Search results for "Godi"

Electronic poetry : understanding poetry in the digital environment

2011

Dynamics in stochastic evolutionary models

2016

We characterize transitions between stochastically stable states and relative ergodic probabilities in the theory of the evolution of conventions. We give an application to the fall of hegemonies in the evolutionary theory of institutions and conflict, and illustrate the theory with the fall of the Qing dynasty and the rise of communism in China.

ON HIGH-SKILL AND LOW-SKILL EQUILIBRIA: A MARKOV CHAIN APPROACH

2006

In this paper we propose to study the dynamics of human capital accumulation by means of a Markov chain. We identify the conditions for the emergence of ergodic and nonergodic dynamics, and relate them to various characteristics of an economic system. The model may generate high-skill and low-skill equilibria as well as intermediate situations. Policy implications are also discussed.

Generalized-ensemble simulations and cluster algorithms

2010

The importance-sampling Monte Carlo algorithm appears to be the universally optimal solution to the problem of sampling the state space of statistical mechanical systems according to the relative importance of configurations for the partition function or thermal averages of interest. While this is true in terms of its simplicity and universal applicability, the resulting approach suffers from the presence of temporal correlations of successive samples naturally implied by the Markov chain underlying the importance-sampling simulation. In many situations, these autocorrelations are moderate and can be easily accounted for by an appropriately adapted analysis of simulation data. They turn out…

STRUCTURAL INSTABILITY IN FERROELECTRICS: SUPERIMPOSING HAMILTONIAN AND STOCHASTIC DYNAMICS

2008

ABSTRACT Structural instability of ferroelectrics distinguished by appearance of coexisting phases and spatial inhomogeneity is at variance with the predictions of statistics in the canonical ensemble. A more refined description includes ergodicity breaking which become apparent at critical temperature when the system resides in metastable state and its development lead to one of possible minimum energy states. In this study the domain growth and switching is reproduced within the framework of Fokker-Planck approach. The mathematical technique is developed for empiric Landau Hamiltonians and improved for application to first principles effective Hamiltonians with supercells and elementary l…

Glass transition for dipolar hard spheres: A mode-coupling approach

1998

Abstract We apply the self-consistent mode-coupling equations, which were recently derived for molecular liquids, to a system of dipolar hard spheres. Making use of the direct correlation function in a mean spherical approximation and with a restriction of the rotational quantum number 1 to zero and one, we find three different phases in the η—T phase space. η and T denote the packing fraction and the temperature respectively. There is one phase where both the transitional degrees of freedom (TDOFs) and the orientational degrees of freedom (ODOFs) are ergodic (liquid), another phase with frozen TDOFs and ergodic ODOFs, and a third phase where TDOFs and ODOFs are frozen (glass). The dynamica…

High Field Polarization Response in Ferroelectrics: Current Solutions and Challenges

2006

Polarization response including ergodicity breaking and the divergence of relaxation time is reproduced for model Hamiltonians of growing complexity. Systematic derivation of the dynamical equations and its solutions is based on the Fokker-Planck and imaginary time Schrödinger equation techniques with subsequent symplectic integration. Test solutions are addressed to finite size and spatially extended problems with microscopically interpretation of the model parameters as a challenge.

Static freezing transition at a finite temperature in a quasi-one-dimensional deuteron glass.

1996

The dipolar freezing process of a quasi-one-dimensional betaine deuteron glass was studied using linear and nonlinear dielectric spectroscopy. The linear response as measured for frequencies $5\mathrm{mHz}l\ensuremath{\nu}l200\mathrm{MHz}$ was analyzed using the recently invented $\ensuremath{\delta}$ plot, providing evidence for a static freezing transition near 30 K. Measurements of the ergodic to nonergodic transition as well as of the incipient divergence of the nonlinear susceptibility yield independent confirmation of this quasistatic freezing transition temperature. The critical exponent describing the nonlinear behavior is found to be $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\p…

ERGODICITY IN RANDOMLY COLLIDING QUBITS

2009

The dynamics of a single qubit randomly colliding with an environment consisting of just two qubits is discussed. It is shown that the system reaches an equilibrium state which coincides with a pure random state of three qubits. Furthermore the time average and the ensemble averages of the quantities used to characterize the approach to equilibrium (purity and tangles) coincide, a signature of ergodic behavior.

Ergodicity breaking in a mean field Potts glass: A Monte Carlo investigation

2002

We use Monte Carlo simulations, single spin-flip as well as parallel tempering techniques to investigate the 10-state fully connected Potts glass for system sizes of up to N = 2560. We find that the α-relaxation shows a strong dependence on N and that for the system sizes considered the system remains ergodic even at temperatures below T D , the dynamical critical temperature for this model. However, if one uses the data for the finite size systems, such as the relaxation times or the time dependence of the spin autocorrelation function, and extrapolates them to the thermodynamic limit, one finds that they are indeed compatible with the results for N = ∞ (which are known from analytical cal…