Percolation for low energy clusters and discrete symmetry breaking in classical spin systems

We consider classical lattice systems in two or more dimensions with general state space and with short-range interactions. It is shown that percolation is a general feature of these systems: If the temperature is sufficiently low, then almost surely with respect to some equilibrium state there is an infinite cluster of spins trying to form a ground state. For systems having several stable sets of symmetry-related ground states we show that at low temperatures spontaneous symmetry breaking occurs because in a two-dimensional subsystem there is a unique infinite cluster of this type.     

Chaotic behavior in nonlinear Hamiltonian systems and equilibrium statistical mechanics

The relation between chaotic dynamics of nonlinear Hamiltonian systems and equilibrium statistical mechanics in its canonical ensemble formulation has been investigated for two different nonlinear Hamiltonian systems. We have compared time averages obtained by means of numerical simulations of molecular dynamics type with analytically computed ensemble averages. The numerical simulation of the dynamic counterpart of the canonical ensemble is obtained by considering the behavior of a small part of a given system, described by a microcanonical ensemble, in order to have fluctuations of the energy of the subsystem. The results for the Fermi-Pasta-Ulam model (i.e., a one-dimensional anharmonic solid) show a substantial agreement between time and ensemble averages independent of the degree of stochasticity of the dynamics. On the other hand, a very different behavior is observed for a chain of weakly coupled rotators, where linear exchange effects are absent. In the high-temperature limit (weak coupling) we have a strong disagreement between time and ensemble averages for the specific heat even if the dynamics is chaotic. This behavior is related to the presence of spatially localized chaos, which prevents the complete filling of the accessible phase space of the system. Localized chaos is detected by the distribution of all the characteristic Liapunov exponents.     

Quenching of self-excited vibrations equilibrium aspects

An analysis is presented of two types of self-excited, two-degree-of-freedom systems. The basic subsystem, in each, is governed by a Van der Pol differential equation. This subsystem is considered attached to a vibration absorber or mounted on a resilient foundation. An examination of the stability of the equilibrium position of the entire system enables one to establish optimal design parameters for either type. The procedure devised for the stability analysis makes it possible to ascertain separately the stability with respect to one or the other natural frequency of the system.     

Switch control for piecewise affine chaotic systems

Switch control can be imposed naturally on the piecewise affine system, where the control action switches from an affine subsystem to another according to switch conditions depending on the system states. In this paper we present such piecewise feedback control for stabilizing unstable equilibrium points of piecewise affine systems. The noise effect on the stabilization is also investigated. The original Chua's circuit is used to illustrate our results.     

Controlling chaos in a satellite power supply subsystem

In this work, we show that chaos control techniques can be used to increase the region that can be efficiently used to supply the power requests for an artificial satellite. The core of a satellite power subsystem relies on its DC/DC converter. This is a very nonlinear system that presents a multitude of phenomena ranging from bifurcations, quasi-periodicity, chaos, coexistence of attractors, among others. The traditional power subsystem design techniques try to avoid these nonlinear phenomena so that it is possible to use linear system theory in small regions about the equilibrium points. Here, we show that chaos control can be used to efficiently extend the applicability region of the satellite power subsystem when it operates in regions of high nonlinearity.     

Exactly Solvable Model of Quantum Diffusion

We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band. The subsystem interacts with its environment by a coupling expressed in terms of correlation functions which are delta-correlated in space and time. For weak coupling, the time evolution of the subsystem density matrix is ruled by a quantum master equation of Lindblad type. Thanks to the invariance under spatial translations, we can apply the Bloch theorem to the subsystem density matrix and exactly diagonalize the time evolution superoperator to obtain the complete spectrum of its eigenvalues, which fully describe the relaxation to equilibrium. Above a critical coupling which is inversely proportional to the size of the subsystem, the spectrum at given wave number contains an isolated eigenvalue describing diffusion. The other eigenvalues rule the decay of the populations and quantum coherences with decay rates which are proportional to the intensity of the environmental noise. An analytical expression is obtained for the dispersion relation of diffusion. The diffusion coefficient is proportional to the square of the width of the energy band and inversely proportional to the intensity of the environmental noise because diffusion results from the perturbation of quantum tunneling by the environmental fluctuations in this model. Diffusion disappears below the critical coupling     

