Quasi-stationary states and incomplete violent relaxation in systems with long-range interactions

We discuss the nature of quasi-stationary states (QSS) with non-Boltzmannian distribution in systems with long-range interactions in relation with a process of incomplete violent relaxation based on the Vlasov equation. We discuss several attempts to characterize these QSS. We show that their distribution is non-universal and explain why their prediction is difficult in general.     

Metastability in the Hamiltonian mean field model and Kuramoto model

We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian mean field (HMF) model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi-stationary states (QSS) observed in the model and the connections to Tsallis statistics and glassy dynamics. We also present new results on the existence of metastable states in the Kuramoto model and discuss the similarities with those found in the HMF model. The existence of metastability seems to be quite a common phenomenon in fully coupled systems, whose origin could be also interpreted as a dynamical mechanism preventing or hindering synchronization.     

General linear response formula for non integrable systems obeying the Vlasov equation

Long-range interacting N-particle systems get trapped into long-living out-of-equilibrium stationary states called quasi-stationary states (QSS). We study here the response to a small external perturbation when such systems are settled into a QSS. In the N → ∞ limit the system is described by the Vlasov equation and QSS are mapped into stable stationary solutions of such equation. We consider this problem in the context of a model that has recently attracted considerable attention, the Hamiltonian mean field (HMF) model. For such a model, stationary inhomogeneous and homogeneous states determine an integrable dynamics in the mean-field effective potential and an action-angle transformation allows one to derive an exact linear response formula. However, such a result would be of limited interest if restricted to the integrable case. In this paper, we show how to derive a general linear response formula which does not use integrability as a requirement. The presence of conservation laws (mass, energy, momentum, etc.) and of further Casimir invariants can be imposed a posteriori. We perform an analysis of the infinite time asymptotics of the response formula for a specific observable, the magnetization in the HMF model, as a result of the application of an external magnetic field, for two stationary stable distributions: the Boltzmann-Gibbs equilibrium distribution and the Fermi-Dirac one. When compared with numerical simulations the predictions of the theory are very good away from the transition energy from inhomogeneous to homogeneous states.     

Origin of the high-and low-frequency K-satellites of 31Ga, 32Ge and 33As

The origin of the high- and low-frequency K-satellites of ³¹Ga, ³²Ge, ³³ As is explain on the basis of Hayasi's theory of quasi-stationary states. It is shown that the same QSS difference gives rise to a particular satellite of either type in all the elements. The results are compared with those of multiple ionisation theory.     

Exploring the thermodynamic limit of Hamiltonian models: convergence to the Vlasov equation

We here discuss the emergence of quasistationary states (QSS), a universal feature of systems with long-range interactions. With reference to the Hamiltonian mean-field model, numerical simulations are performed based on both the original N-body setting and the continuum Vlasov model which is supposed to hold in the thermodynamic limit. A detailed comparison unambiguously demonstrates that the Vlasov-wave system provides the correct framework to address the study of QSS. Further, analytical calculations based on Lynden-Bell's theory of violent relaxation are shown to result in accurate predictions. Finally, in specific regions of parameters space, Vlasov numerical solutions are shown to be affected by small scale fluctuations, a finding that points to the need for novel schemes able to account for particle correlations.     

A Strong Pair Correlation Bound Implies the CLT for Sinai Billiards

We investigate the possibility of proving the Central Limit Theorem (CLT) for Dynamical Systems using only information on pair correlations. A strong bound on multiple correlations is known to imply the CLT (Chernov and Markarian in Chaotic Billiards, 2006). In Chernov’s paper (J. Stat. Phys. 122(6), 2006), such a bound is derived for dynamically Hölder continuous observables of dispersing Billiards. Here we weaken the regularity assumption and subsequently show that the bound on multiple correlations follows directly from the bound on pair correlations. Thus, a strong bound on pair correlations alone implies the CLT, for a wider class of observables. The result is extended to Anosov diffeomorphisms in any dimension. Some non-invertible maps are also considered.     

High-Capacity Quantum Secret Sharing with Hyperdense Coding Assisted by Hyperentangled Photon Pairs

We presents a high-capacity three-party quantum secret sharing (QSS) protocol with a sequence of photon pairs in hyperentangled Bell states in both the polarization and the spatial-mode degrees of freedom. In our scheme, the boss Alice prepares a sequence of photon pairs in hyperentangled Bell states and divides them into two photon sequences which are sent the two agents, respectively. Alice exploits four subsets of decoy photons to assure the security of the photon transmission between her and her agents. The present QSS scheme has the advantage of having a high channel capacity as each photon pair can carry 4 bits of secret message in principle, two times of that by Deng et al. (Phys. Lett. A 372: 1957, 2008). We give out the setups for the preparation of the photon pairs in hyperentangled Bell states with a beta barium borate crystal and the manipulation of the photons with linear optical elements. It will be shown that our QSS protocol is feasible with current experimental technology.     

Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions

Systems of particles interacting with long range interactions present generically ”quasi-stationary states” (QSS), which are approximately time-independent out of equilibrium states. In this proceedings, we explore the generalization of the formation of such QSS and their relaxation from the much studied case of gravity to a generic pair interaction with the asymptotic form of the potential v(r) ∼ 1/r ^γ with γ > 0 in d dimensions. We compute analytic estimations of the relaxation time calculating the rate of two body collisionality in a virialized system approximated as homogeneous. We show that for γ < (d − 1/2), the collision integral is dominated by the size of the system, while for γ > (d − 1/2), it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles if γ < d − 1 (i.e. the force is not integrable) and decreases if γ > d − 1. Using numerical simulations we confirm our analytic results. A corollary of our work gives a ”dynamical” classification of interactions: the dynamical properties of the system depend on whether the pair force is integrable or not.     

High-Capacity Three-Party Quantum Secret Sharing with Single Photons in Both the Polarization and the Spatial-Mode Degrees of Freedom

We present a high-capacity three-party quantum secret sharing (QSS) protocol with a sequence of single photons in both the polarization and the spatial-mode degrees of freedom. By inserting the boss Alice into the middle position between the two agents Bob and Charlie, our QSS protocol is secure in theory. The boss Alice chooses some unitary operations to encode her information on the single photons. It is interesting to point out the fact that Alice does not change the bases of the single photons which are used to carry the useful information about the private key, which improves its success probability for obtaining a private key. Compared with the QSS protocol by Zhou et al. (Chin. Phys. Lett. 24, 2181 (2007)), our QSS protocol has a higher capacity without increasing the difficulty of its implementation in experiment as each correlated photon can carry two bits of useful information. Compared with those QSS protocols based on entangled photon pairs and Bell-state measurements, our QSS protocol is more feasible as it does not require the complete Bell-state analysis which is not easy with linear optics. We give out the setup for the implementation of our QSS protocol with linear optical elements.     

Ⅰ类和Ⅱ类准周期半导体超晶格的电子子带和波函数

本文将包迹函数近似推广用于计算有理数近似下,垂直于超晶格轴的波矢K_⊥不等于零时,准周期半导体超晶格(QSS)的电子子带和波函数,对K_⊥=0的情形,分别计算了Ⅰ类的GaAs/Al_xGa_1-xAs和Ⅱ类的InAs/GaSb QSS的电子子带和波函数,直至代序数m=9和6。对于价带对导带影响强的InAs/GaSb QSS,分别计算了m=5和6时电子子带随K_⊥的变化关系。并提出了利用本文结果计算Ⅰ类的GaAs/Al_xGa_1-xAs QSS带间集体激发的具体方法。     

Central limit behavior in the Kuramoto model at the “edge of chaos”

We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong, the Pdfs of the sums tend to a Gaussian, consistently with the standard CLT. On the other hand, when the system is at the “edge of chaos” (i.e. in a regime with vanishing Lyapunov exponents), robust q-Gaussian-like limit distributions naturally emerge, consistently with recently proved generalizations of the CLT.     

Multi-party d-Level Quantum Secret Sharing Scheme

We develop a multiparty quantum secret sharing (QSS) scheme of classical messages based on arbitrary dimensional multi-particle Greenberger-Horne-Zeilinger (GHZ) states. This scheme can be implemented using only local operations, e.g. generalized Z gate and Hadamard gate, and classical communication (LOCC) between participants. The security of the present scheme against exterior eavesdropping and interior dishonest party has been analyzed and confirmed. Moreover, we discuss the possibility of successful sharing of classical messages in the realistic situation where our QSS scheme is carried out in generalized Pauli channels.     

Stochastic theory of nonlinear rate processes with multiple stationary states

A comparison has been made between the deterministic and stochastic (master equation) formulation of nonlinear chemical rate processes with multiple stationary states. We have shown, via two specific examples of chemical reaction schemes, that the master equations have quasi-stationary state solutions which agree with the various initial condition dependent equilibrium solutions of the deterministic equations. The presence of fluctuations in the stochastic formulation leads to true equilibrium solutions, i.e. solutions which are independent of initial conditions as t → ∞. We show that the stochastic formulation leads to two distinct time scales for relaxation. The mean time for the reaction system to reach the quasi-stationary states from any initial state is of $\text{O}$(N⁰) where N is a measure of the size of the reaction system. The mean time for relaxation from a quasi-stationary state to the true equilibrium state is $\text{O}$(e^N). The results obtained from the stochastic formulation as regards the number and location of the quasi-stationary states are in complete agreement with the deterministic results.     

