We investigate the coarsening dynamics of a simplified version of the persistent voter model in w... more We investigate the coarsening dynamics of a simplified version of the persistent voter model in which an agent can become a zealot-i.e. resistent to change opinion-at each step, based on interactions with its nearest neighbors. We show that such a model captures the main features of the original, non-Markovian, persistent voter model. We derive the governing equations for the one-point and two-point correlation functions. As these equations do not form a closed set, we employ approximate closure schemes, whose validity was confirmed through numerical simulations. Analytical solutions to these equations are obtained and well agree with the numerical results.
We provide a concise review of how chiral and flavor oscillations can be described in quantum fie... more We provide a concise review of how chiral and flavor oscillations can be described in quantum field theory using a finite-time interaction picture approach, where the mass and mixing terms in the Lagrangian can be treated as perturbations. We derive the oscillation formulas for both chiral and flavor transitions and demonstrate that, within the adopted approximations, they match the exact results obtained through non-perturbative methods. Finally, we point out the strong similarities and the differences between these two phenomena.
We demonstrate how chiral oscillations of a massive Dirac field can be described within quantum f... more We demonstrate how chiral oscillations of a massive Dirac field can be described within quantum field theory using a finite-time interaction picture approach, where the mass term in the Lagrangian is treated as a perturbative coupling between massless fields of definite chirality. We derive the formula for chiral oscillations at the fourth order in the perturbative expansion, obtaining a result consistent with the formula derived by means of other methods. Furthermore, we illustrate how the perturbative framework of chiral oscillations can effectively describe production processes where an electron must exhibit both left chirality and positive helicity, as in decay π-→ e-+ νe. Finally, we argue that, in this perturbative view, chiral oscillations are also essential for detecting the decay products in such processes.
We provide a brief overview of the main results of the interaction picture approach to neutrino o... more We provide a brief overview of the main results of the interaction picture approach to neutrino oscillations. In this framework, mixing is treated as an interaction between different neutrino flavors. The oscillation formula is derived by calculating the survival probability of a specific flavor neutrino. Notably, this method yields the same modified oscillation formula as the flavor Fock space approach, exhibiting dependence on both the difference and the sum of neutrino frequencies.
This paper reviews the similarities in the behavior of unstable particles and oscillating neutrin... more This paper reviews the similarities in the behavior of unstable particles and oscillating neutrinos using perturbation theory within the interaction picture of quantum field theory. We begin by examining how decaying systems are studied in the interaction picture and then demonstrate how similar calculations can be performed to determine the transition probabilities for flavor oscillations. Notably, the expressions for neutrino oscillations and particle decays are identical in the short-time range. Furthermore, we show that the flavor oscillation formula derived through this method matches, within the adopted approximation, the one obtained using the flavor Fock space approach.
Journal of Physics A: Mathematical and Theoretical, 2024
We study the non-equilibrium response function $R_{ij}(t,t')$, namely the variation of the local ... more We study the non-equilibrium response function $R_{ij}(t,t')$, namely the variation of the local magnetization $\langle S_i(t)\rangle$ on site $i$ at time $t$ as an effect of a perturbation applied at the earlier time $t'$ on site $j$, in a class of solvable spin models characterized by the vanishing of the so-called {\it asymmetry}.
This class encompasses both systems brought out of equilibrium by the variation of a thermodynamic control parameter, as after a temperature quench, or intrinsically out of equilibrium models with violation of detailed balance. The one-dimensional Ising model and the voter model (on an arbitrary graph) are prototypical examples of these two situations which are used here as guiding examples. Defining the fluctuation-dissipation ratio $X_{ij}(t,t')=\beta R_{ij}/(\partial G_{ij}/\partial t')$, where $G_{ij}(t,t')=\langle S_i(t)S_j(t')\rangle$ is the spin-spin correlation function and $\beta$ is a parameter regulating the strength of the perturbation (corresponding to the inverse temperature when detailed balance holds), we show that, in the quite general case of a kinetics obeying dynamical scaling, on equal sites this quantity has a universal form
$X_{ii}(t,t') = (t+t')/(2t)$, whereas $
\lim _{t\to \infty}X_{ij}(t,t')=1/2$ for any $ij$ couple. The specific case of voter models with long-range interactions is thoroughly discussed.
