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Impact processes of nanoclusters subject to thermal fluctuations are investigated, theoretically. In the former half of the paper, we discuss the basis of quasi-static theory. In the latter part, we carry out the molecular dynamics simulation of collisions between two identical nanoclusters, and report some statistical properties of impacts of nanoclusters.
In linear transport, the fluctuation-dissipation theorem relates equilibrium current correlations to the linear conductance coefficient. For nonlinear transport, there exist fluctuation relations that rely on Onsager's principle of microscopic reversibility away from equilibrium. However, both theory and experiments have shown deviations from microreversibility in the form of magnetic field asymmetric current-voltage relations. We present novel fluctuation relations for nonlinear transport in the presence of magnetic fields that relate current correlation functions at any order at equilibrium to response coefficients of current cumulants of lower order. We illustrate our results with the example of an electrical Mach-Zehnder interferometer.
The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: i.e., the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears. Recently such behavior was observed and some of the earlier predicted exponents were found in experiments on several types of systems described by a model of a modulated oscillator. Here we establish the range where different scaling behavior is displayed and show how the crossover between different types of scaling occurs. The analysis is done for a nonlinear oscillator with two coexisting stable states of forced vibrations. Our numerical calculations, based on the the instanton method allow the mapping of the entire parameter range of bi-stability. We find the regions where the scaling exponents are 1 or 3/2, depending on the damping. The exponent 3/2 is found to extend much further from the bifurcation then were it would be expected to hold as a result of an over-damped soft mode. We also uncover a new scaling behavior with exponent of $\approx$ 1.3 which extends, numerically, beyond the close vicinity of the bifurcation point.
We study phase transition from the Mott insulator to superfluid in a periodic optical lattice. Kibble-Zurek mechanism predicts buildup of winding number through random walk of BEC phases, with the step size scaling as a the third root of transition rate. We confirm this and demonstrate that this scaling accounts for the net winding number after the transition.
In this report, we examine the decoherence of a spin qubits system coupled to counted spin chain with a $1/r^2$ interaction by using influence functional. We also examine the time evolution of density matrix numerically when environment is Gaussian noise.
We consider the energy release associated with first-order transition by Gibbs construction and present such energy release as an accumulation of a series of tiny binding energy differences between over-compressed states and stable ones. Universal formulae for the energy release from one homogeneous phase to the other is given. We find the energy release per converted particle varies with number density. As an example, the deconfinement phase transition at supranuclear densities is discussed in detail. The mean energy release per converted baryon is of order 0.1MeV in RMF theory and MIT bag descriptions for hadronic matter and strange quark matter for a wider parameter region.
The dynamics of a crack propagating in an elastic inhomogeneous material is investigated. The variations of the average crack velocity with the external loading are measured for a brittle rock and are shown to display two distinct regimes: Below a given threshold Gc, the crack velocity is well described by an exponential law v ~ exp^{-(C/(G-(Gamma))} characteristic of subcritical propagation, while for larger values of the driving force G > Gc, the velocity evolves as a power law v ~ (G - G_c)^theta with theta = 0.80 $\pm$ 0.15. These results can be explained extending the continuum theory of Fracture Mechanics to disordered systems. In this description, the motion of a crack is analogue to the one of an elastic line driven in a random medium and critical failure occurs when the loading is sufficiently large to depinne the crack front from the heterogeneities of the material.
This paper has been withdrawn.
This paper is a contribution to the theory of coherent crystals. We present arguments claiming that negative minima in the Fourier transform of a soft pair interaction may give rise to the coexistence of diagonal and off-diagonal long-range order at high densities, and that this coexistence may be detectable due to a periodicity seen on the off-diagonal part of the one-body reduced density matrix, without breaking translation invariance. As an illustration, we study the ground state of a homogenous system of bosons in continuous space, from the interaction retaining only the Fourier modes $v(\k)$ belonging to a single nonzero wave number $|\k|=q$. The result is a mean-field model. We prove that for $v(\k)>0$ the ground state is asymptotically fully Bose-condensed, while for $v(\k)<0$ at densities exceeding a multiple of $\hbar^2 q^2/2m|v(\k)|$ it exhibits both Bose-Einstein condensation and diagonal long-range order, and the latter can be seen on both the one- and the two-body density matrix.
