Acoustic–excitonic effects in a two-dimensional gas of dipolar excitons

The theory of the interaction of a two-dimensional gas of indirect dipolar excitons with Rayleigh surface elastic waves has been developed. The absorption and renormalization of the phase velocity of a surface wave, as well as the drag of excitons by the surface acoustic wave and the generation of bulk acoustic waves by a twodimensional gas of dipolar excitons irradiated by external electromagnetic radiation, have been considered. These effects have been studied both in a normal phase at high temperatures and in a condensed phase of the exciton gas. The calculations have been performed in the ballistic and diffusion limits for both phases.     

Density functional approximation for van der Waals fluids： based on hard sphere density functional approximation

A universal theoretical approach is proposed which enables all hard sphere density functional approximations (DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.     

Thermally induced spin polarization and thermal conductivities in a spin–orbit-coupled two-dimensional electron gas

The thermal conductivities and spin polarization induced by the temperature gradient are investigated in a Rashba spin–orbit-coupled two-dimensional electron gas. In this spin–orbit-coupled system in the presence of nonmagnetic or magnetic electron–impurity scattering, the Wiedemann–Franz law still holds. However, the spin polarization induced by the temperature gradient strongly depends on the property of impurities. The components of spin accumulation both perpendicular and parallel to the direction of the temperature gradient, and the thermally induced charge Hall conductivity may be nonzero for magnetic disorders.     

Optimized local basis set for Kohn–Sham density functional theory

We develop a technique for generating a set of optimized local basis functions to solve models in the Kohn–Sham density functional theory for both insulating and metallic systems. The optimized local basis functions are obtained by solving a minimization problem in an admissible set determined by a large number of primitive basis functions. Using the optimized local basis set, the electron energy and the atomic force can be calculated accurately with a small number of basis functions. The Pulay force is systematically controlled and is not required to be calculated, which makes the optimized local basis set an ideal tool for ab initio molecular dynamics and structure optimization. We also propose a preconditioned Newton–GMRES method to obtain the optimized local basis functions in practice. The optimized local basis set is able to achieve high accuracy with a small number of basis functions per atom when applied to a one dimensional model problem.     

A mesh-free convex approximation scheme for Kohn–Sham density functional theory

Density functional theory developed by Hohenberg, Kohn and Sham is a widely accepted, reliable ab initio method. We present a non-periodic, real space, mesh-free convex approximation scheme for Kohn–Sham density functional theory. We rewrite the original variational problem as a saddle point problem and discretize it using basis functions which form the Pareto optimum between competing objectives of maximizing entropy and minimizing the total width of the approximation scheme. We show the utility of the approximation scheme in performing both all-electron and pseudopotential calculations, the results of which are in good agreement with literature.     

Combined exciton–electron excitation in quantum wells with a two-dimensional electron gas of low density

A combined exciton–cyclotron resonance is found in the photoluminescence excitation and reflectivity spectra of semiconductor quantum wells with an electron gas of low density. In external magnetic fields an incident photon creates an exciton in the ground state and simultaneously excites an electron between Landau levels. A theoretical model is developed and suggests the dominating contribution of the exchange exciton–electron interaction.     

Dynamic density and spin responses of a superfluid Fermi gas in the BCS–BEC crossover: Path integral formulation and pair fluctuation theory

We present a standard field theoretical derivation of the dynamic density and spin linear response functions of a dilute superfluid Fermi gas in the BCS–BEC crossover in both three and two dimensions. The derivation of the response functions is based on the elegant functional path integral approach which allows us to calculate the density–density and spin–spin correlation functions by introducing the external sources for the density and the spin density. Since the generating functional cannot be evaluated exactly, we consider two gapless approximations which ensure a gapless collective mode (Goldstone mode) in the superfluid state: the BCS–Leggett mean-field theory and the Gaussian-pair-fluctuation (GPF) theory. In the mean-field theory, our results of the response functions agree with the known results from the random phase approximation. We further consider the pair fluctuation effects and establish a theoretical framework for the dynamic responses within the GPF theory. We show that the GPF response theory naturally recovers three kinds of famous diagrammatic contributions: the Self-Energy contribution, the Aslamazov–Lakin contribution, and the Maki–Thompson contribution. We also show that unlike the equilibrium state, in evaluating the response functions, the linear (first-order) terms in the external sources as well as the induced order parameter perturbations should be treated carefully. In the superfluid state, there is an additional order parameter contribution which ensures that in the static and long wavelength limit, the density response function recovers the result of the compressibility (compressibility sum rule). We expect that the f$f$-sum rule is manifested by the full number equation which includes the contribution from the Gaussian pair fluctuations. The dynamic density and spin response functions in the normal phase (above the superfluid critical temperature) are also derived within the Nozières–Schmitt–Rink (NSR) theory.     

