Spin Gromov-Witten Invariants

We define and study r-spin Gromov-Witten invariants and r-spin quantum cohomology of a projective variety V, where r≥2 is an integer. The main element of the construction is the space of r-spin maps, the stable maps into a variety V from n-pointed algebraic curves of genus g with the additional data of an r-spin structure on the curve. We prove that is a Deligne-Mumford stack and use it to define the r-spin Gromov-Witten classes of V. We show that these classes yield a cohomological field theory (CohFT) which is isomorphic to the tensor product of the CohFT associated to the usual Gromov-Witten invariants of V and the r-spin CohFT. Restricting to genus zero, we obtain the notion of an r-spin quantum cohomology of V, whose Frobenius structure is isomorphic to the tensor product of the Frobenius manifolds corresponding to the quantum cohomology of V and the r^th Gelfand-Dickey hierarchy (or, equivalently, the A_r−1 singularity). We also prove a generalization of the descent property which, in particular, explains the appearance of the ψ classes in the definition of gravitational descendants.Research of the first author was partially supported by NSA grant number MDA904-99-1-0039Research of the second author was partially supported by NSF grant number DMS-9803427Research of the third author was partially supported by NSF grant DMS-0104397     

Quantum Cryptography in Spin Networks

In this paper we propose a new scheme of long-distance quantum cryptography based on spin networks with qubits stored in electron spins of quantum dots. By＂ conditional Faraday- rotation, single photon polarization measurement, and quantum state transfer, maximal-entangled Bell states for quantum cryptography between two long-distance parties are created. Meanwhile, efficient quantum state transfer over arbitrary＂ distances is obtained in a spin chain by＂ a proper choice of coupling strengths and using spin memory- technique improved. We also analyse the security＂ of the scheme against the cloning-based attack which can be also implemented in spin network and discover that this spin network cloning coincides with the optimal fidelity- achieved by＂ an eavesdropper for entanglement-based cryptography.     

Decoherent Histories of Spin Networks

The decoherent histories formalism, developed by Griffiths, Gell-Mann, and Hartle (in Phys. Rev. A 76:022104, 2007; arXiv:1106.0767v3 [quant-ph], 2011; Consistent Quantum Theory, Cambridge University Press, 2003; arXiv:gr-qc/9304006v2, 1992) is a general framework in which to formulate a timeless, ‘generalised’ quantum theory and extract predictions from it. Recent advances in spin foam models allow for loop gravity to be cast in this framework. In this paper, I propose a decoherence functional for loop gravity and interpret existing results (Bianchi et al. in Phys. Rev. D 83:104015, 2011; Phys. Rev. D 82:084035, 2010) as showing that coarse grained histories follow quasiclassical trajectories in the appropriate limit.     

Generation of Multi-qubit Graph States via Spin Networks

We propose an efficient scheme for preparing multi-qubit graph states via spin networks. The classical types of graph states including cluster state, Greenberger-Horne-Zeilinger state and circle-shaped states can be generated by using imaginary SWAP gate. Our method makes the generation of multipartite entangled graph states more efficient than the ones based on conventional controlled-NOT and controlled phase flip gate for solid-state devices.     

Duality Between Spin Networks and the 2D Ising Model

The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.     

Hojman Exact Invariants and Adiabatic Invariants of Hamilton System

The perturbation to Lie symmetry and adiabatic invariants are studied. Based on the concept of higher-order adiabatic invariants of mechanical systems with action of a small perturbation, the perturbation to Lie symmetry is studied, and Hojman adiabatic invariants of Hamilton system are obtained. An example is given to illustrate the application of the results.     

Invariants in potential scattering

The equivalence of the pictures and representations fails for non-square integrable wave-functions in stationary scattering theory. As an application, a physical interpretation of different types of invariants defined in the Brussels school theory of irreversibility is given.     

