arXiv subjects
Publications and source records attributed to Luca Smaldone.
We present a quantum-field-theoretic treatment of massive chiral fields in which particles possess well-defined chirality and helicity. This framework reproduces the chiral oscillation formula previously obtained in first-quantized approaches and provides a consistent description of weak-interaction processes. We further derive corresponding chiral-energy uncertainty relations.
In this paper, we start reviewing the main features of the one-dimensional Ising model with long-range interactions, where the spin-spin coupling decays as a power law, $J(r) \propto r^{-\alpha}$. We then discuss the key properties of the one-dimensional voter model, in which two agents (spins) at distance $r$ interact with a power-law probability with the same form of $J(r)$. The two models are compared, and the so-called $p$-voter model is presented, which provides a framework to interpolate between them. Specifically, the $p$-voter model reduces to the voter model for $p = 1$ and $p = 2$, while for $p \ge 3$ it falls into the universality class of the Ising model.
In this work, we present a comprehensive and pedagogical review of two quantum field theoretical approaches to neutrino flavor mixing and oscillations: the non-perturbative flavor Fock space formalism and the perturbative interaction picture framework.
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 $\pi^- \to e^- + {\bar \nu}_e$. Finally, we argue that, in this perturbative view, chiral oscillations are also essential for detecting the decay products in such processes.
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 interactions, the $p$-voter model, in one dimension. It is defined in terms of boolean variables $S_{i}$, 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 $P(r)\propto r^{-\alpha}$. 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 $3\le p<\infty$, 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 $p\to \infty$, 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.
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 three-time 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 investigate the aging properties of the one-dimensional voter model with long-range interactions in its ordering kinetics. In this system, an agent $S_i=\pm 1$ positioned at a lattice vertex $i$, copies the state of another one located at a distance $r$, selected randomly with a probability $P(r) \propto r^{-\alpha}$. Employing both analytical and numerical methods, we compute the two-time correlation function $G(r;t,s)$ ($t\ge s$) between the state of a variable $S_i$ at time $s$ and that of another one, at distance $r$, at time $t$. At time $t$, the memory of an agent of its former state at time $s$, expressed by the {\it autocorrelation function} $A(t,s)=G(r=0;t,s)$, decays algebraically for $\alpha >1$ as $[L(t)/L(s)]^{-\lambda}$, where $L$ is a time-increasing coherence length and $\lambda $ is the Fisher-Huse exponent. We find $\lambda =1$ for $\alpha >2$, and $\lambda =1/(\alpha-1)$ for $1<\alpha \le 2$. For $\alpha \le 1$, instead, there is an exponential decay, as in mean-field. Then, at variance with what is known for the related Ising model, here we find that $\lambda $ increases upon decreasing $\alpha$. The space-dependent correlation $G(r;t,s)$ obeys a scaling symmetry $G(r;t,s)=g[r/L(s);L(t)/L(s)]$ for $\alpha >2$. Similarly, for $1<\alpha \le 2$ one has $G(r;t,s)=g[r/{\cal L}(t);{\cal L}(t)/{\cal L}(s)] $, where now the length ${\cal L}$ regulating two-time correlations differs from the coherence length as ${\cal L}\propto L^\delta$, with $\delta=1+2(2-\alpha)$.
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 $\al <4$.
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 time-scale 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.
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.
Space and matter may both be manifestations of a single fundamental quantum dynamics, as it may become evident during black-hole evaporation. Inspired by the fact that quantum electrodynamics underlies the classical theory of elasticity, that in turn has a natural and well-known geometric description in terms of curvature and torsion, related to topological defects, here we move some necessary steps to find the map from such fundamental quantum level to the emergent level of classical space and quantum matter. We proceed by adapting the boson transformation method of standard quantum field theory to the quantum gravity fundamental scenario and successfully obtain the emergence of curvature and torsion, our main focus here. In doing so, we have been able to overcome difficult issues of interpretation, related to the Goldstone modes for rotational symmetry. In fact, we have been able to apply the boson transformation method to disclinations, to relate them to the spin structure and to give an heuristic derivation of the matter field equation on curved space. We also improve results of previous work on the emergence of geometric tensors from elasticity theory, as the non-Abelian contributions to the torsion and curvature tensors, postulated in those papers, here emerge naturally. More work is necessary to identify the type of gravity theories one can obtain in this way.
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 in future neutrino experiments.
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 review the boson transformation method to deal with spontaneous symmetry breaking in quantum field theory, focussing on how it describes the emergence of extended and classical objects in such quantum context. We then apply the method to the emergence of space itself, as an extended and classical object resulting from the evaporation of a quantum black hole. In particular, we show how classical torsion and curvature tensors can emerge as effects of an inhomogeneous Nambu-Goldstone boson condensation in vacuum, in E(3) invariant spinor models with symmetry breaking.
We consider two necessary and sufficient conditions for macrorealism recently appeared in the literature, known as no-signaling-in-time and arrow-of-time conditions, respectively, and study them 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.
Analogs of fundamental physical phenomena can be used in two ways. One way consists in reproducing specific aspects of classical or quantum gravity, of quantum fields in curved space or of other high-energy scenarios, on lower-energy corresponding systems. The ``reverse way'' consists in building fundamental physical theories, for instance, quantum gravity models, inspired by the lower-energy corresponding systems. Here we present the case of graphene and other Dirac materials.
We take the view that the area of a black hole's event horizon is quantized, $A = l_P^2 \, (4 \ln 2) \, N$, and the associated degrees of freedom are finite in number and of fermionic nature. We then investigate general aspects of the entropy, $S_{BH}$, our main focus being black-hole self-similarity. We first find a two-to-one map between the black hole's configurations and the ordered partitions of the integer $N$. Hence we construct from there a composition law between the sub-parts making the whole configuration space. This gives meaning to black hole self-similarity, entirely within a single description, as a phenomenon stemming from the well known self-similarity of the ordered partitions of $N$. Finally, we compare the above to the well-known results on the subleading (quantum) corrections, that necessarily require different (quantum) statistical weights for the various configurations.