Time dependent local field distribution and metastable states in the SK-spin-glass

Different sets of metastable states can be reached in glassy systems below some transition temperature depending on initial conditions and details of the dynamics. This is investigated for the Sherrington-Kirkpatrick spin glass model with long ranged interactions. In particular, the time dependent local field distribution and energy are calculated for zero temperature. This is done for a system quenched to zero temperature, slow cooling or simulated annealing, a greedy algorithm and repeated tapping. Results are obtained from Monte-Carlo simulations and a Master-Fokker-Planck approach. A comparison with replica symmetry broken theory, evaluated in high orders, shows that the energies obtained via dynamics are higher than the ground state energy of replica theory. Tapping and simulated annealing yield on the other hand results which are very close to the ground state energy. The local field distribution tends to zero for small fields. This is in contrast to the Edwards flat measure hypothesis. The distribution of energies obtained for different tapping strengths does again not follow the canonical form proposed by Edwards.     

Testing the Edwards hypothesis in spin systems under tapping dynamics

The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for aaabstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by considering two distinct mechanisms of energy injection: thermal and random tapping. We find that ergodicity depends upon the tapping procedure (i.e. the way the blocked configurations are dynamically accessed): for thermal tapping ergodicity is a good approximation, while it fails to describe the asymptotic stationary state reached by the random tapping dynamics. Received 30 November 2001     

Breakdown of an electric-field driven system: a mapping to a quantum walk

Quantum transport properties of electron systems driven by strong electric fields are studied by mapping the Landau-Zener transition dynamics to a quantum walk on a semi-infinite one-dimensional lattice with a reflecting boundary, where the sites correspond to energy levels and the boundary the ground state. Quantum interference induces a distribution localized around the ground state, and a delocalization transition occurs when the electric field is increased, which describes the dielectric breakdown in the original electron system.     

Aggregation on a membrane of particles undergoing active exchange with a reservoir

We investigate the dynamics of clusters made of aggregating particles on a membrane which exchanges particles with a reservoir. Exchanges are driven by chemical reactions which supply energy to the system, leading to the establishment of a non-equilibrium steady state. We predict the distribution of cluster size at steady state. We show in particular that in a regime, that cannot exist at equilibrium, the distribution is bimodal: the membrane is mainly populated of single particles and finite-size clusters. This work is motivated by the observations that have revealed the existence of submicrometric clusters of proteins in biological membranes.     

Non-linear dynamics of a driven two-level tunnelling defect

With increasing external-field amplitude the dynamics of a driven two-level system shows a cross-over from the weak-coupling or linear-response behaviour to a non-linear regime which is characterised by the appearance of Rabi oscillations, a field-dependent dynamical susceptibility, saturation of energy dissipation and additional frequencies in the correlation function. The system any initial distribution will relax towards a stationary state with a time-dependent polarisation vector. These features are derived from the propagator of the two-level system which is calculated using a perturbative scheme with a well-defined small parameter; the roatating-wave approximation of the Bloch equations is avoided. the dynamical behaviour is discussed by means of correlation and response functions.     

Tapping spin glasses and ferromagnets on random graphs.

We consider a tapping dynamics, analogous to that in experiments on granular media, on spin glasses and ferromagnets on random thin graphs. Between taps, zero temperature single spin flip dynamics takes the system to a metastable state. Tapping corresponds to flipping simultaneously any spin with probability p. This dynamics leads to a stationary regime with a steady state energy E(p). We analytically solve this dynamics for the one-dimensional ferromagnet and +/-J spin glass. Numerical simulations for spin glasses and ferromagnets of higher connectivity are carried out; in particular, we find a novel first order transition for the ferromagnetic systems.     

Quantum dynamics of a mechanical resonator driven by a cavity

We explore the quantum dynamics of a mechanical resonator whose position is coupled to the frequency of an optical (or microwave) cavity mode. When the cavity is driven at a frequency above resonance the mechanical resonator can gain energy and for sufficiently strong coupling this results in limit-cycle oscillations. Using a truncated Wigner function approach, which captures the zero-point fluctuations in the system, we develop an approximate analytic treatment of the resonator dynamics in the limit-cycle regime. We find that the limit-cycle oscillations produced by the cavity are associated with rather low levels of energy fluctuations in the resonator. Compared to a resonator at the same temperature which is driven by a pure harmonic drive to a given average energy, the cavity-driven oscillations can have much lower energy fluctuations. Furthermore, at sufficiently low temperatures, the cavity can drive the resonator into a non-classical state which is number-squeezed.     

