The Geometry of Antiferromagnetic Spin Chains

It has been a conjecture of F.D.M.Haldane that long-wavelength excitations around antiferromagnetic vacua of certain spin chains are related to relativistic two-dimensional σ-models. We construct a class of such spin chains and associated σ-models, using symplectic geometry as a main tool. The target space of the σ-model can be an arbitrary complex flag manifold, and we find universal expressions for the metric and θ-term. The derivation relies on the fact that the flag manifold is a Lagrangian submanifold in a direct product of Grassmannians associated (via geometric quantization) to the representations of spins at consecutive sites of the spin chain. The true goal is not to reach the uttermost limits, but to discover a completeness that knows no boundaries. Rabindranath Tagore      

The Spin Crisis of the Proton

The relationship between the Gerasimov-Drell-Hearn(GDH)sum rule and the first monent,ΓP-the proton spin dependent structure function integral,is established.According to the sum rule and quark structure model of baryon,[SU_sf(6)⊙O(3)]⊙SU_c(3),the spin problem of the proton is discussed The present theoretical results are also compared with the data measured by EMC and SLAC groups.Our prediction is in good agreement with the data.We find that the P₃₃(1232)photo-cxcitation dominates the spin structure function integrals and contributes negatively at low momentum transfer.At higher momentum transfer,the contribution of the P₃₃ is positive,and it decreases rapidly as Q² increasing and finally becomes negligible The integral changes its sign from negative into positive at about Q²=0.3GeV².     

The Isotopic Field Charge Spin Assumption

This paper discusses fundamental physical interactions starting from two preliminary assumptions.

Spin q , Twistor and Spin c

Spin ^q structures induce (Spin ^q style) twistor spaces, which possess canonical Spin ^c structures. Such structures produce Dirac operators. Their indices for the even dimensional case, and the adiabatic limit of their reduced η-invariants for the odd dimensional case, are discussed. Received: 3 October 1995 / Accepted: 2 March 1997     

The Spin Effect of Antiproton-Nucleus Inelastic Collison

If the antiproton optical potential is inclusive of the spin orbit interaction term,the A(p,p)A* inelastic scattering not only can excited the normal parity states,but also can excited the abnormal parity states.There are also induced the polarization P_f(θ) at the inelastic scattering.In the framework of DWIA,we derived the inelastic scattering cross section (dσ/dΩ)_f,i,and polarization P_f(θ),and calculated the (dσ/dΩ)_f,i, and P_f(θ) for ¹²C(p,p)¹²C* with 2⁺,3^－ and 1⁺ states at antiproton energies of 46.8 and 179.7MeV.They fited experiment data quite well.Due to the abnormal partity states in the inelastic process have been measured,the spin orbit term can not be neglect.     

Spin glasses

Recent developments in the theory of spin glasses are discussed. There has been considerable progress, due to Parisi, Sompolinsky, and others, towards understanding the infinite range (mean field) model of Sherrington and Kirkpatrick. Relaxation times diverge in the thermodynamic limit, and this nonergodic behavior is now understood to be the cause of earlier difficulties. There has been less progress in the study of more realistic models with short-range interactions, but numerical studies have shown rather clearly the absence of a finite temperature transition in two dimensions. There is probably no transition ind=3 either, though the evidence is less clearcut, which makes it difficult to understand the sharpness of the freezing observed experimentally. Well below the freezing temperature ESR and torque measurements have been fairly well explained by a theory of Henley, Sompolinsky, and Halperin, in which an important ingredient is anisotropy due to the Dzyloshinsky-Moriya interaction proposed by Fert and Levy.     

自旋超导态

文章综述了近几年来自旋超导领域的研究进展。自旋超导态是由电荷为零自旋非零的玻色子在低温下凝聚成的超流态。文章将介绍自旋超导态的类伦敦方程、类金兹堡—朗道方程及其BCS(Bardeen-Cooper-Schrieffer)型哈密顿量。然后利用这些方程和理论,导出自旋超导体的一些有趣现象,如：零自旋阻现象、电迈斯纳效应和自旋流约瑟夫森效应。此外,作者也讨论了一些很可能是自旋超导体的候选体系,自旋超导体的应用前景,以及该子领域的发展前景展望。     

Spin phase

The existence of a complementary quantity in the Weyl sense for the third component of spin is discussed. This is called the spin phase and the possibilities of measuring this quantity are considered. Connections between the spin phase and the indeterminacy of the direction for the spin are shown. On leave from the Institute of Physics, Nicolas Copernicus University, Torun, Poland.     

Spin Entropy

Two types of randomness are associated with a mixed quantum state: the uncertainty in the probability coefficients of the constituent pure states and the uncertainty in the value of each observable captured by the Born’s rule probabilities. Entropy is a quantification of randomness, and we propose a spin-entropy for the observables of spin pure states based on the phase space of a spin as described by the geometric quantization method, and we also expand it to mixed quantum states. This proposed entropy overcomes the limitations of previously-proposed entropies such as von Neumann entropy which only quantifies the randomness of specifying the quantum state. As an example of a limitation, previously-proposed entropies are higher for Bell entangled spin states than for disentangled spin states, even though the spin observables are less constrained for a disentangled pair of spins than for an entangled pair. The proposed spin-entropy accurately quantifies the randomness of a quantum state, it never reaches zero value, and it is lower for entangled states than for disentangled states.     

The Phase Diagram of a Spin Glass Model

A spin glass problem on a Cayley tree with ferromagnetic interactions is solved rigorously. Using a level-I large deviation argument together with the martingale approach used by Buffet, Patrick and Pulé,⁽¹⁾ explicit expressions for the free energy are derived in different regions of the phase diagram. It is found that there are four phases: a paramagnetic phase, a spin-glass phase, a ferromagnetic phase and a mixed phase. The nature of the phase diagram depends on the power with which the ferromagnetic term occurs in the Hamiltonian.     

The Percolation Signature of the Spin Glass Transition

Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin–Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering—both in short-range (EA) and infinite-range (SK) models—within a two-replica FK representation and also within the different Chayes–Machta–Redner two-replica graphical representation. Based on numerical studies of the ±J EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of two percolating clusters of unequal densities.     

The Semiclassical Study of Nuclear High Spin States

Nuclear high spin states are studied in the extended Thomas-Fermi approximation.Explicit formula for rotational energy and various corrections are given.Concrete calculations are performed for three typical nuclei:¹¹⁶Sn,¹⁵⁸Yb and ²⁴⁰Pu.Qualitatively,the results are similar to that of liquid drop model.Quantum corrections to rotational energy (besides shell corrections) cannot be neglected in a quantitative study.