We study the ordering kinetics of a generalization of the voter model with long-range interaction... more We study the ordering kinetics of a generalization of the voter model with long-range interactions, the p-voter model, in one dimension. It is defined in terms of boolean variables Si, agents or spins, located on sites i of a lattice, each of which takes in an elementary move the state of the majority of p other agents at distances r chosen with probability P (r) ∝ r −α. For p = 2 the model can be exactly mapped onto the case with p = 1, which amounts to the voter model with long-range interactions decaying algebraically. For 3 ≤ p < ∞, instead, the dynamics falls into the universality class of the one-dimensional Ising model with long-ranged coupling constant J(r) = P (r) quenched to small finite temperatures. In the limit p → ∞, a crossover to the (different) behavior of the long-range Ising model quenched to zero temperature is observed. Since for p > 3 a closed set of differential equations cannot be found, we employed numerical simulations to address this case.
We study analytically the ordering kinetics and the final metastable states in the three-dimensio... more We study analytically the ordering kinetics and the final metastable states in the three-dimensional long-range voter model where agents described by a Boolean spin variable can be found in two states (or opinion) . The kinetics is such that each agent copies the opinion of another at distance chosen with probability (). In the thermodynamic limit the system approaches a correlated metastable state without consensus, namely without full spin alignment. In such states the equal-time correlation function (where is the distance) decreases algebraically in a slow, nonintegrable way. Specifically, we find , or , or for , and , respectively. In a finite system metastability is escaped after a time of order and full ordering is eventually achieved. The dynamics leading to metastability is of the coarsening type, with an ever-increasing correlation length (for ). We find for for , and for . For there is not macroscopic coarsening because stationarity is reached in a microscopic time. Such results allow us to conjecture the behavior of the model for generic spatial dimension.
We discuss the role of finite time and energy uncertainty in the quantum field theory description... more We discuss the role of finite time and energy uncertainty in the quantum field theory description of neutrino oscillations. In order to to achieve this goal, we review the flavor Fock-space approach and the time-energy uncertainty relation in the Mandelstam-Tamm form, expressed as a flavor-energy uncertainty relation. Such relation, together with the inequivalence of mass and flavor neutrinos Fock spaces, puts a lower bound on neutrino energy uncertainty. Similar considerations can be derived by a perturbative computation of flavor transitions, which employs the Dirac picture to compute flavor transition probability. Remarkably, both flavor Fock space and interaction picture approach lead to the same oscillation probability, within the approximation adopted in the perturbative calculation.
The dynamical map represents a fundamental concept in quantum field theory, providing a solution ... more The dynamical map represents a fundamental concept in quantum field theory, providing a solution of the field equations in the Fock space of asymptotic fields. In this paper, we show how to express the dynamical map of a scalar field in the language of quantum effective action. This grants us new insights into the study of topological defects in quantum field theory, showing a connection between the usual least-action principle and Umezawa's boson transformation method.
Macrorealism formalizes the intuitive notion that at any given time the system occupies a definit... more Macrorealism formalizes the intuitive notion that at any given time the system occupies a definite state and that the evolution of the system is independent of the measurements performed on it, in contrast to the principles of quantum mechanics. In this study, we carry out a comparative analysis between Leggett--Garg-type inequalities and the conditions of no-signaling-in-time and arrow-of-time for macrorealism within the context of meson oscillations. Our findings indicate that, under given initial conditions, no violations of Leggett--Garg inequalities are observed. However, no-signaling-in-time conditions are found to be violated, thereby revealing the impossibility of applying a macrorealistic description to the analysis of meson physics.
We study analytically the ordering kinetics of the two-dimensional long-range voter model on a tw... more We study analytically the ordering kinetics of the two-dimensional long-range voter model on a two-dimensional lattice, where agents on each vertex take the opinion of others at distance $r$ with probability $P(r) \propto r^{-\al}$. The model is characterized by different regimes, as $\al$ is varied. For $\al > 4$ the behaviour is similar to that of the nearest-neighbor model, with the formation of ordered domains of a typical size growing as $L(t) \propto \sqrt{t}$, until consensus is reached in a time or order $N\ln N$, $N$ being the number of agents. Dynamical scaling is violated due to an excess of interfacial sites whose density decays as slow as $\rho(t) \propto 1/\ln t$. Sizable finite-time corrections are also present, which are absent in the case of nearest-neighbors interactions. For $0<\al \leq 4$ standard scaling is reinstated, and the correlation length increases algebraically as $L(t)\propto t^{1/z}$, with $1/z=2/\al$ for $3<\al<4$ and $1/z=2/3$ for $0<\al<3$. In addition, for $\al \le 3$, $L(t)$ depends on $N$ at any time $t>0$. Such coarsening, however, only leads the system to a partially ordered metastable state where correlations decay algebraically with distance, and whose lifetime diverges in the $N\to \infty$ limit. In finite systems consensus is reached in a time of order $N$ for any $\al <4$.
