It has been known for some time that the exchange-correlation potential in time-dependent densityfunctional theory is an intrinsically nonlocal functional of the density as soon as one goes beyond the adiabatic approximation. In this paper we show that a much more severe nonlocality problem, with a completely different physical origin, plagues the exchange-correlation potentials in time-dependent spin-density functional theory. We show how the use of the spin current density as a basic variable solves this problem, and we provide an explicit local expression for the exchange-correlation fields as functionals of the spin currents. DOI: 10.1103/PhysRevLett.90.066402 PACS numbers: 71.15.Mb, 71.10.Ca, 71.45.Gm For many years the local density approximation (LDA) has provided the much needed handle on the difficult problem of approximating the density dependence of the exchange-correlation (xc) potential-the single particle potential that incorporates the many-body effects in the Kohn-Sham equation for the ground state density [1]. In LDA, the xc potential V xc r r is simply a function of the local density nr r . This approximation is not unreasonable as long as the functional derivative of V xc r r with respect to nr r 0 -the so-called exchange-correlation kernel f xc r r;r r 0 V xc r r = nr r 0 -is a sufficiently shortranged function of the distance jr r ÿr r 0 j [2].However, much recent work [3][4][5][6][7] has demonstrated that the requirement of short rangedness is not always fulfilled in physical systems, and when this happens the local density approximation is flawed. This does not mean that a local description of exchange and correlation is absolutely impossible, only that such a description cannot be achieved in terms of the particle density.For example, in the density-functional theory of crystalline insulators it has been found [4-6] that the xc potential has an ''ultranonlocal'' dependence on the density, due to the fact that the Fourier transform of the xc kernel f xc k k;k k diverges as 1=k 2 for k ! 0. But, the ultranonlocality disappears if one reformulates the theory in terms of the electric polarizationP Pr r and the exchangecorrelation electric fieldẼ E xc r r associated with it. Another instance of the ultranonlocality problem was discovered in the time-dependent density-functional theory (TDDFT) [8] following the realization that the frequency-dependent LDA [9] fails to satisfy Kohn's theorem [10,11]. The pathology was traced to a singularity of the formk kk k 0 k 2 in the xc kernel f xc k k;k k 0 ; ! for k ! 0 at finitek 0 k 0 and !. The ensuing nonlocality problem was solved by upgrading to time-dependent current-density functional theory (TDCDFT), where the basic variable is the current density, and its conjugate field is a vector potential [3]. TDCDFT has since been applied to the calculation of the optical spectra of solids [12] and the polarizability of long polymer chains [13] with considerable success.In this Letter we show that the ultranonlocality problem occurs in an aggravated for...

Long range dewetting forces acting across thin films, such as the fundamental van der Waals interactions, may drive the formation of large clusters (tall multilayer islands) and pits, observed in thin films of diverse materials such as polymers, liquid crystals, and metals. In this study we further develop the methodology of the nonequilibrium statistical mechanics of thin films coarsening within continuum interface dynamics model incorporating long range dewetting interactions. The theoretical test bench model considered here is a generalization of the classical Mullins model for the dynamics of solid film surfaces. By analytic arguments and simulations of the model, we study the coarsening growth laws of clusters formed in thin films due to the dewetting interactions. The ultimate cluster growth scaling laws at long times are strongly universal: Short and long range dewetting interactions yield the same coarsening exponents. However, long range dewetting interactions, such as the van der Waals forces, introduce a distinct long lasting early time scaling behavior characterized by a slow growth of the cluster height/lateral size aspect ratio (i.e., a time-dependent Young angle) and by effective coarsening exponents that depend on cluster size. In this study, we develop a theory capable of analytically calculating these effective size-dependent coarsening exponents characterizing the cluster growth in the early time regime. Such a pronounced early time scaling behavior has been indeed seen in experiments; however, its physical origin has remained elusive to this date. Our theory attributes these observed phenomena to ubiquitous long range dewetting interactions acting across thin solid and liquid films. Our results are also applicable to cluster growth in initially very thin fluid films, formed by depositing a few monolayers or by a submonolayer deposition. Under this condition, the dominant coarsening mechanism is diffusive intercluster mass transport while the cluster coalescence plays a minor role, both in solid and in fluid films.

One contribution of 13 to a theme issue 'The major synthetic evolutionary transitions'. We review lessons learned about evolutionary transitions from a bottom-up construction of minimal life. We use a particular systemic protocell design process as a starting point for exploring two fundamental questions: (i) how may minimal living systems emerge from non-living materials? and (ii) how may minimal living systems support increasingly more evolutionary richness? Under (i), we present what has been accomplished so far and discuss the remaining open challenges and their possible solutions. Under (ii), we present a design principle we have used successfully both for our computational and experimental protocellular investigations, and we conjecture how this design principle can be extended for enhancing the evolutionary potential for a wide range of systems.This article is part of the themed issue 'The major synthetic evolutionary transitions'.

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