Theory of quadratic response

Dynamical Structure Functions, Collective Modes, and Energy Gap in Charged-Particle Bilayers

“…For p ÿ we exploited the fact that P 0 ÿ is identical to the static structure function S ÿ k 0 [7] and that P 1 ÿ is expressible in terms of P 0 ÿ . Borrowing the value of S ÿ k 0 from our earlier static simulation data [17], we have found reasonable numerical agreement between theoretically calculated and measured values of the coefficients, as indicated in Fig. 3(c).…”

Isomorph-based empirically modified hypernetted-chain approach for strongly coupled Yukawa one-component plasmas

“…The proposed isomorph-based empirically modified hypernetted-chain approximation exhibits excellent agreement with computer simulations of dense YOCP liquids. Despite the fact that this approach does not involve tunable or adjustable parameters, it performs consistently better than other rigorous integral theory approximations previously employed for the YOCP [29][30][31][32][33][34] as far as thermodynamic properties and structural quantities are concerned. The generalization of the proposed approach to a broader class of strongly coupled systems beyond the YOCP is discussed and possible further improvements are suggested.…”

“…As a consequence, simple analytical expres-sions have been proposed that allow for an accurate estimation of fundamental thermodynamic properties [27] and even of reduced particle distribution functions [28]. On the theoretical front, the static YOCP characteristics have been investigated with various integral theory methods including the hypernetted-chain [29], the soft mean spherical [30,31], the discretized Rogers-Young [32], the variational modified hypernetted-chain [33] and the empirically modified hypernetted-chain approximations [34] as well as with semi-phenomenological approaches such as the Debye-Hückel plus hole [35] and ion sphere models [36]. It is also worth pointing out that static properties constitute necessary input for advanced theoretical descriptions of dynamic characteristics; for instance the quasi-localized charge approximation of collective modes requires knowledge of the pair correlation function [37], whereas the viscoelastic-dynamic density functional theory of wave dispersion [38], the non perturbative modelfree moment approach of dynamic density-density correlations [39] and the mode coupling theory of the glass transition [40] require knowledge of the structure factor.…”

Quadratic density response function of a two dimensional electron gas

“…As a matter of fact, this vanishing feature in a 2DEG is not entirely unexpected but required by the quadratic compressibility sum rule [26,27,18] lim…”

“…The notation of Eq. (19) means that the imaginary part of the static vðk 1 ; k 2 Þ is simply zero. For a given angle of b 12 , the real part v 0 ðk 1 ; k 2 Þ can be plotted in the Cartesian coordinates ðk 1 ; k 2 Þ.…”