Ultrafast melting of a charge-density wave in the Mott insulator 1T-TaS2

Femtosecond time-resolved core-level photoemission spectroscopy with a free-electron laser is used to measure the atomic-site specific charge-order dynamics of the charge-density?wave in the Mott insulator 1T-TaS2. After strong photoexcitation, a prompt loss of charge order and subsequent fast equilibration dynamics of the electron-lattice system are observed. On the time scale of electron-phonon thermalization, about 1?ps, the system is driven across a phase transition from a long-range charge ordered state to a quasiequilibrium state with domainlike short-range charge and lattice order. The experiment opens the way to study the nonequilibrium dynamics of condensed matter systems with full elemental, chemical, and atomic-site selectivity.     

Non-Gaussian and Clustering Behavior in One-Dimensional Polydisperse Granular Gas System

We present a one-dimensional dynamic model of polydisperse granular mixture with the fractal characteristic of the particle size distribution, in which the particles are subject to inelastic mutual collisions and are driven by Gaussian white noise. The inhomogeneity of the particle size distribution is described by a fractal dimension D. The stationary state that the mixture reaches is the result of the balance between energy dissipation and energy injection. By molecular dynamics simulations, we have mainly studied how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the velocity distribution and distribution of interparticle spacing in the steady-state.The simulation results indicate that, in the inelasticity case, the velocity distribution strongly deviates from the Gaussian one and the system has a strong spatial clustering. Thus the inhomogeneity and the inelasticity have great effects on the velocity distribution and distribution of interparticle spacing. The quantitative information of the non-Gaussian velocity distribution and that of clustering are respectively represented.     

Dissipation Energy in Tapping-Mode Atomic Force Microscopes Caused by Liquid Bridge

The dissipation of energy during the process of contact and separation between a tip and a sample is very important for understanding the phase images in the tapping mode of atomic force microscopes(AFMs). In this study, a method is presented to measure the dissipated energy between a tip and a sample. The experimental results are found to be in good agreement with the theoretical model, which indicates that the method is reliable.Also, this study confirms that liquid bridges are mainly produced by extrusion modes in the tapping mode of AFMs.     

Phase Separation Driven by a Fluctuating Two-Dimensional Self-Affine Potential Field

We study phase separation in a system of hard-core particles driven by a fluctuating two-dimensional self-affine potential landscape which evolves through Kardar–Parisi–Zhang (KPZ) dynamics. We find that particles tend to cluster together on a length scale which grows in time. The final phase-separated steady state is characterized by an unusual cusp singularity in the scaled correlation function and a broad distribution for the order parameter. Unlike the one-dimensional case studied earlier, the cluster-size distribution is asymmetric between particles and holes, reflecting the broken reflection symmetry of the KPZ dynamics, and has a contribution from an infinite cluster in addition to a power law part. A study of the surface in terms of coarse-grained depth variables helps understand many of these features.     

强迫耗散系统的有序结构和系统的发展(Ⅰ)，最小熵产生原理和有序结构

一个系统的发展总是由不可逆热力过程和非线性动力过程所驱动.将大气动力学方程组同考虑了动能变化的Gibbs关系结合起来构建的熵平衡方程，才能更好地描述大气系统的不可逆热力过程和非线性动力过程.至今非平衡态热力学仅利用Onsager线性唯象关系证明了最小熵产生原理.利用新建立的熵平衡方程和大气动力学方程的性质证明，最小熵产生原理在热力学线性区和非线性区都是普遍成立的.且当热量输送平衡、水汽输送平衡和动量输送平衡时，系统达到不可逆过程最弱的最小熵产生热力学状态.当系统又是动力平衡且无平流时，这种最小熵产生态就是 关键词： 非线性热力学 熵产生 最小熵产生原理 有序结构     

A particle in a box in the presence of an electric field and applications to disordered systems

The Green's function and energy eigenvalues of an electron under the influence of a uniform electric field in a box with infinitely high sides is investigated. The second order correction to the energy eigenvalues is calculated by finding zeros of the wronskian and comparing with the value obtained from second order perturbation theory. Comparison is made with the limiting conditions in which the size of the box tends to infinity and the electric field tends towards zero. The results of the investigation suggest a possible criterion for localisation. The value obtained for the ground state energy is used to extend a model of Edwards to study the tail of the density of states of a disordered system in the presence of an electric field.     

