DARWIN Digitale Dissertationen German Version Strich

FU Berlin
Digitale Dissertation

Olivier Fliegans :
Phasenuebergaenge in Kleineren Systemen
Phase transitions in "small" systems

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Abstract

In conventional thermostatistics there is no phase transition in "small" systems ("small" systems are those where the range of the forces is of the order of the system size). In fact, these systems do not exhibit the usual signals of phase transitions, i.e. Yang-Lee singularities. These singularities (divergences) can only occur at the thermodynamical limit. Nevertheless it is possible to define phases and phase transitions for "small" systems by means of local properties of their microcanonical entropy surface without invoking the thermodynamical limit.

In the first part of this thesis, the present status of the theory is summarized. The definitions of phase and phase transitions are recalled. Their relation to the conventional ones is discussed. All these points are illustrated by analytical entropy models.

The two other parts are dedicated to original studies of the microcanonical equilibrium properties of two "small" systems.

First, the liquid-gas phase transition of sodium clusters composed by a few hundreds of atoms is discussed. At low pressure, their caloric curves as functions of the enthalpy show a region characterized by a negative specific heat capacity. This is the signal of a first order phase transition in ``small'' systems. For certain enthalpy-range, their mass distributions have some peculiarities (multifragmentation) which vanish at the thermodynamical limit. High pressures calculations show for the first time the critical point of this first order phase transition. This critical point is located at higher pressure and smaller temperature compared to the critical point of corresponding thermodynamical limit.

The last part deals with self--gravitating systems. Although they are spatially very large they are "small" in the sense given above. These systems are studied in the microcanonical ensemble at constant energy E and total angular momentum L. They are studied without any a priori assumption about their spatial mass distributions (symmetry) and with a "realistic" potential. This is relevant for many astrophysical systems: from galaxies to (multiple-)stars formation. The entropy surface, its derivatives (temperature, angular velocity) and observables probing the mass distribution are worked out for the whole parameter space (E,L). These systems have a rich phase diagram with first order and several second order phase transitions. It is shown that all the properties of (astro-)physical importance are smeared out and lost if the intensive variables are fixed, i.e.\ in the canonical ensemble. Worst, for a given choice of intensive parameters, the partition function diverges for some microcanonical values of these intensive parameters.

Table of Contents

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    Complete version

    Title & Content

    General introduction

    Part I Thermostatistics of "small" systems
    Chapter 1 Introduction and definitions

    1.1 Microcanonical ensemble
    1.2 Canonical ensemble
    1.3 Microcanonical or canonical ensemble?
    1.4 Toy models

    Chapter 2 Thermostatistics of small systems

    2.1 Pure phases
    2.2 First order phase transition
    2.3 Second order phase transition
    2.4 Single event as a signal of phase transition?
    2.5 Alternative theories
    2.6 Conclusions

    Part II Liquid-gas transition of metallic clusters
    Chapter 3 Low pressure and scaling properties

    3.1 Introduction
    3.2 Model
    3.3 Simulation method
    3.4 Results
    3.5 Summary

    Chapter 4 Towards the critical point

    4.1 Introduction
    4.2 MMMC Results
    4.3 Lattice model (CL)
    3.4 Conclusions

    Part III Self-gravitating systems
    Chapter 5 Introduction

    Chapter 6 Microcanonical properties

    6.1 Microcanonical definitions
    6.2 Momentum average and dispersion
    6.3 Numerical method
    6.4 Results
    6.5 Discussion and conclusions

    General conclusion

    Appendices

    A Avoided volume
    B Technical "details"
    C Momentum distribution
    D Temperature at constant pressure

    Bibliography

More Information:

Online available: http://www.diss.fu-berlin.de/2001/93/indexe.html
Language of PhDThesis: english
Keywords: Statistical mechanics, phase transitions, cluster physics, self-gravitating systems
DNB-Sachgruppe: 29 Physik, Astronomie
Classification PACS: 05.20.Cg, 05.70.Fh, 05.10.Ln, 64.70.Dv
Date of disputation: 02-May-2001
PhDThesis from: Fachbereich Physik, Freie Universität Berlin
First Referee: Prof. Dr. Dieter H.E. Gross
Second Referee: Prof. Dr. Alfred Hueller
Contact (Author): fliegans@hmi.de
Contact (Advisor): gross@hmi.de
Date created:05-Jun-2001
Date available:07-Jun-2001

 

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