Dynamics of quantum zeno and anti-zeno effects in an open system

We provide a general dynamical approach for the quantum Zeno and anti-Zeno efects in an open quantum system under repeated non-demolition measurements.In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation.Based on that model,we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements,and derive the measurement-modified decay rates of the excited state.In the cases with frequent ideal measurements at zero-temperature,we re-obtain the same decay rate as that from the wave function collapse postulation(Nature,2000,405:546).The correction to the ideal decay rate is also obtained under the non-ideal measurements.Especially,we find that the quantum Zeno and anti-Zeno efects are possibly enhanced by the non-ideal natures of measurements.For the open system under measurements with arbitrary period,we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum,and show that in the long-time evolution the noise spectrum is efectively tuned by the repeated measurements.Our approach is also able to describe the quantum Zeno and anti-Zeno efects given by the phase modulation pulses,as well as the relevant quantum control schemes.     

Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics

The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach： One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.     

Non-Markovian dynamics of a qubit in a reservoir: different solutions of non-Markovian master equation

We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.     

Dynamical potential approach to dissociation of H--C bond in HCO highly excited vibration

The highly excited vibrational levels of HCO in the electronic ground state, \tilde {X}¹A',are employed to determine the coefficients of an algebraic Hamiltonian, by which the dynamical potential is derived and shown to be very useful for interpreting the intramolecular vibrational relaxation (IVR) which operates via the HCO bending motion. The IVR inhibits the dissociation of H atom and enhances the stochastic degree of dynamical character. This approach is from a global viewpoint on a series of levels classified by the polyad number which is a constant of motion in a certain dynamical domain. In this way, the seemingly complicated level structure shows very regular picture, dynamically.     

Initial-Value Problem of a Coupled Dispersionless System: Dynamical System Approach

We investigate the dynamical behaviour of a coupled dispersionless system （CDS） by solving its initial-value problem following a dynamical system approach. As a result, we unearth a typical miscellaneous travelling waves including the localized and periodic ones. We also investigate the energy density of such waves and find that under some boundary conditions, the localized waves moving towards positive direction are more stable than the periodic waves which on contrary stand for the most conditions. stable travelling waves in another situation of boundary conditions.     

Some dynamical property of the Tsallis distribution from a Fokker-Planck equation

This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.     

Partial entropy change and entanglement in the mixed state for a Jaynes－Cummings model with Kerr medium

By using the algebraic dynamical approach, an atom--field bipartite system in mixed state is employed to investigate the partial entropy change and the entanglement in a cavity filled with Kerr medium. The effects of different nonlinear intensities are studied. One can find that the Kerr nonlinearity can reduce the fluctuation amplitudes of the partial entropy changes and the entanglement of the two subsystems, and also influence their periodic evolution. Meanwhile, increasing the Kerr nonlinear strength can convert the anti-correlated behaviour of the partial entropy change to the positively correlated behaviour. Furthermore, the entanglement greatly depends on the temperature. When the temperature or the nonlinear intensity increases to a certain value, the entanglement can be suppressed greatly.     

Stochastic period-doubling bifurcation analysis of stochastic Bonhoeffer--van der Pol system

In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer--van der Pol (BVP for short) system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter. The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function.     

Chaotic motion of the dynamical system under both additive and multiplicative noise excitations

With both additive and multiplicative noise excitations, the effect on the chaotic behaviour of the dynamical system is investigated in this paper. The random Melnikov theorem with the mean-square criterion that applies to a type of dynamical systems is analysed in order to obtain the conditions for the possible occurrence of chaos. As an example, for the Duffing system, we deduce its concrete expression for the threshold of multiplicative noise amplitude for the rising of chaos, and by combining figures, we discuss the influences of the amplitude, intensity and frequency of both bounded noises on the dynamical behaviour of the Duffing system separately. Finally, numerical simulations are illustrated to verify the theoretical analysis according to the largest Lyapunov exponent and Poincaré map.     

Identification of Chaotic Systems with Application to Chaotic Communication

We propose and develop a novel method to identify a chaotic system with time-varying bifurcation parameters via an observation signal which has been contaminated by additive white Gaussian noise.This method is based on an adaptive algorithm,which takes advantage of the good approximation capability of the radial basis function neural network and the ability of the extended Kalman filter for tracking a time-varying dynamical system.It is demonstrated that,provided the bifurcation parameter varies slowly in a time window,a chaotic dynamical system can be tracked and identified continuously,and the time-varying bifurcation parameter can also be retrieved in a sub-window of time via a simple least-square-fit method.     

