Theoretical studies of condensed matter

Quasi-solid state microscopic dynamics in equilibrium classical liquids: Self-consistent relaxation theory

“…The existence of this regime is quite understandable because the transition to quasisolid-state dynamics occurs in some domain of spatial scales and consequently in some wave number domain. An analysis of expression (42) for C T (k, ω) shows that such a transition is realized for the correspondence between frequency relaxation parameters…”

“…In the framework of the general statistical mechanics approach, we can regard an equilibrium liquid as a multiparticle system, an ensemble of atoms and molecules [42]. In this case, it is convenient to use the mathematical apparatus of correlation functions, distribution functions, moments, and cumulants of these functions to describe both structural and dynamical properties of this liquid [43][44][45][46].…”

“…where the coefficients A T 1 (k) and A T 2 (k) are defined by (37b) and (37c). We note several important properties of expression (42). First, because the spectral density can take only nonnegative values, C T (k, ω) ≥ 0, the relation between the frequency parameters ∆ 2 T, 3 (k) and ∆ 2 T, 4 (k)…”

“…Second, for a fixed k, the form of the spectrum C T (k, ω) is defined by the biquadratic polynomial in the denominator in (42). Almost all features of the spectrum C T (k, ω) can be rather easily determined in the framework of the usual mathematical analysis of (42).…”

“…Finally, expression (42) allows estimating the values of physical quantities characterizing the propagation of shear oscillations in a liquid: the propagation velocity v (T ) and the damping coefficient Γ (T ) of transverse sound oscillations. Hence, for the velocity v (T ) , from dispersion relation (44b), we obtain…”