Two Hard Spheres in a Spherical Pore: Exact Analytic Results in Two and Three Dimensions

The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a relation valid for any dimension between these partition functions, second virial coefficient for inhomogeneous systems in a spherical pore, and third virial coefficients for polydisperse hard spheres mixtures. Using the established relation we were able to evaluate the cluster integral b ₂(V) related with the second virial coefficient for the Hard Disc system into a circular pore. Finally, we analyse the behaviour of the obtained expressions near the maximum density.     

Large Bipolarons in Two and Three Dimensions

The large bipolaron in two and three dimensions is investigated by combining the reasonable asymptotic relative wavefunctions and the Lee-Low-Pines-Huybrechts (LLP-H) variational method. The values of the critical coupling constant α_C above which bipolarons may exist and the critical ratio of dielectric constants η_c below which bipolarons may exist are evaluated, which are very close to the recent results obtained within totally different variational approaches. It is also found that low-dimensional materials are more favorable for the formation of bipolarons.     

Superdiffusivity of Asymmetric Exclusion Process in Dimensions One and Two

We prove that the diffusion coefficient for the asymmetric exclusion process diverges at least as fast as t ^1/4 in dimension d=1 and (logt)^1/2 in d=2. The method applies to nearest and non-nearest neighbor asymmetric exclusion processes.     

Single-Particle Momentum Distributions for Bosonic Trimer States in Two and Three Dimensions

For a system formed by three bosons interacting by a pairwise zero-range potential we show how the functional form of the asymptotic momentum distribution changes drastically when passing from bi (2D) to tridimensional (3D) regime, mainly affected by the absence/presence of the Efimov effect in 2D/3D. The spectator functions and the momentum distribution are calculated analytically for both regimes.     

Enhanced Correlation of Electron-Positron Pair in Two and Three Dimensions

Early time electron-positron correlation in vacuum pair-production in an external field is investigated. The entangled electron and positron wave functions are obtained analytically in the configuration and momentum spaces. It is shown that, relative to that of the one-dimensional theory, two- and three-dimensional calculations yield enhanced spatial correlation and broadened momentum spectra. In fact, at early times the electron and positron almost coincide spatially. The correlation also depends on the direction of the applied field. For the spatial correlation, the transverse correlation is stronger than the longitudinal correlation.     

Ground and Excited States of Bipolarons in Two and Three Dimensions

The properties of large bipolarons in two and three dimensions are investigated by averaging over the relative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method. The ground-state (GS) and excited-state energies of the Fröhlich bipolaron for the whole range of electron-phonon coupling constants can be obtained. The energies of the first relaxed excited state (RES) and Franck-Condon (FC) excited state of the bipolaron are also calculated. It is found that the first RES energy is lower than the FC state energy. The comparison of our GS and RES energies with those in literature is also given.     

Ground and Excited States of Bipolarons in Two and Three Dimensions

The properties of large bipolarons in two and three dimensions are investigated by averaging over the relative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method. The groundstate (GS) and excited-state energies of the Fr(o)hlich bipolaron for the whole range of electron-phonon coupling constants can be obtained. The energies of the first relaxed excited state (RES) and Franck-Condon (FC) excited state of the bipolaron are also calculated. It is found that the first RES energy is lower than the FC state energy. The comparison of our GS and RES energies with those in literature is also given.     

三维无网格法中权函数影响半径的优化

从函数逼近的角度建立三维无网格法中权函数影响半径的优化计算模型,针对一次基、二次基情形求解该模型.分析不同影响半径下函数的逼近误差,以及计算量、条件数等因素对无网格法计算性能的影响,结合数值试验,确认给出的权函数影响半径是有效、可靠、综合最优的.     

The Temperley-Lieb-Jones Algebra and Symmetry Group in Heisenberg Spin Models in One and Two Dimensions

We present a systematic method to construct the spin models of Heisenberg type in higher dimensions with nearesband non-nearest neighbour interactions. These models constructed in this way are of Temperley-Lieb-Jones (TLJ) algebraic structures and SU(2)-invariances. The TLJ algebra is generalized to adjusting the lattice spin models. The Hamiltonians of Heisenberg spin models in one dimension (including second nearest neighbour interactions) and in two-dimensional triangular lattice (with nearest interaction) are constructed explicitly. The hidden symmetries are shown to be the SU(2) group, and the terms in Ilamiltonian for different lattice cells are explicitly shown to be the representations of elements of (TLJ) algebra.     

Differing Averaged and Quenched Large Deviations for Random Walks in Random Environments in Dimensions Two and Three

We consider the quenched and the averaged (or annealed) large deviation rate functions I _q and I _a for space-time and (the usual) space-only RWRE on \mathbbZ^d{\mathbb{Z}^d} . By Jensen’s inequality, I _a  ≤ I _q . In the space-time case, when d ≥ 3 + 1, I _q and I _a are known to be equal on an open set containing the typical velocity ξ _o . When d = 1 + 1, we prove that I _q and I _a are equal only at ξ _o . Similarly, when d = 2 + 1, we show that I _a  < I _q on a punctured neighborhood of ξ _o . In the space-only case, we provide a class of non-nestling walks on \mathbbZ^d{\mathbb{Z}^d} with d = 2 or 3, and prove that I _q and I _a are not identically equal on any open set containing ξ _o whenever the walk is in that class. This is very different from the known results for non-nestling walks on \mathbbZ^d{\mathbb{Z}^d} with d ≥ 4.     

The Periodic Oscillation of an Adiabatic Piston in Two or Three Dimensions

We study a heavy piston of mass M that separates finitely many ideal, unit mass gas particles moving in two or three dimensions. Neishtadt and Sinai previously determined a method for finding this system’s averaged equation and showed that its solutions oscillate periodically. Using averaging techniques, we prove that the actual motions of the piston converge in probability to the predicted averaged behavior on the time scale M ^1/2 when M tends to infinity while the total energy of the system is bounded and the number of gas particles is fixed.     

R-T不稳定性发展的二维和三维对比研究

 应用摄动方法研究不同密度流体交界面上的Rayleigh-Taylor（R-T）不稳定性问题，分别研究了二维（2D）与三维（3D）R-T不稳定性的线性与非线性增长，并进行了对比。得出的结论为：（1） 三维不稳定性的线性增长比二维情况要快，且同维度上相同的初始扰动波长，其时间增长指数受另一维度上的初始波长影响。（2） R-T不稳定性发展在考虑了非线性增长的影响之后，二维与三维扰动增长的图像也不一样。     

Reduced Mobility of Triple Nodes and Lines on Grain Growth in Two and Three Dimensions

Vertex dynamics models in two and three dimensions are applied to study grain growth including a limited mobility of triple points (two dimensions) and triple lines (three dimensions). A recent experiment on a triple node is used to validate the proposed model. The reduced triple node/line mobility in the case of a polycrystalline sample is shown to influence both, the grain growth kinetics and the grain size distribution function.     

Path Integration and Separation of Variables in Spaces of Constant Curvature in Two and Three Dimensions

In this paper path integration in two- and three-dimensional spaces of constant curvature is discussed: i.e. the flat spaces R² and R³, the two- and three-dimensional sphere and the two- and three-dimensional pseudosphere. We are going to discuss all coordinates systems where the Laplace operator admits separation of variables. In all of them the path integral formulation will be stated, however in most of them an explicit solution in terms of the spectral expansion can be given only on a formal level. What can be stated in all cases, are the propagator and the corresponding Green function, respectively, depending on the invariant distance which is a coordinate independent quantity. This property gives rise to numerous identities connecting the corresponding path integral representations and propagators in various coordinate systems with each other.