Operations on Cyclic Homology, the X Complex, and a Conjecture of Deligne

We prove that there is a product on the Hochschild and cyclic chain complex of a homotopy Gerstenhaber algebra. By restricting to the special case of the algebra of Hochschild cochains (the so called deformation complex), we obtain operations on cyclic homology of associative algebras.     

Periodic Driving Induced Anomalous End Modes in a Superconducting Wire with the Second-Neighbor Pairing Potential

The anomalous end modes are generated in a one-dimensional p-wave superconducting wire with second-neighbor couplings and a periodic driving in pairing potential. We show that the driving on the amplitude or the phase of the first-neighbor and second-neighbor pairing potential can both generate conventional end modes and anomalous end modes, with corresponding Floquet eigenvalues equal to ± 1 or appear in complex conjugate pairs. We have numerically studied the driving of the first-neighbor and second-neighbor pairing potential, and also analyzed the end modes, Floquet eigenvalues and the Fourier transform of these end modes.

     

Numerical Simulations of Screened Coulomb Systems. A Comparison Between Hyperspherical and Periodic Boundary Conditions

Numerical simulations or Coulomb systems can be performed in various geometries, for instance in a cube with periodic boundary conditions ( ³) or on the surface of a hypersphere or on the surface of a hypersphere ( ³). We show how to extend these methods of simulations to the case of screened (Yukawa) potentials. We make a detailed comparison between the properties of Yukawa systems in these two geometries and derive the correct configurational energies of some models such as the Yukawa restricted primitive model and the Yukawa one component plasma.     

A Separable Pairing Force in Nuclear Matter

The method introduced by Duguet is adopted to derive a separable form of the pairing interaction in the ^1So channel from a bare or an effective nucleon-nucleon （NN） interaction in nuclear matter. With this approach the separable pairing interaction reproduces the pairing properties provided by its corresponding NN interaction. In this work, separable forms of pairing interactions in the ^1So channel for the bare NN interaction, Bonn potential and the Gogny effective interaction are obtained. It is found that the separable force of the Gogny effective interaction in the 1So channel has a clear link with the bare NN interaction. With such a simple separable form pairing properties provided by the Gogny force in nuclear matter can be reproduced.     

Interactions Between Solitons and Cnoidal Periodic Waves of the Boussinesq Equation

The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this peper, two equivalent very simple methods, the truncated Painlevé analysis and the generalized tanh function expansion approaches, are developed to find interaction solutions between solitons and any other types of Boussinesq waves.     

Interactions Between Solitons and Cnoidal Periodic Waves of the Boussinesq Equation

The Boussinesq equation is one of important prototypic models in nonlinear physics.Various nonlinear excitations of the Boussinesq equation have been found by many methods.However,it is very difcult to find interaction solutions among diferent types of nonlinear excitations.In this peper,two equivalent very simple methods,the truncated Painlev′e analysis and the generalized tanh function expansion approaches,are developed to find interaction solutions between solitons and any other types of Boussinesq waves.     

A Possible Pairing Mechanism in Two-Band Hubbard Model

A theoretical scheme for describing the quasiparticle-pair superconductivity in doped CuO₂ system is suggested based on the model put forward by Emery and Reiter. The doped O holes and associated two neighboring Cu-spins form spin-1/2 quasiparticles. Through the magnetic interaction with the spin background, the quasiparticles interact with each other and lead to pair condensation which is responsible for the superconductivity.     

A p-d Hybridization Pairing Model in the Cuprates

A new mechanism for the pairing in cuprate superconductors ia proposed and studied by using the mean-field approximations. A hybridieation singlet pair is formed by media of strong hybridization between a d hole on Cu site and a p doped hole with opposite spin on the nearest-neighbor O site in the CuO₂ plane. The transition temperature can be found to reach a peak around δ～0.1-0.3 and the ratio of energy gap to T_c has a maximum 4.0. This is in good agreement with experiments. The specific heat jump as a function of doping fraction δ, the upper critical field and the coherence length, are obtained.     