We study analytically the ordering kinetics of the two-dimensional long-range voter model on a tw... more We study analytically the ordering kinetics of the two-dimensional long-range voter model on a two-dimensional lattice, where agents on each vertex take the opinion of others at distance $r$ with probability $P(r) \propto r^{-\al}$. The model is characterized by different regimes, as $\al$ is varied. For $\al > 4$ the behaviour is similar to that of the nearest-neighbor model, with the
formation of ordered domains of a typical size growing as $L(t) \propto \sqrt{t}$, until consensus is reached in a time of the order of $N\ln N$, with $N$ being the number of agents. Dynamical scaling is violated due to an excess of interfacial sites whose density decays as slowly as $\rho(t) \propto 1/\ln t$.
Sizable finite-time corrections are also present, which are absent in the case of nearest-neighbors interactions. For $0<\al \leq 4$ standard scaling is reinstated, and the correlation length increases algebraically as $L(t)\propto t^{1/z}$, with $1/z=2/\al$ for $3<\al<4$ and $1/z=2/3$ for $0<\al<3$. In addition, for $\al \le 3$, $L(t)$ depends on $N$ at any time $t>0$. Such coarsening, however, only leads the system to a partially ordered metastable state where correlations decay algebraically with distance, and whose lifetime diverges in the $N\to \infty$ limit. In finite systems consensus is reached in a time of order $N$ for any $\al <4$.
We briefly review recent developments in the study of the quantum nature of flavor mixing; in par... more We briefly review recent developments in the study of the quantum nature of flavor mixing; in particular, the attention will be devoted to neutrino and neutral meson oscillations. We employ Leggett-Garg type inequalities and no-signaling-in-time conditions to probe the intrinsic quantumness of such a physical manifestation, showing how the analysis is not affected by the wave-packet spreading (for neutrinos) and the intrinsic particle instability (for mesons).
Time-energy uncertainty relation (TEUR) plays a fundamental role in quantum mechanics, as it allo... more Time-energy uncertainty relation (TEUR) plays a fundamental role in quantum mechanics, as it allows to grasp peculiar aspects of a variety of phenomena based on very general principles and symmetries of the theory. Using the Mandelstam-Tamm method, TEUR has been recently derived for neutrino oscillations by connecting the uncertainty on neutrino energy with the characteristic timescale of oscillations. Interestingly enough, the suggestive interpretation of neutrinos as unstable-like particles has proved to naturally emerge in this context. Further aspects have been later discussed in semiclassical gravity by computing corrections to the neutrino energy uncertainty in a generic stationary curved spacetime, and in quantum field theory, where the clock observable turns out to be identified with the non-conserved flavor charge operator. In the present work, we give an overview on the above achievements. In particular, we analyze the implications of TEUR and explore the impact of gravitational and non-relativistic effects on the standard condition for neutrino oscillations. Correlations with the quantum-information theoretic analysis of oscillations and possible experimental consequences are qualitatively discussed.
We analyze the dynamics of neutrino Gaussian wave-packets, the damping of flavor oscillations and... more We analyze the dynamics of neutrino Gaussian wave-packets, the damping of flavor oscillations and decoherence effects within the framework of extended theories of gravity. In particular, we show that, when the underlying description of the gravitational interaction admits a violation of the strong equivalence principle, the parameter quantifying such a violation modulates the wave-packet spreading, giving rise to potentially measurable effects.
We investigate Leggett-Garg temporal inequalities in flavor-mixing processes. We derive an exact ... more We investigate Leggett-Garg temporal inequalities in flavor-mixing processes. We derive an exact flavor-mass uncertainty relation and we prove that this gives an upper bound to the violation of the inequalities. This finding relates temporal nonclassicality to quantum uncertainty and provides a time analog of the Tsirelson upper bound to the violation of the spatial Bell inequalities. By studying the problem both in the exact field-theoretical setting and in the limiting quantum mechanical approximation, we show that the inequalities are violated more strongly in quantum field theory than in quantum mechanics.
