TWO WEEKS TRENTO MEETING



 
 
 

PHASE TRANSITIONS IN FINITE SYSTEMS 

 
 
 

11th to the 22nd of September, 2000.

Trento Italy

Organizing Committee

Ph.Chomaz(1), M. D'Agostino(2), D. Gross(3), F.Gulminelli(4), H. Haberland(5)

(1) GANIL, B.P.5027, F-14021 Caen c\'edex, France

(2) Università di Bologna, Italy

(3) HMI, 14109 Berlin, Germany

(4) LPC Caen,F-14050 Caen c\'edex, France 

(5) Universitaet Freiburg, D-79104 Freiburg, Germany

Abstract

Phase transitions are universal properties of interacting matter which have been widely studied in the thermodynamical limit of infinite systems. However, in many physical situations this limit cannot be accessed and phase transitions should be reconsidered from a more general point of view. This is for example the case of matter under long range forces like gravitation : even if self - gravitating systems are very large they cannot be considered as infinite because of the non saturating nature of the force. Other cases are provided by microscopic or mesoscopic systems. Metallic clusters can melt before being vaporized. Small drops of quantum fluids may undergo Bose condensation or super-fluid phase transition. Dense hadronic matter is predicted to merge in a quark and gluon plasma phase while nuclei are expected to exhibit a liquid - gas phase transition. For all these systems the experimental issue is how to sign a possible phase transition in a finite system.

Recently, many different groups have made considerable progresses on these issues on experimental as well as on the theoretical side. In particular, it seems that phase transitions of different order can be unambigously defined even in finite systems through topological anomalies in the relevant thermostatistical potentials. These concepts have been tested in different models and observable signals have been proposed to infer thermodynamical properties from experimental data. Very promising attempts to measure direct evidences of thermodynamical phase transitions in mesoscopic systems have been also reported in the past months by the nuclear as well as the atomic cluster communities. In particular, melting and vaporisation points have been reported as well as topological anomalies such as negative heat capacities. These results can be considered as important discoveries in general physics.

In order to share the progresses and to join the efforts of the various groups we believe that it is time to organize a Trento workshop on thermodynamical phase transitions in finite systems. Many ''hot'' issues and new ideas need to be discussed and criticized by a pluridisciplinary community. Moreover, other fields of physics dealing with various phase transitions in finite systems can bring important contributions to the debate and can benefit from these discoveries and progresses.

Program of subjects :

  • Thermodynamics without the thermodynamical limit
  • Definition of thermostatistical phase transition
  • Signals of phase transitions and critical points
  • Theoretical signals from mass partitions
  • Experimental status for low-energy nuclear systems
  • Results on clusters
  • Phase transition of self-gravitating systems
  • Equilibrium, thermometers and other observables
  • Applications to other phase transitions
  • Open problems and new propositions

Schedule
 
 

  • Morning from 9:00 to 12:30 : Lectures and Review talks
  • Afternoon from 15:00 to 19:00 : Presentations and Discussion

First Week

Thermodynamics

Subjects

Speakers of the morning lectures

 

9h00 - 11h00

11h30 -12h30

Possible Intervenants of the afternoon discussion

15h 00 - 17h00

17h30 - 19h00

Monday

Thermodynamic Theory

D. Gross (Berlin)

Ph. Chomaz (GANIL)

P. Borrmann (Oldenburg)

F. Gulminelli (Caen)

L.G. Moretto (LBL)

J. Jellinek (Argonne)

P. Labastie (Toulouse)

F. Spiegelmann (Toulouse)

M. Pettini (Firenze)

J. Doye (Cambridge)

A.H. Raduta (Bucharest)

A.R. Raduta (Bucharest)

Tuesday

Dynamics, Ergodicity et c.

J. Jellinek (Argonne)

P. Labastie (Toulouse)

Ph. Chomaz (GANIL) 

A. Bonasera (Catania) 

F. Spiegelmann (Toulouse)

F. Gulminelli (Caen)

B. Borderie (Orsay)

M.F. Rivet (Orsay)

D. Gross (Berlin)

D.J. Wales (Cambridge)

P. Borrmann (Oldenburg)

M. Pettini (Firenze)

H. Posch (Wien)

A.H. Raduta (Bucharest)

A.R. Raduta (Bucharest)

C. Dorso

Wenesday

Observables

F. Gulminelli (Caen)

L.G. Moretto (LBL)

F. Spiegelmann (Toulouse)

Ph. Chomaz (GANIL)

