Solution of the Eliashberg equations for a very strong electron-phonon coupling with a low-energy cutoff

We solve the Eliashberg equations for the case of an explicit k dependence of the interactions, and of the resulting self-energies Σ₁(k,ω), Σ₂(k,ω). We consider a strong energy-dependence of the electron-electron scattering-rate τ, which is associated with a strong energy-dependence of the electron-phonon matrix element g(k,k′). We characterize this energy-dependence by a cutoff ζ₁, which is of the order of the phonon frequency ω_ph. We find that we can account for a large number of unexpected features of the superconductivity of the cuprates by the BCS electron-phonon theory, if we consider very large values of the McMillan coupling constant λ_ph, and small values of the cutoff ζ₁. Specifically, the Coulomb interaction is found not to depress T_c; the isotope effect is strongly reduced when ζ₁ < ω_ph. We find solutions in which the gap function Δ(k, ω) has extended s-wave symmetry but is very anisotropic. These large anisotropies are in good agreement with various experiments. We suggest that the underlying cause of the strong energy-dependence is a very small electronic screening parameter at the Fermi surface; the electron-phonon matrix element g is abnormally large, and this accounts for the high transition temperatures of the cuprates. An order of magnitude estimate suggests that the electron-phonon mechanism can account for transition temperatures up to about 200 K. We thus propose a very-strong-coupling theory, in which the renormalization functions, in particular the energy-renormalization X, depend very strongly on the superconducting gap Δ, and thus display a very strong temperature-dependence between T_c and T = 0. An experimental manifestation of the very strong coupling with a small cutoff is a zero bias anomaly sometimes observed in tunneling experiments.     

形如Coulomb势的本征值微扰计算

用超位力定理(HVT)和赫尔曼-费恩曼(Hellman-Feynman)定理(HFT)计算了Coulomb势加上径向线性项和常数项的本征能量的微扰系数,这种计算方法优于通常的瑞利-薛定谔微扰理论,不需要计算本征函数系数,并且用这种方法可以既快捷又有效地计算大量本征能量的微扰系数.     

Two-body correlations and pair formation in the two-dimensional Coulomb gas

We investigate pair correlations in the two-dimensional Coulomb gas made up of two species of point ions carrying electric charges Z₁ e(>0) and Z₂ e(<0), and interaction by the logarithmic Coulomb potential. This system is known to be classically stable for couplings=e ²/k _BTc=2/¦Z₁Z₂¦ (whereT is the temperature). Correlations between equally charged ions are shown to be greatly modified at short distances, in the range _c/2<< _c, due to gradual ion condensation. The usual integral equations for the pair correlation functions admit no solutions in that range. Preliminary Monte Carlo simulations for the symmetric case (Z₁=–Z₂) reveal a striking chemical equilibrium between tightly bound ion pairs and free ions, which is reasonably well described by a simple Bjerrum model.     

Ab initio potential energy surface for the nitrogen molecule pair and thermophysical properties of nitrogen gas

A four-dimensional potential energy hypersurface (PES) for the interaction of two rigid nitrogen molecules was determined from high-level quantum-chemical ab initio computations. A total of 408 points for 26 distinct angular configurations were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory and basis sets up to aug-cc-pV5Z supplemented with bond functions. The calculated interaction energies were extrapolated to the complete basis set limit and complemented by corrections for core–core and core–valence correlations, relativistic effects and higher coupled-cluster levels up to CCSDT(Q). An analytical site–site potential function with five sites per nitrogen molecule was fitted to the interaction energies. The PES was validated by computing second and third pressure virial coefficients as well as shear viscosity and thermal conductivity in the dilute-gas limit. An improved PES was obtained by scaling the CCSDT(Q) corrections for all 408 points by a constant factor, leading to quantitative agreement with the most accurate experimental values of the second virial coefficient over a wide temperature range. The comparison with the best experimental data for shear viscosity shows that the values computed with the improved PES are too low by about 0.3% between 300 and 700?K. For thermal conductivity large systematic deviations are found above 500?K between the calculated values and most of the experimental data.     

