
Roberto FranzosiUniversity of Siena | UNISI · Department of Environment, Earth and Physical Sciences
Roberto Franzosi
PhD
Phase-Transitions
Quantum Phase-Transitions
Entanglement Estimation
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117
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Introduction
Thermodynamic Phase Transitions
Bose-Einstein Condensates Dynamics
Dynamics and Thermodynamics of Classical and Quantum Systems
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Publications
Publications (117)
Resorting to microcanonical ensemble Monte Carlo simulations, we study the geometric 1 and topological properties of the state space of a model of network glass-former. This model, a 2 Lennard-Jones binary mixture, does not crystallize due to frustration. We found, at equilibrium and 3 at low energy, two peaks of specific heat, in correspondence wi...
Dicke states form a class of entangled states that has attracted much attention for their applications in various quantum algorithms. They emerge as eigenstates of the Tavis–Cummings (TC) Hamiltonian, a simplification of the Dicke model, which describes an assembly of two‐level atoms trapped in an electromagnetic cavity. In this letter, it is showe...
In the present paper we address the general problem of selective electrodynamic interactions between DNA and protein, which is motivated by decades of theoretical study and our very recent experimental findings (M. Lechelon et al, \textit{Sci Adv} \textbf{8,} eabl5855 (2022)). Inspired by the Davydov and Holstein-Fr\"{o}hlich models describing elec...
Dicke states form a class of entangled states that has attracted much attention for their applications in various quantum algorithms. They emerge as eigenstates of the Tavis-Cummings Hamiltonian, a simplification of the Dicke model, which describes an assembly of two-level atoms trapped in an electromagnetic cavity. In this letter, we show that in...
We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure. We derive the Fubini–Study metric of the projective Hilbert space of a multi-qubit quantum system, endowing it with a Riemannian metric structure, and investigate its deep link with the entanglement of the states of this space. As a measure, we ad...
This work presents a comprehensive exploration of the entanglement and graph connectivity properties of Graph States (GSs). Qubit entanglement in Pseudo Graph States (PGSs) is quantified using the Entanglement Distance (ED), a recently introduced measure of bipartite entanglement. In addition, a new approach is proposed for probing the underlying g...
In this work, we present a comprehensive exploration of the entanglement and graph connectivity properties of graph states. We quantify the entanglement in pseudo graph states using the entanglement distance, a recently introduced measure of entanglement. Additionally, we propose a novel approach to probe the underlying graph connectivity of genuin...
We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure. We derive the Fubini-Study metric of the projective Hilbert space of a quantum system, endowing it with a Riemannian metric structure, and investigate its deep link with the entanglement of the states of this space. As a measure we adopt the \emph...
We consider a spin network resembling an α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-helix structure and study quantum information transfer...
Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science, such as quantum communication, quantum computing, and quantum interferometry. Nevertheless, to our best knowledge, a directly or numerically computable measure for the entanglement of multipartite mixed states...
Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science, such as quantum communication, quantum computing, and quantum interferometry. Nevertheless, to our best knowledge, a directly or numerically computable measure for the entanglement of multipartite mixed states...
We consider a spin network resembling an $\alpha$-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 uppe...
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...
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...
Engineering a stationary entanglement between atoms or ions placed at small distances is a challenging problem in quantum information science. In this paper, the stationary and dynamics of entanglement in a system of dipole-coupled qubits interacting with a single-mode optical cavity in the strong coupling regime are theoretically investigated. We...
Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science, such as, for instance, quantum communication, quantum computing, and quantum interferometry. Nevertheless, to our best knowledge, a directly computable measure for the entanglement of multipartite mixed-states...
We study the out-of-equilibrium properties of the antiferromagnetic Hamiltonian Mean-Field model at low energy. In this regime, the Hamiltonian dynamics exhibits the presence of a long-lived metastable state where the rotators are gathered in a bicluster. This state is not predicted by equilibrium statistical mechanics in the microcanonical ensembl...
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...
