2025/03/30 by Amir Dembo, Eliran Subag, Dembo, Amir +1
Physics and Astronomy · Materials Science · #Theoretical and Computational Physics #Material Dynamics and Properties #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2503.23342
We derive the coupled non-linear integro-differential equations for the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics at temperature T, for spherical mixed p-spin disordered mean-field models, initialized according to a Gibbs measure for temperature T0, in the replica-symmetric (RS) or 1-replica-symmetry-breaking (RSB) phase. For any T0=T above the dynamical phase transition point Tc\rm dyn the resulting stationary relaxation dynamics coincide with the FDT solution for these equations, while for lower T0=T in the 1-RSB phase, the relaxation dynamics coincides with the FDT solution, now concentrated on the single spherical band within the Gibbs measure's support on which the initial point lies.