The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Wolfhard Janke - One of the best experts on this subject based on the ideXlab platform.
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transition barrier at a first order phase transition in the canonical and Microcanonical Ensemble
arXiv: Statistical Mechanics, 2017Co-Authors: Wolfhard Janke, Philipp Schierz, Johannes ZierenbergAbstract:We compare the transition barrier that accompanies a first-order phase transition in the canonical and Microcanonical Ensemble. This is directly encoded in the probability distributions of standard Metropolis Monte Carlo simulations and a proper Microcanonical sampling technique. For the example of droplet formation, we find that in both Ensembles the transition barrier scales as expected but that the barrier is much smaller in the Microcanonical Ensemble. In addition its growth with system size is weaker which will enhance this difference for larger systems. We provide an intuitive physical explanation for this observation.
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first order phase transitions in the real Microcanonical Ensemble
Physical Review E, 2016Co-Authors: Philipp Schierz, Johannes Zierenberg, Wolfhard JankeAbstract:: We present a simulation and data analysis technique to investigate first-order phase transitions and the associated transition barriers. The simulation technique is based on the real Microcanonical Ensemble where the sum of kinetic and potential energy is kept constant. The method is tested for the droplet condensation-evaporation transition in a Lennard-Jones system with up to 2048 particles at fixed density, using simple Metropolis-like sampling combined with a replica-exchange scheme. Our investigation of the Microcanonical Ensemble properties reveals that the associated transition barrier is significantly lower than in the canonical counterpart. Along the line of investigating the Microcanonical Ensemble behavior, we develop a framework for general Ensemble evaluations. This framework is based on a clear separation between system-related and Ensemble-related properties, which can be exploited to specifically tailor artificial Ensembles suitable for first-order phase transitions.
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molecular dynamics and monte carlo simulations in the Microcanonical Ensemble quantitative comparison and reweighting techniques
Journal of Chemical Physics, 2015Co-Authors: Philipp Schierz, Johannes Zierenberg, Wolfhard JankeAbstract:Molecular Dynamics (MD) and Monte Carlo (MC) simulations are the most popular simulation techniques for many-particle systems. Although they are often applied to similar systems, it is unclear to which extent one has to expect quantitative agreement of the two simulation techniques. In this work, we present a quantitative comparison of MD and MC simulations in the Microcanonical Ensemble. For three test examples, we study first- and second-order phase transitions with a focus on liquid-gas like transitions. We present MD analysis techniques to compensate for conservation law effects due to linear and angular momentum conservation. Additionally, we apply the weighted histogram analysis method to Microcanonical histograms reweighted from MD simulations. By this means, we are able to estimate the density of states from many Microcanonical simulations at various total energies. This further allows us to compute estimates of canonical expectation values.
L Ferroni - One of the best experts on this subject based on the ideXlab platform.
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the Microcanonical Ensemble of the ideal relativistic quantum gas
European Physical Journal C, 2007Co-Authors: F Becattini, L FerroniAbstract:We derive the Microcanonical partition function of the ideal relativistic quantum gas of spinless bosons in a quantum field framework as an expansion over fixed multiplicities. Our calculation generalizes well known expressions in the literature in that it does not introduce any large-volume approximation and it is valid at any volume. We discuss the issues concerned with the definition of the Microcanonical Ensemble for a free quantum field at volumes comparable with the Compton wavelength and provide a consistent prescription for calculating the Microcanonical partition function that is finite at finite volume and yielding the correct thermodynamic limit. Besides an immaterial overall factor, the expression obtained turns out to be the same as in the non-relativistic multi-particle approach. This work is an introduction to the derivation of the most general expression of the Microcanonical partition function fixing the maximal set of observables of the Poincare group.
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statistical model and Microcanonical Ensemble
Journal of Physics G, 2005Co-Authors: F Becattini, L FerroniAbstract:The study of the Microcanonical Ensemble of hadron-resonance gas is needed to probe the statistical model of hadronization and to settle some long-standing issues about its scope and meaning. We present a formulation of the Microcanonical Ensemble suitable for relativistic systems and numerical Monte Carlo techniques purposely developed for the multi-species hadron-resonance system.
