Heat conduction in a three-dimensional momentum-conserving anharmonic lattice

Heat conduction in three-dimensional anharmonic lattices was numerically studied by the Green-Kubo theory. For a given lattice width W, a dimensional crossover is generally observed to occur at a W-dependent threshold of the lattice length. Lattices shorter than W will display a 3D behavior while lattices longer than W will display a 1D behavior. In the 3D regime, the heat current autocorrelation function was found to show a power-law decay as a function of the time lag τ as τ^{β} with β=-1.2. This indicates normal heat conduction. However, the decay exponent deviates significantly from the conventional theoretical value of β=-1.5. A flat power spectrum S(ω) of the global heat current in the low-frequency limit was also observed in the 3D regime. This provides not only an alternative verification of normal heat conduction but also a clear physical insight into its origin.     

Simulation studies of the scattering of a solitary wave by a mass impurity in a chain of nonlinear oscillators

We have simulated large amplitude motion in cyclic one-dimensional lattices of Morse potential oscillators with a mass impurity, and have observed an unexpected persistence of solitary wave behavior for which we are unable to discover a satisfactory explanation. In solitary wave motion as a function of cycle length and of initial energy, the most common feature of the dynamics is an initial energy plateau with regular oscillatory energy exchange between the solitary wave and other excitations of the lattice, followed by rapid decay. Some systems show no decay at all through 1000 impurity interactions, while others show no significant plateau before decaying. For some cycle lengths there are energy bands in which the solitary wave propagates indefinitely long, with small amplitude oscillatory exchange of energy with the lattice. No regularities were found.     

Topological phase transition and electrically tunable diamagnetism in silicene

The movement and relaxation of the localized energy on FPU lattices have been studied by using Wavelet transforms methods. The energy relaxation mechanism for nonlinear chains involves the degradation of higher frequency excitations into lower frequencies. It is shown that low frequency modes decay more slowly in nonlinear chains. The wavelet spectrum exhibits a behavior involving the interplay of phonon modes and breather modes.     

合肥光源高亮度模式Lattice设计

介绍了一组合肥光源新高亮度模式的Lattice. 新的设计维持了储存环上所有元件和光束线位置不变,也没有加入新的元件. 取得了较低发射度. 所有直线节处的垂直方向β函数值都很小，适合插入件的运行. 跟踪计算表明新Lattice具有足够大的动力学孔径用于注入和储存粒子.     

Critical Study of Hierarchical Lattice Renormalization Group in Magnetic Ordered and Quenched Disordered Systems: Ising and Blume–Emery–Griffiths Models

Renormalization group based on the Migdal–Kadanoff bond removal approach is often considered a simple and valuable tool to understand the critical behavior of complicated statistical mechanical models. In presence of quenched disorder, however, predictions obtained with the Migdal–Kadanoff bond removal approach quite often fail to quantitatively and qualitatively reproduce critical properties obtained in the mean-field approximation or by numerical simulations in finite dimensions. In an attempt to overcome this limitation we analyze the behavior of Ising and Blume–Emery–Griffiths models on more structured hierarchical lattices. We find that, apart from some exceptions, the failure is not limited to Midgal–Kadanoff cells but originates right from the hierarchization of Bravais lattices on small cells, and shows up also when in-cell loops are considered.     

Dynamical invariants in the deterministic fixed-energy sandpile

The non-ergodic behavior of the deterministic Fixed Energy Sandpile (DFES), with Bak-Tang-Wiesenfeld (BTW) rule, is explained by the complete characterization of a class of dynamical invariants (or toppling invariants). The link between such constants of motion and the discrete Laplacians properties on graphs is algebraically and numerically clarified. In particular, it is possible to build up an explicit algorithm determining the complete set of independent toppling invariants. The partition of the configuration space into dynamically invariant sets, and the further refinement of such a partition into basins of attraction for orbits, are also studied. The total number of invariant sets equals the graphs complexity. In the case of two dimensional lattices, it is possible to estimate a very regular exponential growth of this number vs. the size. Looking at other features, the toppling invariants exhibit a highly irregular behavior. The usual constraint on the energy positiveness introduces a transition in the frozen phase. In correspondence to this transition, a dynamical crossover related to the halting times is observed. The analysis of the configuration space shows that the DFES has a different structure with respect to dissipative BTW and stochastic sandpiles models, supporting the conjecture that it lies in a distinct class of universality.     

Depolarization of transverse spin rotation by random walks on lattices

The depolarization of rotating spins that perform random walks on 1,2, and 3-dimensional lattices is investigated. If the random rotation frequencies are taken from Gaussian distributions, an asymptotic exponential decay is found in all dimensions. The decay constant depends on a noninteger power of the width of the frequency distribution in d=1 and 2. The effect of different frequency distributions is also discussed.     

