Boundary Driven Zero-Range Processes in Random Media

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the stationary state is found to be trivial in absence of boundary drive. Out of equilibrium, two further cases are distinguished according to the tail of the disorder distribution. For strong disorder, the fugacity profiles are found to be governed by the paths of normalized α-stable subordinators. The expectations of integrated functions of the tagged particle position are calculated for three types of routes.     

在无标度网络上基于偏好聚集机理的零区域凝聚现象

为了理解在真实网络中偏好聚集机理如何影响交通输运系统的粒子稳定态分布,研究了基于偏好聚集机理的零区域作用(zero range process,ZRP)凝聚现象.与以往采用巨正则系综方法处理ZRP问题不同,通过平均场速率方程解析得到了系统的相变点和稳定态分布情况.研究发现当存在正偏好聚集时,随着粒子跳跃速率的增大,系统呈现出三种不同的相：完全凝聚相、部分凝聚相、均匀相;当存在负偏好聚集机理时,系统只出现两相：部分凝聚相、均匀相.不同于无权与加权网络交通情况,系统的稳定态分布依赖于边权、粒子跳跃速率以及偏好 关键词： 无标度网络 零区域作用 偏好聚集 平均场速率方程     

Spontaneous pattern formation in a polariton condensate

Exciton-polariton condensation can be regarded as a self-organization phenomenon, where phase ordering is established among particles in the system. In such condensed systems, further ordering can occur in the particle density distribution, under particular experimental conditions. In this work we report on spontaneous pattern formation in a polariton condensate under nonresonant optical pumping. The slightly elliptical ring-shaped excitation laser that we employ forces condensation to occur into a single-energy state with periodic boundary conditions, giving rise to a multilobe standing-wave patterned state.     

Physics of <Emphasis Type="Italic">π</Emphasis>-meson condensation and high temperature cuprate superconductors

The idea of condensation of the Goldstone π-meson field in nuclear matter had been put forward a long time ago. However, it was established that the normal nuclear density is too low, it is not sufficient to condensate π mesons. This is why the π condensation has never been observed. Recent experimental and theoretical studies of high-temperature cuprate superconductors have revealed condensation of Goldstone magnons, the effect fully analogous to the π condensation. The magnon condensation has been observed. It is clear now that quantum fluctuations play a crucial role in the condensation, in particular they drive a quantum phase transition that destroys the condensate at some density of fermions. The text was submitted by the author in English.     

Ring diagrams,Landau parameters,pion condensation and the binding energy of nuclear matter

We calculate all direct π-exchange ring diagrams to arbitrary orders in nuclear matter. Our model incorporates intermediate Δ(1236) resonances, correlations, ρ- as well as π-meson exchange and mesonic form factors. We find that the convergence of the diagram summation is governed by two quantities which have an immediate physical interpretation: the Landau parameter G'₀ and the threshold for pion condensation. The contribution to the energy of nuclear matter from terms of third and higher order is 2 MeV/particle (repulsion) at normal density, with a strong density dependence.     

Bose-Einstein condensation at finite momentum and magnon condensation in thin film ferromagnets

We use the Gross-Pitaevskii equation to determine the spatial structure of the condensate density of interacting bosons whose energy dispersion ϵ _k has two degenerate minima at finite wave-vectors ± q. We show that in general the Fourier transform of the condensate density has finite amplitudes for all integer multiples of q. If the interaction is such that many Fourier components contribute, the Bose condensate is localized at the sites of a one-dimensional lattice with spacing 2 π/|q|; in this case Bose-Einstein condensation resembles the transition from a liquid to a crystalline solid. We use our results to investigate the spatial structure of the Bose condensate formed by magnons in thin films of ferromagnets with dipole-dipole interactions.     

Density of states in the bilayer graphene with the excitonic pairing interaction

In the present paper, we consider the excitonic effects on the single particle normal density of states (DOS) in the bilayer graphene (BLG). The local interlayer Coulomb interaction is considered between the particles on the non-equivalent sublattice sites in different layers of the BLG. We show the presence of the excitonic shift of the neutrality point, even for the noninteracting layers. Furthermore, for the interacting layers, a very large asymmetry in the DOS structure is shown between the particle and hole channels. At the large values of the interlayer hopping amplitude, a large number of DOS at the Dirac’s point indicates the existence of the strong excitonic coherence effects between the layers in the BLG and the enhancement of the excitonic condensation. We have found different competing orders in the interacting BLG. Particularly, a phase transition from the hybridized excitonic insulator phase to the coherent condensate state is shown at the small values of the local interlayer Coulomb interaction.     

