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The transport of photoinjected charges in disordered organic films is often interpreted using a formula based on a Gaussian disorder model (GDM) that neglects spatial correlations due to chargedipole interactions, even though such correlations have recently been shown to explain the universal electric field dependence observed in these systems. Based on extensive computer simulations of a 3D disorder model that includes such correlations, we present a new formula for analyzing experiments that accurately describes transport in these materials. [S0031-9007(98)07626-1] PACS numbers: 73.50.Yg, 72.10.Bg, 72.80.LeRecent efforts by a number of workers [1-7] have increased our understanding of nearly universal features of photoinjected charge transport in many disordered organic materials, including molecularly doped polymers [8,9], low molecular weight organic glasses [10,11], and certain polyconjugated polymers [12,13]. In particular, it is now recognized that the Poole-Frenkel (PF) dependence [8][9][10][11][12], m~exp͑gof the drift mobility m on electric field E observed in these materials results from slowly varying spatial fluctuations in the potential energy of a charge migrating through the material. Such energetic fluctuations can arise [1] from a random distribution of molecules in the medium possessing permanent electric dipole moments; a carrier's interaction with the latter provides a significant contribution U d to the total site energy. More importantly, the energy correlation function [1,3] C͑r͒ ͗U d ͑0͒U d ͑r͒͘ ϳ s 2 d a͞r (2) decays very slowly with intersite separation r. Here, s d ͗U 2 d ͘ 1͞2 is the rms width of the dipolar energetic disorder, and a is a minimal charge-dipole separation. In a previous Letter [3], an analytical result equivalent to (1) was derived for carriers diffusing along one spatial dimension through a medium with correlations as in (2). This same behavior was also observed in 3D charge transport simulations [4]. Moreover, very recent studies on both 1D and 3D systems suggest that this mechanism producing PF behavior is stable under additional sources of disorder less correlated than those that arise from dipoles [5,6], and indicate that the PF factor g in (1) is insensitive to all but the dipolar component of the disorder.These recent advances raise questions regarding the way materials have been experimentally characterized in the past. Most measurements in the last decade have been interpreted using an uncorrelated Gaussian disorder model, developed and extensively studied by Bässler and co-workers prior to the recent recognition of the importance of spatial correlations [14]. In the GDM, transport occurs through hops among localized states characterized by a Gaussian distribution of site energies, with hopping rates obeying an asymmetric detailed balance relation [14]. Numerical simulations capture well many features of experiment; its Gaussian density of states (DOS) leads to a temperature dependence ln m~2͑T 0 ͞T͒ 2 routinely observed, and the GDM reproduces low temperature...

A simple tractable theory of vibrational relaxation of polyatomic molecules in polyatomic solvents, which is also applicable to solid solutions, is presented. The theory takes as its starting point Fermi's golden rule, avoids additional assumptions such as the rotating wave or random phase approximations, and treats both the internal degrees of freedom of the relaxing molecule and the bath degrees of freedom in a fully quantum mechanical manner. The results yield intuitively understandable expressions for the relaxation rates. The treatment of the annihilation as well as the creation of all participating bosons allows the theory to go beyond earlier analyses which treated only cascade processes. New predicted features include temperature effects and asymmetry effects in the frequency dependence. The theory is constructed in a manner which facilitates the use of recent developments in the analysis of instantaneous normal modes of liquids.

