research

Classical and Quantum Fluids


“Aim of the research is to develop analytical and computational methods for condensed and soft matter starting from the fundamental many-body equations. Apart from the few analytically exactly solvable models our principal instruments, guided by the various sum-rules, are Integral Equation Theory, Density Functional Theory, Thermodynamic Perturbation Theory, Association Theory, and Monte Carlo simulations which can find exact properties of many-body systems. We are combining these approaches to create new methods and to test the accuracy of calculations on materials. Current studied materials include colloidal suspensions, ionic liquids, polymer mixtures, the electron fluid, the polaron, and boson fluids (like 4He, 4He-H2 mixtures, ...). We investigate the structure and thermodynamic properties of the materials including their phase transitions like the gas-liquid-(glass)-solid first order ones and the superfluid-superconducting second order ones, the percolation threshold, the clustering, the localization, the demixing, the polydispersity, and surface properties.
Lately we started working on euclidean relativistic covariant and ultralocal quantum scalar field theories through Path integral Monte Carlo of lattice field theory subject to different kinds of quantization procedures. ”


Soft and Biological Matter:
publications
14.14. Fantoni R., Gazzillo D., Giacometti A., Miller M. A., and Pastore G., J. Chem. Phys. 127, 234507 (2007), (*)
"Patchy sticky hard spheres: Analytical study and Monte Carlo simulations"
(arXiv:0710.2356)
18.18. Fantoni R., Giacometti A., Malijevský A., and Santos A., J. Chem. Phys. 131, 124106 (2009),
"Penetrable-Square-Well fluids: Analytical study and Monte Carlo simulations"
(arXiv:0907.5559) Featured in the SkLogWiki
23.23. Fantoni R., Giacometti A., Sciortino F., and Pastore G., Soft Matter 7, 2419 (2011), (*)
"Cluster theory of Janus particles", erratum
(arXiv:1012.1820) Featured among the Top 10 most downloaded SM articles in February 2011 RSC Blog RSC Blog
24.24. Fantoni R., Malijevský A., Santos A., and Giacometti A., Europhys. Lett. 93, 26002 (2011),
"Phase diagram of the penetrable square well-model"
(arXiv:1101.0708) Featured in the SkLogWiki
26.26. Fantoni R., Malijevský A., Santos A., and Giacometti A., Mol. Phys. 109, 2723 (2011),
"The penetrable square-well model: Extensive versus non-extensive phases"
(arXiv:1106.1750) Featured in the SkLogWiki
35.35. Maestre M. A. G., Fantoni R., Giacometti A., and Santos A., J. Chem. Phys. 138, 094904 (2013), (*)
"Janus fluid with fixed patch orientations: Theory and simulations"
(arXiv:1212.5540)


Condensed Matter:
publications


Exact results:
publications


Field theory:
publications


Education:



Some lecture notes:


Notes on Jellium


We discuss the static screening in the Random Phase Approximation (RPA) of the Hartree potential of a degenerate electron gas explaining the Friedel oscillations as extracted from the book "Coulomb liquids" by Norman H. March and Mario P. Tosi (3 pages).


Notes on Quantum Monte Carlo


We discuss random walk methods in the first lecture. In the second lecture we discuss variational Monte Carlo which is a straightforward application of the Metropolis Monte Carlo method, the only complication being that the wavefunction for fermion systems is a determinant. In the third lecture we discuss the projector Monte Carlo methods. Finally in the fourth lecture we discuss the Path Integral Monte Carlo method (19 pages).


Notes on Symmetries and Particles in relativistic quantum theory and proof of the spin-statistics theorem


We describe a pointwise, structureless, elementary, free particle by a finite dimensional irreducible unitary representation of its group symmetries (51 pages).


Notes on the Renormalization Group of real fluids


We describe the theory of the Renormalization Group and apply it to the theory of real fluids. We review some of the ideas of the Renormalization Group in the statistical physics of classical and quantum fluids. The origin, the nature, the basis, the formulation, the critical exponents and scaling, relevance, irrelevance, and marginality, universality, and Wilson's concept of flows and fixed point in a space of Hamiltonians (16 pages).


Notes on the angular momentum in quantum mechanics


We describe the angular momentum in quantum mechanics as the generator of rotations starting from Wigner theorem (9 pages).