Higher Hochschild Homology,Topological Chiral Homology and Factorization Algebras

We study the higher Hochschild functor, factorization algebras and their relationship with topological chiral homology. To this end, we emphasize that the higher Hochschild complex is a functor sSet _∞ × CDGA _∞ where sSet and CDGA _∞ are the (∞,1)-categories of simplicial sets and commutative differential graded algebras, and give an axiomatic characterization of this functor. From the axioms, we deduce several properties and computational tools for this functor. We study the relationship between the higher Hochschild functor and factorization algebras by showing that, in good cases, the Hochschild functor determines a constant commutative factorization algebra. Conversely, every constant commutative factorization algebra is naturally equivalent to a Hochschild chain factorization algebra. Similarly, we study the relationship between the above concepts and topological chiral homology. In particular, we show that on their common domains of definition, the higher Hochschild functor is naturally equivalent to topological chiral homology. Finally, we prove that topological chiral homology determines a locally constant factorization algebra and, further, that this functor induces an equivalence between locally constant factorization algebras on a manifold and (local system of) E _n -algebras.     

Pairing symmetries in cuprates: A Gorkov formalism

Inspite of the direct evidence for Cooper pairing in the cuprates as in conventional superconductors, the pairing symmetry in the cuprate superconductors is still considered to be a controversial and a highly debatable topic. The microscopic equations appropriate for these new materials, essentially the yttrium based compounds, are discussed following Gorkov's formalism for the conventional superconductors. Various types of symmetry of the pairing parameter are considered. In this study we consider the anisotropic nature of the gap parameter to write the mean-field equations of the cuprates. We observe that the symmetry of the potential is fundamental in deciding the nature of the anisotropy in the gap parameter.     

Pairing rotations and separation energies

Recent experiments exhibit a strong regularity of the two-neutron (proton) binding energies in superconducting nuclei. Using BCS calculations by Soloviev and by Kisslinger and Sorensen for the rare earth and tin region, respectively, we show that the pairing rotational model accounts for this behaviour provided the deformation does not change appreciably when two neutrons or protons are added to the system. The model relates the degree of pairing to the ground state energies of neighbouring even-even nuclei and supplements the information coming from the odd-even effect.     

Cyclic Representations of Quantum (Super) Algebras At qp=1

Cyclic representations of quantum (super) algebras are studied at q^p=1 using two methods:the quotient module method and the q-boson realization method.For the quantum algebras associated with any finite dimensional simple Lie algebra the general theory of two methods is given,and is generated to the quantum superalgebra U_qosp(1.2).By constructing the cyclic representation of q-Heisenberg-Wey1 superalgebras the q-boson realization method is generated to construction of cyclic representations of some high-rank quantum superalgebras.     

A Variant of the Mukai Pairing via Deformation Quantization

Let X be a smooth projective complex variety. The Hochschild homology HH_?(X) of X is an important invariant of X, which is isomorphic to the Hodge cohomology of X via the Hochschild?CKostant?CRosenberg isomorphism. On HH_?(X), one has the Mukai pairing constructed by Caldararu. An explicit formula for the Mukai pairing at the level of Hodge cohomology was proven by the author in an earlier work (following ideas of Markarian). This formula implies a similar explicit formula for a closely related variant of the Mukai pairing on HH_?(X). The latter pairing on HH_?(X) is intimately linked to the study of Fourier?CMukai transforms of complex projective varieties. We give a new method to prove a formula computing the aforementioned variant of Caldararu??s Mukai pairing. Our method is based on some important results in the area of deformation quantization. In particular, we use part of the work of Kashiwara and Schapira on Deformation Quantization modules together with an algebraic index theorem of Bressler, Nest and Tsygan. Our new method explicitly shows that the ??Noncommutative Riemann?CRoch?? implies the classical Riemann?CRoch. Further, it is hoped that our method would be useful for generalization to settings involving certain singular varieties.     