The Schrödinger–Langevin equation with and without thermal fluctuations

The Schrödinger–Langevin equation (SLE) is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues relative to its solutions: the stationarity of the excited states of the non-interacting subsystem when one considers the dissipation only and the thermal relaxation toward asymptotic distributions with the additional stochastic term. We first show that a proper application of the Madelung/polar transformation of the wave function leads to a non zero damping of the excited states of the quantum subsystem. We then study analytically and numerically the SLE ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states and quantum noises are discussed and a detailed analysis is carried with two kinds of noise and potential. We show that within our assumptions the use of the SLE as an effective open quantum system formalism is possible and discuss some of its limitations.     

General approach to quantum-classical hybrid systems and geometric forces

We present a general theoretical framework for a hybrid system that is composed of a quantum subsystem and a classical subsystem. We approach such a system with a simple canonical transformation which is particularly effective when the quantum subsystem is dynamically much faster than the classical counterpart, which is commonly the case in hybrid systems. Moreover, this canonical transformation generates a vector potential which, on one hand, gives rise to the familiar Berry phase in the fast quantum dynamics and, on the other hand, yields a Lorentz-like geometric force in the slow classical dynamics.     

Quad-rotor unmanned helicopter control via novel robust terminal sliding mode controller and under-actuated system sliding mode controller

This paper uses the recently developed novel robust terminal sliding mode control (NRTSMC) and under-actuated system sliding mode control (USSMC) approaches to solve the strong coupling and under-actuated problems of a small quad-rotor unmanned helicopter (QRUH). The two controllers have been widely adopted to act as a single control algorithm in many fields, respectively. However, this paper just displays the useful composite application of the two controllers. The QRUH model can be divided into two subsystems, including a fully actuated subsystem (FAS) and an under-actuated subsystem (UAS). For the FAS, the NRTSMC is used to solve the strong coupling problem, it can guarantee the FAS states converge to the desired equilibrium in a very short time, then the states are treated as time invariants and the UAS gets simplified. For the UAS, the USSMC is utilized to solve the under-actuated problem. The obtained simulation results show the applicability of the composite control when faced with external disturbances.     

Complex pole approach in thermodynamic description of fluid mixtures with small number of molecules

The subject matter of classical thermodynamics is the asymptotic behavior of equilibrium systems in thermodynamic limit, for small molecular systems, when transition to thermodynamic limit is impossible, the extension of thermodynamics is required. This work studies novel approach for the evaluation of partition functions of small systems by complex pole analysis. Several cases for molecular systems in small cavities are studied numerically. In particular size-dependent additional pressure for small systems is evaluated analytically and numerically. Similar approach was developed earlier in nuclear physics for finite systems of nucleons. The obtained results correspond to published experimental data and molecular dynamics simulations.     

Two problems concerning hot hadronic matter and high energy collisions (Equilibrium formation,plasma deflagration)

This paper addresses two questions concerning the hydrodynamical approach to high energy collisions producing large multiplicities of hadrons. The first one concerns the difficulty of understanding in terms of successive parton interactions the formation of local thermal equilibrium for the small and short-lived blobs of excited hadronic matter created in such collisions. We argue that the number of successive parton interactions is not the only relevant factor for equilibrium formation, another factor being the early randomization present in all experiments which observe a subsystem of the complete final state and average over many unobserved degrees of freedom. This conjecture helps to understand the high degree of universality of hadronic jets and the fact that quite different dynamical models manage to describe the same data. The second problem concerns the hadronization of a blob of quark-gluon plasma as could be produced in a very high energy collision. Assuming the transition of plasma to hadron gas to have high latent heat, we show for small chemical potential that the plasma can deflagrate and convert a fraction of its latent heat into collective flow of the hadron gas. In such deflagrations very little entropy is produced, but the flow velocity of the hadron gas with respect to the plasma can be more than half of the velocity of light.     

