arXiv subjects

Matteo Gori

Publications and source records attributed to Matteo Gori.

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

How Atoms Interact Within Molecules

Fundamental understanding of interatomic forces in molecules must emerge from quantum mechanics, yet widely used empirical force fields rely on simplified mechanistic approximations that often fail to capture the complexity of many-body systems. Here we employ recent developments in quantum field theory (QFT) for long-range electron correlation and machine learning force fields (MLFFs) to directly compute the depth and scatter of interatomic forces for molecular systems containing hundreds of atoms. We find that while the average interaction strength decays polynomially with interatomic separation, the interaction scatter remains robust and exhibits substantial anisotropy. Both QFT and MLFFs demonstrate that increasing the molecular size further amplifies this scatter and anisotropy -- a phenomenon not considered in traditional textbook empirical models. These results provide new benchmarks for force models, shift the focus from interacting atoms to interacting ``hotspots'' that might determine the folding pathways of (bio)polymers, and rationalize why MLFFs are uniquely successful in capturing the nuances of complex molecular systems. Our findings offer a roadmap for the development of more accurate and quantum-aware molecular force fields.

physics.chem-ph↗

arXiv2026

Quantum Field Approaches to Chemical Systems

Quantum-matter theory (QMT), based on the Schr\"odinger or Dirac equations, is firmly established for both intra- and intermolecular interactions. However, there are two key issues with QMT. First, its applicability to large molecular complexes is hindered by the relatively high computational cost of the calculations required to achieve high accuracy. Second, fields are also quantum objects that produce many intriguing effects beyond standard QMT approaches to molecular systems. This review focuses on recent developments in quantum-field theory (QFT) approaches to both covalent and non-covalent interactions for molecules in vacuum and subject to environments such as cavities and solvents. QFT provides a rich playground for novel chemical theories and insights. For example, chemical reactions and van der Waals interactions can be manipulated by cavities, boundaries, and optical excitations; novel interactions emerge when molecules interact with quantized fields; systems with millions of atoms could soon be treated with coarse-grained QFT formalisms; and unexpected scaling laws for atomic and molecular properties can emerge when QFT is applied to sets of chemical systems. This review sets the stage for an exciting QFT-driven path for further development of chemical theory.

physics.chem-ph↗

arXiv2025

Repulsive Inverse-Distance Interatomic Interaction from Many-Body Quantum Electrodynamics

Interactions between objects can be classified as fundamental or emergent. Fundamental interactions are either extremely short-range or decay inversely with the separation distance, such as the Coulomb potential between charges or the gravitational attraction between masses. In contrast, emergent quantum van der Waals (vdW) and Casimir interactions decay considerably faster ($R^{-6}$ or $R^{-7}$) with distance $R$. Here we apply perturbative quantum electrodynamics (QED) to a many-body (MB) system of atoms modeled as charged harmonic oscillators, and reveal a persistent inverse-distance MB-QED interaction stemming from the coupling between virtual photons and molecular plasmons in the non-retarded regime. This interaction, scaling with the third power of the fine-structure constant, is reminiscent of the Lamb shift for a single atom. Although weaker than vdW forces, this MB-QED $R^{-1}$ interaction may substantially surpass gravitational attraction in future experiments probing quantum gravity at microscopic scales.

quant-ph↗

arXiv2024

Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory

Computationally feasible multipartite entanglement measures are needed to advance our understanding of complex quantum systems. An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers, showing several advantages over existing methods, including ease of computation, a deep geometrical interpretation, and applicability to multipartite entanglement. Here, we present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states, based on the purity of fragments of the whole systems. Our analysis includes the application of GEM to a two-mode Gaussian state coupled through a combined beamsplitter and a squeezing transformation. Additionally, we explore 3-mode and 4-mode graph states, where each vertex represents a bosonic mode, and each edge represents a quadratic transformation for various graph topologies. Interestingly, the ratio of the geometric entanglement measures for graph states with different topologies naturally captures properties related to the connectivity of the underlying graphs. Finally, by providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory on $\mathbb R_t\times S^1$, going beyond the standard bipartite entanglement entropy approach between different regions of spacetime. The results presented herein suggest how the GEM paves the way for using quantum information-theoretical tools to study the topological properties of the space on which a quantum field theory is defined.

quant-ph↗

arXiv2023

Phase Transitions in Abelian Lattice Gauge Theory: Production and Dissolution of Monopoles and Monopole-Antimonopole Pairs