Concise presentation of the Coulomb electrostatic potential of a uniformly charged cube

We use a novel method to calculate in closed form the Coulomb electrostatic potential created by a uniformly charged cube at an arbitrary point in space. We apply a suitable transformation of variables that allows us to obtain a simple presentation of the electrostatic potential in one-dimensional integral form. The final concise closed form expression of the Coulomb electrostatic potential of the uniformly charged cube is obtained after completing the calculation of the resulting one-dimensional integrals. Such integrals consist of combinations of products of error functions and power functions that can be solved exactly despite their intimidating appearance. The exact analytic formula for the Coulomb electrostatic potential that we derive reflects the symmetry of the cube and is easy to implement. We illustrate its use by calculating the exact values of the electrostatic potential at some points of symmetry such as the center of cube, center of face of cube, center of edge of cube and corner of cube.     

Molecular field theory for nematic liquid crystal film with finite layers

The nematic liquid crystal film composed of n molecular layers is studied based upon a spatially anisotropic pair potential, which reproduces approximately the elastic free energy density. On condition that the system has perfect nematic order, as in the Lebwohl—Lasher model, the director in the film is isotropic. The effect of the temperature is investigated by means of molecular field theory. Some new results are obtained. Firstly, symmetry breaking takes place when taking account of the temperature, and the state with the director along the normal of the film has the lowest free energy. Secondly, the N—I phase transition temperature increases as an effect of finite sizes instead of decreasing as in the Lebwohl—Lasher model. Thirdly, the nematic order is induced in the layers near the surface in the isotropic phase.     

Effective potentials in the Lifshitz scalar field theory

We study the one-loop effective potentials of the four-dimensional Lifshitz scalar field theory with the particular anisotropic scaling z=2, and the mass and the coupling constants renormalization are performed whereas the finite counterterm is just needed for the highest order of the coupling because of the mild UV divergence. Finally, we investigate whether the critical temperature for the symmetry breaking can exist or not in this approximation.     

Low-temperature effective potential of the Ising model

We study the low-temperature effective potential of the Ising model. We evaluate the three-point and four-point zero-momentum renormalized coupling constants that parametrize the expansion of the effective potential near the coexistence curve. These results are obtained by a constrained analysis of the ε-expansion that uses accurate estimates for the two-dimensional Ising model.     

Correspondence between Electrostatics and Contact Mechanics with Further Results in Equilibrium Charge Distributions

It is common in mesoscopic systems to find instances where several charges interact among themselves. These particles are usually confined by an external potential that shapes the symmetry of the equilibrium charge configuration. In the case of classical charges moving on a plane and repelling each other via the Coulomb potential, they possess a ground state à la Thomson or Wigner crystal. As the number of particles N increases, the number of local minima grows exponentially and direct or heuristic optimization methods become prohibitively costly. Therefore the only feasible approximation to the problem is to treat the system in the continuum limit. Since the underlying framework is provided by potential theory, we shall by-pass the corresponding mathematical formalism and list the most common cases found in the literature. Then we prove a (albeit known) mathematical correspondence that will enable us to re-discover analytical results in electrostatics. In doing so, we shall provide different methods for finding the equilibrium surface density of charges, analytical and numerical. Additionally, new systems of confined charges in three-dimensional surfaces will be under scrutiny. Finally, we shall highlight exact results regarding a modified power-law Coulomb potential in the d-dimensional ball, thus generalizing the existing literature.     

CO2-CO分子间等效作用势与液态CO冲击压缩特性研究

二氧化碳(CO2)和一氧化碳(CO)是高含碳凝聚态炸药爆轰混合产物中两种重要成分,因此,在研究爆轰反应平衡问题以及爆轰产物状态方程时,必然要涉及到CO2-CO分子间等效作用势的确定问题.本文从反应体系化学平衡的角度,采用分子流体的微扰变分理论(MCR)以及分子混合物的范德瓦耳斯单相流体模型(vdW-1f),对过去和最近发表的液态CO的冲击压缩实验数据进行了详细分析,重新优化了CO2-CO分子间exp-6型势函数中的参数值.讨论了本文确定的CO2-CO分子间等效作用势与过去所采用的势函数之间存在的差别.     

