arXiv subjects

Marco Pettini

Publications and source records attributed to Marco Pettini.

At least 19 recordsLinked to original sources

arXiv2026

Hamiltonian Dynamics and Fundamental Phenomena in Biophysics: A Review

We review a theoretical and experimental programme addressing two closely related phenomena in biophysics: the classical analogue of Fr\"ohlich phonon condensation in macromolecules driven out of thermal equilibrium, and the resulting activation of long-range resonant electrodynamic intermolecular forces.The first is obtained by applying the time-dependent variational principle (TDVP) to the quantum Wu-Austin model,yielding a fully classical Hamiltonian in action-angle variables whose nonlinear rate equations display a nonequilibrium phase transition: supplied energy is channelled into the lowest-frequency collective mode. The second is based on a classical electrodynamic Hamiltonian for two coupled oscillating dipoles, whose normal modes predict long-range (1/r^3) resonant interactions. These are absent at thermal equilibrium but emerge under out-of-equilibrium coherent oscillations.We also discuss how to link Fr\"ohlich rate equations directly to Hamilton equations, clarifying the role of bath-mediated nonlinear couplings and the conditions for strong condensation at room temperature.In addition, TDVP is applied to a Davydov-Holstein-Fr\"ohlich model describing electron-phonon dynamics along a specific DNA sequence and its cognate restriction enzyme EcoRI. The time-domain Fourier cross-spectrum of the resulting electron currents shows a sharp co-resonance peak for the canonical recognition sequence, which disappears under randomisation, providing a sequence-specific electrodynamic signature of DNA-protein recognition.Experimental evidence from THz near-field spectroscopy, fluorescence correlation spectroscopy, and direct protein clustering is reviewed. Together these results support the view that metabolic energy can drive macromolecules into coherent oscillatory states, activating selective long-range electrodynamic forces relevant to biochemical organisation in living matter.

physics.bio-ph↗

arXiv2026

A Dynamical Spacetime Mechanism for Quantum Entanglement with a Falsifiable Experimental Signature

Quantum entanglement is a central resource of quantum information science, yet its correlations are ordinarily treated as properties of the quantum state rather than as the outcome of an underlying physical process. Here we explore the hypothesis that these correlations are mediated dynamically by a field propagating locally at finite velocity through an extension of ordinary spacetime. The model embeds physical $(3,1)$-dimensional spacetime in a warped five-dimensional geometry containing an additional timelike coordinate. Within the adopted geometric ansatz, the form of the extended spacetime metric is determined by the five-dimensional vacuum Einstein equations. A massless field propagating through the resulting five-dimensional bulk can mediate correlations whose projection onto observable four-dimensional spacetime connects arbitrarily distant locations at equal laboratory time, while preserving operational no-signaling. Coupling this field to a Bohm--Bub-inspired collapse scheme provides a possible dynamical realization of entanglement correlations and, under a stated statistical consistency condition, reproduces Born statistics. The framework leads to a concrete experimental test. Two nominally independent Bell pairs are predicted to develop a weak, distance-dependent contextual correlation between particles belonging to different pairs, as a consequence of bulk-field mediation. This cross-pair correlation is absent in standard quantum mechanics for independently prepared systems and is predicted to decrease as the inverse square of their separation. It could therefore be tested by varying the distance between two simultaneous Bell experiments using existing photonic technology. Observation of such a signal would support a dynamical spacetime account of quantum entanglement and could have implications for quantum networks employing multiple independent entangled resources.

quant-ph↗

arXiv2025

Hamiltonian model for energy condensation in classical systems: Relevance to proteins

Recent experimental evidence for collective protein vibrations in the terahertz (THz) domain indicates that energy in biomolecular systems can self-organize in an orderly manner, as anticipated by Fr\"ohlich's theory of condensates within a quantum framework. As a first step to bridge THz experiments with theory, we study the Hamiltonian dynamics of a classical network of coupled normal modes representing Fr\"ohlich-type systems. Our results demonstrate that biologically relevant condensates can emerge at room temperature under appropriate nonlinear coupling schemes. The condensation mechanism remains robust also when the original Fr\"ohlich resonance conditions are relaxed.

physics.bio-ph↗

arXiv2024

Unveiling Long-Range Forces in Light Harvesting Proteins: Pivotal Roles of Temperature and Light

Electrodynamic interactions between biomolecules are of potential biological interest for signaling warranting investigation of their activation through various mechanisms in living systems. Here, using as model system a light harvesting protein within the phycobilisome antenna system of red algae, we proved that not only light exposure but also thermal energy alone can trigger attractive electrodynamic interactions up to hundreds of nanometer. The latter are sustained by low frequency collective modes and while the second mode appears only upon illumination, the fundamental one can be activated by temperature alone. Activation of such collective modes and ED interactions might influence conformational rearrangements and energy transport within the phycobilisome antenna system. This is a paradigm-shift that underscores the immense potential of biological systems in exploiting different forms of input energy to achieve optimal energy transfer.