The resonant activation effect (RA) has been well studied in different ways during the last two decades. It consists in the presence of a minimum in the mean time spent by a Brownian particle to exit from a potential well in the presence of a fluctuating external force, as a function of the mean frequency (or the correlation time) of the latter. This work studies the role played by the asymmetry of a piecewise linear potential in the RA effect, and, in general, the behavior of the mean first passage time and the mean velocity of the particle crossing through the potential barrier. A strong dependence on the asymmetry of the potential has been found which can be put in relationship with the current in the ratchet whose the potential here used is an elementary module. In this case a current reversal as a function of the frequency of the switching potential occurs. Comparison of the calculations with the Doering-Gadua model have been performed, as well as comparison with smooth symmetrical potentials, by checking for the robustness of the resonant correlation time. The calculations have been done by solving numerically the Langevin equation in the presence of an uncorrelated Gaussian noise. The resonant mean first passage times show an unexpected behavior as a function of the thermal noise intensity. The related curves present for the different symmetries an unexpected inversion of their relative behavior beyond a certain threshold value of the noise. This means that the current reversal can only occur for weak noise intensities, lower than that threshold value.
We study productivity dispersions across workers, firms and industrial sectors. Empirical study of the Japanese data shows that they all obey the Pareto law, and also that the Pareto index decreases with the level of aggregation. In order to explain these two stylized facts, we propose a theoretical framework built upon the basic principle of statistical physics. In this framework, we employ the concept of superstatistics which accommodates fluctuations of aggregate demand.
We extend a result by Ojima on spontaneous symmetry breaking of Lorentz boosts in thermal (KMS) states and show that it is in fact a special case in a more general class of examples of spontaneous symmetry breaking of Lorentz symmetry in relativistic many-body systems. Furthermore we analyse the nature of the corresponding Goldstone phenomenon and the type of Goldstone excitations (provided they have particle character).
An algorithm based on Renormalization Group (RG) to analyze time series forecasting was proposed in cond-mat/0110285. In this paper we explicitly code and test it. We choose in particular some financial time series (stocks, indexes and commodities) with daily data and compute one step ahead forecasts. We then construct some indicators to evaluate performances. The algorithm is supposed to prescribe the future development of the time series by using the self-similarity property intrinsically present in RG approach. This property could be potentially very attractive for the purpose of building winning trading systems. We discuss some relevant points along this direction. Although current performances have to be improved the algorithm seems quite reactive to various combinations of input parameters and different past values sequences. This makes it a potentially good candidate to detect sharp market movements. We finally mention current drawbacks and sketch how to improve them.
The dynamics of a "peeling front" or an elastic line is studied under creep (constant load) conditions. Our experiments show an exponential dependence of the creep velocity on the inverse force (mass) applied. In particular, the dynamical correlations of the avalanche activity are discussed here. We compare various avalanche statistics to those of a line depinning model with non-local elasticity, and study various measures of the experimental avalanche-avalanche and temporal correlations such as the autocorrelation function of the released energy and aftershock activity. From all these we conclude, that internal avalanche dynamics seems to follow "line depinning" -like behavior, in rough agreement with the depinning model. Meanwhile, the correlations reveal subtle complications not implied by depinning theory. Moreover, we also show how these results can be understood from a geophysical point of view.
In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as to quantum state reconstruction on the basis of incomplete data. There are two appendices in which I outline how generalised canonical distributions link to the conventional formulation of statistical mechanics, and how classical probability calculus emerges at the macroscopic level.
It is demonstrated that a two-parameter deformed oscillator with the deformation parameters q,p such that 0 < q,p \le 1 exhibits the property of "accidental" two-fold (pairwise) energy level degeneracy of the classes E_m=E_{m+1} and E_0=E_{m}. The most general case of degeneracy of q,p-oscillators of the form E_{m+k}=E_m (with k\ge 1 for m\ge 1 or k\ge 2 for m=0) is briefly discussed.
It is shown that a sufficiently strong external electric field causes a decrease in the transition temperature of ferroelectric, antiferroelectric, and metal-insulator transitions. The temperature dependence of the critical electric field suppressing a low-temperature phase is obtained. The relation between the low-temperature charge gap (the band gap) in the insulating phase and the metal-insulator transition temperature is also inferred.
By using topological current theory, we study the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it is found topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting, and merging of disclinations are given.