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statistical hadronization and hadronic Microcanonical Ensemble i
European Physical Journal C, 2004Co-Authors: F Becattini, L FerroniAbstract:We present a full treatment of the Microcanonical Ensemble of the ideal hadron-resonance gas starting from a quantum-mechanical formulation which is appropriate for the statistical model of hadronization. By using a suitable transition operator for hadronization we are able to recover the results of the statistical theory, particularly the expressions of the rates of different channels. Explicit formulae are obtained for the phase space volume or density of states of the ideal relativistic gas in quantum statistics as a cluster decomposition, generalizing previous ones in the literature. The problem of the computation of averages in the hadron gas Microcanonical Ensemble and the comparison with canonical ones will be the main subject of a forthcoming second paper.
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statistical hadronization and Microcanonical Ensemble
Acta Physica Polonica B, 2004Co-Authors: F Becattini, L FerroniAbstract:Author(s): Becattini, F; Ferroni, L | Abstract: We present a Monte Carlo calculation of the Microcanonical Ensemble of the of the ideal hadron-resonance gas including all known states up to a mass of 1. 8 GeV, taking into account quantum statistics. The computing method is a development of a previous one based on a Metropolis Monte Carlo algorithm, with a the grand-canonical limit of the multi-species multiplicity distribution as proposal matrix. The Microcanonical average multiplicities of the various hadron species are found to converge to the canonical ones for moderately low values of the total energy. This algorithm opens the way for event generators based for the statistical hadronization model.
Philipp Schierz - One of the best experts on this subject based on the ideXlab platform.
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transition barrier at a first order phase transition in the canonical and Microcanonical Ensemble
arXiv: Statistical Mechanics, 2017Co-Authors: Wolfhard Janke, Philipp Schierz, Johannes ZierenbergAbstract:We compare the transition barrier that accompanies a first-order phase transition in the canonical and Microcanonical Ensemble. This is directly encoded in the probability distributions of standard Metropolis Monte Carlo simulations and a proper Microcanonical sampling technique. For the example of droplet formation, we find that in both Ensembles the transition barrier scales as expected but that the barrier is much smaller in the Microcanonical Ensemble. In addition its growth with system size is weaker which will enhance this difference for larger systems. We provide an intuitive physical explanation for this observation.
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first order phase transitions in the real Microcanonical Ensemble
Physical Review E, 2016Co-Authors: Philipp Schierz, Johannes Zierenberg, Wolfhard JankeAbstract:: We present a simulation and data analysis technique to investigate first-order phase transitions and the associated transition barriers. The simulation technique is based on the real Microcanonical Ensemble where the sum of kinetic and potential energy is kept constant. The method is tested for the droplet condensation-evaporation transition in a Lennard-Jones system with up to 2048 particles at fixed density, using simple Metropolis-like sampling combined with a replica-exchange scheme. Our investigation of the Microcanonical Ensemble properties reveals that the associated transition barrier is significantly lower than in the canonical counterpart. Along the line of investigating the Microcanonical Ensemble behavior, we develop a framework for general Ensemble evaluations. This framework is based on a clear separation between system-related and Ensemble-related properties, which can be exploited to specifically tailor artificial Ensembles suitable for first-order phase transitions.
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molecular dynamics and monte carlo simulations in the Microcanonical Ensemble quantitative comparison and reweighting techniques
Journal of Chemical Physics, 2015Co-Authors: Philipp Schierz, Johannes Zierenberg, Wolfhard JankeAbstract:Molecular Dynamics (MD) and Monte Carlo (MC) simulations are the most popular simulation techniques for many-particle systems. Although they are often applied to similar systems, it is unclear to which extent one has to expect quantitative agreement of the two simulation techniques. In this work, we present a quantitative comparison of MD and MC simulations in the Microcanonical Ensemble. For three test examples, we study first- and second-order phase transitions with a focus on liquid-gas like transitions. We present MD analysis techniques to compensate for conservation law effects due to linear and angular momentum conservation. Additionally, we apply the weighted histogram analysis method to Microcanonical histograms reweighted from MD simulations. By this means, we are able to estimate the density of states from many Microcanonical simulations at various total energies. This further allows us to compute estimates of canonical expectation values.
Jan Naudts - One of the best experts on this subject based on the ideXlab platform.
