Quenched dynamics of classical isolated systems: The spherical spin model with two-body random interactions or the Neumann integrable model

• Autores: Cugliandolo, Leticia Fernanda; Lozano, Gustavo Sergio; Nessi, Emilio Nicolás; Picco, Marcos Fernando; Tartaglia, Alessandro
• Año de publicación: 2018
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: DYNAMICAL PROCESSES; ENERGY LANDSCAPES; ERGODICITY BREAKING; NUMERICAL SIMULATIONS
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body random interactions. In the statistical physics framework, the potential energy is of the so-called p = 2 kind, closely linked to the scalar field theory. Most importantly for our setting, the energy conserving dynamics are equivalent to the ones of the Neumann integrable model. We take initial conditions from the Boltzmann equilibrium measure at a temperature that can be above or below the static phase transition, typical of a disordered (paramagnetic) or of an ordered (disguised ferromagnetic) equilibrium phase. We subsequently evolve the configurations with Newton dynamics dictated by a different Hamiltonian, obtained from an instantaneous global rescaling of the elements in the interaction random matrix. In the limit of infinitely many degrees of freedom, , we identify three dynamical phases depending on the parameters that characterise the initial state and the final Hamiltonian. We next set the analysis of the system with finite number of degrees of freedom in terms of N non-linearly coupled modes. We argue that in the limit the modes decouple at long times. We evaluate the mode temperatures and we relate them to the frequency-dependent effective temperature measured with the fluctuation-dissipation relation in the frequency domain, similarly to what was recently proposed for quantum integrable cases. Finally, we analyse the N - 1 integrals of motion, notably, their scaling with N, and we use them to show that the system is out of equilibrium in all phases, even for parameters that show an apparent Gibbs-Boltzmann behaviour of the global observables. We elaborate on the role played by these constants of motion after the quench and we briefly discuss the possible description of the asymptotic dynamics in terms of a generalised Gibbs ensemble.
Fil: Cugliandolo, Leticia Fernanda. Université Pierre et Marie Curie; Francia. Université Pierre et Marie Curie. Laboratoire de Physique Théorique et Hautes Energies; Francia
Fil: Lozano, Gustavo Sergio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Nessi, Emilio Nicolás. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Picco, Marcos Fernando. Université Pierre et Marie Curie. Laboratoire de Physique Théorique et Hautes Energies; Francia
Fil: Tartaglia, Alessandro. Université Pierre et Marie Curie. Laboratoire de Physique Théorique et Hautes Energies; Francia