Dynamics of the peel front and the nature of acoustic emission during peeling of an adhesive tape

We investigate the peel front dynamics and acoustic emission (AE) of an adhesive tape within the context of a recent model by including an additional dissipative energy that mimics bursts of acoustic signals. We find that the nature of the peeling front can vary from a smooth to a stuck-peeled configuration depending on the values of dissipation coefficient, inertia of the roller, and mass of the tape. Interestingly, we find that the distribution of AE bursts shows power law statistics with two scaling regimes with increasing pull velocity as observed in experiments. In these regimes, the stuck-peeled configuration is similar to the "edge of peeling" reminiscent of a system driven to a critical state.     

Stochastic Thermodynamics of a Piezoelectric Energy Harvester Model

We experimentally study a piezoelectric energy harvester driven by broadband random vibrations. We show that a linear model, consisting of an underdamped Langevin equation for the dynamics of the tip mass, electromechanically coupled with a capacitor and a load resistor, can accurately describe the experimental data. In particular, the theoretical model allows us to define fluctuating currents and to study the stochastic thermodynamics of the system, with focus on the distribution of the extracted work over different time intervals. Our analytical and numerical analysis of the linear model is succesfully compared to the experiments.     

Dissipative Dynamics and the Statistics of Energy States of a Hookean Model for Protein Folding

A generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean spring connecting pairs of hydrophobic residues, reproduces the energy probability distribution of real proteins over a very large range of energies. We show that this system with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional Ornstein–Uhlenbeck process and giving rise to the so-called Wigner distribution. A tunably fine- or coarse-grained sampling of the energy landscape yields a family of distributions for the energies and energy spacings.     

Molecular-dynamics simulations with explicit hydrodynamics II: On the collision of polymers with molecular obstacles

We present a study of the dynamics of single polymers colliding with molecular obstacles using Molecular-dynamics simulations. In concert with these simulations we present a generalized polymer-obstacle collision model which is applicable to a number of collision scenarios. The work focusses on three specific problems: i) a polymer driven by an external force colliding with a fixed microscopic post; ii) a polymer driven by a (plug-like) fluid flow colliding with a fixed microscopic post; and iii) a polymer driven by an external force colliding with a free polymer. In all three cases, we present a study of the length-dependent dynamics of the polymers involved. The simulation results are compared with calculations based on our generalized collision model. The generalized model yields analytical results in the first two instances (cases i) and ii)), while in the polymer-polymer collision example (case iii)) we obtain a series solution for the system dynamics. For the case of a polymer-polymer collision we find that a distinct V-shaped state exists as seen in experimental systems, though normally associated with collisions with multiple polymers. We suggest that this V-shaped state occurs due to an effective hydrodynamic counter flow generated by a net translational motion of the two-chain system.     

Jamming, freezing and metastability in one-dimensional spin systems

We consider in parallel three one-dimensional spin models with kinetic constraints: the paramagnetic constrained Ising chain, the ferromagnetic Ising chain with constrained Glauber dynamics, and the same chain with constrained Kawasaki dynamics. At zero temperature the dynamics of these models is fully irreversible, leading to an exponentially large number of blocked states. Using a mapping of these spin systems onto sequential adsorption models of, respectively, monomers, dimers, and hollow trimers, we present exact results on the statistics of blocked states. We determine the distribution of their energy or magnetization, and in particular the large-deviation function describing its exponentially small tails. The spin and energy correlation functions are also determined. The comparison with an approach based on a priori statistics reveals systematic discrepancies with the Edwards hypothesis, concerning in particular the fall-off of correlations. Received 26 February 2002 Published online 6 June 2002     

Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences

There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability distribution of nonequilibrium systems. Another recently discovered far from equilibrium expression relates nonequilibrium measurements of the work done on a system to equilibrium free energy differences. In this paper, we derive a generalized version of the fluctuation theorem for stochastic, microscopically reversible dynamics. Invoking this generalized theorem provides a succinct proof of the nonequilibrium work relation.     

Fluctuation theorem for currents in the Spinning Lorentz Gas

We study the fluctuation theorem formulated in terms of the currents present in a Hamiltonian system with coupled mass and energy transport. To drive the system out of equilibrium, we assume it to be connected to two ideal thermodynamical baths. The fluctuation symmetry is, thus, expressed in terms of the joint probability distribution of energy and particle currents in the system. This relation is verified numerically for the stationary state in the Spinning Lorentz Gas (SLG), driven out of equilibrium by temperature and/or chemical potential differences between the baths, as well as in the presence of an applied field.