We combine the microcanonical formulation of lattice gauge theories (LGTs) developed by Callaway and the microcanonical inflection point analysis (MIPA) proposed by Bachmann et al. to achieve a systematic characterization of phase transitions (PTs) in U(1) lattice electrodynamics. Besides identifying the well-known deconfinement PT (DPT) due to the neutral pair dissolution, which we classify as a first-order PT, we unequivocally detect three higher-order PTs. According to MIPA, we observe two independent third-order PTs in the confined phase; instead, in the deconfined (Coulomb) phase, we observe a dependent third-order PT. For a deeper understanding of the physical meaning of these PTs, we numerically compute the average number density of monopolar and pair defects as a function of energy. Our analysis reveals that DPT is only one of the major mechanisms observable in LGT. The independent third-order PTs are associated, respectively, to the first occurrence of monopolar topological defects and to the production of pairs.

hep-lat↗

arXiv2022

Examining the origins of observed terahertz modes from an optically pumped atomistic model protein in aqueous solution

The microscopic origins of terahertz (THz) vibrational modes in biological systems are an active and open area of current research. Recent experiments [Physical Review X 8, 031061 (2018)] have revealed the presence of a pronounced mode at $\sim$0.3 THz in fluorophore-decorated bovine serum albumin (BSA) protein in aqueous solution under nonequilibrium conditions induced by optical pumping. This result was heuristically interpreted as a collective elastic fluctuation originating from the activation of a low-frequency phonon mode. In this work, we show that the sub-THz spectroscopic response emerges in a statistically significant manner (> 2$\sigma$) from such collective behavior, illustrating how specific THz vibrational modes can be triggered through optical excitations and other charge reorganization processes. We revisit the theoretical analysis with proof-of-concept molecular dynamics that introduce optical excitations into the simulations. Using information theory techniques, we show that these excitations can induce a multiscale response involving the two optically excited chromophores (tryptophans), other amino acids in the protein, ions, and water. Our results motivate new experiments and fully nonequilibrium simulations to probe these phenomena, as well as the refinement of atomistic models of Fr\"ohlich condensates that are fundamentally determined by nonlinear interactions in biology.

physics.bio-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

Configurational microcanonical statistical mechanics from Riemannian geometry of equipotenital level sets

In the present work, we present a detailed discussion of a Riemannian metric structure originally introduced in [Gori et al., \textit{J. Stat. Mech.}, \textbf{9} 093204 (2018)] on the configuration space and on phase space allowing us to interpret the derivatives of the configurational microcanonical entropy and of the canonical entropy in terms of integrals of extrinsic geometrical quantities associated with the equipotential level sets.

cond-mat.stat-mech↗

arXiv2022

Second Quantization Approach to Many-Body Dispersion Interactions

The many-body dispersion (MBD) framework is a successful approach for modeling the long-range electronic correlation energy and optical response of systems with thousands of atoms. Inspired by field theory, here we develop a second-quantized MBD formalism (SQ-MBD) that recasts a system of atomic quantum Drude oscillators in a Fock-space representation. SQ-MBD provides (I) tools for projecting observables (interaction energy, transition multipoles, polarizability tensors) on coarse-grained representations of the atomistic system ranging from single atoms to large structural motifs, (ii) a quantum-information framework to analyze correlations and (non)separability among fragments in a given molecular complex, and (iii) a path toward the applicability of the MBD framework to molecular complexes with millions of atoms. The SQ-MBD approach offers novel insights into quantum fluctuations in molecular systems and enables direct coupling of collective plasmon-like MBD degrees of freedom with arbitrary environments, providing a tractable computational framework to treat dispersion interactions and polarization response in intricate systems.

physics.chem-ph↗

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

The Berezinskii Kosterlitz Thouless phase transition is of second-order in the microcanonical ensemble

A paradigmatic example of a phase transition taking place in the absence of symmetry-breaking is provided by the Berezinkii-Kosterlitz-Thouless (BKT) transition in the two-dimensional XY model. In the framework of canonical ensemble, this phase transition is defined as an infinite-order one. To the contrary, by tackling the transitional behavior of the two dimensional XY model in the microcanonical ensemble, we show that the BKT phase transition is of second order. This provides a new example of statistical ensemble inequivalence that could apply to a broad class of systems undergoing BKT phase transitions.

cond-mat.stat-mech↗

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

Geometrical aspects in the analysis of microcanonical phase-transitions

In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the energy level sets of the Hamiltonian of a system under investigation. In particular, it turns out that peculiar behaviours of thermodynamic observables at a phase transition point are rooted in more fundamental changes of the geometry of the energy level sets in phase space. More specifically, we discuss how microcanonical and geometrical descriptions of phase-transitions are shaped in the special case of $ϕ^4$ models with either nearest-neighbours and mean-field interactions.

cond-mat.stat-mech↗

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

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↗

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↗