlated disorder and localization of interacting quantum particles.

@article{Giamarchi1996VariationalTO,
  title={Variational theory of elastic manifolds with correlated disorder and localization of interacting quantum particles.},
  author={Giamarchi and P LeDoussal},
  journal={Physical review. B, Condensed matter},
  year={1996},
  volume={53 22},
  pages={
          15206-15225
        }
}
We apply the gaussian variational method (GVM) to study the equilibrium statistical mechanics of the two related systems: (i) classical elastic manifolds, such as flux lattices, in presence of columnar disorder correlated along the $\tau$ direction (ii) interacting quantum particles in a static random potential. We find localization by disorder, the localized phase being described by a replica symmetry broken solution confined to the mode $\omega=0$. For classical systems we compute the… 
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References

SHOWING 1-10 OF 49 REFERENCES
Path Integrals and The Relation Between Classical and Quantum Mechanics
Our perception of the world outside ourselves can best be described in the terms of classical physics. The phenomena on the atomic scale require the ideas of quantum mechanics for their understanding
Many-particle physics
1. Introductory Material.- 1.1. Harmonic Oscillators and Phonons.- 1.2. Second Quantization for Particles.- 1.3. Electron - Phonon Interactions.- A. Interaction Hamiltonian.- B. Localized Electron.-
Phys. Rev. B
  • Phys. Rev. B
  • 1995
Phys. Rev. B
  • Phys. Rev. B
  • 1995
Phys. Rev. B
  • Phys. Rev. B
  • 1995
Phys. Rev. E
  • Phys. Rev. E
  • 1995
Phys. Rev. Lett
  • Phys. Rev. Lett
  • 1995
Phys. Rev. Lett
  • Phys. Rev. Lett
  • 1995
Ecole Normale Supérieure etetà l'Université Paris- Sud
  • Rev. Mod. Phys
  • 1994
...
1
2
3
4
5
...