Nonlinear order-parameter relaxation in the nonlinear?-model

Naeem Jan, Dietrich Stauffer

Manoj Kumar, G. S. Agarwal

The effect of cross relaxation, i.e., the transfer of coherence between transitions coupled by inelastic collisions, on third-order nonlinear processes, namely, saturated absorption and four-wave mixing, is studied within the context of a model four-level system. Numerical results displaying changes in the resonant structures in four-wave-mixing signals for a range of collisional parameters are presented.

Mustafa KESKİN, Rıza Erdem

Dynamic behavior of a spin-1 Ising model [1] with arbitrary bilinear (J) and biquadratic (K) pair interactions is studied by using the path probability method [2]. First the equilibrium behavior of the model is given briefly in order to understand the nonequilibrium behavior. Then the path probability method is applied to the spin-1 Ising model with J and K Hamiltonian and the system of nonlinear differential equations, which are also called the dynamic equations or rate equations, is found. The dynamic equations are solved using the Runga-Kutta method and the solutions, namely relaxation of order parameters are examined to see the "flatness" property of metastable states. It is found that the system relaxes to either stable or metastable states depending upon the initial values of the order parameters. Moreover, if there are more than one metastable states, the relaxation occurs according to the initial values of the order parameters or free energy values. Finally, the results are compared with the flow diagrams which are the solutions of the dynamic equations in two-dimensional phase space [3] and it is seen that the same results are found except for the "flatness" property of metastable states.

H K Janssen, Klaus Oerding

We study the purely relaxational tricritical dynamics of a non-conserved order parameter (model A) in the upper critical dimension d c =3 and in 3- epsilon dimensions. We are especially interested in the relaxation, starting from a macroscopically prepared initial state with a small correlation length. Using the methods of renormalized field theory we obtain the scaling behaviour of the correlation and response functions and study the nonlinear relaxation of the order parameter M(t). In three dimensions M(t) displays a crossover from the purely logarithmic short-time behaviour M(t) approximately (In(t/t 0 )) -a to a t - 1 4 / power law with logarithmic corrections. For dimensions d<3 we obtain the exponents which govern the tricritical relaxation at lowest non-trivial order in epsilon =3-d. The dynamic scaling exponent z is calculated at second order in epsilon .

Razvan Teodorescu, I. L. Aleǐner