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the Microcanonical Ensemble
2011Co-Authors: Jan NaudtsAbstract:The harmonic oscillator is used to illustrate the ergodic theorem, which is the basis of statistical mechanics. The Microcanonical Ensemble is defined. Its entropy is discussed and is used to define the Microcanonical temperature. Examples are given of Microcanonical instabilities.
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entanglement of a Microcanonical Ensemble
Journal of Physics A, 2007Co-Authors: Tobias Verhulst, Jan NaudtsAbstract:We replace time-averaged entanglement by Ensemble-averaged entanglement and derive a simple expression for the latter. We show how to calculate the Ensemble average for a two-spin system and for the Jaynes–Cummings model. In both cases the time-dependent entanglement is known as well so that one can verify that the time average coincides with the Ensemble average.
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a generalized quantum Microcanonical Ensemble
Journal of Statistical Mechanics: Theory and Experiment, 2006Co-Authors: Jan Naudts, Erik Van Der StraetenAbstract:We discuss a generalized quantum Microcanonical Ensemble. It describes isolated systems that are not necessarily in an eigenstate of the Hamilton operator. Statistical averages are obtained by combining a time average and a maximum entropy argument to resolve the lack of knowledge about initial conditions. As a result, statistical averages of linear observables coincide with values obtained in the canonical Ensemble. Non-canonical averages can be obtained by taking into account conserved quantities which are non-linear functions of the microstate.
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boltzmann entropy and the Microcanonical Ensemble
EPL, 2005Co-Authors: Jan NaudtsAbstract:Boltzmann's entropy is slightly modified to make it suitable for discussing phase transitions in finite systems. As an example, it is shown that the pendulum undergoes a second-order phase transition when passing from a vibrational to a rotating state.
Johannes Zierenberg - One of the best experts on this subject based on the ideXlab platform.
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transition barrier at a first order phase transition in the canonical and Microcanonical Ensemble
arXiv: Statistical Mechanics, 2017Co-Authors: Wolfhard Janke, Philipp Schierz, Johannes ZierenbergAbstract:We compare the transition barrier that accompanies a first-order phase transition in the canonical and Microcanonical Ensemble. This is directly encoded in the probability distributions of standard Metropolis Monte Carlo simulations and a proper Microcanonical sampling technique. For the example of droplet formation, we find that in both Ensembles the transition barrier scales as expected but that the barrier is much smaller in the Microcanonical Ensemble. In addition its growth with system size is weaker which will enhance this difference for larger systems. We provide an intuitive physical explanation for this observation.
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first order phase transitions in the real Microcanonical Ensemble
Physical Review E, 2016Co-Authors: Philipp Schierz, Johannes Zierenberg, Wolfhard JankeAbstract:: We present a simulation and data analysis technique to investigate first-order phase transitions and the associated transition barriers. The simulation technique is based on the real Microcanonical Ensemble where the sum of kinetic and potential energy is kept constant. The method is tested for the droplet condensation-evaporation transition in a Lennard-Jones system with up to 2048 particles at fixed density, using simple Metropolis-like sampling combined with a replica-exchange scheme. Our investigation of the Microcanonical Ensemble properties reveals that the associated transition barrier is significantly lower than in the canonical counterpart. Along the line of investigating the Microcanonical Ensemble behavior, we develop a framework for general Ensemble evaluations. This framework is based on a clear separation between system-related and Ensemble-related properties, which can be exploited to specifically tailor artificial Ensembles suitable for first-order phase transitions.
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molecular dynamics and monte carlo simulations in the Microcanonical Ensemble quantitative comparison and reweighting techniques
Journal of Chemical Physics, 2015Co-Authors: Philipp Schierz, Johannes Zierenberg, Wolfhard JankeAbstract:Molecular Dynamics (MD) and Monte Carlo (MC) simulations are the most popular simulation techniques for many-particle systems. Although they are often applied to similar systems, it is unclear to which extent one has to expect quantitative agreement of the two simulation techniques. In this work, we present a quantitative comparison of MD and MC simulations in the Microcanonical Ensemble. For three test examples, we study first- and second-order phase transitions with a focus on liquid-gas like transitions. We present MD analysis techniques to compensate for conservation law effects due to linear and angular momentum conservation. Additionally, we apply the weighted histogram analysis method to Microcanonical histograms reweighted from MD simulations. By this means, we are able to estimate the density of states from many Microcanonical simulations at various total energies. This further allows us to compute estimates of canonical expectation values.