The Chern‐Simons Current in Systems of DNA‐RNA Transcriptions

A Chern‐Simons current, coming from ghost and anti‐ghost fields of supersymmetry theory, can be used to define a spectrum of gene expression in new time series data where a spinor field, as alternative representation of a gene, is adopted instead of using the standard alphabet sequence of bases . After a general discussion on the use of supersymmetry in biological systems, we give examples of the use of supersymmetry for living organism, discuss the codon and anti‐codon ghost fields and develop an algebraic construction for the trash DNA, the DNA area which does not seem active in biological systems. As a general result, all hidden states of codon can be computed by Chern‐Simons 3 forms. Finally, we plot a time series of genetic variations of viral glycoprotein gene and host T‐cell receptor gene by using a gene tensor correlation network related to the Chern‐Simons current. An empirical analysis of genetic shift, in host cell receptor genes with separated cluster of gene and genetic drift in viral gene, is obtained by using a tensor correlation plot over time series data derived as the empirical mode decomposition of Chern‐Simons current.     

Extension of the Chern–Simons Theory: Conservation Laws,Lagrange Structures,and Stability

Russian Physics Journal - We consider the class of higher derivative 3d vector field models with the wave operator being a polynomial of the Chern–Simons operator. For the nth order theory of...     

SO（d,d;Z) Transformation Property for Gauge Fluxes and Ramond-Ramond Fields in Noncommutative Geometry

In this paper we study the spinor constructions of gauge fluxes and Ramond-Ramond fields on noncommutative tori T^d up to d=6. In which the spinor and conjugate spinor are distinguished and dual bases are also introduced.So that we can express the Chern-Simons Lagrangian in toroidal compactification as a product of spinors.     

二维模糊球上的量子霍尔流体

在回顾了Haldane对量子Hall效应在二维球面S2上的描述后,本文构造了二维模糊球S2上的非对易代数及其Hilbert空间的Moyal结构.通过构造模糊球上不可压缩量子霍尔流体的非对易Chern-Simons理论,求解具有准粒子源的Gaussian约束,找出模糊球上的Calogero矩阵及最低Landau能级Laughlin波函数的完全集,此Laughlin波函数由旋量坐标推广的Jack多项式表示.     

Modelling of Bound States of Dirac Particles in Singular Background in Framework of Symanzik Approach

The problem of interaction of the fields of quantum electrodynamic with material macro-object is considered by employing the Symanzik approach on modelling the interaction of quantum field with space-time inhomogeneities. Results obtained in the models with Chern–Simons interaction of photon field with 2-dimensional material are briefly reviewed. In the model of interaction of spinor field with homogeneous isotropic material plane constructed in framework of Symanzik approach, the bound states are considered. For localized near plane Dirac particle the dispersion relation and the expressions for current, charge and density are analyzed. The bound states with massless dispersion law is considered. The presented methods of modelling can find application to a wide class of phenomena emerging from the interaction of quantum fields with extended material structures.     

{SL(2, \mathbb{C})} Chern–Simons Theory and the Asymptotic Behavior of the Colored Jones Polynomial

It has been proposed that the asymptotic behavior of the colored Jones polynomial is equal to the perturbative expansion of the Chern–Simons gauge theory with complex gauge group ${SL(2, \mathbb{C})}$ on the hyperbolic knot complement. In this note we make the first step toward verifying this relation beyond the semi-classical approximation. This requires a careful understanding of some delicate issues, such as normalization of the colored Jones polynomial and the choice of polarization in Chern–Simons theory. Addressing these issues allows us to go beyond the volume conjecture and to verify some predictions for the behavior of the subleading terms in the asymptotic expansion of the colored Jones polynomial.     

