Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Improved quasiparticle wave functions and mean field for G(0)W(0) calculations: Initialization with the COHSEX operator

The GW approximation to the electron self-energy has become a standard method for ab initio calculation of excited-state properties of condensed-matter systems. In many calculations, the G W self-energy operator, E, is taken to be diagonal in the density functional theory (DFT) Kohn-Sham basis within the G0 W0 scheme. However, there are known situations in which this diagonal Go Wo approximation starting from DFT is inadequate. We present two schemes to resolve such problems. The first, which we called sc-COHSEX-PG W, involves construction of an improved mean field using the static limit of GW, known as COHSEX (Coulomb hole and screened exchange), which is significantly simpler to treat than GW W. In this scheme, frequency-dependent self energy E(N), is constructed and taken to be diagonal in the COHSEX orbitals after the system is solved self-consistently within this formalism. The second method is called off diagonal-COHSEX G W (od-COHSEX-PG W). In this method, one does not self-consistently change the mean-field starting point but diagonalizes the COHSEX Hamiltonian within the Kohn-Sham basis to obtain quasiparticle wave functions and uses the resulting orbitals to construct the G W E in the diagonal form. We apply both methods to a molecular system, silane, and to two bulk systems, Si and Ge under pressure. For silane, both methods give good quasiparticle wave functions and energies. Both methods give good band gaps for bulk silicon and maintain good agreement with experiment. Further, the sc-COHSEX-PGW method solves the qualitatively incorrect DFT mean-field starting point (having a band overlap) in bulk Ge under pressure.

Evidence of clustering in an aqueous electrolyte solution: a small-angle X-ray scattering study

The work reported hen was motivated by a desire to verify the existence of structure - specifically MP-rich clusters induced by sodium bromide (NaBr) in the ternary liquid mixture 3-methylpyridine (Mf) + water(W) + NaBr. We present small-angle X-ray scattering (SAXS) measurements in this mixture. These measurements were obtained at room temperature (similar to 298 K) in the one-phase region (below the relevant lower consolute points, T(L)s) at different values of X (i.e., X = 0.02 - 0.17), where X is the weight fraction of NaBr in the mixture. Cluster-size distribution, estimated on the assumption that the clusters are spherical, shows systematic behaviour in that the peak of the distribution shifts rewards larger values of cluster radius as X increases. The largest spatial extent of the clusters (similar to 4.5 nm) is seen at X = 0.17. Data analysis assuming arbitrary shapes and sizes of clusters gives a limiting value of cluster size (- 4.5 nm) that is not very sensitive to X. It is suggested that the cluster size determined may not be the same as the usual critical-point fluctuations far removed from the critical point (T-L). The influence of the additional length scale due to clustering is discussed from the standpoint of crossover from Ising to mean-field critical behaviour, when moving away from the T-L.

Universality in the fast orientational relaxation near isotropic-nematic transition

Detailed molecular dynamics simulations of Lennard-Jones ellipsoids have been carried out to investigate the emergence of criticality in the single-particle orientational relaxation near the isotropic-nematic (IN) phase transition. The simulations show a sudden appearance of a power-law behavior in the decay of the second-rank orientational relaxation as the IN transition is approached. The simulated value of the power-law exponent is 0.56, which is larger than the mean-field value (0.5) but less than the observed value (0.63) and may be due to the finite size of the simulated system. The decay of the first-rank orientational time correlation function, on the other hand, is nearly exponential but its decay becomes very slow near the isotropic-nematic transition, The zero-frequency rotational friction, calculated from the simulated angular Velocity correlation function, shows a marked increase near the IN transition.

Dipolar reorientation and phase-transition in mixed alkali-halide crystals

We show that the results of Lüty and Ortiz-Lopez relating the cyanide reorientation rates to the high-temperature phase diagrams of alkali-halide-alkali-cyanide mixed crystals can be understood within simple mean-field theory.

Adsorption isotherms for neutral organic compounds-A hierarchy in modelling: Part II

A two-state model allowing for size disparity between the solvent and the adsorbate is analysed to derive the adsorption isotherm for electrosorption of organic compounds. Explicity, the organic adsorbate is assumed to occupy "n" lattice sites at the interface as compared to "one" by the solvent. The model parameters are the respective permanent and induced dipole moments apart from the nearest neighbour distance. The coulombic interactions due to permanent and induced dipole moments, discreteness of charge effects, and short-range and specific substrate interactions have all been incorporated. The adsorption isotherm is then derived using mean field approximation (MFA) and is found to be more general than the earlier multi-site versions of Bockris and Swinkels, Mohilner et al., and Bennes, as far as the entropy contributions are concerned. The role of electrostatic forces is explicity reflected in the adsorption isotherm via the Gibbs energy of adsorption term which itself is a quadratic function of the electrode charge-density. The approximation implicit in the adsorption isotherm of Mohilner et al. or Bennes is indicated briefly.