Towards a dynamical temperature of finite Hamiltonian systems

With the aid of numerical simulations of the β Fermi-Pasta-Ulam (FPU) system, we compare the different definitions of dynamical temperature for Hamiltonian systems. We have shown that each definition gives different values of temperature for a system with a small number of degrees of freedom (DOF). Only for systems with a sufficiently large number of DOF, do all the definitions of dynamical temperature approach the same value.     

A measure of conductivity for lattice fermions at finite density

We study the linear response to an external electric field of a system of fermions in a lattice at zero temperature. This allows to measure numerically the Euclidean conductivity which turns out to be compatible with an analytical calculation for free fermions. The numerical method is generalizable to systems with dynamical interactions where no analytical approach is possible.     

Dynamics of quantum zeno and anti-zeno efects in an open system

We provide a general dynamical approach for the quantum Zeno and anti-Zeno efects in an open quantum system under repeated non-demolition measurements.In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation.Based on that model,we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements,and derive the measurement-modified decay rates of the excited state.In the cases with frequent ideal measurements at zero-temperature,we re-obtain the same decay rate as that from the wave function collapse postulation(Nature,2000,405:546).The correction to the ideal decay rate is also obtained under the non-ideal measurements.Especially,we find that the quantum Zeno and anti-Zeno efects are possibly enhanced by the non-ideal natures of measurements.For the open system under measurements with arbitrary period,we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum,and show that in the long-time evolution the noise spectrum is efectively tuned by the repeated measurements.Our approach is also able to describe the quantum Zeno and anti-Zeno efects given by the phase modulation pulses,as well as the relevant quantum control schemes.     

Thermodynamics based on the principle of least abbreviated action: Entropy production in a network of coupled oscillators

We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several examples are worked out to show that this formalism yields the right microcanonical (equilibrium) quantities. The relevance of this approach to nonequilibrium situations is illustrated with an application to a network of coupled oscillators (Kuramoto model). We provide an expression for the entropy production in this system finding that its positive value is directly related to dissipation at the steady state in attaining order through synchronization.     

Exact Dynamical Equations of Three-State Ising Neural Network Derived from a Generating Functional

The exact equations of parallel dynamics for three-Ising neural networks at zero temperature are derived from a generating functional. The generating functional is proposed to be a δ-function to fit the dynamical rule of three-Ising model. The dynamical equations obtained in the case without self-coupling terms are in agreement with the published results derived with a probabilistic approach, which shows that this approach can be used to advantage in calculating the exact dynamical equations and other order parameters for multistate Ising neural networks.     

Quasi-linearization and stability analysis of some self-dual,dark equations and a new dynamical system†

We describe a class of self-dual dark nonlinear dynamical systems a priori allowing their quasi-linearization, whose integrability can be effectively studied by means of a geometrically based gradient-holonomic approach. A special case of the self-dual dynamical system, parametrically dependent on a functional variable is considered, and the related integrability condition is formulated. Using this integrability scheme, we study a new self-dual, dark nonlinear dynamical system on a smooth functional manifold, which models the interaction of atmospheric magneto-sonic Alfvén plasma waves. We prove that this dynamical system possesses a Lax representation that allows its full direct linearization and compatible Poisson structures. Moreover, for this self-dual nonlinear dynamical system we construct an infinite hierarchy of mutually commuting conservation laws and prove its complete integrability.     

Neutron scattering evidence of a boson peak in protein hydration water

Measurement of the low temperature neutron excess of scattering of H2O-hydrated plastocyanin relative to D2O-hydrated protein allowed us to reveal the presence of an inelastic peak at about 3.5 meV. This excess of vibrational modes, elsewhere termed "boson peak," is due to the dynamical behavior of the water molecules belonging to the H2O-hydration shell surrounding the protein. The relevance of the boson peak to the dynamical coupling between the solvent and the protein, and hence to the protein functionality is addressed.     

中能重离子碰撞中的气–液相变和同位旋分馏

利用核物质理论研究气–液相变结果表明,气–液相变中临界温度T_c随系统质量的增加而增加,但随碰撞系统同位旋的增加而减小.利用改进的同位旋相关的量子分子动力学模型,研究了中能重离子碰撞过程中同位旋分馏强度随碰撞系统的同位旋和系统质量的变化,结果表明,同位旋分馏强度与气–液相变临界温度T_c有对应的关系,特别是气–液相变和同位旋分馏都发生在正常核密度以下低密度的spinodal不稳定区.这表明气–液相变和同位旋分馏具有相类似的动力学行为和内在联系,也预示着可以通过对同位旋分馏强度的研究和测量来揭示中能重离子碰撞过程中气–液相变的动力学特征