Influence of shell structure and pairing correlations on the nuclear state density

A microscopic calculation of nuclear state densities was performed starting from realistic single-particle levels. Within this concept, a correspondence between microscopic ground state energy corrections and microscopic effects on state densities was deduced. It is shown that the approximations introduced by a simple analytical expression for the nuclear state density are comparable to the uncertainties of microscopically calculated state densities for nuclei in their ground state configuration. Guidelines for the determination of the parameters of this analytical expression were deduced from the microscopic computations.     

Particle density and non-local kinetic energy density functional for two-dimensional harmonically confined Fermi vapors

We evaluate analytically some ground state properties of two-dimensional harmonically confined Fermi vapors with isotropy and for an arbitrary number of closed shells. We first derive a differential form of the virial theorem and an expression for the kinetic energy density in terms of the fermion particle density and its low-order derivatives. These results allow an explicit differential equation to be obtained for the particle density. The equation is third-order, linear and homogeneous. We also obtain a relation between the turning points of kinetic energy and particle densities, and an expression of the non-local kinetic energy density functional. Received 27 March 2001 and Received in final form 12 June 2001     

Level density parameters for the back-shifted fermi gas model in the mass range 40 < A < 250

The parameters a and Δ for the Fermi gas model with fictive ground state are determined for about 220 nuclei from experimental level densities at low excitation energy and at the neutron binding energy. In. agreement with previous results it is found that for most nuclei the fictive ground state is back-shifted relative to the conventionally shifted ground state as determined by the pairing energy. Shell effects are evident at the mass numbers 90, 140 and 208 for both the level density parameter a and the back-shift. A comparison is given with previous results and different experimental data on level densities.     

非对称量子点中极化子的性质

采用线性组合算符和幺正变换方法研究了非对称量子点中强、弱耦合极化子的性质,导出了非对称量子点中强、弱耦合极化子的基态能量和基态结合能随量子点的横向、纵向有效受限长度,电子-声子耦合强度的变化关系.通过数值计算,结果表明,量子点中强、弱耦合极化子的基态能量和基态结合能随量子点的横向、纵向有效受限长度的减小而迅速增大.     

Out of equilibrium dynamics of supersymmetry at high energy density

We investigate the out of equilibrium dynamics of global chiral supersymmetry at finite energy density. We concentrate on two specific models. The first is the massive Wess–Zumino model which we study in a self-consistent one-loop approximation. We find that for energy densities above a certain threshold, the fields are driven dynamically to a point in field space at which the fermionic component of the superfield is massless. The state, however, is found to be unstable, indicating a breakdown of the one-loop approximation. To investigate further, we consider an O(N) massive chiral model which is solved exactly in the large N limit. For sufficiently high energy densities, we find that for late times the fields reach a nonperturbative minimum of the effective potential degenerate with the perturbative minimum. This minimum is a true attractor for O(N) invariant states at high energy densities, and this provides a mechanism for determining which of the otherwise degenerate vacua is chosen by the dynamics. The final state for large energy density is a cloud of massless particles (both bosons and fermions) around this new nonperturbative supersymmetric minimum. By introducing boson masses which softly break the supersymmetry, we demonstrate a see-saw mechanism for generating small fermion masses. We discuss some of the cosmological implications of our results.     

Ab-initio local density approximation description of the electronic properties of zinc blende cadmium sulfide (zb-CdS)

Ab-initio, self-consistent electronic energy bands of zinc blende CdS are reported within the local density functional approximation (LDA). Our first principle, non-relativistic and ground state calculations employed a local density potential and the linear combination of atomic orbitals (LCAO). Within the framework of the Bagayoko, Zhao, and Williams (BZW) method, we solved self-consistently both the Kohn-Sham equation and the equation giving the ground state density in terms of the wavefunctions of the occupied states. Our calculated, direct band gap of 2.39 eV, at the Γ point, is in accord with the experiment. Our calculation reproduced the peaks in the conduction and valence bands density of states, within experimental uncertainties. The calculated electron effective mass agrees with experimental findings.     

Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem

Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide proof of existence of a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of the density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism. Numerical results for one-dimensional non-interacting systems illustrate the formalism. Some direct formal and practical implications of the present reformulation of DFT are also discussed.     

Gauge model of disordered magnets

A model of disordered magnets with their ground state degenerate in energy is proposed. It is shown that the presence of singularities in the field of an order parameter leads to the appearance of additional degrees of freedom described by the gauge field of the rotation group. The gauge fields arise as coefficients of the connection of some non-trivial fibre bundle. The lagrangian of disordered magnets with linear singularities (disclinations) in the field of the order parameter is constructed, and the spectrum of hydrodynamic modes is found.     

Charged kaon condensation in high density quark matter

We show that at asymptotically high densities the “color-flavor-locked+neutral kaon condensate” phase of QCD develops a charged kaon condensate through the Coleman–Weinberg mechanism. At densities achievable in neutron stars a charged kaon condensate forms only for some (natural) values of the low energy constants describing the low-lying excitations of the ground state.     

