Recurrence relations and time evolution in the three-dimensional Sawada model

Abstract

Time-dependent behavior of the three-dimensional Saeada model is obtained by a method of recurrence relations, Exactly calculated quantities are the time evolution of the density-fluctuation operator and its random force. As an application, their linear coefficients, the relaxation and memory functions, are used to obtain certain dynamic quantities, e.g. , the mobility.

Non-exponential relaxation for anomalous diffusion

“…Applying the Laplace transform yields Π(z) = (2γ/π) arctan(ω s /z). It is interesting to note that this memory function is realized in electron gas models [27]. We now show that it is possible to find at least three time scales for this memory.…”

Time Evolution in a Two-dimensional Ultrarelativistic-like Electron Gas by Recurrence Relations Method

“…The basal autocorrelation a 0 is unknown a priori, however it is possible to determine it through the analytical theory of continued fractions due to Mori [16]. By taking the Laplace transform of 1 It is worth mentioning that the KSP (6) has already been used in several situations where β → ∞ (see, e.g., [6,7]). It is a standard linear response relation whose validity at T = 0 was established many years ago [2,17,18].…”

“…The apparatus we are going to employ to solve the equation of motion of the density fluctuation is the well established RRM. This approach has already been successfully applied in the study of the nonrelativistic dense electron gas (2DEG), at the long wavelength and zero temperature limits, in one [5], two [6], three [7], and D dimensions [8]. Applications of the RRM to many-body systems, in general, are also available in the literature (see, e.g., reference [9]).…”

The topology of Hilbert spaces and the dynamics of molecular processes

“…To order k, D, = u2n2/ (4n2 -l), nb 1, where u is defined in (C). Then, R(Z) = tan-' u/z and R(t) =jo(ut), where/, is the spherical Bessel function of order n. An interacting version of this model has been obtained [57].…”