Kauffman Cellular Automata on Quasicrystal Topology

In this paper, we perform numerical simulations to study Kauffman cellular automata (KCA) on quasiperiod lattices. In particular, we investigate phase transition, magnetic entropy, and propagation speed of the damage on these lattices. Both the critical threshold parameter \(p_{c}\) and the critical exponents are estimated with good precision. In order to investigate the increase of statistical fluctuations and the onset of chaos in the critical region of the model, we have also defined a magnetic entropy to these systems. It is seen that the magnetic entropy behaves in a different way when one passes from the frozen regime (p < p_c) to the chaotic regime (p > p_c). For a further analysis, the robustness of the propagation of failures is checked by introducing a quenched site dilution probability q on the lattices. It is seen that the damage spreading is quite sensitive when a small fraction of the lattice sites are disconnected. A finite-size scaling analysis is employed to estimate the critical exponents. From these numerical estimates, we claim that on both pure (q =?0) and diluted (q =?0.05) quasiperiodic lattices, the KCA model belongs to the same universality class than on square lattices. Furthermore, with the aim of comparing the dynamical behavior between periodic and quasiperiodic systems, the propagation speed of the damage is also calculated for the square lattice assuming the same conditions. It is found that on square lattices the propagation speed of the damage obeys a power law as \(v\sim (p-p_{c})^{\alpha }\), whereas on quasiperiod lattices, it follows a logarithmic law as \(v \sim \ln (p-p_{c})^{\alpha }\).     

Universal Long-Time Relaxation on Lattices of Classical Spins: Markovian Behavior on Non-Markovian Timescales

The long-time behavior of certain fast-decaying infinite temperature correlation functions on one-, two-, and three-dimensional lattices of classical spins with various kinds of nearest-neighbor interactions is studied numerically, and evidence is presented that the functional form of this behavior is either simple exponential or exponential multiplied by cosine. Due to the fast characteristic timescale of the long-time decay, such a universality cannot be explained on the basis of conventional Markovian assumptions. It is suggested that this behavior is related to the chaotic properties of the spin dynamics.     

Localization and Propagation in Random Lattices

We analyze the motion of a particle on random lattices. Scatterers of two different types are independently distributed among the vertices of such a lattice. A particle hops from a vertex to one of its neighboring vertices. The choice of neighbor is completely determined by the type of scatterer at the current vertex. It is shown that on Poisson and vectorizable random triangular lattices the particle will either propagate along some unbounded strip or be trapped inside a closed strip. We also characterize the structure of a localization zone contained within a closed strip. Another result shows that for a general class of random lattices the orbit of a particle will be bounded with probability one.     

Localized heat perturbation in harmonic 1D crystals: Solutions for the equation of anomalous heat conduction

In this paper exact analytical solutions for the equation that describes anomalous heat propagation in a harmonic 1D lattices are obtained. Rectangular, triangular and sawtooth initial perturbations of the temperature field are considered. The solution for an initially rectangular temperature profile is investigated in detail. It is shown that the decay of the solution near the wavefront is proportional to \(1/\sqrt t \). In the center of the perturbation zone the decay is proportional to 1/t. Thus, the solution decays slower near the wavefront, leaving clearly visible peaks that can be detected experimentally.     

Identification of molecules through the fluorescence enhancement by a metal tip

A fluorescence enhancement phenomenon, which is realized as a result of a sharp increase in the radiative decay rate of a quantum dipole emitter (QDE) is investigated theoretically in the vicinity of a conical metal tip. The QDE relaxation process is considered as a self-stimulated transition from an excited state into the ground state due to the feedback field formation from the tip. The dynamics of the system shows a stepped relaxation behavior that differs significantly from the conventional exponential decay. This effect can be observed in a small region of the resonance frequency, which is defined by an angle of conical tip. The increase of fluorescence when approaching of molecule to the metal tip on the surface enables one to determine its location.     

Critical Behavior of the Gaussian Model with Periodic Interactions on Diamond—Type Hierarchical Lattices in External Magnetic Fields

The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences.The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction onds.The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method.The critical points and all the critical exponents are obtained.The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices.When all the Gaussian distribution constants are the same,the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.     

Eight-parameter renormalization group for Penrose lattices

The Ising model and the bond percolation model are set up with eight parameters on two-dimensional Penrose lattices. The behavior of their phase transition is studied by the use of a real-space renormalization group method. The resulting critical indices suggest that they belong to the universality class of two-dimensional periodic lattices.     