physics.bio-ph↗

arXiv2023

Quantum Entanglement without nonlocal causation in (3,2)-dimensional spacetime

This work aims at exploring whether the nonlocal correlations due to quantum entanglement could exist without nonlocal causation. This is done with the aid of a toy model to investigate whether the ability of two quantum entangled particles to "correlate" their behaviors even at very large distances and in the absence of any physical connection can be seen as due to an exchange of information through an extra-temporal dimension. Since superluminal information exchange is forbidden in our (3,1) spacetime, an extra-temporal dimension is needed to recover the physical picture of finite velocity information exchange between entangled entities. Assuming that the geometry of space-time of dimension (3,2) is described by a metric containing a warping factor, the confinement of the massive particles in the extra time dimension follows. Therefore, why we do not experience an infinitely large extra time dimension can be explained. The toy model proposed here is defined by borrowing Bohm-Bub's proposal to describe the wavefunction collapse using nonlinear (non-unitary) dynamical equations and then elaborating this approach for an entangled system. The model so obtained is just speculative without any claim of being robust against any criticism, nevertheless, it satisfies the purpose of giving the possibility to the hypotheses formulated above to be verified experimentally; in fact, it proposes an experiment potentially interesting which would otherwise be immediately dismissed as manifestly trivial. The proposed experiment would consist of checking the possible violation of Bell's inequality between two identical but independent systems under appropriate conditions. Beyond its theoretical interest, entanglement is a key topic in quantum computing and quantum technologies, so any attempt to gain a deeper understanding of it could be useful.

physics.gen-ph↗

arXiv2023

Routing a quantum state in a bio-inspired network

We consider a spin network resembling an $α$-helix structure and study quantum information transfer over this bio-inspired network. The model we use is the Davydov model in its elementary version without a phononic environment. We investigate analytically and numerically the perfect state transfer (PST) in such a network which provides an upper bound on the probability of quantum states transfer from one node to another. We study PST for different boundary conditions on the network and show it is reachable between certain nodes and with suitable spin-spin couplings.

quant-ph↗

arXiv2022

Topological Theory of Phase Transitions

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 mechanical manifolds that are found to stem from changes of their topology. These findings, together with two theorems, have suggested that a topological theory of phase transitions can be formulated to go beyond the limits of the existing theories. Among other advantages, the new theory applies to phase transitions in small $N$ systems (that is, at nanoscopic and mesoscopic scales), and in the absence of symmetry-breaking. However, the preliminary version of the theory was incomplete and still falsifiable by counterexamples. The present work provides a relevant leap forward leading to an accomplished development of the topological theory of phase transitions paving the way to further developments and applications of the theory that can be no longer hampered.

cond-mat.stat-mech↗

arXiv2022

Experimental evidence for long-distance electrodynamic intermolecular forces

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 and functioning of the molecular machines at work in living organisms. Here, using two independent experiments, on the basis of different physical effects detected by fluorescence correlation spectroscopy and terahertz spectroscopy, respectively, we demonstrate experimentally the activation of resonant electrodynamic intermolecular forces. This is an unprecedented experimental proof of principle of a physical phenomenon that, having been observed for biomacromolecules and with long-range action (up to 1000 Angstroms), could be of importance for biology. In addition to thermal fluctuations that drive molecular motion randomly, these resonant (and thus selective) electrodynamic forces may contribute to molecular encounters in the crowded cellular space.

physics.bio-ph↗

arXiv2021

Transition between random and periodic electron currents on a DNA chain

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 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 Principle to work out the dynamical equations of the system. It is found that under the action of an external source of energy transferred to the electron, and according to the excitation site, the electron current can display either a broad frequency spectrum or a sharply peaked frequency spectrum. This sequence-dependent charge transfer phenomenology is suggestive of a potentially rich variety of electrodynamic interactions of DNA molecules under the action of electron excitation. This could imply the activation of interactions between DNA and transcription factors, or between DNA and external electromagnetic fields.

physics.bio-ph↗

arXiv2020

Hamiltonian chaos and differential geometry of configuration space-time

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 the present work. In a Riemannian-geometric context, the stability/instability of the dynamics depends on the curvature properties of the ambient manifold and is investigated by means of the Jacobi--Levi-Civita (JLC) equation for geodesic spread. It is confirmed that the dominant mechanism at the ground of chaotic dynamics is parametric instability due to curvature variations along the geodesics. A comparison is reported of the outcomes of the JLC equation written also for the Jacobi metric on configuration space and for another metric due to Eisenhart on an extended configuration space-time. This has been applied to the Hénon-Heiles model, a two-degrees of freedom system. Then the study has been extended to the 1D classical Heisenberg XY model at a large number of degrees of freedom. Both the advantages and drawbacks of this geometrization of Hamiltonian dynamics are discussed. Finally, a quick hint is put forward concerning the possible extension of the differential-geometric investigation of chaos in generic dynamical systems, including dissipative ones, by resorting to Finsler manifolds.