Partition density functional theory and its extension to the spin-polarized case

Partition density functional theory (PDFT) [P. Elliott, K. Burke, M.H. Cohen, and A. Wasserman, Phys. Rev. A 82 (2), 024501 (2010)] is a formally exact method for obtaining molecular properties from Kohn–Sham calculations on isolated fragments. Here, we express the partition energy of PDFT as an implicit functional of the molecular spin-densities for a given choice of fragmentation, and use the principle of von Barth and Hedin to formulate the spin-decomposed version of PDFT. We introduce a partition energy functional of the spin-up and spin-down electronic densities and derive the associated polarized partition potentials, which are found to be global quantities that influence every fragment in the molecule. Along with the formal theory, we propose a simplified approach to computing the spin-partition potentials, and illustrate its utility and accuracy with two simple examples. Finally, we propose a viable approach to including external electric and magnetic fields in the framework of spin-PDFT.     

Solutions of the two-body Salpeter equation under the Coulomb and exponential potential for any l state with Laplace approach

In this paper we have solved the two-body spinless-Salpeter (SS) equation under the Coulomb and exponential type potentials. We have applied an approximation for the centrifugal term in our calculations. The energy eigenvalues and the corresponding eigenfunctions are reported by using the Laplace transform approach for any n, l states.     

Inhomogeneous similarity solutions of the Boltzmann equation with confining external forces

The Nikolskii transform makes it possible to construct inhomogeneous solutions of the Boltzmann equation from homogeneous ones. These solutions correspond to a gas in expansion, but if we introduce external forces, they can relax toward absolute Maxwellians. This property holds independently of the assumed intermolecular inverse power force. Consequently, for Maxwell molecules and from energy-dependent homogeneous distributions, we construct effectively a class of inhomogeneous similarity distributions with Maxwellian equilibrium relaxation. We review and investigate again the homogeneous distributions which can be written in closed form, for instance, we show that an elliptic exact solution proposed some years ago violates positivity. For Maxwell interaction with singular cross sections, we numerically construct inhomogeneous distributions having Maxwellian equilibrium states and study the Tjon overshoot effect. We show that both the sign and the time decrease of the external force as well as the microscopic model of the cross section contribute to the asymptotic behavior of the distribution. These inhomogeneous similarity solutions include a class of distributions that asymptotically oscillate between different Maxwellians. Two classes of external forces are considered: linear spatial-dependent forces or linear velocity-dependent forces plus source term.     

On the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids

It is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density. We derive the explicit form that the functional takes for a system of hard rods, and propose an approximate one for hard spheres. Attractive interactions are also considered in mean-field approximation. In all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated.     

Vibrational analysis of nitrosamine,a molecule with an almost constant potential along the inversion coordinate

ABSTRACT

The fundamental vibrational transitions of nitrosamine and its doubly deuterated isotopologue have been computed by vibrational configuration interaction theory including up to 6-tuple excitations. The potential energy surface has been represented by an n-mode expansion up to 4-mode couplings terms obtained from explicitly correlated coupled-cluster theory, CCSD(T)-F12a. Very good agreement with experimental data has been been achieved and a number of new assignments is provided.     

Microscopic theory of single particle and pair condensation of an attracting bose gas as the basis for superfluidity and superconductivity

A consistent and unified microscopic theory of superfluidity and superconductivity is developed on the basis of two-stage Fermi-Bose-liquid (FBL) (in particular case, one-stage Bose-liquid) scenarios. It is shown that these phase transition scenarios is accompanied, as a rule, by the formation of composite bosons (Cooper pair and bipolarons) with their subsequent single particle (SPC) and pair condensation (PC). A brief outline of the modified and generalized BCS-like pairing theory of fermions is presented. In an analogy to that, a detailed boson pairing theory is developed. The SPC and PC features of an attracting 3d- and 2d-BG as a function of the interboson coupling constant in the complete range 0≤T≤T _B is studied in detail. It is argued that the coexistence of the order parameters of attracting fermions Δ_F and bosons Δ_B leads to the superfluidity (in³He) and superconductivity (in superconductors) by two FBL scenarios. One of these scenarios is realized in the so-called fermion superconductors (FSC) and the other in the boson superconductors (BSC) in which the gapless superconductivity is caused by the absence of the gap Δ_SF in the excitation spectrum of bosons and not by the presence of point or line nodes of the BCS-like gap Δ_F. The new adequate definitions for basic superconducting parameters of FSC and BSC are given. The theory proposed is consistent with the experimental data available.