Front Propagation Dynamics with Exponentially-Distributed Hopping

We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B → 2A reaction. We find that the effect of fluctuations is especially pronounced at small hopping rates. Fluctuations are treated heuristically via a density cutoff in the reaction rate. We then consider the case of propagating up a reaction rate gradient. The effect of fluctuations here is pronounced, with the front velocity increasing without limit with increasing bulk particle density. The rate of increase is faster than in the case of a reaction-gradient with nearest-neighbor hopping. We derive analytic expressions for the front velocity dependence on bulk particle density. Computer simulations are performed to confirm the analytical results.     

<Emphasis Type="Italic">Ab initio</Emphasis> study of a Y-doped ∑31 grain boundary in alumina

The atomic structures and energetics of clean and Y-doped general grain boundary (GB) ∑31/(0001) models in α-Al₂O₃ are studied by a series of high precision ab initio calculations. A large supercell with 700 atoms and periodic boundary conditions is adopted for undoped and Y-doped GB with different substitution sites and concentrations. It is shown that Y atoms preferably segregate to the central column of the 7-member Al ring. This is explained as more favorable bond formation for Y in this position and lower GB energy. The calculated GB formation energy for the clean and Y-doped cases is respectively 3.99 and 3.67 J/m². On the average, the GB region in ∑31 has a slightly lower charge density than the bulk crystalline region. In addtition, the GB induces a long ranged asymmetric electrostatic potential distribution on each side of the grain boundary.     

A Fleming–Viot Particle Representation¶of the Dirichlet Laplacian

We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. For large N, the particle distribution density converges to the normalized heat equation solution in D with Dirichlet boundary conditions. The stationary distributions converge as N→∞ to the first eigenfunction of the Laplacian in D with the same boundary conditions. Received: 11 November 1999 / Accepted: 19 May 2000     

Multiply connected Fermi sphere and fermion condensation

We examine the structure of the ground state of a homogeneous Fermi liquid beyond the instability point of the Fermi-like quasiparticle momentum distribution in the effective-functional method with a strong repulsive effective interaction. A numerical study of the initial stage of rearrangement of the ground state, based on a simple effective functional, showed that there exists a temperature T ₀, above which the behavior of the system is the same as in the theory of fermion condensation, and for T<T ₀ the scenario of rearrangement of the ground state is different. At low temperatures an intermediate structure arises, with a multiply connected quasiparticle momentum distribution. The transition of this structure with growth of the coupling constant to a state with a fermion condensate is discussed. Zh. éksp. Teor. Fiz. 114, 2078–2088 (December 1998)     

Duality relations for asymmetric exclusion processes

We derive duality relations for a class ofU _q [SU(2)]-symmetric stochastic processes, including among others the asymmetric exclusion process in one dimension. Like the known duality relations for symmetric hopping processes, these relations express certainm-point correlation functions inN-particle systems (Nm) in terms of sums of correlation functions of the same system but with onlym particles. For the totally asymmetric case we obtain exact expressions for some boundary density correlation functions. The dynamical exponent for these correlators isz=2, which is different from the dynamical exponent for bulk density correlations, which is known to bez=3/2.     

Dark Matter as a Cosmic Bose-Einstein Condensate and Possible Superfluid

Dark matter arising from spontaneous symmetry breaking of a neutral scalar field coupled to gravity comprises ultra low mass bosons with a Bose-Einstein condensation temperature far above the present background temperature. Assuming galactic halos to consist of a Bose-Einstein condensate of astronomical extent, we calculate the condensate coherence length, transition temperatures, mass distribution, and orbital velocity curves, and deduce the particle mass and number density from the observed rotation curves for the Andromeda and Triangulum galaxies. We also consider the possibility of superfluid behaviour in the halos of rotating galaxies, and estimate the critical angular frequency and line density for formation of quantised vortices.     

The role of the interfacial SiOx layer in SnO2/n-Si photocells

It is proposed that the charge transport across the SiO _x layer at the interface SnO₂/Si proceeds by a hopping mechanism. During heat treatment of the photovoltaic cells, in air, chemical reactions occur with O₂/H₂O, which lead to a drastic reduction of the density of hopping sites near the Si conduction band edge. The SiO _x hopping sites of energy near the valence band edge are less affected by these chemical reactions. Thus, photogenerated holes can still pass the barrier while the dark current flow is strongly inhibited.     