On Pointwise Decay of Linear Waves on a Schwarzschild Black Hole Background

We prove sharp pointwise t ⁻³ decay for scalar linear perturbations of a Schwarzschild black hole without symmetry assumptions on the data. We also consider electromagnetic and gravitational perturbations for which we obtain decay rates t ⁻⁴, and t ⁻⁶, respectively. We proceed by decomposition into angular momentum ℓ and summation of the decay estimates on the Regge-Wheeler equation for fixed ℓ. We encounter a dichotomy: the decay law in time is entirely determined by the asymptotic behavior of the Regge-Wheeler potential in the far field, whereas the growth of the constants in ℓ is dictated by the behavior of the Regge-Wheeler potential in a small neighborhood around its maximum. In other words, the tails are controlled by small energies, whereas the number of angular derivatives needed on the data is determined by energies close to the top of the Regge-Wheeler potential. This dichotomy corresponds to the well-known principle that for initial times the decay reflects the presence of complex resonances generated by the potential maximum, whereas for later times the tails are determined by the far field. However, we do not invoke complex resonances at all, but rely instead on semiclassical Sigal-Soffer type propagation estimates based on a Mourre bound near the top energy.     

Numerical results for spin glass ground states on Bethe lattices: Gaussian bonds

The average ground state energies for spin glasses on Bethe lattices of connectivities r = 3,...,15 are studied numerically for a Gaussian bond distribution. The Extremal Optimization heuristic is employed which provides high-quality approximations to ground states. The energies obtained from extrapolation to the thermodynamic limit smoothly approach the ground-state energy of the Sherrington-Kirkpatrick model for r ↦ ∞. Consistently for all values of r in this study, finite-size corrections are found to decay approximately with ~N^-4/5. The possibility of ~N^-2/3 corrections, found previously for Bethe lattices with a bimodal ± J bond distribution and also for the Sherrington-Kirkpatrick model, are constrained to the additional assumption of very specific higher-order terms. Instance-to-instance fluctuations in the ground state energy appear to be asymmetric up to the limit of the accuracy of our heuristic. The data analysis provides insights into the origin of trivial fluctuations when using continuous bonds and/or sparse networks.     

B decays to baryons

From inclusive measurements, it is known that about 7% of all B mesons decay into final states with baryons. In these decays, some striking features become visible compared to mesonic decays. The largest branching fractions come with quite moderate multiplicities of 3?C4 hadrons. We note that two-body decays to baryons are suppressed relative to three- and four-body decays. In most of these analyses, the invariant baryon?Cantibaryon mass shows an enhancement near the threshold. We propose a phenomenological interpretation of this quite common feature of hadronization to baryons.     

Breaking of Ergodicity in Expanding Systems of Globally Coupled Piecewise Affine Circle Maps

To identify and to explain coupling-induced phase transitions in coupled map lattices (CML) has been a lingering enigma for about two decades. In numerical simulations, this phenomenon has always been observed preceded by a lowering of the Lyapunov dimension, suggesting that the transition might require changes of linear stability. Yet, recent proofs of co-existence of several phases in specially designed models work in the expanding regime where all Lyapunov exponents remain positive. In this paper, we consider a family of CML composed by piecewise expanding individual map, global interaction and finite number $N$ of sites, in the weak coupling regime where the CML is uniformly expanding. We show, mathematically for $N=3$ and numerically for $N\ge 3$ , that a transition in the asymptotic dynamics occurs as the coupling strength increases. The transition breaks the (Milnor) attractor into several chaotic pieces of positive Lebesgue measure, with distinct empiric averages. It goes along with various symmetry breaking, quantified by means of magnetization-type characteristics. Despite that it only addresses finite-dimensional systems, to some extend, this result reconciles the previous ones as it shows that loss of ergodicity/symmetry breaking can occur in basic CML, independently of any decay in the Lyapunov dimension.     

Quenched light hadron spectrum

We present results of a large-scale simulation for the flavor nonsinglet light hadron spectrum in quenched lattice QCD with the Wilson quark action. Hadron masses are calculated at four values of lattice spacing in the range a approximately 0.1-0.05 fm on lattices with a physical extent of 3 fm at five quark masses corresponding to m(pi)/m(rho) approximately 0.75-0.4. The calculated spectrum in the continuum limit shows a systematic deviation from experiment, though the magnitude of deviation is contained within 11%. Results for decay constants and light quark masses are also reported.     

Force-induced desorption of self-avoiding walks on Sierpinski gasket fractals

In this work we investigate force-induced desorption of linear polymers in good solvents in non-homogeneous environment, by applying the model of self-avoiding walk on two- and three-dimensional fractal lattices, obtained as generalization of the Sierpinski gasket fractal. For each of these lattices one of its boundaries represents an adsorbing wall, whereas along one of the fractal edges, not lying in the adsorbing wall, an external force acts on the self-avoiding walk. The hierarchical nature of the lattices under study enables an exact real-space renormalization group treatment, which yields the phase diagram of polymer critical behavior. We show that for this model there is no low-temperature reentrance in the cases of two-dimensional lattices, whereas in all studied three-dimensional cases the force-temperature dependance is reentrant. We also find that in all cases the force-induced desorption transition is of first order.