Memory in time-dependent density functional theory

Exact time-dependent density functionals remember both the entire history of the density and the initial wave function. We show that the two effects are intimately related, and all history dependence can be written as initial-state dependence, including that of the exchange-correlation kernel. For states that can be evolved from a ground state, all initial-state dependence is a dependence on a pseudo-prehistory, providing a route to excited-state densities from time-dependent density functional theory.     

InAs量子环中类氢杂质能级

在有效质量近似下,利用微扰法研究了InAs量子环内类氢杂质基态及低激发态的能级分布。受限势采用抛物形势,在二维平面极坐标下,用薛定谔方程的精确解析解进行计算。数值计算结果显示,电子能级敏感地依赖于量子环半径,能级存在极小值,这是由于限制势采用抛物势的结果。如果减小环的半径,可以增加能级间距。第一激发态类氢杂质能级的简并没有消除,n≥2时简并的能级发生分裂并且间距随半径的增大而增大。电子能级间距还敏感地依赖于角频率并随角频率的增大而增大。第一激发态的简并没有消除,第二激发态的简并被部分地消除。在计算InAs量子环中类氢杂质的基态和低激发态的能级时,角频率改变的影响也是很深刻的。文章结果对研究量子环的光跃迁及光谱结构有重要指导意义。     

简并基态最陡下降微扰理论

本文证明,Cioslowski所引入的一个全新的量子力学计算方案,非简并基态最陡下降微扰理论,通过按对称性选择合适的零级试探波函数后,可以处理简并基态的微扰分裂问题由于最陡下降微扰理论既避免了通常的其他微扰理论需要对各个基矢量无限求和的或求解一组微分方程的缺陷,又具有逐步迭代改善计算结果的优点,本文引进的计算方案可望在原子分子及其他多粒子体系能级的微扰分裂计算中得到广泛应用。 关键词：     

Broken symmetry in antiferromagnets

We discuss limitations of the conventional ‘broken symmetry’ picture of the Heisenberg antiferromagnet. The exact results on the ground state of the linear chain and of the three-dimensional Hamiltonian do not show a ‘degeneracy of the vacuum’. With the help of a solvable model it is shown that the correlations in the ground state may have the Néel character, as revealed by the neutron experiments, even though the ground state is quite different from the Néel states. There is no Goldstone mode in the linear chain. The spin of the antiferromagnetic spin wave is 1/2. But the physical states have a doublet of the spin waves which could be regarded as degenerate states of spin 1 and spin 0. The fermionic character is suppressed and the bosonic character revealed, as in the decolouring phenomena in quantum field theory. It is plausible that in the three-dimensional case also there is no Goldstone mode.     

温度对抛物量子阱中极化子能量的影响

采用线性组合算符法和幺正变换法研究温度对抛物型量子阱中极化子基态能和基态结合能的影响. 通过理论推导得到极化子基态能和基态结合能的表达式. 结合量子统计力学中平均声子数的表达式, 得到极化子基态能量和基态结合能与温度的函数关系. 在不同温度下, 分别讨论了极化子基态能量和基态结合能与电子-声子耦合强度和阱宽的关系, 阱深取不同值时讨论了极化子基态能和基态结合能随温度的变化规律. 计算结果表明, 极化子的基态能量和基态结合能都是温度的递增函数.     

The multilevel pairing Hamiltonian versus the degenerate case

We study the pairing Hamiltonian in a set of non-degenerate levels. First, we review in the path integral framework the spontaneous breaking of the U(1) symmetry occurring in such a system for the degenerate situation. Then the behaviors with the coupling constant of the ground state energy in the multilevel and in the degenerate case are compared. Next we discuss, in the multilevel case, an exact strong coupling expansion for the ground state energy which introduces the moments of the single particle level distribution. The domain of validity of the expansion, which is known in the macroscopic limit, is explored for finite systems and its implications for the energy of the latter is discussed. Finally the seniority and Gaudin excitations of the pairing Hamiltonian are addressed and shown to display the same gap in leading order.     

Quantum Phase Transition and Ferromagnetic Spin Correlation in Parallel Double Quantum Dots

We investigate electronic transport through a parallel double quantum dot （DQD） system with strong on-site Coulomb interaction, as well as the interdot tunnelling. By applying numerical renormalization group method, the ground state of the system and the transmission probability at zero temperature are obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit （2e^2/h） due to the Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to anti-ferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.     

Vortex-Peierls states in optical lattices

We show that vortices, induced in cold atom superfluids in optical lattices, may order in a novel vortex-Peierls ground state. In such a state vortices do not form a simple lattice but arrange themselves in clusters, within which the vortices are partially delocalized, tunneling between classically degenerate configurations. We demonstrate that this exotic quantum many-body state is selected by an order-from-disorder mechanism for a special combination of the vortex filling and lattice geometry that has a macroscopic number of classically degenerate ground states.     

Meta-generalized gradient approximation: non-empirical construction and performance of a density functional

The local ingredients of a meta-generalized gradient approximation (meta-GGA) include the electron density, its gradient, and the Kohn–Sham orbital kinetic energy density. We discuss the strategy of constructing a successful meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The new feature of this functional is that it simultaneously respects the two paradigms of electronic structure theory: one- or two-electron densities and slowly-varying densities, and so is uniformly accurate for atoms, molecules and solids. Results of extensive numerical tests of the new functional are summarized and evaluated.     

Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids

The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.