Using the general result that the mobility m of charge carriers driven in a spatially correlated random potential by an electric field E can be expressed in terms of the Laplace transform of a particular correlation function related to the random potential, we demonstrate that the exponential dependence of m on p E universally observed in molecularly doped polymers arises naturally from the interaction of charge carriers with randomly distributed permanent dipoles. [S0031-9007(96)00689-8] PACS numbers: 72.10.Bg, 72.80.Le High-field time-of-flight experiments have been used for over two decades to characterize carrier mobilities in photoexcited molecularly doped polymers and amorphous molecular glasses [1-3]. Numerous measurements over a large range of fields E and temperatures T have established that, in many materials, the carrier mobility m exhibits a universal Poole-Frenkel behavior [4]where m 0 is a temperature independent prefactor and k is Boltzmann's constant. In a particular form of this phenomenological expression proposed by Gill [5], the activation energy Q is temperature independent, and the Poole-Frenkel factor is written g B͑b 2 b 0 ͒, where b 1͞kT , and B and b 0 1͞kT 0 are constants. In a second form, motivated by extensive numerical simulations on the Gaussian disorder model (GDM) of Bässler and coworkers [2], Q͞kT ͑2s͞3kT͒ 2 , and g C͑b 2 s 2 2 S 2 ͒, where s is the width of the energetic disorder, and C and S are constants. Many recent theoretical attempts to explain this observed proportionality between lnm and p E have focused on the role played by spatial and energetic disorder [2,6-8]. The GDM, for example, describes transport as a biased random walk among dopant molecules with Gaussian-distributed random site energies [2]. Of the various mechanisms proposed as the source of this disorder, it has been shown that the interaction of charge carriers with permanent dipoles (located on either dopant or host molecules) can give rise to a Gaussian-like density of states of the type assumed in the GDM [9,10]. Considerable data establishing a relationship between carrier mobilities and group dipole moments of molecular constituents support this view of charge-dipole interactions as the source of energetic disorder in these systems [9,[11][12][13][14][15].Unfortunately, although the standard GDM satisfactorily explains many features of experiment, such as the time-of-flight transients, it displays a field dependence similar to (1) only in a relatively narrow range and only at large fields (E . 10 5 V͞cm). Indeed, a general feature of Monte Carlo simulations [2,6] and other numerical work [8] on this problem is a significant regime at low fields in which the field dependence is much weaker than that described by (1). In experiments, by contrast, the linear dependence of lnm on p E often [16] persists down to the lowest fields probed (8 3 10 3 V͞cm).In this Letter we develop an analytical theory for the field dependence based upon an idea introduced recently by Gartstein and Conwell [17]. We show, usin...

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An important characteristic of flocks of birds, school of fish, and many similar assemblies of selfpropelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system. PACS numbers: 05.70. Fh, 87.17.Jj, The collective motion of a group of autonomous particles is a subject of intense research that has potential applications in biology, physics and engineering [1,2,3]. One of the most remarkable characteristics of systems such as a flock of birds, a school of fish or a swarm of locusts, is the emergence of ordered states in which the particles move in the same direction, in spite of the fact that the interactions between the particles are (presumably) of short range. Given that these systems are generally out of equilibrium, the emergence of ordered states cannot be accounted for by the standard theorems in statistical mechanics that explain the existence of ordered states in equilibrium systems typified by ferromagnets.A particularly simple model to describe the collective motion of a group of self-propelled particles was proposed by Vicsek et al. [4]. In this model each particle tends to move in the average direction of motion of its neighbors while being simultaneously subjected to noise. As the amplitude of the noise increases the system undergoes a phase transition from an ordered state in which the particles move collectively in the same direction, to a disordered state in which the particles move independently in random directions. This phase transition was originally thought to be of second order. However, due to a lack of a general formalism to analyze the collective dynamics of the Vicsek model, the nature of the phase transition (i.e. whether it is second or first order) has been brought into question [5].In this letter we show that the nature of the phase transition can depend strongly on the way in which the noise is introduced into these systems. We illustrate this by presenting analytical results on two different network systems that are closely related to the self-propelled particle models. We show that in these two network models the phase transition switches from second to first order when the way in which the noise is introduced changes from the one presented in [4] to the one described in [5].The first network model, which we will refer to as the vectorial network model, consists of a network of N 2D-vectors (represented as complex numbers), {σ 1 = e iθ...

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We consider a model for population dynamics such as for the evolution of bacterial colonies which is of the Fisher type but where the competitive interaction among individuals is nonlocal, and show that spatial structures with interesting features emerge. These features depend on the nature of the competitive interaction as well as on its range, specifically on the presence or absence of tails in, and the central curvature of, the influence function of the interaction.