Quantum technologies able to manipulating single quantum systems, are presently developing. Among the dowries of the quantum realm, entanglement is one of the basic resources for the novel quantum revolution. Within this context, one is faced with the problem of protecting the entanglement when a system state is manipulated. In this paper, we inves...
Quantum technologies able to manipulating single quantum systems, are presently developing. Among the dowries of the quantum realm, entanglement is one of the basic resources for the novel quantum revolution. Within this context, one is faced with the problem of protecting the entanglement when a system state is manipulated. In this paper, we inves...
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...
We study the out-of-equilibrium properties of the antiferromagnetic Hamiltonian Mean-Field model at low energy. In this regime, the Hamiltonian dynamics exhibits the presence of a stationary state where the rotators are gathered in a bicluster. This state is not predicted by equilibrium statistical mechanics in the microcanonical ensemble. Performi...
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...
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...
The achievement of quantum supremacy boosted the need for a robust medium of quantum information. In this task, higher-dimensional qudits show remarkable noise tolerance and enhanced security for quantum key distribution applications. However, to exploit the advantages of such states, we need a thorough characterization of their entanglement. Here,...
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 peculia...
The achievement of quantum supremacy boosted the need for a robust medium of quantum information. In this task, higher-dimensional qudits show remarkable noise tolerance and enhanced security for quantum key distribution applications. However, to exploit the advantages of such states, we need a thorough characterisation of their entanglement. Here,...
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 peculia...
In the last years, a relationship has been established between the quantum Fisher information (QFI) and quantum entanglement. In the case of two-qubit systems, all pure entangled states can be made useful for sub-shot-noise interferometry while their QFI meets a necessary and sufficient condition (Hyllus et al., 2010). In M-qubit systems, the QFI p...
We propose a measure of entanglement that can be computed for any pure state of an M-qubit system. The entanglement measure has the form of a distance that we derive from an adapted application of the Fubini-Study metric. This measure is invariant under local unitary transformations and defined as trace of a suitable metric that we derive, the enta...
We propose a measure of entanglement that can be computed for any pure state of an $M$-qubit system. The entanglement measure has the form of a distance that we derive from an adapted application of the Fubini-Study metric. This measure is invariant under local unitary transformations and defined as trace of a suitable metric that we derive, the en...
In a recent paper [Franzosi, Physica A 494, 302 (2018)], we have suggested to use of the surface entropy, namely the logarithm of the area of a hypersurface of constant energy in the phase space, as an expression for the thermodynamic microcanonical entropy, in place of the standard definition usually known as Boltzmann entropy. In the present manu...
In a recent paper, we have suggested to use of the surface entropy, namely the logarithm of the area of a hypersurface of constant energy in the phase space, as an expression for the thermodynamic microcanonical entropy, in place of the standard definition usually known as Boltzmann entropy. Our proposal was aimed to fix some issues encountered in...
In the case of two qubits, all pure entangled states can be made useful for sub-shot-noise interferometry [1]. However, with non-optimal two-qubit states, the value of quantum Fisher information provides just a sufficient condition in the task of detecting the degree of entanglement of a generic state. We show analytically that for a large class of...
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...
We aimed to characterise and quantify the entanglement properties in many-qubit systems, starting from 1-D arrays of interacting qubits and focusing on two-qubit systems.
The work begins considering the system analysed in [1] and the initial theory is highly extracted from [2].
1. Hans J. Briegel and Robert Raussendorf. Persistent entanglement in...
We investigate the origin of spectral collapse occurring in nonlinear Rabi Hamiltonians with an su(1,1) coupling scheme, showing how the collapse can be triggered by the competition between the Rabi parameter g and the field frequency W. The collapse already appears in the model Hamiltonian where the atomic-energy term is absent. After showing that...
The entropy definition in the microcanonical ensemble is revisited. We propose a novel definition for the microcanonical entropy that resolve the debate on the correct definition of the microcanonical entropy. In particular we show that this entropy definition fixes the problem inherent the exact extensivity of the caloric equation. Furthermore, th...
