# Marco PettiniAix-Marseille Université | AMU · Centre de Physique Théorique

Marco Pettini

HDR

## About

162

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Introduction

## Publications

Publications (162)

The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase transitions. In fact, in correspondence of a phase transition there are peculiar geometrical changes of the mechanica...

Both classical and quantum electrodynamics predict the existence of dipole-dipole long-range electrodynamic intermolecular forces; however, these have never been hitherto experimentally observed. The discovery of completely new and unanticipated forces acting between biomolecules could have considerable impact on our understanding of the dynamics a...

Both classical and quantum electrodynamics predict the existence of dipole-dipole long-range electrodynamic intermolecular forces; however, these have never been hitherto experimentally observed. The discovery of completely new and unanticipated forces acting between biomolecules could have considerable impact on our understanding of the dynamics a...

Agent-based modelling and simulation have been effectively applied to the study of complex biological systems, especially when composed of many interacting entities. Representing biomolecules as autonomous agents allows this approach to bring out the global behaviour of biochemical processes as resulting from local molecular interactions. In this p...

Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase tran...

Agent-based modelling and simulation have been effectively applied to the study of complex biological systems, especially when composed by a large number of interacting entities. Representing biomolecules as autonomous agents allows this approach to bring out the global behaviour of biochemical processes as resulting from local molecular interactio...

By resorting to a model inspired to the standard Davydov and Holstein-Fr\"ohlich models, in the present paper we study the motion of an electron along a chain of heavy particles modelling a sequence of nucleotides proper to a DNA fragment. Starting with a model Hamiltonian written in second quantization, we use the Time Dependent Variational Princi...

By resorting to a model inspired to the standard Davydov and Holstein-Fröhlich models, in the present paper we study the motion of an electron along a chain of heavy particles modeling a sequence of nucleotides proper to a DNA fragment. Starting with a model Hamiltonian written in second quantization, we use the Time Dependent Variational Principle...

In the present paper we address the problem of the energy downconversion of the light absorbed by a protein into its internal vibrational modes. We consider the case in which the light receptors are fluorophores either naturally co-expressed with the protein or artificially covalently bound to some of its amino acids. In a recent work [Phys. Rev. X...

This paper tackles Hamiltonian chaos by means of elementary tools of Riemannian geometry. More precisely, a Hamiltonian flow is identified with a geodesic flow on configuration space–time endowed with a suitable metric due to Eisenhart. Until now, this framework has never been given attention to describe chaotic dynamics. A gap that is filled in th...

Phase transitions do not necessarily correspond to a symmetry breaking phenomenon. This is the case of the Kosterlitz–Thouless (KT) phase transition in a two-dimensional classical XY model, a typical example of a transition stemming from a deeper phenomenon than a symmetry-breaking. Actually, the KT transition is a paradigmatic example of the succe...

In the present paper we address the problem of the energy downconversion of the light absorbed by a protein into its internal vibrational modes. We consider the case in which the light receptors are fluorophores either naturally co-expressed with the protein or artificially covalently bound to some of its amino acids. In a recent work [Phys. Rev. X...

In the present paper we address the problem of the energy downconversion of the light absorbed by a protein into its internal vibrational modes. We consider the case in which the light receptors are fluorophores either naturally co-expressed with the protein or artificially covalently bound to some of its amino acids. In a recent work [Phys. Rev. X...

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

By identifying Hamiltonian flows with geodesic flows of suitably chosen Riemannian manifolds, it is possible to explain the origin of chaos in classical Newtonian dynamics and to quantify its strength. There are several possibilities to geometrize Newtonian dynamics under the action of conservative potentials and the hitherto investigated ones prov...

By identifying Hamiltonian flows with geodesic flows of suitably chosen Riemannian manifolds, it is possible to explain the origin of chaos in classical Newtonian dynamics and to quantify its strength. There are several possibilities to geometrize Newtonian dynamics under the action of conservative potentials and the hitherto investigated ones prov...

The present work reports about the dynamics of a collection of randomly distributed, and randomly oriented, oscillators in 3D space, coupled by an interaction potential falling as $1/r^3$, where r stands for the inter-particle distance. This model schematically represents a collection of identical biomolecules, coherently vibrating at some common f...

We describe the activation of out-of-equilibrium collective oscillations of a macromolecule as a classical phonon condensation phenomenon. If a macromolecule is modeled as an open system—that is, it is subjected to an external energy supply and is in contact with a thermal bath to dissipate the excess energy—the internal nonlinear couplings among t...

Different arguments led us to surmise that the deep origin of phase transitions has to be identified with suitable topological changes of potential-related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase tra...

In this paper we investigate the Hamiltonian dynamics of a lattice gauge model in three spatial dimension. Our model Hamiltonian is defined on the basis of a continuum version of a duality transformation of a three dimensional Ising model. The system so obtained undergoes a thermodynamic phase transition in the absence of symmetry-breaking. Besides...

