Classical particle in a box with random potential: Exploiting rotational symmetry of replicated Hamiltonian

@article{Fyodorov2007ClassicalPI,
  title={Classical particle in a box with random potential: Exploiting rotational symmetry of replicated Hamiltonian},
  author={Yan V. Fyodorov and H.-J. Sommers},
  journal={Nuclear Physics},
  year={2007},
  volume={764},
  pages={128-167}
}

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References

SHOWING 1-10 OF 82 REFERENCES
Localization of a polymer in random media: relation to the localization of a quantum particle.
TLDR
It is shown how the end-to-end distance of a polymer that is free to move can be obtained from the density of states of the quantum particle using extreme value statistics, and a physical interpretation to the recently discovered one-step replica-symmetry-breaking solution is given.
Variational theory of elastic manifolds with correlated disorder and localization of interacting quantum particles.
TLDR
It is shown that the marginality condition appears as the condition to obtain the correct physical behavior in quantum systems, and agreement with renormalization group results is found whenever it can be compared.
Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
Abstract: By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick
Large time nonequilibrium dynamics of a particle in a random potential.
  • Cugliandolo, Le Doussal P
  • Physics, Mathematics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
TLDR
The existence of two asymptotic time regimes: stationary dynamics, slow aging dynamics with violation of equilibrium theorems are demonstrated and an analytical solution of these equations is obtained.
Density of stationary points in a high dimensional random energy landscape and the onset of glassy behavior
The density of stationary points and minima of a N ≫ 1 dimensional Gaussian energy landscape has been calculated. It is used to show that the point of zero-temperature replica symmetry breaking in
Inertial effects in the short-range Toy Model
We examine the dynamics of the so-called Toy Model with an added inertial term. The problem is essentially the Kramers problem for a massive particle in a flow field given by the gradient of a
Large-time dynamics and aging of a polymer chain in a random potential.
  • Y. Goldschmidt
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2006
TLDR
The out-of-equilibrium large-time dynamics of a Gaussian polymer chain in a quenched random potential is studied and two possible dynamical behaviors are identified depending upon the time separation: a stationary regime and an aging regime.
Exactly solvable model of a quantum spin glass.
TLDR
A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered, which exhibits replica symmetry breaking and the thermodynamics is now regular at small temperatures.
...
...