Effective field theory of a topological insulator and the Foldy–Wouthuysen transformation

Employing the Foldy–Wouthuysen transformation, it is demonstrated straightforwardly that the first and second Chern numbers are equal to the coefficients of the 2+1 and 4+1 dimensional Chern–Simons actions which are generated by the massive Dirac fermions coupled to the Abelian gauge fields. A topological insulator model in 2+1 dimensions is discussed and by means of a dimensional reduction approach the 1+1 dimensional descendant of the 2+1 dimensional Chern–Simons theory is presented. Field strength of the Berry gauge field corresponding to the 4+1 dimensional Dirac theory is explicitly derived through the Foldy–Wouthuysen transformation. Acquainted with it, the second Chern numbers are calculated for specific choices of the integration domain. A method is proposed to obtain 3+1 and 2+1 dimensional descendants of the effective field theory of the 4+1 dimensional time reversal invariant topological insulator theory. Inspired by the spin Hall effect in graphene, a hypothetical model of the time reversal invariant spin Hall insulator in 3+1 dimensions is proposed.     

Quantization of the Chern invariant polynomial and its topological quantum ground state

The symplectic quantization of the Chern invariant polynomial on a 2n-dimensional manifold is considered. The ground state wave functional as a representation of the vacuum state of the theory is constructed in terms of the Chern-Simons form. An important consequence of these results is that the existence of the Chern-Simons wave functional is not exclusive of topological four-dimensional gauge theory.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

Graph invariants of Vassiliev type and application to 4D quantum gravity

We consider graph invariants of Vassiliev type extended by the quantum group link invariants. When they are expanded byx whereq=e ^x , the expansion coefficients are known as the Vassiliev invariants of finite type. In the present paper, we define tangle operators of graphs given by a functor from a category of colored and oriented graphs embedded into a 3-space to a category of representations of the quasi-triangular ribbon Hopf algebra extended byU _q (sl(2),C)), which are subject to a quantum group analog of the spinor identity. In terms of them, we obtain the graph invariants of Vassiliev type expressed to be identified with Chern Simons vacuum expectation values of Wilson loops including intersection points. We also consider the 4d canonical quantum gravity of Ashtekar. It is verified that the graph invariants of Vassiliev type satisfy constraints of the quantum gravity in the loop space representation of Rovelli and Smolin.This is not the author's present address.     

Creating macroscopic atomic Einstein-Podolsky-Rosen states from Bose-Einstein condensates

We present a scheme for creating quantum entangled atomic states through the coherent spin-exchange collision of a spinor Bose-Einstein condensate. The state generated possesses macroscopic Einstein-Podolsky-Rosen correlation and the fluctuation in one of its quasispin components vanishes. We show that an elongated condensate with large aspect ratio is most suitable for creating such a state.     

基于非线性放大环镜和Lyot滤波器的多波长与耗散孤子锁模态开关型掺铥光纤激光器

报道了一种基于非线性放大环镜和Lyot滤波器技术的态开关型掺铥光纤激光器.通过仔细调节偏振控制器和泵浦功率,掺铥光纤激光器可以分别在多波长态和耗散孤子锁模态运行,并且两种态之间可以相互切换.对于多波长态,在光谱半功率值范围内能生成8个稳定的波长;对于耗散孤子锁模态,在1996 nm的中心波长处产生脉冲能量高达41.49 nJ,脉冲持续时间为2.4 ns,光谱带宽为29 nm的耗散孤子.不同运行态间的切换归因于偏振控制器导致的非线性放大环镜的功能的改变.     

Higher order theories and their relationship with noncommutativity

We present a relationship between noncommutativity and higher order time derivative theories using a perturbation method. We make a generalization of the Chern–Simons quantum mechanics for higher order time derivatives. This model presents noncommutativity in a natural way when we project to low-energy physical states without the necessity of taking the strong field limit. We quantize the theory using a Bopp's shift of the noncommutative variables and we obtain a spectrum without negative energies, under the perturbation limits. In addition, we extent the model to high order time derivatives and noncommutativity with variable dependent parameter.     

Higher derivative extensions of 3<Emphasis Type="Italic">d</Emphasis> Chern–Simons models: conservation laws and stability

We consider the class of higher derivative 3d vector field models with the field equation operator being a polynomial of the Chern–Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.     