The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an explicit relation between entropy and topological invariants of certain submanifolds of configuration space, and,...

The present paper deals with an experimental feasibility study concerning the detection of long- range intermolecular interactions through molecular diffusion behavior in solution. This follows previous analyses, theoretical and numerical, where it was found that inter-biomolecular long-range force fields of electrodynamic origin could be detected...

A longstanding, and still present, proposal relates the activation of collective intramolecular oscillations of biomolecules with their biological functioning. These collective oscillations are predicted to occur in the THz frequency domain. Collective oscillations of an entire molecule, or of a substantial fraction of its atoms, are essential to g...

Fluorescence Correlation Spectroscopy (FCS) is widely used to detect and quantify diffusion processes at the molecular level. The molecules of which diffusion is studied are marked with fluorescent dyes. It is commonly maintained that this technique only applies to systems where the concentration of fluorescent molecules is low. Even if this is the...

A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size...

A central issue in the science of complex systems is the quantitative characterization of complexity. In the
present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate with a—in principle, any—network a differentiable object (a Riemannian manifold) whose volume is used to deﬁne the e...

Background
This study is mainly motivated by the need of understanding how the diffusion behavior of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range...

The topological theory of phase transitions has its strong point in two theorems proving that, for a wide class of physical systems, phase transitions necessarily stem from topological changes of some submanifolds of configuration space. It has been recently argued that the $2D$ lattice $\phi^4$-model provides a counterexample that falsifies this t...

Persistent homology analysis, a recently developed computational method in
algebraic topology, is applied to the study of the phase transitions undergone
by the so-called XY-mean field model and by the phi^4 lattice model,
respectively. For both models the relationship between phase transitions and
the topological properties of certain submanifolds...

In the present work we intend to investigate how to detect the behaviour of the immune system reaction to an external stimulus in terms of phase transitions. The immune model considered follows Jerne’s idiotypic network theory. We considered two graph complexity measures—the connectivity entropy and the approximate von Neumann entropy—and one entro...

We propose a method to associate a differentiable Riemannian manifold to a generic many-degrees-of-freedom discrete system which is not described by a Hamiltonian function. Then, in analogy with classical statistical mechanics, we introduce an entropy as the logarithm of the volume of the manifold. The geometric entropy so defined is able to detect...

Introduction
In psychotherapy, the object of study is not directly perceptible and material, but involves human mind complexity and specific content
Objectives
In psychotherapeutic relationship we propose a method to inspect by deduction non-conscious mind, patient hidden mood, hate, affectivity.
Aims
The aim of this work is using a modern physic...

In the present work we intend to investigate how to detectthe behaviour of the immune system reaction to an external stimulus interms of phase transitions. The immune model considered follows Jerne'sidiotypic network theory. We considered two graph complexity measures- the connectivity entropy and the approximate von Neumann entropy -and one entrop...

Self-organization of living organisms is of an astonishing complexity and efficiency. More specifically, biological systems are the site of a huge number of very specific reactions that require the right biomolecule to be at the right place, at the right time. From a dynamical point of view, this raises the fundamental question of how biomolecules...

In order to define a new method for analyzing the immune system within the realm of Big Data, we bear on the metaphor provided by an extension of Parisi’s model, based on a mean field approach. The novelty is the multilinearity of the couplings in the configurational variables. This peculiarity allows us to compare the partition function \documentc...

The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is shown that when the particles are uniformly distributed throughout the accessible space, the self-diffusion coef...

The issue of retarded long-range resonant interactions between two molecules
with oscillating dipole moments is reinvestigated within the framework of
classical electrodynamics. By taking advantage of a theorem in complex
analysis, we present a simple method to calculate the frequencies of the normal
modes, which are then used to estimate the inter...

The dynamical properties and diffusive behavior of a collection of mutually
interacting particles are numerically investigated for two types of long-range
interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It
is shown that when the particles are uniformly distributed throughout the
accessible space, the self-diffusion coef...

The beam-plasma instability, i.e., the response of the plasma bulk to the injection of supra thermal charged-particle beams, results to be appropriately characterized by a long-range interaction system. This physical system hosts a number of very interesting phenomena and, in particular, the emergence of long-lived quasi-stationary states. We chara...

We consider a Gaussian statistical model whose parameter space is given by
the variances of random variables. Underlying this model we identify networks
by interpreting random variables as sitting on vertices and their correlations
as weighted edges among vertices. We then associate to the parameter space a
statistical manifold endowed with a Riema...

The beam-plasma instability, i.e., the response of the plasma bulk to the
injection of supra thermal charged-particle beams, results to be appropriately
characterized by a long-range interaction system. This physical system hosts a
number of very interesting phenomena and, in particular, the emergence of
long-lived quasi-stationary states. We consi...

