Exactly quantized dynamics of classical incommensurate sliders

We report peculiar velocity quantization phenomena in the classical motion of an idealized 1D solid lubricant, consisting of a harmonic chain interposed between two periodic sliders. The ratio upsilon(c.m.)/upsilon(ext) of the chain center-of-mass velocity to the externally imposed relative velocity of the sliders stays pinned to exact "plateau" values for wide ranges of parameters, such as slider corrugation amplitudes, external velocity, chain stiffness, and dissipation, and is strictly determined by the commensurability ratios alone. The phenomenon is explained by one slider rigidly dragging the kinks that the chain forms with the other slider. Possible consequences of these results for some real systems are discussed.     

Hysteresis from dynamically pinned sliding states

We report a surprising hysteretic behavior in the dynamics of a simple one-dimensional nonlinear model inspired by the tribological problem of two sliding surfaces with a thin solid lubricant layer in between. In particular, we consider the frictional dynamics of a harmonic chain confined between two rigid incommensurate substrates which slide with a fixed relative velocity. This system was previously found, by explicit solution of the equations of motion, to possess plateaus in parameter space exhibiting a remarkable quantization of the chain center-of-mass velocity (dynamic pinning) solely determined by the interface incommensurability. Starting now from this quantized sliding state, in the underdamped regime of motion and in analogy to what ordinarily happens for static friction, the dynamics exhibits a large hysteresis under the action of an additional external driving force F_ext. A critical threshold value F_c of the adiabatically applied force F_ext is required in order to alter the robust dynamics of the plateau attractor. When the applied force is decreased and removed, the system can jump to intermediate sliding regimes (a sort of “dynamic” stick-slip motion) and eventually returns to the quantized sliding state at a much lower value of F_ext. Hysteretic behavior is also observed as a function of the external driving velocity.     

Propagation of excitation in long 1D chains: Transition from regular quantum dynamics to stochastic dynamics

The quantum dynamics problem for a 1D chain consisting of 2N + 1 sites (N ? 1) with the interaction of nearest neighbors and an impurity site at the middle differing in energy and in coupling constant from the sites of the remaining chain is solved analytically. The initial excitation of the impurity is accompanied by the propagation of excitation over the chain sites and with the emergence of Loschmidt echo (partial restoration of the impurity site population) in the recurrence cycles with a period proportional to N. The echo consists of the main (most intense) component modulated by damped oscillations. The intensity of oscillations increases with increasing cycle number and matrix element C of the interaction of the impurity site n = 0 with sites n = ±1 (0 < C ≤ 1; for the remaining neighboring sites, the matrix element is equal to unity). Mixing of the components of echo from neighboring cycles induces a transition from the regular to stochastic evolution. In the regular evolution region, the wave packet propagates over the chain at a nearly constant group velocity, embracing a number of sites varying periodically with time. In the stochastic regime, the excitation is distributed over a number of sites close to 2N, with the populations varying irregularly with time. The model explains qualitatively the experimental data on ballistic propagation of the vibrational energy in linear chains of CH₂ fragments and predicts the possibility of a nondissipative energy transfer between reaction centers associated with such chains.     

Rotational motion,shell structure and coherent state dynamics

We analyze the dynamics of coherent states in a two-dimensional model of rotational motion using the unitary group and the schematic Q·Q force. We find a uniform rotation of the nuclear quadrupole. Application of the gauge invariant periodic quantization method yields the exact rotational spectrum.     

利用取帧技术在气轨上验证变力做功

在气垫导轨上研究了滑块在变力作用下的运动规律.利用质量较为均匀的细铁链的下落改变作用在滑块上的力,利用摄像机记录随铁链下落滑块的运动过程,通过取帧技术获得滑块运动的位移、速度和时间关系.     

Drift velocity in the necklace model for reptation in a two-dimensional square lattice

We report the chain dynamics in the necklace model that mimics the reptation of a chain of N particles in a two-dimensional square lattice. We focus on the drift velocity under an applied static field. The characteristics of the model allow us to determine the effects of the forces on the chains and the resulting mechanisms that affect the drift velocity. Results obtained through Monte Carlo simulations were analyzed and discussed and distinct regimes as a function of the force strength and N were identified. We found that for small total applied forces, the drift velocity scales as 1/N. When the applied force to every particle is small but the total applied force is not, the tube deforms in such a way that the drift velocity does not depend on N. Large forces, applied to every particle, can straight chains such that the distance between the chain ends increases faster than the number of particles. Also, large forces can deform the chain within the tube what is directly related to a decrease of the drift velocity.     

Zener tunneling between the landau levels in quasi-two-dimensional electronic Corbino disks at large filling factors

The magnetotransport characteristics of quasi-two-dimensional electronic Corbino disks based on a wide GaAs quantum well with two filled subbands of size quantization are studied. At low temperatures and high magnetic fields, the Corbino disks exhibit the oscillations of differential conductivity, which are periodic with respect to dc electric field E _dc. It is shown that the observed oscillations are related to the Zener tunneling induced by E _dc. The tunneling occurs between the filled and empty Landau levels under conditions corresponding to the absence of the Hall field.     