Small polaron hopping conduction mechanism in Ni-doped LaFeO3

The electrical transport properties of LaFe_{1? x} Ni _x O₃ (0.1 ≤ x ≤ 0.6) bulk samples were investigated over a wide temperature range, i.e. 9–300 K. Powder x-ray diffraction patterns at room temperature showed that all samples were formed in a single phase. However, a structural transformation was observed from orthorhombic (Pnma) to rhombohedral crystal symmetry at x > 0.5 in Ni-doped samples, which is supported by the electrical transport analysis. Temperature-dependent resistivity data were fitted using Mott's variable-range hopping model for a limited range of temperatures to calculate the hopping distance and the density of states at Fermi level. It was found that all parameters vary systematically with an increase in Ni concentration. Moreover, the resistivity data were also fitted using the small polaron hopping (SPH) model. The non-adiabatic SPH conduction mechanism is followed up to 50% Ni concentration, whereas an adiabatic hopping conduction mechanism is active above it. Such a change in the conduction mechanism is accompanied by subtle electronically induced structural changes involving Fe³⁺–O–Fe³⁺ and Fe³⁺–O–Ni³⁺ bond angles and bond lengths. Thus, we suggest that the transport properties can be explained according to the additional delocalization of charge carriers induced by Ni doping.     

Canonical Analysis of Condensation in Factorised Steady States

We study the phenomenon of real space condensation in the steady state of a class of mass transport models where the steady state factorises. The grand canonical ensemble may be used to derive the criterion for the occurrence of a condensation transition but does not shed light on the nature of the condensate. Here, within the canonical ensemble, we analyse the condensation transition and the structure of the condensate, determining the precise shape and the size of the condensate in the condensed phase. We find two distinct condensate regimes: one where the condensate is gaussian distributed and the particle number fluctuations scale normally as L ^1/2 where L is the system size, and a second regime where the particle number fluctuations become anomalously large and the condensate peak is non-gaussian. Our results are asymptotically exact and can also be interpreted within the framework of sums of random variables. We further analyse two additional cases: one where the condensation transition is somewhat different from the usual second order phase transition and one where there is no true condensation transition but instead a pseudocondensate appears at superextensive densities. PACS numbers: 05.40.-a, 02.50.Ey, 64.60.-i.     

Role of next-nearest-neighbour hopping in the internal structure of the ground state and finite temperature quantities of 2D t-J model

An exact diagonalization calculation for a small cluster in the two-dimensional t-J model has been studied to calculate two-hole correlation. Calculations reveal dominant hole-hole correlation for holes sitting on next-nearest-neighbour (NNN) sites and critical coupling occurs at J/t = 0.8. With the increase in negative-type NNN hopping, correlation decreases at NNN sites whereas it increases at other sites. The thermodynamic properties such as entropy and specific heat are studied as functions of temperature with various NNN hopping strength. Results show that with the inclusion of negative NNN hopping, the system becomes more ordered. A qualitative transition temperature region has been estimated. It is shown that with the increase in NNN hopping strength, T _c increases. Specific heat results show non-Fermi liquid-type behaviour of the system. All our calculations establish the importance of negative-type NNN hopping.     

All-electron study of ultra-incompressible superhard material ReB2: structural and electronic properties

This paper investigates the structural and electronic properties of rhenium diboride by first-principles calculation based on density functional theory. The obtained results show that the calculated equilibrium structural parameters of ReB2 are in excellent agreement with experimental values. The calculated bulk modulus is 361 GPa in comparison with that of the experiment. The compressibility of ReB2 is lower than that of well-known OsB2. The anisotropy of the bulk modulus is confirmed by c/a ratio as a function of pressure curve and the bulk modulus along different axes along with the electron density distribution. The high bulk modulus is attributed to the strong covalent bond between Re-d and B-p orbitals and the wider pseudogap near the Fermi level, which could be deduced from both electron charge density distribution and density of states. The band structure and density of states of ReB2 exhibit that this material presents metallic behavior. The good metallicity and ultra-incompressibility of ReB2 might suggest its potential application as pressure-proof conductors.     

Mott Law as Lower Bound for a Random Walk in a Random Environment

We consider a random walk on the support of an ergodic stationary simple point process on ℝ^d, d≥2, which satisfies a mixing condition w.r.t. the translations or has a strictly positive density uniformly on large enough cubes. Furthermore the point process is furnished with independent random bounded energy marks. The transition rates of the random walk decay exponentially in the jump distances and depend on the energies through a factor of the Boltzmann-type. This is an effective model for the phonon-induced hopping of electrons in disordered solids within the regime of strong Anderson localization. We show that the rescaled random walk converges to a Brownian motion whose diffusion coefficient is bounded below by Mott's law for the variable range hopping conductivity at zero frequency. The proof of the lower bound involves estimates for the supercritical regime of an associated site percolation problem.