Topological Invariants in Braid Theory

Many invariants of knots and links have their counterparts in braid theory. Often, these invariants are most easily calculated using braids. A braid is a set of n strings stretching between two parallel planes. This review demonstrates how integrals over the braid path can yield topological invariants. The simplest such invariant is the winding number – the net number of times two strings in a braid wrap about each other. But other, higher-order invariants exist. The mathematical literature on these invariants usually employs techniques from algebraic topology that may be unfamiliar to physicists and mathematicians in other disciplines. The primary goal of this paper is to introduce higher-order invariants using only elementary differential geometry.Some of the higher-order quantities can be found directly by searching for closed one-forms. However, the Kontsevich integral provides a more general route. This integral gives a formal sum of all finite order topological invariants. We describe the Kontsevich integral, and prove that it is invariant to deformations of the braid.Some of the higher-order invariants can be used to generate Hamiltonian dynamics of n particles in the plane. The invariants are expressed as complex numbers; but only the real part gives interesting topological information. Rather than ignoring the imaginary part, we can use it as a Hamiltonian. For n = 2, this will be the Hamiltonian for point vortex motion in the plane. The Hamiltonian for n = 3 generates more complicated motions.     

Invariants of the Reflection Coefficient

Optics and Spectroscopy - The reflection coefficient of a plane monochromatic wave from a three-layer structure is analyzed in detail in the case in which the wave is linearly polarized in the...     

Subfactor Realisation of Modular Invariants

 We study the problem of realising modular invariants by braided subfactors and the related problem of classifying nimreps. We develop the fusion rule structure of these modular invariants. This structure is a useful tool in the analysis of modular data from quantum double subfactors, particularly those of the double of cyclic groups, the symmetric group on 3 letters and the double of the subfactors with principal graph the extended Dynkin diagram D ₅ ⁽¹⁾. In particular for the double of S ₃, 14 of the 48 modular modular invariants are nimless, and only 28 of the remaining 34 nimble invariants can be realised by subfactors. Received: 14 February 2003 / Accepted: 3 April 2003 Published online: 19 May 2003 Communicated by H. Araki, D. Buchholz and K. Fredenhagen     

事件驱动的无线传感器网络嵌入式操作系统研究

针对无线传感器网络节点能量敏感和多任务的特点,提出了基于事件驱动的嵌入式实时操作系统;采用分层结构的设计思想,构建模块化的系统组件,利用内存控制块链表,实现简易高效的内存管理;基于事件驱动和任务优先级,实现系统低功耗和抢占式的任务调度;实验结果表明,系统功耗低,实时性好。     

Invariants of Multi-Component Ermakov Systems

It is shown that certain multi-component Ermakov systems admit Lewis-Ray-Reid invariants. This extends the result to the two-component Ermakov system.     

Invariants of chaotic Hamiltonian systems

The invariants of chaotic bounded Hamiltonian systems and their relation to the solutions of the first variational equations of the equations of motion are studied. We show that these invariants are characterized by the fact that they either lose the property of differentiability as functions on phase space or that a certain formal power series defined in terms of the derivatives of the invariants has zero radius of convergence. For a specific example, we show that the former possibility appears to apply.     

Invariants of topological quantum mechanics

We investigate a new topological invariant of the punctured plane using a Hamiltonian approach. The Hamiltonian is built out of topological invariants available on the punctured plane. On the other hand it is shown that the model is a generalized version, using the appropriate language of homotopy, of the superconformal quantum mechanics (gauge approach) recently proposed by L. Baulieuet al. This relationship allows a better understanding of the structure and results of the gauge approach and makes possible a proper identification of the topological invariants which emerge from it.     

Invariants of Multi-Component Ermakov Systems

It is shown that certain multi-component Ermakov systems admit Lewis-Ray-Reid invariants. This extends the result to the two-component Ermakov system.     

One-Step Implementation of Single Spin Measurement in Spin Star Network

We present an efficient one-step scheme for a single spin measurement based on nuclear magnetic resonance （NMR） techniques. This scheme considerably reduces the time of operation using a spin star network where a target spin and an ancillary spin are coupled to a ring of N spins. As opposed to the proposal in [Phys. Rev. Lett. 97 （2006） 100501] using a cubic lattice crystal to achieve a cubic speedup, the distinct advantage of this scheme is that under ideal conditions it requires the application of only one step to create a system of N correlated spins. In the process of single spin measurement, the total macroscopic magnetization, the individual magnetization and the transfer fidelity are calculated analytically as simple cosine functions of time and the amplitude of irradiation.