Nonclassicality of Coherent Photon-Subtracted Two Single-Modes Squeezed Vacuum State

We introduce a two-mode non-Gaussian state, generated by nonlocal coherent photon-subtraction (CPS) from two single-mode squeezed vacuum states (TSSV). Its normalized factor is turned out to be related with a Legendre polynomial. We further investigate the nonclassical properties of the CPS-TSSV through cross-correlation function, antibunching effect, photon number distribution, wave function and Wigner function. It is shown that the CPS operation can produce the vortex state and can exhibit the highly nonclassical properties.     

Classical hamiltonian reduction on D(2|1;α) Chern–Simons gauge theory and large N=4 superconformal symmetry

3d Chern–Simons gauge theory has a strong connection with 2d CFT and link invariants in knot theory. We impose some constraints on the D(2|1;α) CS theory in the similar context of the hamiltonian reduction of 2d superconformal algebras. There Hilbert states in D(2|1;α) CS theory are partly identified with characters of the large N=4 SCFT by their transformation properties.     

Spinor slow-light and dirac particles with variable mass

We consider the interaction of two weak probe fields of light with an atomic ensemble coherently driven by two pairs of standing wave laser fields in a tripod-type linkage scheme. The system is shown to exhibit a Dirac-like spectrum for light-matter quasiparticles with multiple dark states, termed spinor slow-light polaritons. They posses an "effective speed of light" given by the group velocity of slow light, and can be made massive by inducing a small two-photon detuning. Control of the two-photon detuning can be used to locally vary the mass including a sign flip. Particularly, this allows the implementation of the random-mass Dirac model for which localized zero-energy (midgap) states exist with unusual long-range correlations.     

Differential characters and cohomology of the moduli of flat connections

Let \(\pi {:}\, P\rightarrow M\) be a principal bundle and p an invariant polynomial of degree r on the Lie algebra of the structure group. The theory of Chern–Simons differential characters is exploited to define a homology map \(\chi ^{k} {:}\, H_{2r-k-1}(M)\times H_{k}({\mathcal {F}}/{\mathcal {G}})\rightarrow {\mathbb {R}}/{\mathbb {Z}}\), for \(k<r-1\), where \({\mathcal {F}} /{\mathcal {G}}\) is the moduli space of flat connections of \(\pi \) under the action of a subgroup \({\mathcal {G}}\) of the gauge group. The differential characters of first order are related to the Dijkgraaf–Witten action for Chern–Simons theory. The second-order characters are interpreted geometrically as the holonomy of a connection in a line bundle over \({\mathcal {F}}/{\mathcal {G}}\). The relationship with other constructions in the literature is also analyzed.

     

Toward $$\mathrm {U}(N|M)$$ knot invariant from ABJM theory

We study \(\mathrm {U}(N|M)\) character expectation value with the supermatrix Chern–Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half-BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives \(\mathrm {U}(N|M)\) character expectation values in terms of \(\mathrm {U}(1|1)\) averages for a particular type of character representations. This means that the \(\mathrm {U}(1|1)\) character expectation value is a building block for the \(\mathrm {U}(N|M)\) averages and also, by an appropriate limit, for the \(\mathrm {U}(N)\) invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern–Simons matrix model. We obtain the Rosso–Jones-type formula and the spectral curve for this case.     

Shell model study of 52V and 52Cr and gamma decay of isobaric analogue states in 52Cr

The spectrum of ⁵²V is studied with the Kuo-Brown (KB) renormalized interaction and with Vervier's interactions. Wave functions of isobaric analogue states (IAS) in ⁵²Cr are generated from ⁵²V wave functions. Wave functions of low-lying levels of ⁵²Cr are obtained by a shell model calculation with the KB interaction and with the phenomenological effective interaction of Lips and McEllistrem. Electromagnetic decay of IAS to low-lying states via the isovector part of the transition operator is considered. Transition rates are first calculated by assuming that the final state configurations do have the proper isospin. A projection operator is defined in isospace to construct basis states having the proper isospin, starting with excited configurations of ⁵²Cr which do not have well-defined isospin. Two methods — diagonalization after projection and projection after diagonalization — are developed in which the definite isospin of basis states can be handled.