A. Bonasera (Catania)

R. Bougault (Caen)

M. D'Agostino (Bologna)

J.B. Elliott (Berkeley)

D. Gross (Berlin)

P. Labastie (Toulouse)

D.J. Wales (Cambridge)

C. Brechignac (Orsay)

H. Haberland (Freiburg)

M. Schmidt (Freiburg)

A.H. Raduta (Bucharest)

A.R. Raduta (Bucharest)

J. Jellinek (Argonne)

Thursday

Experimental results

R. Bougault (Caen),

C. Brechignac (Orsay)

M. D'Agostino (Bologna)

A. Chbihi (Ganil)

L.G. Moretto (LBL)

B. Borderie (Orsay)

M. Bruno (Bologna)

J.B. Elliott (Berkeley)

M.F. Rivet (Orsay)

C. Brechignac (Orsay)

M. Schmidt (Freiburg)

F. Cannata (Bologna)

Friday

Experimental Results

B. Borderie (Orsay)

H. Haberland (Freiburg)

M.F. Rivet (Orsay)

L.G. Moretto (LBL)

R. Bougault (Caen)

M. Bruno (Bologna)

M. D'Agostino (Bologna)

J.B. Elliott (Berkeley)

A. Chbihi (Ganil)

H. Haberland (Freiburg)

M. Schmidt (Freiburg)

Second Week

Critical behaviors

Speakers of the morning lectures

 

9h00 - 11h00

11h30 -12h30

Possible Intervenants of the afternoon discussion

 

15h 00 - 17h00

17h30 - 19h00

Monday

Critical Phenomena Theory

J. Richert (Strasbourg) 

F. Gulminelli (Caen)

A. Bonasera (Catania)

Ph. Chomaz (GANIL)

D. Gross (Berlin)

J. Jellinek (Argonne)

M. Antoni (Marseille)

P. Borrmann (Oldenburg)

M. Pettini (Firenze)

A. Botvina.(GSI)

C. Dorso

Tuesday

Dynamics

A. Bonasera (Catania),

M. Antoni (Marseille)

M. Pettini (Firenze)

J. Richert (Strasbourg)

D. Gross (Berlin) 

J. Jellinek (Argonne)

P. Borrmann (Oldenburg)

H. Posch (Wien)

A. Botvina.(GSI)

C. Dorso

Wenesday

Experimental results

M. D'Agostino (Bologna)

J.B. Elliott (Berkeley)

Michel Farizon (Lyon)

J. Richert (Strasbourg) 

D. Gross (Berlin)

A. Botvina.(GSI)

F. Gramegna

J. Leygnier (Orsay)

Thursday

Young physicists seminars and general discussion

V. Duflot 

B. Bouriquet

F. Gobet 

E. Geraci  

L. Casetti

Olivier Fliegans

 

F. Calvo

E. Galichet

N. Leneindre

 

Friday

Self gravitating systems and other phase transitions

H. Posch (Wien)

D. Gross (Berlin)

M. Antoni (Marseille)

J. Jellinek (Argonne)

F. Gulminelli (Caen)

Ph. Chomaz (GANIL)

P. Borrmann (Oldenburg)

M. Pettini (Firenze)

T. Maruyama (Catania)

A. Botvina.(GSI)

Key speakers
 

Subject

Financial Support

Dates

First Week

Second Week

Nuclear theory

A. Bonasera (Catania)

'18-23 '

yes

Ph. Chomaz (GANIL)

10 23

yes

yes

C. Dorso (Buenos Aires)

Yes(+travel)

10 23

yes

yes

H. Feldmeier (Darmstadt)

10 20

yes

yes

F. Gulminelli (Caen)

10 23

yes

yes

A. Botvina (GSI)

Yes

17 23

yes

L.G. Moretto (LBL)

10 16

yes

A.H. Raduta (Bucharest)

Yes

10 24

yes

yes

A.R. Raduta (Bucharest)

Yes

10 24

yes

Yes

Nuclear Experiments

B. Borderie (Orsay)

9 22

yes

yes

R. Bougault (Caen)

10 17

yes

M. Bruno (Bologna)

10 23

yes

A. Chbihi (Ganil)

'10 17'

yes

M. D'Agostino (Bologna)

10 23

yes

yes

J.B. Elliott (Berkeley)

Yes

10 22

yes

yes

F. Gramegna

'18-23'

yes

W. Mueller (GSI)

10 23 - Cancelled

A. Pagano (LNS-Catania)

10 15 - Cancelled

M.F. Rivet (Orsay)

yes

9 18

yes

Cluster Theory

J. Doye(Cambridge)

Yes?