Transport properties of the two-dimensional electron gas in AlP quantum wells at finite temperature including magnetic field and exchange–correlation effects

We investigate the transport scattering time, the single-particle relaxation time and the magnetoresistance of a quasi-two-dimensional electron gas in a GaP/AlP/GaP quantum well at zero and finite temperatures. We consider the interface-roughness and impurity scattering, and study the dependence of the mobility, scattering time and magnetoresistance on the carrier density, temperature and local-field correction. In the case of zero temperature and Hubbard local-field correction our results reduce to those of Gold and Marty (Physica E 40 (2008) 2028; Phys. Rev. B 76 (2007) 165309). We also discuss the possibility of a metal–insulator transition which might happen at low density.     

Turbulence modulation model for gas–particle flow based on probability density function approach

The paper focuses on the turbulence modulation problem in gas–particle flow with the use of probability density function(PDF) approach. By means of the PDF method, a general statistical moment turbulence modulation model without considering the trajectory difference between two phases is derived from the Navier–Stokes equations. A new turbulence production term induced by the dispersed-phase is analyzed and considered. Furthermore, the trajectory difference between two media is taken into account. Subsequently, a new k–ε turbulence modulation model in dilute particle-laden flow is successfully set up. Then, the changes to several terms, including the turbulence production, dissipation, and diffusion terms, are well described consequently. The promoted model provides a more probable explanation for the modification of particles on the turbulence. Finally, we applied the model to simulate a gas–particle turbulence flow case in a wall jet, and found that the simulation results agree well with the experimental data.     

Polaron and molecular states of a spin–orbit coupled impurity in a spinless Fermi sea

We investigate the polaron and molecular states of a fermionic atom with one-dimensional spin–orbit coupling(SOC)coupled to a three-dimensional spinless Fermi sea. Because of the interplay among the SOC, Raman coupling and spinselected interatomic interactions, the polaron state induced by the spin–orbit coupled impurity exhibits quite unique features. We find that the energy dispersion of the polaron generally has a double-minimum structure, which results in a finite center-of-mass(c.m.) momentum in the ground state, different from the zero-momentum polarons where SOC are introduced into the majority atoms. By further tuning the parameters such as the atomic interaction strength, a discontinuous transition between the polarons with different c.m. momenta may occur, signaled by the singular behavior of the quasiparticle residue and effective mass of the polaron. Meanwhile, the molecular state as well as the polaron-to-molecule transition is also strongly affected by the Raman coupling and the effective Zeeman field, which are introduced by the lasers generating SOC on the impurity atom. We also discuss the effects of a more general spin-dependent interaction and mass ratio. These results would be beneficial for the study of impurity physics brought by SOC.     

Calculation of the Kirkwood–Frohlich correlation factor and dielectric constant of methanol using a statistical model and density functional theory

The geometries of methanol monomer and methanol clusters, (CH₃OH) _m , m = 2–10, were optimized using the DFT/B3LYP/6-31++G(d,p) method. For each m > 2, a number of conformers were found to satisfy the optimization condition, showing no imaginary frequency in their calculated IR spectra. With increasing m, five- and six-membered rings begin to appear with open chain branches and the calculated IR spectra approach the experimentally observed IR spectrum of liquid methanol. Using the average energy of formation of one hydrogen bond and a statistical model, the Kirkwood–Frohlich (K–F) correlation factor (g) and dielectric constant (ε) were calculated for each methanol cluster. From a plot of ε versus cluster size (m), the bulk dielectric constant was obtained by extrapolation to m→∞. The value of g averaged over all conformers is in almost complete agreement with the g value obtained in an earlier molecular dynamics simulation study by Fonseca and Ladanyi [J. Chem. Phys. 93, 8148 (1990)]. Using this value of g in the K–F equation, the dielectric constant (ε) of methanol was calculated and found to be in fair agreement with (～17% lower than) the experimental value and also with an earlier molecular dynamics simulation [Mol. Phys. 94, 435 (1998)]. The calculated ε follows the same trend in variation with temperature as the experimental ε in the range 288–318 K.     

Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation

Kohn–Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn–Sham Hamiltonian generally results in a large number of basis functions per atom in order to resolve the rapid oscillations of the Kohn–Sham orbitals around the nuclei. Previous attempts to reduce the number of basis functions per atom include the usage of atomic orbitals and similar objects, but the atomic orbitals generally require fine tuning in order to reach high accuracy. We present a novel discretization scheme that adaptively and systematically builds the rapid oscillations of the Kohn–Sham orbitals around the nuclei as well as environmental effects into the basis functions. The resulting basis functions are localized in the real space, and are discontinuous in the global domain. The continuous Kohn–Sham orbitals and the electron density are evaluated from the discontinuous basis functions using the discontinuous Galerkin (DG) framework. Our method is implemented in parallel and the current implementation is able to handle systems with at least thousands of atoms. Numerical examples indicate that our method can reach very high accuracy (less than 1 meV) with a very small number (4–40) of basis functions per atom.     

Instability of a two-dimensional Bose–Einstein condensate with Rashba spin–orbit coupling at finite temperature

We prove that in a two-dimensional homogeneous boson system with Rashba spin–orbit coupling, Bose–Einstein condensate with plane-wave order is unstable at finite temperature. The calculations are based on a nonlinear sigma model scheme. The density wave contributions to the thermal deletions are divergent in the infrared limit. The behavior of the divergence is different from that without spin–orbit coupling.     

Measurement of the neutron-proton spin correlation coefficient Ayy at 90° c.m. by elastic scattering of 13.7 MeV polarized neutrons from a polarized proton target

The neutron-proton spin correlation coefficient A_yy was measured at 90° c.m. by elastic scattering of 13.7 MeV polarized neutrons from a polarized proton target. The target polarization of about 60% was produced in a LMN single crystal by dynamic nuclear orientation using 70 GHz microwaves. The target was thin enough to allow the detection of the recoil protons in coincidence with the associated scattered neutrons. Our result for A_yy is the first experimental determination of a neutron-proton spin correlation parameter at such a low energy. To determine the influence of A_yy on the ³S₁-³D₁ mixing parameter ε₁, a single-energy n-p phase shift analysis was performed using the experimentally determined value of A_yy= 0.078 ± 0.014 along with analyzing power and cross section data. As expected, the result for ε₁ changes drastically upon the inclusion of A_yy. An unexpectedly small value of ε₁ = −0.16°±0.54° has been obtained in the present analysis.     

On a solution of the self-interaction problem in Kohn–Sham density functional theory

We report on a methodology for the treatment of the Coulomb energy and potential in Kohn–Sham density functional theory that is free from self-interaction effects. Specifically, we determine the Coulomb potential given as the functional derivative of the Coulomb energy with respect to the density, where the Coulomb energy is calculated explicitly in terms of the pair density of the Kohn–Sham orbitals. This is accomplished by taking advantage of an orthonormal and complete basis that is an explicit functional of the density that then allows for the functional differentiation of the pair density with respect to the density to be performed explicitly. This approach leads to a new formalism that provides an analytic, closed-form determination of the exchange potential. This method is applied to one-dimensional model systems and to the atoms Helium through Krypton based on an exchange only implementation. Comparison of our total energies (denoted SIF) to those obtained using the usual Hartree–Fock (HF) and optimized effective potential (OEP) methods reveals the hierarchy $E_{\mathrm{HF}}\le E_{\mathrm{OEP}}\le E_{\mathrm{SIF}}$ that is indicative of the greater variation freedom implicit in the former two methods.     

Effect of Coulomb repulsion on spin and orbital magnetism of cobalt–benzene complex: A relativistic density functional study

We have demonstrated electronic configurations and magnetic properties of single Co adatom on benzene (Bz) molecule in the framework of relativistic density functional theory. A sequence of fixed spin moment (FSM) calculations were carried out with and without Coulomb repulsion (U). We have investigated that varying the strength of Coulomb repulsion results to different equilibrium positions for the Co adatom on benzene molecule. It was shown that inclusion of the on-site Coulomb repulsion in the Co 3d orbitals affects significantly the geometry of Co–Bz complex. We also found two stable low-spin and high-spin multiplicities for the complex. The nature of the high-spin configuration was explained according to the Hubbard electron–electron correlation in 3d shell of the Co adatom. Our FSM results indicate that the high-spin state is a global minimum in the presence of Hubbard parameter U. The relativistic spin–orbit coupling and using orbital polarization correction induce considerable orbital magnetism in both low and high spin states of the Co–Bz complex. We have also calculated magnetic anisotropy energies for two spin states and we found out that an out-of-plane magnetic orientation of Co adatom is more favorable in the low spin state whereas the Coulomb repulsion (U = 2 eV and U = 4 eV) predicts an in-plane magnetic orientation for Co adatom. Our findings can be implicitly taken into account for the extended system of added single Co atom on graphene.