The entropy definition in the microcanonical ensemble is revisited. We propose a novel definition for the microcanonical entropy that resolve the debate on the correct definition of the microcanonical entropy. In particular we show that this entropy definition fixes the problem inherent the exact extensivity of the caloric equation. Furthermore, th...
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...
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,...
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 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...
The validity of the concept of negative temperature has been recently challenged by arguing that the Boltzmann entropy (that allows negative temperatures) is inconsistent from a mathematical and statistical point of view, whereas the Gibbs entropy (that does not admit negative temperatures) provides the correct definition for the microcanonical ent...
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...
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...
Very recently, the validity of the concept of negative temperature has been
challenged by several authors since they consider Boltzmann's entropy (that
allows negative temperatures) inconsistent from a mathematical and statistical
point of view, whereas they consider Gibbs' entropy (that does not admit
negative temperatures) the correct definition...
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...
The notion of negative absolute temperature emerges naturally from
Boltzmann's definition of "surface" microcanonical entropy in isolated systems
with a bounded energy density. Recently, the well-posedness such construct has
been challenged, on account that only Gibbs "volume" entropy --and the strictly
positive temperature thereof-- would give ris...
We propose a possible experimental realization of a quantum analogue of Newton’s cradle
using a configuration which starts from a Bose–Einstein condensate. The system consists of
atoms with two internal states trapped in a one-dimensional tube with a longitudinal optical
lattice and maintained in a strong Tonks–Girardeau regime at maximal filling....
We propose a possible experimental realization of a quantum analogue of
Newton's cradle using a configuration which starts from a Bose-Einstein
condensate. The system consists of atoms with two internal states trapped in a
one dimensional tube with a longitudinal optical lattice and maintained in a
strong Tonks-Girardeau regime at maximal filling....
We explore the statistical behaviour of the discrete nonlinear Schrödinger equation as a test bed for the observation of negative-temperature (i.e. above infinite temperature) states in Bose–Einstein condensates in optical lattices and arrays of optical waveguides. By monitoring the microcanonical temperature, we show that there exists a parameter...
In the general case of a many-body Hamiltonian system, described by an
autonomous Hamiltonian $H$, and with $K\geq 0$ independent conserved
quantities, we derive the microcanonical thermodynamics. By a simple approach,
based on the differential geometry, we derive the microcanonical entropy and
the derivatives of the entropy with respect to the con...
We explore the statistical behavior of the discrete nonlinear Schroedinger
equation. We find a parameter region where the system evolves towards a state
characterized by a finite density of breathers and a negative temperature. Such
a state is metastable but the convergence to equilibrium occurs on astronomical
time scales and becomes increasingly...
Discrete breathers, originally introduced in the context of biopolymers and coupled nonlinear oscillators, are also localized modes of excitation of Bose–Einstein condensates (BEC) in periodic potentials such as those generated by counter-propagating laser beams in an optical lattice. Static and dynamical properties of breather states are analysed...
The dynamics of repulsive bosons condensed in an optical lattice is effectively described by the Bose-Hubbard model. The classical
limit of this model, reproduces the dynamics of Bose-Einstein condensates, in a periodic potential, and in the superfluid
regime. Such dynamics is governed by a discrete nonlinear Schrödinger equation. Several papers, a...
Discrete breather solitons correspond to states at negative temperatures for BEC in optical lattices. Under the action of boundary losses that decrease energy and atomic density, the system relaxes from positive to negative temperature states.
We discuss the possibility of exponential quantum localization in systems of ultracold bosonic atoms with repulsive interactions in open optical lattices without disorder. We show that exponential localization occurs in the maximally excited state of the lowest energy band. We establish the conditions under which the presence of the upper energy ba...
We discuss the possibility of exponential quantum localization in systems of ultracold bosonic atoms with repulsive interactions in open optical lattices without disorder. We show that exponential localization occur in the maximally excited state of the lowest energy band. We establish the conditions under which the presence of the upper energy ban...
We consider a generic classical many particle system described by an
autonomous Hamiltonian $H(x^{_1},...,x^{_{N+2}})