10 16

yes

J. Jellinek (Argonne)

Yes(+Travel)

10 16

yes

P. Labastie (Toulouse)

Yes

yes

F. Spiegelmann (Toulouse)

Yes

10 16

yes

Cluster Experiments

C. Brechignac (Orsay)

10 16

yes

M. Farizon (Lyon)

with the Professor Tilmann Maerk (Innsbruck) the 14, 15 and 16

14 22

Part * 2

yes

C. Guet (Grenoble)

Cancelled

H. Haberland (Freiburg)

10 16

yes

J. Leygnier (Orsay)

17 22

yes

M. Schmidt (Freiburg)

10 22

yes

yes

General physics,and other fields

M. Antoni (Marseille)

yes

17 22

yes

P. Borrmann (Oldenburg)

Yes

yes

yes

F. Cannata (Bologna)

10 23 - Cancelled

D. Gross (Berlin)

Yes

9 22

yes

yes

H. Krivine (Orsay)

Cancelled

T. Maruyama (Catania) 

yes

16 23

yes

M. Pettini (Firenze)

Yes

10 12 and 18-19

yes

yes

H. Posch (Wien)

Yes

16 23

yes

J. Richert (Strasbourg)

Yes

17 23

yes

Etudiants, 

post doc,

young physicists

Working with

V. Duflot 

F. Gulminelli

Yes

10 23

yes

yes

B. Bouriquet

A. Chbihi

Yes

'17 23'

yes

F. Gobet 

Michel Farizon

Yes

'10 23'

yes

yes

F. Calvo 

Labastie

Yes

10 16

yes

N. Leneindre

D'Agostino-Bougault

Yes

10 23

yes

yes

E. Geraci

D'Agostino

Yes (one week)

10 22

yes

yes

M.-Ch. Firpo

Antoni

Yes?

E. Galichet

Borderie

Yes

9 23

yes

yes

L. Casetti

Pettini

Cancelled

R. Franzosi

Pettini

Yes

yes

L. Spinelli

Pettini

Yes

yes

yes

G. Fabbri

Bonasera

Yes

Cancelled

David d'Enterria

Cancelled

Olivier Fliegans

Gross

If possible

10 24

Yes

yes

34

30

 

Abstracts (by order of receipt):

Reverse collaboration

Elena Geraci:

The Reverse experiment intends to study isospin effects and cluster productions
in nuclear multifragmentation in heavy ion collisions as a function of the mass
and the excitation energy of the colliding nuclear systems in reverse
kinematics. The peculiarities of the experiment, isotopic identification of the
nuclear clusters and good particle-particle correlation, are important
requirements for studying phase transition in finite nuclear system. The
experiment has been performed using the forward part of Chimera
multidetector at Laboratori Nazionali del Sud using 112Sn and 124Sn beams
impinging on 58Ni,64Ni and Al targets. Data analyses are in progress.
 
 

DYNAMICS AND THERMODYNAMICS OF FINITE SYSTEMS

J. Jellinek

Chemistry Division, Argonne National Laboratory, Argonne, IL 60439, USA

 

The correspondence between dynamics and thermodynamics/statistical
mechanics of finite systems will be examined, and a new axiomatic
approach for introducing thermodynamic concepts and quantities through
dynamics will be formulated. Illustrations will be given through
analysis of phase changes in one- and two-component metal clusters.

 

 

Caloric Curves for Atomic Clusters.

Hellmut Haberland

Caloric curves of small, free and mass selected sodium clusters are
measured by using the photofragmentation pattern of thermalized and laser
excited clusters as a "nano-calorimeter". The solid/liquid phase change is
studied for clusters containing between 50 and 200 atoms. The influence of
the finite size on the thermodynamics of the clusters is investigated.

 

 

Ergodicity.

Pierre Labastie

 

MD simulation of quark system

or

Multifragmentation of expanding nuclear matter.