Universality of Short-Range Nucleon-Nucleon Correlations in Nuclei

We investigate the short-range correlations in light nuclei. The highly correlated many-body states are obtained with an explicitly correlated basis which enables us to get a precise solution of a many-body Schrödinger equation for a realistic interaction. We show two-body density distributions for the different spin-isospin channels calculated from three- and four-body states to investigate the short-range correlations between nucleon pairs. At distances below 1 fm a universal behavior is found which does not depend on the many-body states. The universality is also seen in high momentum components of the two-body momentum distributions.     

束缚纠缠态量子秘密共享的不安全性分析

分析了以Smolin束缚纠缠态作为通道量子态的量子秘密共享方案的安全性.给出了一个简单的来自通信方内部的截获重发攻击策略,这个攻击策略是依赖比对单量子比特测量结果的窃听检测程序所不能检测出来的.结果表明,仅以束缚纠缠Smolin态作为通道量子态的量子秘密共享方案对于来自内部的窃听攻击不是无条件的.     

Relative intensities in X-ray photoelectron spectra: Part XI. Calculation of photoionization cross sections for valence levels of SiF4

Partial photoionization cross sections for valence MOs of SiF₄ have been calculated by the method of multiple scattering with atomic amplitudes (MSAA) for excitation energies ranging from the ionization threshold to 60 eV. The cross section behavior near the ionization thresholds is determined mainly by the shape resonances of t₂ and e symmetries. The resonance structure of photoionization cross sections is treated in terms of deviations from the additive model, and of conceptions of “quasi-stationary” states and “quasi-forbidden” bands. The energy positions of quasi-stationary states in SiF₄ are compared with the data obtained from X-ray absorption spectra. The dependence of theoretical cross sections on the inter-nuclear distances is studied.     

The Vlasov equation and the Hamiltonian mean-field model

We show that the quasi-stationary states of homogeneous (zero magnetization) states observed in the N-particle dynamics of the Hamiltonian mean-field (HMF) model are nothing but Vlasov stable homogeneous states. There is an infinity of Vlasov stable homogeneous states corresponding to different initial momentum distributions. Tsallis q-exponentials in momentum, homogeneous in angle, distribution functions are possible, however, they are not special in any respect, among an infinity of others. All Vlasov stable homogeneous states lose their stability because of finite N effects and, after a relaxation time diverging with a power-law of the number of particles, the system converges to the Boltzmann–Gibbs equilibrium.     

Graph State-Based Quantum Secret Sharing with the Chinese Remainder Theorem

Quantum secret sharing (QSS) is a significant quantum cryptography technology in the literature. Dividing an initial secret into several sub-secrets which are then transferred to other legal participants so that it can be securely recovered in a collaboration fashion. In this paper, we develop a quantum route selection based on the encoded quantum graph state, thus enabling the practical QSS scheme in the small-scale complex quantum network. Legal participants are conveniently designated with the quantum route selection using the entanglement of the encoded graph states. Each participant holds a vertex of the graph state so that legal participants are selected through performing operations on specific vertices. The Chinese remainder theorem (CRT) strengthens the security of the recovering process of the initial secret among the legal participants. The security is ensured by the entanglement of the encoded graph states that are cooperatively prepared and shared by legal users beforehand with the sub-secrets embedded in the CRT over finite fields.     

利用光束的轨道角动量实现高密度数据存储的机理研究

光束的轨道角动量本征态可以构建高维Hilbert空间，将之应用于数据存储中，可以实现比传统方法更高的数据存储密度.提出了一种用光束轨道角动量实现高密度数据存储的方法，对存储区域进行相位编码，通过探测透射光束轨道角动量谱(螺旋谱)的特征来区分由相位编码形成的不同数据态.四台阶结构相位编码可以实现57个不同的数据态，有望将数据密度提高为传统方法的近6倍. 关键词： 光束轨道角动量 光学存储 高密度存储     

Action in Hamiltonian Models Constructed by Yang-Baxter Equation: Entanglement and Measures of Correlation

By using the quantum Yang-Baxterization approach, we investigate the dynamics of quantum entanglement under the actions of different Hamiltonians on the different two-qubit input states and analyze the effects of the Yang-Baxter operations on it. During any quantum process that takes place in a noisy environment, quantum correlations display behavior that does not increase. We point out that for two-qubit systems subject to actions of different Yang-Baxter operations the loss of correlations can be mitigated by the appropriate choice of the initial states and the Yang-Baxterization process. We show that in a noisy environment it possible to create the optimal conditions for performing any quantum information task.