Motivated by its prospective biological relevance, the issue of resonant long-range interactions between two molecules displaying oscillating dipole moments is reinvestigated within the framework of classical electrodynamics. In particular, our findings shed new light on Fröhlichʼs theory of selective long-range interactions between biomolecules. F...

Highly specific spatiotemporal interactions between cognate molecular partners essentially sustain all biochemical transactions in living matter. That such an exquisite level of accuracy may result from encountering forces solely driven by thermal diffusive processes is unlikely. Here we propose a yet unexplored strategy to experimentally tackle th...

The issue of retarded long-range resonant interactions between two molecules
with oscillating dipole moments is reinvestigated within the framework of
classical electrodynamics. By taking advantage of a theorem in complex
analysis, we present a simple method to work out the frequencies of the normal
modes, which are then used to estimate the intera...

We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a...

The Fermi–Pasta–Ulam (FPU) nonlinear oscillator chain has proved to be a seminal system for investigating problems in nonlinear dynamics. First proposed as a nonlinear system to elucidate the foundations of statistical mechanics, the initial lack of confirmation of the researchers expectations eventually led to a number of profound insights into th...

This submission has been withdrawn by arXiv administrators because it is incomplete and thus violates arXiv policy. Comment: This submission has been withdrawn

The ${\bm E}\times{\bm B}$ drift motion of charged test particle dynamics in the Scrape Off Layer (SOL)is analyzed to investigate a transport control strategy based on Hamiltonian dynamics. We model SOL turbulence using a 2D non-linear fluid code based on interchange instability which was found to exhibit intermittent dynamics of the particle flux....

Elsevier journal. The attached copy is furnished to the author for non-commercial research and education use, including for instruction at the author's institution, sharing with colleagues and providing to institution administration. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institu...

Elsevier journal. The attached copy is furnished to the author for non-commercial research and education use, including for instruction at the author's institution, sharing with colleagues and providing to institution administration. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institu...

Molecular-dynamics calculations performed on a model of a Xe solid with diluted impurities made of I2 molecules indicate the existence of a crossover energy, below which the time to reach thermodynamic equilibrium increases rapidly. This effect is associated with the existence of long-living out-of-equilibrium states typical of many-degrees-of-free...

This book explores the foundations of Hamiltonian dynamical systems and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. A broad participation of topology in these fields has been lacking and this book will provide a welcome overview of the current research in the area, in which the author him...

We study a mean-field Hamiltonian system whose potential energy V({qi}i = 1...N) is expressed as a sum of k-body interactions and we show that in the thermodynamic limit the presence and the energy position of first-order phase transitions can be inferred by the study of the topology of configuration space induced by V, without resorting to any sta...

In this first chapter we will give an outline of some fundamental elements of statistical mechanics, of Hamiltonian dynamics, and of the relationship between them.
The general problem of statistical physics is the following. Given a collection–in general a large collection–of atoms or molecules, given the interaction laws among the constituents of...

In the preceding chapter we have seen that configuration-space topology is suspected to play a significant role in the emergence of phase transition phenomena. We have summarized all the clues in the form of a working hypothesis that we called the topological hypothesis. Then this has been given strong support by a direct numerical investigation of...

The preceding chapter contains a major theoretical achievement: the unbounded growth with N of certain thermodynamic observables, eventually leading to singularities in the N → ∞limit, which are used to define the occurrence of an equilibrium phase transition, is necessarily due to appropriate topological transitions in configuration space. The rel...

This book reports on an unconventional explanation of the origin of chaos in Hamiltonian dynamics and on a new theory of the origin of thermodynamic phase transitions. The mathematical concepts and methods used are borrowed from Riemannian geometry and from elementary differential topology, respectively. The new approach proposed also unveils deep...

The theoretical scenario depicted in this monograph is not a rephrasing of already known facts in an unusual mathematical language.
In fact, the Riemannian theory of Hamiltonian chaos, though still formulated at a somewhat primitive level (in that it does not yet include the role of nontrivial topology of the mechanical manifolds), provides a natur...

In the preceding chapters, we discussed the conceptual development that, starting from the Riemannian theory of Hamiltonian chaos, led us first to conjecture the involvement of topology in phase transition phenomena— formulating what we called the topological hypothesis—and then provided both indirect and direct numerical evidence of this conjectur...

The problem of integrability in classical mechanics has been a seminal one. Motivated by celestial mechanics, it has stimulated a wealth of analytical methods and results. For example, as we have discussed in Chapter 2, the weaker requirement of only approximate integrability over finite times, or the existence of integrable regions in the phase sp...

In the previous chapters we have shown how simple concepts belonging to classical differential geometry can be successfully used as tools to build a geometric theory of chaotic Hamiltonian dynamics. Such a theory is able to describe the instability of the dynamics in classical systems consisting of a large number N of mutually interacting particles...