Adsorption isitherms for neutral organic compounds-A hierarchy in modelling: Part IV. Charge of maximum adsorption-Statistical mechanical basis

The charge at which adsorption of orgamc compounds attains a maximum ( \sigma MAX M) at an electrochenucal interface is analysed using several multi-state models in a hierarchical manner The analysis is based on statistical mechamcal results for the following models (A) two-state site parity, (B) two-state muhl-slte, and (C) three-state site parity The coulombic interactions due to permanent and reduced dipole effects (using mean field approximation), electrostatic field effects and specific substrate interactions have been taken into account. The simplest model in the hierarchy (two-state site parity) yields the exphcit dependence of ( \sigma MAX M) on the permanent dipole moment, polarizability of the solvent and the adsorbate, lattice spacing, effective coordination number, etc Other models in the baerarchy bring to hght the influence of the solvent structure and the role of substrate interactions, etc As a result of this approach, the "composition" of oM.x m terms of the fundamental molecular constants becomes clear. With a view to use these molecular results to maxamum advantage, the derived results for ( \sigma MAX M) have been converted into those involving experimentally observable parameters lake Co, C 1, E N, etc Wherever possible, some of the earlier phenomenologlcal relations reported for ( \sigma MAX M), notably by Parsons, Damaskm and Frumkln, and Trasattl, are shown to have a certain molecular basis, vlz a simple two-state sate panty model.As a corollary to the hxerarcbacal modelling, \sigma MAX M and the potential corresponding to at (Emax) are shown to be constants independent of 0max or Corg for all models The lmphcatlon of our analysis f o r OmMa x with respect to that predicted by the generalized surface layer equation (which postulates Om~ and Ema x varlaUon with 0) is discussed in detail Finally we discuss an passing o M. and the electrosorptlon valency an this context.

Adsorption isotherms-Microscopic modelling: Part II

A lattice formahsm using "spin variables" is employed to analyse multi-state models for the adsorption of neutral dipoles.In particular, a spin-1/2 (two-state) model incorporating permanent and reduced dipole moments of the solvent and the organic adsorbate,substrate interactions, and &screteness of charge effects is analysed The resulting Generalized Islng Hamaltonian is solved under mean field approximation (MFA) in order to derive the adsorption isotherm for organic molecules A few spin-1 (three-state) models are also analysed under MFA to describe the competitive adsorption of multi-state solvent and organic dipoles, and the appropriate equilibrium relations are derived The unification and isomorphism existing at the Hamlltonlan level for several diverse realizations, such as adsorption of ions and solvent/orgamc molecules, is indicated The possibility of analysing phase transitions using this generalized approach is briefly indicated.

Theoretical description of time-resolved pump/probe photoemission in TaS2: a single-band DFT+DMFT(NRG) study within the quasiequilibrium approximation

In this work, we theoretically examine recent pump/probe photoemission experiments on the strongly correlated charge-density-wave insulator TaS2.We describe the general nonequilibrium many-body formulation of time-resolved photoemission in the sudden approximation, and then solve the problem using dynamical mean-field theory with the numerical renormalization group and a bare density of states calculated from density functional theory including the charge-density-wave distortion of the ion cores and spin-orbit coupling. We find a number of interesting results: (i) the bare band structure actually has more dispersion in the perpendicular direction than in the two-dimensional planes; (ii) the DMFT approach can produce upper and lower Hubbard bands that resemble those in the experiment, but the upper bands will overlap in energy with other higher energy bands; (iii) the effect of the finite width of the probe pulse is minimal on the shape of the photoemission spectra; and (iv) the quasiequilibrium approximation does not fully describe the behavior in this system.

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

The two-dimensional,q-state (q>4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.

Theory of the mixed valent state

After briefly discussing the question of a distinct mixed valent state and theoretical models for it, the area of greatest theoretical success, namely the mixed valent impurity, is reviewed. Applications to spectroscopy, energetics and Hall effect are then putlined. The independent impurity approximation is inadequate for many properties of the bulk system, which depend on lattice coherence. A recent auxiliary or slave boson approach with a simple mean field limit and fluctuation corrections is summarized. Finally the mixed valent semiconductor is discussed as an outstanding problem.

