Eigenvalue Crossing as a Phase Transition in Relaxation Dynamics
Gianluca Teza, Ran Yaacoby, Oren Raz
Abstract
When a system's parameter is abruptly changed, a relaxation toward the new equilibrium of the system follows. We show that a crossing between the second and third eigenvalues of the relaxation operator results in a singularity in the dynamics analogous to a first-order equilibrium phase transition. While dynamical phase transitions are intrinsically hard to detect in nature, here we show how this kind of transition can be observed in an experimentally feasible four-state colloidal system. Finally, analytical proof of survival in the thermodynamic limit of a many body (1D Ising) model is provided.
Topics & Concepts
Level crossingPhase transitionRelaxation (psychology)Dynamics (music)Eigenvalues and eigenvectorsStatistical physicsPhysicsPhase (matter)Transition (genetics)Condensed matter physicsQuantum mechanicsChemistryHistoryGeneArchaeologySocial psychologyAcousticsBiochemistryPsychologyAdvanced Thermodynamics and Statistical MechanicsNonlinear Dynamics and Pattern FormationMaterial Dynamics and Properties