nlin.CD↗

arXiv2020

Exciting out-of-equilibrium states in macromolecules through light pumping

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 8, 031061 (2018)], it has been experimentally found that by shining a laser light on the fluorophores attached to a protein the energy fed to it can be channeled into the normal mode of lowest frequency of vibration thus making the subunits of the protein coherently oscillate. Even if the phonon condensation phenomenon has been theoretically explained, the first step - the energy transfer from electronic excitation into phonon excitation - has been left open. The present work is aimed at filling this gap.

physics.bio-ph↗

arXiv2019

Coherent Riemannian-geometric description of Hamiltonian order and chaos with Jacobi metric

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 provide consistent results. However, it has been recently argued that endowing configuration space with the Jacobi metric is inappropriate to consistently describe the stability/instability properties of Newtonian dynamics because of the non-affine parametrization of the arc length with physical time. To the contrary, in the present paper, it is shown that there is no such inconsistency and that the observed instabilities in the case of integrable systems using the Jacobi metric are artefacts.

cond-mat.stat-mech↗

arXiv2018

Out-of-equilibrium collective oscillation as phonon condensation in a model protein

In the first part of the present paper (theoretical), the activation of out-of-equilibrium collective oscillations of a macromolecule is described 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 the normal modes make the system undergo a non-equilibrium phase transition when the energy input rate exceeds a threshold value. This transition takes place between a state where the energy is incoherently distributed among the normal modes, to a state where the input energy is channeled into the lowest frequency mode entailing a coherent oscillation of the entire molecule. The model put forward in the present work is derived as the classical counterpart of a quantum model proposed long time ago by H. Fröhlich in the attempt to explain the huge speed of enzymatic reactions. In the second part of the present paper (experimental), we show that such a phenomenon is actually possible. Two different and complementary THz near-field spectroscopic techniques, a plasmonic rectenna, and a micro-wire near-field probe, have been used in two different labs to get rid of artefacts. By considering a aqueous solution of a model protein, the BSA (Bovine Serum Albumin), we found that this protein displays a remarkable absorption feature around 0.314 THz, when driven in a stationary out-of-thermal equilibrium state by means of optical pumping. The experimental outcomes are in very good qualitative agreement with the theory developed in the first part, and in excellent quantitative agreement with a theoretical result allowing to identify the observed spectral feature with a collective oscillation of the entire molecule.

cond-mat.soft↗

arXiv2018

Density filtered Fluorescence Correlation Spectroscopy for highly concentrated solutions

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 optimal operational condition, we show that FCS can be used also at high concentrations (up to 50$μ$M) of fluorescent molecules: the detector blinding due to highly fluorescent solutions of concentrated dyes can be avoided by using neutral optic density (OD) filters, and the initial condition of very bad signal to noise ratio (SNR) can be hampered by suitable statistical averaging, as usual in other contexts of signal analysis.

physics.bio-ph↗

arXiv2018

Toward a refining of the topological theory of phase transitions

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, finally, two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of some submanifolds of configuration space. It has been recently shown that the $2D$ lattice $ϕ^4$-model provides a counterexample that falsifies the mentioned theorems. On the basis of a numerical investigation, the present work indicates the way to overcome this difficulty: in spite of the absence of critical points of the potential in correspondence of the transition energy, the phase transition of this model stems from an asymptotic ($N\to\infty$) change of topology of the energy level sets.

cond-mat.stat-mech↗

arXiv2018

On the origin of Phase Transitions in the absence of Symmetry-Breaking

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 well known use of quantities like the Wilson loop we show how else the phase transition in such a kind of models can be detected. It is found that the first order phase transition undergone by this model is characterised according to an Ehrenfest-like classification of phase transitions applied to the configurational entropy. On the basis of the topological theory of phase transitions, it is discussed why the seemingly divergent behaviour of the third derivative of configurational entropy can be considered as the "shadow" of some suitable topological transition of certain submanifolds of configuration space.

cond-mat.stat-mech↗

arXiv2017

Riemannian-geometric entropy for measuring network complexity

A central issue of 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 to a - in principle any - network a differentiable object (a Riemannian manifold) whose volume is used to define an entropy. The effectiveness of the latter to measure networks complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale--free networks, as well as of characterizing small Exponential random graphs, Configuration Models and real networks.

math-ph↗

arXiv2017

Collective behavior of oscillating electric dipoles

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 frequency, coupled with a $1/r^3$ potential stemming from the electrodynamic interaction between oscillating dipoles. The oscillating dipole moment of each molecule being a direct consequence of its coherent (collective) vibration. By changing the average distance among the molecules, neat and substantial changes in the power spectrum of the time variation of a collective observable are found. As the average intermolecular distance can be varied by changing the concentration of the solvated molecules, and as the collective variable investigated is proportional to the projection of the total dipole moment of the model biomolecules on a coordinate plane, we have found a prospective experimental strategy of spectroscopic kind to check whether the mentioned intermolecular electrodynamic interactions can be strong enough to be detectable, and thus to be of possible relevance to biology.

cond-mat.dis-nn↗