Decreasing of the finite-size effects through the twisted boundary conditions II

In the large-N limit it is shown that a model with twisted boundary conditions becomes equivalent to the U(N) invariant theory which has a volume N² times larger than the theory with periodic boundary conditions. Even for finite N, it is confirmed that the finite-size effects in the models with twisted boundary conditions rather decrease, compared with the ones with periodic boundary conditions, by performing a Monte Carlo simulation for the two-dimensional SU(3) chiral models.     

Tagged Particle Diffusion in One-Dimensional Gas with Hamiltonian Dynamics

We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special case where all particles have the same mass, we obtain analytic results for the velocity auto-correlation function in the short time diffusive regime and the long time approach to the saturation value when finite-size effects become relevant. In the case where the masses are unequal, numerical simulations indicate sub-diffusive behaviour with mean square displacement of the tagged particle growing as t/ln(t) with time t. Also various correlation functions, involving the velocity and position of the tagged particle, show damped oscillations at long times that are absent for the equal mass case.     

The quantum mechanical Toda lattice,II

The periodic Toda lattice consists of N particles which move along a closed line and are coupled with an exponential spring to their immediate neighbors. This system, in contrast to the open Toda lattice, has only bound states. In the method of Kac and Van Moerbeke, the classical periodic Toda chain is transformed to a new of set of canonically conjugate variables, μ and ν, which are closely related to the natural coordinates of an open Toda chain with one particle less. The quantum mechanical eigenfunctions for this reduced system are constructed explicitly, and this allows the quantum mechanical analogs of μ and ν to be defined. The bounds states for the periodic Toda chain are then written as linear combinations of functions resembling the wave functions of the reduced open chain. These functions satisfy a set of remarkably simple recursion formulas, and the coefficients in the expansion can be written essentially as a product of as many factors as pairs of conjugate variables μ and ν. Each factor is given as a solution of a second order difference equation which can be recognized as a quantum analog for the equations of motion of one pair μ and ν. The quantization conditions result from cancelling out the exponential growth in the overall wave function, and are phrased in terms of certain phase angles being submultiples of π according as the representation of the group of cyclic permutations. The calculations are simple for N = 3, and moderately tricky for N = 4 although the results are always fairly obvious.     

Algebraic quantization of the SU(3) skyrmion

The algebraic quantization of the SU(3) skyrmion is presented. We discuss the role of the number of colors (N_c) in QCD and the Wess-Zumino term in the quantization. Two distinct dynamical group chains are shown to correspond to different methods of semiclassical quantization. We obtain most of the SU(6) quark model predictions for the skyrmion quantized with N_c=3.     

基于椭圆偏振显微镜的纳米级磁头润滑膜观测方法

针对磁头飞行导致液体润滑膜的转移研究以及润滑膜在磁头上的动态变化特性观测问题,基于改进的垂直物镜的椭圆偏振显微镜,提出起偏器相移方法的磁头表面润滑膜厚度计算模型,实现了润滑膜厚度的测量。实验以非极性润滑剂Z03覆盖的磁头为样品对椭圆偏振显微镜进行标定,以极性润滑剂Zdol4000作为样品,对其在磁头表面的去湿现象进行观察。该方法测量精度可达0.37 nm,分辨力约0.36 μm,可为其他纳米级薄膜观测提供一定的技术参考。     

Weak Finite—Size Dependence of Velocity and Strong Phase Dependence of Central Charge

We study the finite-size scaling behavior of velocity and central charge for different coupling constants and different phases in (1 1)-dimensional lattice model in very short chains.Using XXZ spin 1/2 chains with 15 or fewer sites,we demonstrate the weak finite-size dependence of spinon velocity for any magnitude of coupling strength Jz and the strong phase dependence of central charge.This behavior of velocity and central charge in different coupling constants and different phases gives a method to determine phase transitions of (1 1)-dimensional models.This method is simple and efficient by utilizing only the ground state energy of very short finite-size chains.It is also general and powerfur for various one-dimensional lattice models and it uncovers eventhe weakest berezinski-Kosterlitz-Thouless phase transitions.     

Anomalous conductance oscillations and half-metallicity in atomic Ag-O chains

Using spin density functional theory, we study the electronic and magnetic properties of atomically thin, suspended chains containing silver and oxygen atoms in an alternating sequence. Chains longer than 4 atoms develop a half-metallic ground state implying fully spin-polarized charge carriers. The conductances of the chains exhibit weak even-odd oscillations around an anomalously low value of 0.1G0 (G0=2e2/h) which coincide with the averaged experimental conductance in the long chain limit. The unusual conductance properties are explained in terms of a resonating-chain model, which takes the reflection probability and phase shift of a single bulk-chain interface as the only input. The model also explains the conductance oscillations for other metallic chains.     

