王先谦庄学研究初探

王先谦《庄子集解》是庄学中非常重要的书。地方也“间下己意”，标揭对庄子思想和写作艺术的见解。性质和作者等，王先谦也有独到的观点。它基本上是由郭庆藩的《庄子集释》删略辑成，有的对于庄学研究中一直存在的问题，如《庄子》一书的     

Raman active collective mode in underdoped cuprates

We report experimental observation of Bardasis–Schrieffer-type s-symmetry collective mode in the d-wave high T_c superconductors. The mode persists above T_c in the pseudogap phase of the underdoped superconductors — direct spectroscopic evidence of the correlations in the particle–particle channel above T_c.     

Collective modes in a one-dimensional nonuniform fluid model

A one-dimensional fluid with short-range repulsive interaction and one period of cosinusoidal attraction in a periodic container is transformed to a two-mode format. The system has both high-temperature single-phase regions and lowtemperature two-phase regions with a very broad spatial interface that can be stabilized by a weak external field. The case of vanishing external field brings out properties of the mode amplitude dependence which one expects to extend to more complex systems.     

Effective theory for deformed nuclei

Techniques from effective field theory are applied to nuclear rotation. This approach exploits the spontaneous breaking of rotational symmetry and the separation of scale between low-energy Nambu–Goldstone rotational modes and high-energy vibrational and nucleonic degrees of freedom. A power counting is established and the Hamiltonian is constructed at next-to-leading order.     

Path integral approach to the full Dicke model

The full Dicke model describes a system of N identical two level-atoms coupled to a single mode quantized bosonic field. The model considers rotating and counter-rotating coupling terms between the atoms and the bosonic field, with coupling constants g₁ and g₂, for each one of the coupling terms, respectively. We study finite temperature properties of the model using the path integral approach and functional methods. In the thermodynamic limit, N→∞, the system exhibits phase transition from normal to superradiant phase, at some critical values of temperature and coupling constants. We distinguish between three particular cases, the first one corresponds to the case of rotating wave approximation, where g₁≠0 and g₂=0, the second one corresponds to the case of g₁=0 and g₂≠0, in these two cases the model has a continuous symmetry. The last one, corresponds to the case of g₁≠0 and g₂≠0, where the model has a discrete symmetry. The phase transition in each case is related to the spontaneous breaking of its respective symmetry. For each one of these three particular cases, we find the asymptotic behaviour of the partition function in the thermodynamic limit, and the collective spectrum of the system in the normal and the superradiant phase. For the case of rotating wave approximation, and also the case of g₁=0 and g₂≠0, in the superradiant phase, the collective spectrum has a zero energy value, corresponding to the Goldstone mode associated to the continuous symmetry breaking of the model. Our analysis and results are valid in the limit of zero temperature, β→∞, in which, the model exhibits a quantum phase transition.     

Collectivity of plasmon excitations in small sodium clusters with planar structure

The collectivity of the electronic motion in small sodium clusters with planar structure is studied by the time-dependent density functional theory (TDDFT). The formation and development of collective resonances in the absorption spectra were obtained as the function of the size and shape of the plane. We find the symmetry plays an important role in the collective excitation. Resonance peaks increase with the reduction of the symmetries and, on the contrary, resonance peaks decrease with the increase of the symmetries. In the planar cluster, there are two main excitation modes: the higher-energy mode and the competitive mode, which is due to the coupling and competition of the quasi-lower-energy effect and the quasi-higher-energy effect. With the increase of the interatomic distance, peaks of the absorption spectra are all red-shifted and the evolutionary trend is also discussed.     

Testing Dirac-Brueckner models in collective flow of heavy-ion collisions

We investigate differential in-plane and out-of-plane flow observables in heavy-ion reactions at intermediate energies from 0.2-2 AGeV within the framework of relativistic BUU transport calculations. The mean field is based on microscopic Dirac-Brueckner-Hartree-Fock (DB) calculations. We apply two different sets of DB predictions, those of ter Haar and Malfliet and more recent ones from the Tübingen group, which are similar in general but differ in details. The latter DB calculations exclude spurious contributions from the negative-energy sector to the mean field which results in a slightly softer equation of state and a less repulsive momentum dependence of the nucleon-nucleus potential at high densities and high momenta. For the application to heavy-ion collisions in both cases non-equilibrium features of the phase space are taken into account on the level of the effective interaction. The systematic comparison to experimental data favours the less repulsive and softer model. Relative to non-relativistic approaches one obtains larger values of the effective nucleon mass. This produces a sufficient amount of repulsion to describe the differential flow data reasonably well. Received: 8 January 2001 / Accepted: 12 November 2001     

High-spin nuclear states and persistent currents in mesoscopic rings

An analogy is presented between periodic persistent currents in mesoscopic rings and staggerings of gamma energy transitions from some nuclear high-spin states. Various sources of damping of the expected periodic structures in both physical systems are compared. This discussion provides, in the nuclear case, a tentative explanation of the scarcity of such staggerings, their appearance near ¹⁵⁰Gd and the existence of a spin-window for their observation. Received: 21 July 1997 / Revised version: 13 October 1997     

集合风险模型的可分解性

本文讨论了集合风险模型中 ,在复合二项分布和复合负二项分布两种情况下的可分解性问题 ,得到了同复合泊松分布情况下类似的结果