Synchronization in nonidentical complex Ginzburg-Landau equations

A cross-correlation coefficient of complex fields has been investigated for diagnosing spatiotemporal synchronization behavior of coupled complex fields. We have also generalized the subsystem synchronization way established in low-dimensional systems to one- and two-dimensional Ginzburg-Landau equations. By applying the indicator to examine the synchronization behavior of coupled Ginzburg-Landau equations, it is shown that our subsystem approach may be of better synchronization performance than the linear feedback method. For the linear feedback Ginzburg-Landau equation, the nonidentical system exhibits generalized synchronization characteristics in both amplitude and phase. However, the nonidentical subsystem may exhibit complete-like synchronization properties. The difference between complex fields for driven and response systems gives a linear scaling with the change of their parameter difference.     

Berry phase in a bipartite system with general subsystem–subsystem couplings

The Berry phase in a bipartite system described by the XXZ model is studied in this Letter. We calculate the Berry phase acquired by the bipartite system as well as the geometric phase gained by each subsystem. The results show that as the coupling constants tend to infinity all geometric phases go to zero, this confirms the prediction given by us previously [X.X. Yi, L.C. Wang, T.Y. Zheng, Phys. Rev. Lett. 92 (2004) 150406] for bipartite systems with a specific subsystem–subsystem coupling.     

HL-2A装置实时等离子体位形重建系统的加速优化

现有的HL-2A实时平衡重建系统采用的是网格尺寸为33×33,将无法满足HL-2M装置对控制精度和速度要求。为此开发了网格尺寸为129×129的重建系统,并通过GPU并行、算法重构等优化方法,使得新的重建系统在保证计算精度的情况下能够使得每一次平均重建计算维持在600μs内,可满足HL-2A和HL-2M中周期为1ms等离子体控制系统对重建系统精度和速度要求。     

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现有的HL-2A实时平衡重建系统采用的是网格尺寸为33×33,将无法满足HL-2M装置对控制精度和速度要求.为此开发了网格尺寸为129×129的重建系统,并通过GPU并行、算法重构等优化方法,使得新的重建系统在保证计算精度的情况下能够使得每一次平均重建计算维持在600μs内,可满足HL-2A和HL-2M中周期为1ms等离子体控制系统对重建系统精度和速度要求.     

Scaling and interleaving of subsystem Lyapunov exponents for spatio-temporal systems

The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the spectrum of a subsystem by a suitable rescaling in a very cost effective way. We compute the Lyapunov spectrum for the subsystem by truncating the original Jacobian without modifying the original dynamics and thus taking into account only a portion of the information of the entire system. In doing so we notice that the Lyapunov spectra for consecutive subsystem sizes are interleaved and we discuss the possible ways in which this may arise. We also present a new rescaling method, which gives a significantly better fit to the original Lyapunov spectrum. We evaluate the performance of our rescaling method by comparing it to the conventional rescaling (dividing by the relative subsystem volume) for one- and two-dimensional lattices in spatio-temporal chaotic regimes. Finally, we use the new rescaling to approximate quantities derived from the Lyapunov spectrum (largest Lyapunov exponent, Lyapunov dimension, and Kolmogorov-Sinai entropy), finding better convergence as the subsystem size is increased than with conventional rescaling. (c) 1999 American Institute of Physics.     

Theoretical evidence for a reentrant phase diagram in ortho-para mixtures of solid H2 at high pressure

We develop a multiorder parameter mean-field formalism for systems of coupled quantum rotors. The scheme is developed to account for systems where ortho-para distinction is valid. We apply our formalism to solid H2 and D2. We find an anomalous reentrant orientational phase transition for both systems at thermal equilibrium. The correlation functions of the order parameter indicate short-range order at low temperatures. As the temperature is increased the correlation increases along the phase boundary. We also find that even extremely small odd-J concentrations (1%) can trigger short-range orientational ordering.     

Integrable Mott insulators driven by a finite electric field

We develop a method for extracting the steady nonequilibrium current from studies of driven isolated systems, applying it to the model of a one-dimensional Mott insulator at high temperatures. While in the nonintegrable model the nonequilibrium conditions can be accounted for by internal heating, the integrability leads to a strongly nonlinear dc response with a vanishingly small dc conductivity in the linear-response regime. The finding is consistent with equilibrium results for the dc limit of the optical conductivity determined in the presence of a weak and decreasing perturbation.