Thermodyamic Bounds on Drude Weights in Terms of Almost-conserved Quantities

We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions. Namely, the commutator between the Hamiltonian and the conservation law of a finite chain may result in boundary terms only. No reference to techniques used in Suzuki’s proof of Mazur bound is made (which strictly applies only to finite-size systems with exact conservation laws), but Lieb-Robinson bounds and exponential clustering theorems of quasi-local C* quantum spin algebras are invoked instead. Our result has an important application in the transport theory of quantum spin chains, in particular it provides rigorous non-trivial examples of positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ spin 1/2 chain (Prosen, in Phys Rev Lett 106:217206, 2011).     

Unified approach to Thermodynamic Bethe Ansatz and finite size corrections for lattice models and field theories

We present a unified approach to the Thermodynamic Bethe Ansatz (TBA) for magnetic chains and field theories that includes the finite size (and zero-temperature) calculations for lattice BA models. In all cases, the free energy follows by quadratures from the solution of a single nonlinear integral equation (NLIE) (a system of NLIE appears for nested BA). We derive the NLIE for: (a) the six-vertex model with twisted boundary conditions, (b) the XXZ chain in an external magnetic field h_z and (c) the massive Thirring sine-Gordon model (mT-sG) in a periodic box of size β ≡ T^-1 using the light-cone approach. This NLIE is solved by iteration in one regime (high T in the XXZ chain and low T in the sG-mT model). In the opposite (conformal) regime, the leading behaviors are obtained in closed form. Higher corrections can be derived from the Riemann-Hilbert form of the NLIE that we present.     

Anomalous mass dependence of radiative quark energy loss in a finite-size quark-gluon plasma

We demonstrate that for a finite-size quark-gluon plasma the induced gluon radiation from heavy quarks is stronger than that for light quarks when the gluon formation length becomes comparable with (or exceeds) the size of the plasma. The effect is due to oscillations of the light-cone wave function for the in-medium q→gq transition. The dead cone model by Dokshitzer and Kharzeev neglecting quantum finite-size effects is not valid in this regime. The finite-size effects also enhance the photon emission from heavy quarks.     

On the periodic orbits of a strongly chaotic system

A point particle sliding freely on a two-dimensional surface of constant negative curvature (Hadamard-Gutzwiller model) exemplifies the simplest chaotic Hamiltonian system. Exploiting the close connection between hyperbolic geometry and the group SU(1,1)/⦅±1⦆, we construct an algorithm (symboliv dynamics), which generates the periodic orbits of the system. For the simplest compact Riemann surface having as its fundamental group the “octagon group”, we present an enumeration of more than 206 million periodic orbits. For the length of the nth primitive periodic orbit we find a simple expression in terms of algebraic numbers of the form m + √2n (m, nϵN are governed by a particular Beatty sequence), which reveals a strange arithmetical structure of chaos. Knowledge of the length spectrum is crucial for quantization via the Selberg trace formula (periodic orbit theory), which in turn is expected to unravel the mystery of quantum chaos.     

Detailed unsteady dynamics of flame-flow interactions during combustion instability and its transition scenario for lean-premixed low-swirl hydrogen turbulent flames

This experimental study elucidates the unsteady dynamics of flame-flow interactions during unique thermoacoustic instability (TI) and the transition mechanism from stable combustion to TI for lean-premixed hydrogen turbulent jet flames in a low-swirl combustor (LSC), where a swirler assembly consists of an unswirled central region (CR) and an annular swirler region (SR). Simultaneous 200-kHz pressure fluctuation p’ measurements and 10-kHz OH* chemiluminescence imaging, as well as 40-kHz stereoscopic particle image velocimetry (SPIV) and two-dimensional PIV measurements for steady-state and transient data acquisitions, respectively, were conducted. The SPIV was performed in multiple planes to explore three-dimensional velocity fields. During TI, periodic flashback was possibly caused by significant axial velocity oscillations, resulting in the local mixture velocity falling below the turbulent flame speed. The large-scale vortex ring generated by the velocity oscillations caused axisymmetric radial velocity V_r oscillations with switching signs during the TI period. Similar to a typical low-swirl flow, the positive V_r away from the combustor axis created diverging flow, whereas unlike the typical flowfield, the negative V_r toward the combustor axis generated converging flow while flattening the axial velocity distributions, which was the signature phenomenon for this TI. Using the transient data and dynamic mode decomposition, variations in delay times between the mixture injection and its convection to a region with positive local Rayleigh indices were investigated. During stable combustion, the mixture jet from the SR predominantly induced thermoacoustic coupling (TC). As the combustion transitioned into the TI, the mixture jet from the CR began to induce TC and, eventually, achieved predominance in inducing TC during fully evolved TI. The transition from the SR jet- into CR jet-dominant TI arising from the dynamic flame-flow interactions resulted from the inherent physical characteristics of hydrogen flames, thereby yielding the larger p’ amplitude compared to typical TIs.