Linear and Nonlinear Response Theory with Applications

Ravinder Rupchand Puri

A.‐S. F. Obada, Saad S. M. Hassan, M. H. Mahran

Janka Petravic, Denis J. Evans

We generalize nonlinear response theory for autonomous systems so that it describes the response of classical many-body systems to large time-dependent external fields. Our formalism represents the first practical application of response theory to such problems. Our expressions for the nonlinear time-dependent response are tested against nonequilibrium molecular dynamics computer simulation. The relation of our results to known special cases (time-dependent linear response and time-independent nonlinear response) is discussed.

James H. Luscombe

The nonequilibrium response of a two-dimensional, paramagnetic system to a rapid and arbitrarily large change (quench) in a symmetry-breaking field is investigated. The complete time dependence of the conjugate order parameter is calculated with a real-space renormalization-group (RG) method. The nonlinear relaxation "rate" is found to be time dependent. Its approach to the corresponding prediction of linear-response theory is characterized. The nonlinear response is found to go over to linear response via an early, exponential regime followed by a crossover to an asymptotic, algebraic approach to linear response at long times. The initial transient decay is quench-strength dependent in contrast with the final behavior, which is largely "universal" and quench insensitive. We study a nearest-neighbor Ising model in a magnetic field in the paramagnetic, "disordered" phase. The dynamics are controlled by a kinetic Ising model with simultaneous spin-flip (adsorption-desorption) and spin-exchange (diffusion) kinetics. The model is applicable to non-equilibrium "dosing" experiments on adsorbed systems. Diffusion is shown not to affect the growth rate of the total order parameter (magnetization or coverage). General recursion relations for the temperature and magnetic field are derived for the entire thermodynamic plane. The RG analysis reproduces linear-response theory for arbitrary magnetic field and is consistent with known scaling laws concerning nonlinear relaxation. The time-dependent magnetization in the critical region has a power-law regime before crossing over into its final exponential decay.

Fabrizio Tafuri, C. A. Perroni, G. De Filippis

Shun Ogawa, Yoshiyuki Y. Yamaguchi

A nonlinear response theory is provided by use of the transient linearization method in the spatially one-dimensional Vlasov systems. The theory inclusively gives responses to external fields and to perturbations for initial stationary states, and is applicable even to the critical point of a second-order phase transition. We apply the theory to the Hamiltonian mean-field model, a toy model of a ferromagnetic body, and investigate the critical exponent associated with the response to the external field at the critical point in particular. The obtained critical exponent is the nonclassical value 3/2, while the classical value is 3. However, interestingly, one scaling relation holds with another nonclassical critical exponent of susceptibility in the isolated Vlasov systems. Validity of the theory is numerically confirmed by directly simulating temporal evolutions of the Vlasov equation.