Toshiki Maruyama

JAERI (staying in Catania for one year)

 

Hamiltonian dynamics, Geometrical and Topological

concept in the study of phase transitions

Marco Pettini

Osservatorio Astrofisico di Arcetri

and I.N.F.N. Sezione di Firenze

and I.N.F.M. UdR di Firenze

 

A reseach work performed with L. Casetti, R. Franzosi and L.Spinelli during
the last years has made use of differential-geometric and topological concepts
in the study of classical Hamiltonian dynamics and phase transitions.
New important steps forward have been made for what concerns the topological
hypothesis about the deep origin of phase transitions. In this framework the
the main idea is to link the appearance of phase transitions to some major
topology change of equipotential submanifolds of phase space instead of
linking them to non-analyticity, as is usual in the Yang-Lee and in the
Dobrushin-Ruelle theories. The implications are far reaching because, in
principle, the thermodynamic limit dogma can be overcome and from the
topological point of view a possibility appears of properly defining a new
mathematical counterpart of phase transitions, also at finite number of degrees
of freedom. This is of prospective interest to the study of phase transitions
in finite N systems, like nano and mesoscopic systems, nuclear or atomic
clusters and so on.
The results so far obtained concern: an analytic result for a mean field XY
model; the numerical computation of the potential energy dependence
of a topologic invariant (the Euler characteristic) of the equipotential
surfaces of the configuration space of a lattice phi^4 model directly
confirming the tight link between topology and phase transitions and suggesting
which kind of topology changes are involved; a first successful attempt
at working out some sufficiency conditions, in order to restrict the domain of
topology changes that can be responsible for the appearance of a first or
second order thermodynamic phase transition, reported in; finally,
the proof of a general theorem about the necessity of topology changes of
equipotential submanifolds of the microscopic configuration space for the
occurrence of first or second order phase transitions.

Some Aspects of Ergodicity and Chaos inGravitational systems

 

Harald A. Posch

Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria

E-mail: posch@ls.exp.univie.ac.at

 

Walter Thirring

Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria

E-mail: fwagner@ap.univie.ac.at

 

Recently, we have studied many-body systems in $d$ dimensions interacting
with a purely attractive pair potential $\sim |{x}_i - {x}_j|^{\nu}$, where $\nu$
is a positive parameter. The case $\nu = d = 1$ corresponds to the well-known
linear sheet model. We derive the temperature in microcanonical equilibrium for
arbitrary $\nu$ and $d$ and, for $d=1$, the corresponding velocity distribution
for a finite number $N$ of particles. We verified these theoretical expressions by
comparing them to extensive computer simulation results for various $\nu$. We
also computed full Lyapunov spectra and the Kolmogorov-Sinai entropy and found
that the maximum exponent increases linearly as a function of $|\nu - 2|$, where
$\nu = 2$ represents a regular harmonic oscillator chain with vanishing expoents.
For the linear sheet model, we find indications for the existence of sticky phase-space
regions and non ergodicity even if more than 16 particles are involved.

We also studied some stability and ergodic properties of the famous reduced three
body problem (``Sun, Jupiter, and a test particle''). We propose a simple oscillator
model to understand the stability of orbits with small eccentricity of the test particle.
It models the main short-time features for small mass ratios of the other bodies. These
results are confronted with simulation results for bigger mass ratios, where chaotic
features emerge. For larger energies, for which the test particle may reach the
neighborhood of the Sun and of Jupiter, the density in configuration space is nearly
homogeneous indicating almost ergodic behavior. In the case of the more general problem
of three particles in a planar box (circular or square) with reflecting boundaries, the
existence or lack of conserved quantities other than the energy leads to a converging or
diverging kinetic energy, respectively.

 

 What do we learn from the Caloric curve ?

Walter F.J. Mueller

GSI, Abteilung KP3, D-64291 Darmstadt

Mail: W.F.J.Mueller@gsi.de

 

Critical behaviour and hydrogen cluster multifragmentation

Michel FARIZON

IPNL, Lyon.

We report on a cluster fragmentation study involving collisions of fast
(c/88) hydrogen cluster ions with atomic helium and fullerenes. The
experimental characterization of cluster fragmentation by a statistical
analysis of the fragmentation events, has become possible because of a
multicoincidence technique in which all fragments are detected on an event
by event basis. From the break-up in two fragments to the complete
disintegration of the cluster, these molecular systems of small size
exhibit a transition with an increase of the fluctuations.

 

Statistical description of finite systems

Philippe CHOMAZ

GANIL Caen France

 

 

Measurable observables of phase coexistence.

Critical behaviour in first order phase transition

Francesca GULMINELLI

LPC Caen FRANCE

 

Thermodynamics of hot drops at fragmentation times

Claudio Dorso

Buenos Aires, Argentina