Testi

La seguente lista riporta alcuni testi ed articoli di riferimento relativi agli argomenti trattati nel corso. Gli studenti possono comunque utilizzare qualsiasi testo pertinente agli argomenti trattati.
  • Referenze Principali
    • Handbook of Stochastic Methods,
      C.W. Gardiner
      Springer (1985)

    • Stochastic Runge-Kutta algoritms. I. White noise,
      R. L. Honeycutt
      Phys. Rev. A 45, 600 (1992)

    • Path integral methods for dynamics of stochastic and disordered systems,
      J.A. Hertz, Y. Roudi and P. Sollich
      J. Phys. A: Math. Theor. 50 (2017) 033001
      doi:10.1088/1751-8121/50/3/033011

    • Path integral methods for Stocahstic Differential Equations,
      C C. Chow and M. A. Buice
      J. Math. Neuroscience (2015) 5:8
      doi:10.1186/s13408-015-0018-5

    • State-dependent diffusion: Thermodynamic consistency and its path integral formulation,
      A W.C. Lau and T.C. Lubensky
      Phys. Rev. E 76, 011123 (2007)
      doi:10.1103/PhysRevE.76.011123

    • Field Theory of Non-Equilibrium Systems,
      Alex Kamenev
      Cambridge University Press (2023)

    • The Spherical p-spin Interaction Spin Glass Model: The Dynamics,
      A. Crisanti, H. Horner, H.-J. Sommers
      Zeitschrift fur Physik B 92, 257-271 (1993)
      doi: 10.1007/BF01312184


  • Additional References
    • The Fokker-Planck Equation,
      H. Risken
      Springer (1989)

    • Stochastic Differential Equations: An introduction with applications,
      B Øksendal
      Springer (1998)

    • Quantum Field Theory of Non-equilibrium States,
      J. Rammer
      Cambridge University Press (2007)

    • Effective action for composite operators,
      J.M. Conrwall, R. Jackiw and E. Tomboulis
      Phys. Rev. D 10, 2428 (1974)

    • Spherical 2+p spin-glass model: An analytically solvable model with a glass-to-glass transition,
      A. Crisanti, L. Leuzzi
      Physical Review B 73, 14412 (2006)
      doi: 10.1103/PhysRevB.73.014412

    • Chaos in Random Neural Networks,
      H. Sompolinsky, A. Crisanti, H-J. Sommers
      Phys. Rev. Lett. 61, 259 (1988)
      doi: 10.1103/PhysRevLett.61.259

    • Path integral approach to random neural networks,
      A. Crisanti, H. Sompolinsky
      Phys. Rev. E 98, 062120 (2018)
      doi: 10.1103/PhysRevE.98.062120

    • Chaos in Random Neural Networks,
      A. Crisanti
      Slides Goetingen May 2016.