Scientific collaborations:


1. Mario Pio Tosi, Scuola Normale Superiore (SNS) of Pisa, Italy (Laurea thesis and 3 publications)
2. Bernard Jancovici, University of Paris-Sud at Orsay, France (1 publication)
3. Angel Alastuey, Ecole Normale Sup\'erieure de Lyon, France (1 publication)
4. Giorgio Pastore, University of Trieste, Italy (Ph.D. thesis and 10 publications)
5. Domenico Gazzillo, University Ca' Foscari of Venezia, Italy (8 publications)
6. Achille Giacometti, University Ca' Foscari di Venezia, Italy (18 publications)
7. Francesco Sciortino, University La Sapienza of Rome, Italy (1 publication)
8. Gabriel Téllez, University of Los-Andes in Bogota', Colombia (2 publications)
9. Peter Sollich, King's college of London, United Kingdom (2 publications)
10. Mark Miller, University of Cambridge, United Kingdom (1 publication)
11. Andrés Santos, University of Extremadura at Badajoz, Spain (14 publications)
12. Alexandr Malijevský, University of Prague, Czech Republic (4 publications)
13. Kristian Müller-Nedebock, University of Stellenbosch, South Africa (1 publication)
14. Bert Klumperman, University of Stellenbosch, South Africa (1 publication)
15. Johannes Salari, University of Technology Eindhoven, The Netherlands (1 publication)
16. Miguel Angel Maestre, University of Extremadura at Badajoz, Spain (3 publications)
17. Saverio Moroni, CNR Rome-Trieste, Italy (1 publication)
18. Paola Gori-Giorgi, University of Amsterdam, The Netherlands
19. John R. Klauder, University of Florida, U.S.A. (9 publications)
20. Ana María Montero Martínez, University of Extremadura at Badajoz, Spain




Some past undergraduate and graduate projects:


I. Integral Equation Theories for Simple and Complex Classical Fluids

theory collaborators: Giorgio Pastore, Domenico Gazzillo, Achille Giacometti, Andrés Santos

II. Mesoscopic Physics: colloids, reverse micelles and globular proteins

theory collaborators: Domenico Gazzillo, Achille Giacometti

III. Coulomb Liquids

theory collaborators: Mario P. Tosi, Bernard Jancovici, Gabriel Téllez, Angel Alastuey
simulation collaborators: David M. Ceperley
example project: "Thermodynamic limit of the free 1DEG on a circle"
example project: "Static screening in a degenerate electron plasma"
example project: "The Jellium"

IV. Compact Objects: black holes, white dwarfs and neutron stars

theory collaborator: Stuart L. Shapiro
simulation collaborator: Luciano Rezzolla
example project: "scalar gravitation"

V. Phase transitions

theory collaborator: Nigel D. Goldenfeld
example project: "the Wigner crystal"

VI. Fractional statistics

theory collaborators: Eduardo H. Fradkin and Michael Stone
example project: "introduction to anyons"

VII. Monte Carlo Methods

for classical and quantum statistical physics: David M. Ceperley
for biological systems: Klaus Schulten
example project: "Ewald's sums"

VIII. Polymer Physics

theory collaborator: Kristian Müller-Nedebock
experimental collaborator: Bert Klumperman




Some ongoing projects:


I. Soft Matter

II. Condensed Matter

III. Compact Objects: black holes, white dwarfs and neutron stars

IV. Phase transitions

V. Fractional statistics

VI. Integral Equation Theories for Simple and Complex Fluids

VII. Monte Carlo Methods

VIII. Polymers

IX. Non Equilibrium Statistical Mechanics

X. Relativistic Euclidean Quantum Field Theory




Some conference presentations:


Conference Name Year Place
Milano 2017 Milano (Italy)
Sphinx 2017 Badajoz (Spain)
Sphinx 2013 Badajoz (Spain)
Sphinx 2010 Badajoz (Spain)
FisMat 2015 Palermo (Italy)
FisMat 2013 Milano (Italy)
CECAM 2007 Lyon (France)
8th LMC 2011 Vienna (Austria)
8th LMC 2011 Vienna (Austria)
7th LMC 2008 Lund (Sweden)
6th LMC 2005 Utrecht (Netherlands)
ICTP 2011 Trieste (Italy)
MECO 38 2013 Trieste (Italy)
MECO 35 2010 Pont-à-Mousson (France)
MECO 31 2006 Primosten (Croatia)
StatPhys 24 2010 Cairns (Australia)
StatPhys 23 2007 Genova (Italy)
SigmaPhi 2014 Rhodes (Greece)
NITheP 2012 Stellenbosch (South Africa)
NITheP 2011 Stellenbosch (South Africa)
NITheP 2010 Stellenbosch (South Africa)
NITheP 2009 Stellenbosch (South Africa)
Parma 2004 Parma (Italy)
Giovanni Paladin Memorial 2004 Rome (Italy)
6th World Congress and Expo on Nanotechnology and Material Science 2018 Valencia (Spain)



Research table:


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Riccardo Fantoni, via Udine 29, 34135 Trieste, Italy