A Cyclic Induction Accelerator

The main feature of the examined cyclic induction accelerator is the separation of control and accelerating electromagnetic fluxes. The control magnetic field is formed by analogy with the magnetic field of a weakly focusing synchrotron, and the accelerating vortex electric field is generated by electromagnetic cores – inductors. Such a design of the cyclic induction accelerator allows the active steel volume and the power of a supply unit to be reduced significantly, and the separation of control and accelerating magnetic fluxes allows the energy lost by particles by synchrotron emission to be compensated using a relatively simple method. Recent investigations have demonstrated that in this accelerator, electrons can be accelerated to energies exceeding 300 MeV.     

Pairing and quarteting correlations in nuclei

The Gorkov approach to the pairing problem has been generalized in order to take into account pairing and quarteting correlations with a model Hamiltonian including a charge independent pairing interaction and a n-p isopairing term. The single quasi-particle and quasi-hole energies calculated for all the doubly even nuclei of the $\text{7}\text{2}$^? shell show the importance of quarteting correlations in nuclei.     

Khovanov-Rozansky Homology and Topological Strings

We conjecture a relation between the sl(N) knot homology, recently introduced by Khovanov and Rozansky, and the spectrum of BPS states captured by open topological strings. This conjecture leads to new regularities among the sl(N) knot homology groups and suggests that they can be interpreted directly in topological string theory. We use this approach in various examples to predict the sl(N) knot homology groups for all values of N. We verify that our predictions pass some non-trivial checks Mathematics Subject Classifications (2000): 57M25, 57M27, 18G60, 18E30, 14J32, 14N35, 81T30, 81T45 Dedicated to the memory of F.A. Berezin     

Pairing and quartetting in exotic nuclei

A review is given of pair correlations in nuclei with an emphasis on the symmetry character of the superfluid solution which depends on (i) the isospin of the nucleus and (ii) the relative strength of the T=0 and T=1 pairing forces. The most general SO(8) model which accommodates neutrons and protons as well as T=0 and T=1 pairing, is solvable in three limits: only T=0 pairing, only T=1 pairing and equal strengths in the two channels. In these limits, the superfluid ground-state solution of N=Z nuclei exhibits a quartet structure. The competition between superfluidity and magicity is discussed with reference to integrable models. To cite this article: P. Van Isacker, C. R. Physique 4 (2003).     

稀土区对力强度的研究

在相对论平均场框架下系统地研究了稀土区同位素链的对力强度, 首次发现了 中子的对力强度G_n在中子幻数N=82处突然增大以及质子的对力强度G_p和中子的奇、偶性有关的特性, 证明了对力强度本质上是和核的壳层结构紧切相关. 另外, 还给出了计算对力强度G_n和G_p的一般公式.     

Topological Field Theories and Harrison Homology

Tools and arguments developed by Kevin Costello are adapted to families of “Outer Spaces” or spaces of graphs. This allows us to prove a version of Deligne’s conjecture: the Harrison homology associated with a homotopy commutative algebra is naturally a module over a cobordism category of 3-manifolds.     

Asymmetric Bethe-Salpeter Equation for Pairing and Condensation

The Martin-Schwinger hierarchy of correlations are reexamined and the three-particle correlations are investigated under various partial summations. Besides the known approximations of screened, ladder and maximally crossed diagrams the pair-pair correlations are considered. It is shown that the recently proposed asymmetric Bethe-Salpeter equation to avoid unphysical repeated collisions is derived as a result of the hierarchical dependencies of correlations. Exceeding the parquet approximation we show that an asymmetry appears in the selfconsistent propagators. This form is superior over the symmetric selfconsistent one since it provides the Nambu-Gorkov equations and gap equation for fermions and the Beliaev equations for bosons while from the symmetric form no gap equation results. The selfenergy diagrams which account for the subtraction of unphysical repeated collisions are derived from the pair-pair correlation in the three-particle Green’s function. It is suggested to distinguish between two types of selfconsistency, the channel-dressed propagators and the completely dressed propagators, with the help of which the asymmetric expansion completes the Ward identity and is Φ-derivable.