We study the mixing of different kind of fields (scalar in 0+1D, scalar in 3+1D, fermion in 3+1D)... more We study the mixing of different kind of fields (scalar in 0+1D, scalar in 3+1D, fermion in 3+1D) treating the mixing term as an interaction. To this aim, we employ the usual perturbative series in the interaction picture. We find that expression for flavor changing probability exhibits corrections with respect to the usual quantum mechanical (e.g. neutrino) oscillation formula, in agreement with the result previously obtained in the non-perturbative flavor Fock space approach.
We study necessary and sufficient conditions for macrorealism (known as no-signaling-in-time and ... more We study necessary and sufficient conditions for macrorealism (known as no-signaling-in-time and arrow-of-time conditions) in the context of neutrino flavor transitions, within both the plane wave description and the wave packet approach. We then compare the outcome of the above investigation with the implication of various formulations of Leggett-Garg inequalities. In particular, we show that the fulfillment of the addressed conditions for macrorealism in neutrino oscillations implies the fulfillment of Leggett-Garg inequalities, whereas the converse is not true. Finally, in the framework of wave packet approach, we also prove that, for distances longer than the coherence length, the no-signaling-in-time condition is always violated whilst Leggett-Garg inequalities are not.
The quantum field theory formalism describing the phenomenon of neutrino mixing and oscillations ... more The quantum field theory formalism describing the phenomenon of neutrino mixing and oscillations is reviewed in its essential aspects. The condensate structure of the flavor vacuum state is considered and its non-perturbative nature is discussed within the existence in the quantum field theory of the manifold of unitarily inequivalent representations of the anticommutation relations. The Poincaré structure of the theory is discussed in connection with the gauge theory features of neutrino mixing, where the possibility arises to describe flavored neutrinos as on-shell fields with definite masses. The flavor vacuum state may be thought of as a refractive medium where different refraction indexes are related to the different neutrino masses. Neglecting the condensate structure of the flavor vacuum implies neglecting second-order contributions in the gauge field coupling and leads to experimentally inconsistent results.
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Papers by Luca Smaldone
In this study, we carry out a comparative analysis between Leggett--Garg-type inequalities and the conditions of no-signaling-in-time and arrow-of-time for macrorealism within the context of meson oscillations. Our findings indicate that, under given initial conditions, no violations of Leggett--Garg inequalities are observed. However, no-signaling-in-time conditions are found to be violated, thereby revealing the impossibility of applying a macrorealistic description to the analysis of meson physics.
formation of ordered domains of a typical size growing as $L(t) \propto \sqrt{t}$, until consensus is reached in a time or order $N\ln N$, $N$ being the number of agents. Dynamical scaling is violated due to an excess of interfacial sites whose density decays as slow as $\rho(t) \propto 1/\ln t$.
Sizable finite-time corrections are also present, which are absent in the case of nearest-neighbors interactions. For $0<\al \leq 4$ standard scaling is reinstated, and the correlation length increases algebraically as $L(t)\propto t^{1/z}$, with $1/z=2/\al$ for $3<\al<4$ and $1/z=2/3$ for $0<\al<3$. In addition, for $\al \le 3$, $L(t)$ depends on $N$ at any time $t>0$. Such coarsening, however, only leads the system to a partially ordered metastable state where correlations decay algebraically with distance, and whose lifetime diverges in the $N\to \infty$ limit. In finite systems consensus is reached in a time of order $N$ for any $\al <4$.
formation of ordered domains of a typical size growing as $L(t) \propto \sqrt{t}$, until consensus is reached in a time of the order of $N\ln N$, with $N$ being the number of agents. Dynamical scaling is violated due to an excess of interfacial sites whose density decays as slowly as $\rho(t) \propto 1/\ln t$.
Sizable finite-time corrections are also present, which are absent in the case of nearest-neighbors interactions. For $0<\al \leq 4$ standard scaling is reinstated, and the correlation length increases algebraically as $L(t)\propto t^{1/z}$, with $1/z=2/\al$ for $3<\al<4$ and $1/z=2/3$ for $0<\al<3$. In addition, for $\al \le 3$, $L(t)$ depends on $N$ at any time $t>0$. Such coarsening, however, only leads the system to a partially ordered metastable state where correlations decay algebraically with distance, and whose lifetime diverges in the $N\to \infty$ limit. In finite systems consensus is reached in a time of order $N$ for any $\al <4$.