Spin Statistics and CPT for Solitons

Conditions are analysed under which the statistics of soliton sectors of massive two-dimensional field theories can be properly defined. A soliton field algebra is defined as a crossed product with the group of soliton sectors. In this algebra, the nonlocal commutation relations are determined and weak locality, spin statistics and CPT theorems are proven. These theorems depart from their usual appearance due to the broken symmetry connecting the inequivalent vacua. An interpretation of these results in terms of modular theory is given. For the neutral subalgebra of the soliton algebra, the theorems hold in a familiar form, and twisted duality is derived.     

Connecting Spin and Statistics in Quantum Mechanics

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (?1)^2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required.     

Local Energy Statistics in Spin Glasses

Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. We review some rigorous results confirming the validity of this conjecture. In the context of the SK models, we analyse the limits of the validity of the conjecture for energy levels growing with the volume of the system. In the case of the Generalised Random energy model, we give a complete analysis for the behaviour of the local energy statistics at all energy scales. In particular, we show that, in this case, the REM conjecture holds exactly up to energies E _N < β _c N, where β _c is the critical temperature. We also explain the more complex behaviour that sets in at higher energies. Research supported in part by the DFG in the Dutch-German Bilateral Research Group “Mathematics of Random Spatial Models from Physics and Biology” and by the European Science Foundation in the Programme RDSES.     

Spin,Statistics, and Reflections II. Lorentz Invariance

The analysis of the relation between modular P₁CT-symmetry—a consequence of the Unruh effect—and Pauli’s spin-statistics relation is continued. The result in the predecessor to this article is extended to the Lorentz symmetric situation. A model G _L of the universal covering of the restricted Lorentz group is modelled as a reflection group at the classical level. Based on this picture, a representation of G _L is constructed from pairs of modular P₁CT-conjugations, and this representation can easily be verified to satisfy the spin-statistics relation.Dedicated to Professor H.-J. Borchers on the occasion of his 80th birthdayEmmy-Noether fellow of the Deutsche Forschungsgemeinschaft     

Propagating Torsion from First Principles

A propagating torsion model is derived from the requirement of compatibility between minimal action principle and minimal coupling procedure in Riemann-Cartan spacetimes. In the proposed model, the trace of the torsion tensor is derived from a scalar potential that determines the volume element of the spacetime. The equations of the model are written down for the vacuum and for various types of matter fields. Some of their properties are discussed. In particular, we show that gauge fields can interact minimally with the torsion without the breaking of gauge symmetry.     

Proof of the Spin Statistics Connection 2: Relativistic Theory

The traditional standard theory of quantum mechanics is unable to solve the spin–statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle” but by the adoption of the complex standard relativistic quantum field theory. In a recent paper (Santamato and De Martini in Found Phys 45(7):858–873, 2015) we presented a proof of the spin–statistics problem in the nonrelativistic approximation on the basis of the “Conformal Quantum Geometrodynamics”. In the present paper, by the same theory the proof of the spin–statistics theorem is extended to the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin–statistics connection observed in Nature (Santamato and De Martini in Found Phys 45(7):858–873, 2015). The present proof of the spin–statistics theorem is simpler than the one presented in Santamato and De Martini (Found Phys 45(7):858–873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary.     

Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems

We obtain new principles for transferring log-Sobolev and Spectral-Gap inequalities from a source metric-measure space to a target one, when the curvature of the target space is bounded from below. As our main application, we obtain explicit estimates for the log-Sobolev and Spectral-Gap constants of various conservative spin system models, consisting of non-interacting and weakly-interacting particles, constrained to conserve the mean-spin. When the self-interaction is a perturbation of a strongly convex potential, this partially recovers and partially extends previous results of Caputo, Chafaï Grunewald, Landim, Lu, Menz, Otto, Panizo, Villani, Westdickenberg and Yau. When the self-interaction is only assumed to be (non-strongly) convex, as in the case of the two-sided exponential measure, we obtain sharp estimates on the system’s Spectral-Gap as a function of the mean-spin, independently of the size of the system.     

聚丙烯腈PAN分子链的第一性原理研究

利用RHF方法,选择基组STO3G,对聚丙烯腈PAN分子链CH3(CHCNCH2)9CH2CN的10个单体进行理论研究.在结构优化方面,PAN分子链稳定结构为反式构象.主链C-C平均键长155.6pm,支链C-C平均键长149.7pm,C-N平均键长115.5pm.在电荷分布方面,主链C原子电荷分布呈现出一定的周期性,与C-N键相连的主链C原子电荷量小于相邻的主链C原子的电荷量,两者的电负性有一定的差异.存在这种差异的原因在于支链N原子的存在,支链N原子具有更强的电负性.最后对PAN结构链的振动模式进行分析得出,在对PAN进行预氧化及碳化处理时,先发生的是脱氢反应,随着温度的升高,产生环化,从而使环化与脱氢同时存在.     