State Dependent Attempt Rate Modeling of Single Cell IEEE 802.11 WLANs with Homogeneous Nodes and Poisson Arrivals

Analytical models of IEEE 802.11-based WLANs are invariably based on approximations, such as the well-known mean-field approximations proposed by Bianchi for saturated nodes. In this paper, we provide a new approach for modeling the situation when the nodes are not saturated. We study a State Dependent Attempt Rate (SDAR) approximation to model M queues (one queue per node) served by the CSMA/CA protocol as standardized in the IEEE 802.11 DCF. The approximation is that, when n of the M queues are non-empty, the attempt probability of the n non-empty nodes is given by the long-term attempt probability of n saturated nodes as provided by Bianchi's model. This yields a coupled queue system. When packets arrive to the M queues according to independent Poisson processes, we provide an exact model for the coupled queue system with SDAR service. The main contribution of this paper is to provide an analysis of the coupled queue process by studying a lower dimensional process and by introducing a certain conditional independence approximation. We show that the numerical results obtained from our finite buffer analysis are in excellent agreement with the corresponding results obtained from ns-2 simulations. We replace the CSMA/CA protocol as implemented in the ns-2 simulator with the SDAR service model to show that the SDAR approximation provides an accurate model for the CSMA/CA protocol. We also report the simulation speed-ups thus obtained by our model-based simulation.

Appearance of "Fragile" Fermi Liquids in Finite-Width Mott Insulators Sandwiched between Metallic Leads

Using inhomogeneous dynamical mean-field theory, we show that the normal-metal proximity effect could force any finite number of Mott-insulating "barrier" planes sandwiched between semi-infinite metallic leads to become "fragile" Fermi liquids. They are fully Fermi-liquid-like at T=0, leading to a restoration of lattice periodicity at zero frequency, with a well-defined Fermi surface, and perfect (ballistic) conductivity. However, the Fermi-liquid character can rapidly disappear at finite omega, V, T, disorder, or magnetism, all of which restore the expected quantum tunneling regime, leading to fascinating possibilities for nonlinear response in devices.

Long-range Coulomb interactions and nanoscale electronic inhomogeneities in correlated oxides

Electronic, magnetic, or structural inhomogeneities ranging in size from nanoscopic to mesoscopic scales seem endemic and are possibly generic to colossal magnetoresistance manganites and other transition metal oxides. They are hence of great current interest and understanding them is of fundamental importance. We show here that an extension, to include long-range Coulomb interactions, of a quantum two-fluid l-b model proposed recently for manganites [Phys. Rev. Lett. 92, 157203 (2004)] leads to an excellent description of such inhomogeneities. In the l-b model two very different kinds of electronic states, one localized and polaronic (l) and the other extended or broad band (b) coexist. For model parameters appropriate to manganites and even within a simple dynamical mean-field theory (DMFT) framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance (CMR), qualitatively and quantitatively. However, in the absence of long-ranged Coulomb interaction, a system described by such a model would actually phase separate, into macroscopic regions of l and b electrons, respectively. As we show in this paper, in the presence of Coulomb interactions, the macroscopic phase separation gets suppressed and instead nanometer scale regions of polarons interspersed with band electron puddles appear, constituting a kind of quantum Coulomb glass. We characterize the size scales and distribution of the inhomogeneity using computer simulations. For realistic values of the long-range Coulomb interaction parameter V-0, our results for the thresholds for occupancy of the b states are in agreement with, and hence support, the earlier approach mentioned above based on a configuration averaged DMFT treatment which neglects V-0; but the present work has features that cannot be addressed in the DMFT framework. Our work points to an interplay of strong correlations, long-range Coulomb interaction, and dopant ion disorder, all inevitably present in transition metal oxides as the origin of nanoscale inhomogeneities rather than disorder frustrated phase competition as is generally believed. As regards manganites, it argues against explanations for CMR based on disorder frustrated phase separation and for an intrinsic origin of CMR. Based on this, we argue that the observed micrometer (meso) scale inhomogeneities owe their existence to extrinsic causes, e.g., strain due to cracks and defects. We suggest possible experiments to validate our speculation.

A theoretical model for the magnetic helicity of solar active regions

Active regions on the solar surface are known to possess magnetic helicity, which is predominantly negative in the northern hemisphere and positive in the southern hemisphere. Choudhuri et al. [Choudhuri, A.R. On the connection between mean field dynamo theory and flux tubes. Solar Phys. 215, 31–55, 2003] proposed that the magnetic helicity arises due to the wrapping up of the poloidal field of the convection zone around rising flux tubes which form active regions. Choudhuri [Choudhuri, A.R., Chatterjee, P., Nandy, D. Helicity of solar active regions from a dynamo model. ApJ 615, L57–L60, 2004] used this idea to calculate magnetic helicity from their solar dynamo model. Apart from getting broad agreements with observational data, they also predict that the hemispheric helicity rule may be violated at the beginning of a solar cycle. Chatterjee et al. [Chatterjee, P., Choudhuri, A.R., Petrovay, K. Development of twist in an emerging magnetic flux tube by poloidal field accretion. A&A 449, 781–789, 2006] study the penetration of the wrapped poloidal field into the rising flux tube due to turbulent diffusion using a simple 1-d model. They find that the extent of penetration of the wrapped field will depend on how weak the magnetic field inside the rising flux tube becomes before its emergence. They conclude that more detailed observational data will throw light on the physical conditions of flux tubes just before their emergence to the photosphere.