第一原理研究铝锂金属间化合物

运用密度泛函理论系统地研究了二元铝锂金属间化合物Al₃Li、AlLi、Al₂Li₃和Al₄Li₉的结构、形成热、弹性和电子结构.通过计算四种金属间化合物的形成热,证明了金属间化合物中铝和锂之间具有强烈的化学作用. 在富锂金属间化合物中,随着锂的含量的增加,金属间化合物热力学稳定性呈线性减弱. 计算金属间化合物的单晶弹性常数可以得出四种金属间化合物都是机械稳定的. 运用Voigt-Reuss-Hil     

First Principles Study on FeAs Single Layers

在广义梯度近似(GGA)和GGA+U的框架下,用第一性原理方法研究了用FeAs单层的简单模型来研究LaFeAsO和BaFe2As2的合理性. 对未掺杂的FeAs单层,优化的几何结构及其对应的电子结构与本体的性质差异较大,并且在单层中没有发现体相中的共线反铁磁基态. 另外,在单层中,As与Fe层之间在z方向的间距随电子和空穴掺杂浓度的变化也与实验结果不符,这些结果表明,在LaFeAsO和BaFe2As2中,FeAs层与其他层之间的相互作用是不可忽略的,用简单的FeAs单层来处理Fe基超导体需要考虑更多的修正     

First Investigation of 115In in the High Spin Regime

The ¹¹⁵In nucleus was studied by means of γ-ray spectroscopic measurements. This nucleus was populated with the ¹⁰⁰Mo(¹⁸O, p2n)¹¹⁵In reaction and a charged-particle detector array was used to identify the proton evaporation channel. A level scheme with 17 new transitions is presented and compared with theoretical predictions based on the particle + core model.     

NH3分子在LiH（100）表面吸附的第一性原理研究

采用第一性原理方法研究了NH₃分子在LiH（100）晶面的表面吸附情况.通过研究LiH（100）/NH₃体系的吸附位置、吸附能和电子结构,发现NH₃分子在LiH（100）晶面主要是化学吸附,初始位置为NH₃分子中N-H键在Li顶住时失去一个H原子,并在LiH（100）面形成NH₂基,其吸附能为0.511 eV,属于强化学吸附,吸附作用最强.此时NH₂基与附近H原子和Li原子之间为离子键作用,NH₂基中N—H键为共价键;NH₃分子中另一个H原子与LiH表面的一个H原子形成一个H₂分子逸出表面.H₂分子中H-H键为明显的共价键.     

NH3分子在LiH(100)表面吸附的第一性原理研究

采用第一性原理方法研究了NH3分子在LiH(100)晶面的表面吸附情况. 通过研究LiH(100) /NH3体系的吸附位置、吸附能和电子结构,发现NH3分子在Li3N (100)晶面主要是化学吸附,初始位置为NH3分子中N-H键在Li顶位时失去一个H原子,并在LiH(110)面形成NH2基,其吸附能为0.511 eV,属于强化学吸附,吸附作用最强. 此时NH2基与附近H原子和Li原子之间为离子键作用,NH2基中N—H键为共价键;NH3分子中另一个H原子与LiH表面的一个H原子形成一个H2分子逸出表面. H2分子中H-Ｈ键为明显的共价键.     

高压下硫化钙的弹性和热力学性质的第一性原理计算

利用基于密度泛函理论的第一性原理平面波赝势方法结合准谐德拜模型研究NaCl结构的CaS在高压下的弹性和热力学性质.计算得到的零温零压下的晶格常数、体弹模量与实验值符合得很好.弹性常数和弹性模量随着压强的增大而增大.压强对体弹模量和热膨胀系数的影响大于温度的影响.热容随压强的升高而降低,在高温下热容接近于Dulong-Petit极限.通过求解Gibbs自由能计算得到B1结构和B2结构CaS的相变压为36.61 GPa.     

Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs taking values in a countable space, but under the stronger assumptions of \(\alpha \)-mixing (for local statistics) and exponential \(\alpha \)-mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.     

Statistics of Energy Levels and Zero Temperature Dynamics for Deterministic Spin Models with Glassy Behaviour

We consider the zero-temperature dynamics for the infinite-range, non translation invariant one-dimensional spin model introduced by Marinari, Parisi and Ritort to generate glassy behaviour out of a deterministic interaction. It is argued that there can be a large number of metastable (i.e., one-flip stable) states with very small overlap with the ground state but very close in energy to it, and that their total number increases exponentially with the size of the system.     

Physical Properties of III-Antiminodes -- a First Principles Study

A comprehensive first principles study of III-Antimonide binary compounds is hardly found in literature. We report a broad study of structural and electronic properties of boron antimonide （BSb）, aluminium antimonide （AlSb）, gallium antimonide （GaSb） and indium antimonide （InSb） in zineblende phase based on density functional theory （DFT）. Our calculations are based on Full-PotentiM Lineaxized Augmented Plane wave plus local orbitals （FP- L（APWq-lo）） method. Different forms of exchange-correlation energy functional and corresponding potential are employed for structural and electronic properties. Our computed results for lattice parameters, bulk moduli, their pressure derivatives, and cohesive energy are consistent with the available experimental data. Boron antimonide is found to be the hardest compound of this group. For band structure calculations, in addition to LDA and GGA, we used GGA-EV, an approximation employed by Engel and Vosko. The band gap results with GGA-EV are of significant improvement over the earlier work.     

Physical Properties of III-Antiminodes --- a First Principles Study

A comprehensive first principles study of III-Antimonide binary compounds ishardly found in literature. We report a broad study of structural and electronicproperties of boron antimonide (BSb), aluminium antimonide (AlSb), galliumantimonide (GaSb) and indium antimonide (InSb) in zincblende phase based on density functional theory (DFT). Our calculations are based onFull-Potential Linearized Augmented Plane wave plus local orbitals(FP-L(APW+lo)) method. Different forms of exchange-correlation energyfunctional and corresponding potential are employed for structural andelectronic properties. Our computed results for lattice parameters, bulkmoduli, their pressure derivatives, and cohesive energy are consistent withthe available experimental data. Boron antimonide is found to be the hardestcompound of this group. For band structure calculations, in addition to LDAand GGA, we used GGA-EV, an approximation employed by Engel and Vosko. The band gap results with GGA-EV are of significant improvement over the earlier work.