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Quantum mechanics started out as a theory to describe the smallest scales of energy in Nature. After hundred years of development it is now routinely employed to describe, for example, quantum computers with thousands of qubits. This tremendous progress turns the debate of foundational questions into a technological imperative. In what follows we introduce a model of a quantum measurement process that consistently includes the impact of having access only to finite resources when describing a macroscopic system, like a measurement apparatus. Leveraging modern tools from equilibration of closed systems and typicality, we show how the collapse can be seen as an effective description of a closed dynamics, of which we do not know all its details. Our model is then exploited to address the ``Wigner Friend Scenario'', and we observe that an agreement is reached when both Wigner and his friend acknowledge their finite resources perspective and describe the measurement process accordingly., Comment: 7+2 pages, 2 figures. Comments are welcome

In this comment, we obtain the complete energy levels for Dvornikov's paper, that is, the energy levels dependent on two quantum numbers, namely, the radial quantum number (given by $N$) and the angular quantum number (given by $J_z$). In particular, what motivated us to do this was the fact that the quantized energy levels for particles (fermions or bosons) in polar, cylindrical, or spherical coordinates depend on two quantum numbers: a radial quantum number and an angular quantum number. From this, the following question/doubt arose: Why do the energy levels in Dvornikov's paper only depend on one quantum number? That is, Where did the angular quantum number given by $J_z$ go? So, using Studenikin's paper as a starting point (as well as others in the literature), we write one of the equations from Dvornikov's paper in a matrix form. Next, we use the four-component Dirac spinor and obtain a set/system of four coupled first-order differential equations. From the first two equations with $m\simeq 0$, we obtain a (compact) second-order differential equation for two spinor components. So, solving this equation, we obtain the neutrino energy levels, which explicitly depend on both $N$ and $J_z$. Finally, we note that for $J_z>0$ (positive angular momentum) with $u=+1$ (component $\psi_3$), we obtain exactly the particular energy levels of Dvornikov's paper., Comment: 8 pages, no figure. Comment on arXiv:1408.2735

In this paper, we determine the relativistic bound-state solutions for the charged (DO) Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime in $(2+1)$-dimensions, where such solutions are given by the two-component Dirac spinor and by the relativistic energy spectrum. In this way, we work with the curved DO with minimal coupling in polar coordinates, where we use the tetrad formalism. To analytically solve our problem, we consider two approximations, where the first is that the cosmological constant is very small (conical approximation), and the second is that the linear velocity of the rotating frame is much less than the speed of light (slow rotation regime). So, after solving a second-order differential equation, we obtain a generalized Laguerre equation, whose solutions are the generalized Laguerre polynomials. Consequently, we obtain the energy spectrum, which is quantized in terms of the radial and total magnetic quantum numbers $n$ and $m_j$, and explicitly depends on the angular frequency $\omega$ (describes the DO), cyclotron frequency $\omega_c$ (describes the external magnetic field), angular velocity $\Omega$ (describes the rotating frame), spin parameter $s$ (describes the ``spin''), spinorial parameter $u$ (describes the components of the spinor), effective rest mass $m_{eff}$ (describes the rest mass modified by the spin-rotation coupling), and on a real parameter $\sigma$ and cosmological constant $\Lambda$ (describes the Bonnor-Melvin-Lambda spacetime). In particular, we note that this spectrum is asymmetrical (due to the presence of $\Omega$) and has its degeneracy broken (due to the presence of $\sigma$ and $\Lambda$) for $m_js<0$. Besides, we also graphically analyze the behavior of the spectrum and of the probability density as a function of the parameters of the system for different values of $n$ and $m_j$., Comment: 33 pages, and 21 figures

Understanding how macroscopic systems exhibit irreversible thermal behavior has been a long-standing challenge, first brought to prominence by Boltzmann. Recent advances have established rigorous conditions for isolated quantum systems to equilibrate to a maximum entropy state, contingent upon weak assumptions. These theorems, while powerful, apply for a sudden quench. However, natural processes involve finite-time perturbations or quenches, which raises a crucial question: Can these systems still equilibrate under more realistic, finite-time dynamics? In this work, we extend the established results to account for finite-time quenches, demonstrating that even under finite-time perturbations, the system will equilibrate provided it populates many significant energy levels. While the mathematical proof is more intricate than in the instantaneous case, the physical conclusion remains the same: sufficient perturbation leads to equilibration. Our results provide a broader and more physically realistic framework for understanding thermalization in isolated quantum systems, Comment: comments are welcome

In this work we introduce an idempotent pressure to level-2 functions and its associated density entropy. All this is related to idempotent pressure functions which is the natural concept that corresponds to the meaning of probability in the level-2 max-plus context. In this general framework the equilibrium states, maximizing the variational principle, are not unique. We investigate the connections with the general convex pressure introduced recently to level-1 functions by Bi\'{s}, Carvalho, Mendes and Varandas. Our general setting contemplates the dynamical and not dynamical framework. We also study a characterization of the density entropy in order to get an idempotent pressure invariant by dynamical systems acting on probabilities; this is therefore a level-2 result. We are able to produce idempotent pressure functions at level-2 which are invariant by the dynamics of the pushforward map via a form of Ruelle operator., Comment: 27 pages

Federated Learning (FL) allows devices to train a global machine learning model without sharing data. In the context of wireless networks, the inherently unreliable nature of the transmission channel introduces delays and errors that compromise the regularity of updating the global model. Furthermore, limited resources and energy consumption of devices are factors that affect FL performance. Therefore, this work proposes a new FL algorithm called FL-E2WS that considers both the requirements of federated training and a wireless network within the scope of the Internet of Things. To reduce the energy cost of devices, FL-E2WS schedules communication resources to allocate the ideal bandwidth and power for the transmission of models under certain device selection and uplink resource block allocation, meeting delay requirements, power consumption, and packet error rate. The simulation results demonstrate that FL-E2WS reduces energy consumption by up to 70.12% and enhances the accuracy of the global model by up to 10.21% compared to the FL algorithms that lacks transmission channel knowledge. Additionally, when compared to FL versions that scale communication resources, FL-E2WS achieves up to a 38.61% reduction in energy consumption and improves the accuracy of the global model by up to 1.61%.

In this comment, we point out a series of errors made by Senjaya in your paper (2024) \cite{Senjaya}. In particular, these errors involved the Dirac equation in the 3+1 dimensional Schwarzschild spacetime, tetrad field, curved gamma matrices, and the time-independent Dirac equation written in terms of the inner/scalar product between the gamma matrices and the orbital angular momentum (i.e., $\vec{\gamma}\cdot\vec{L}$). Besides, the strange/peculiar thing about all this is that even Senjaya \cite{Senjaya} citing Collas and Klein \cite{Collas}, where the (mathematical) formalism is correct, everything indicates that he ``ignored'' or ``forgot'' to use such formalism in your paper. Therefore, using Ref. \cite{Collas}, we show here the correct form of the errors made by Senjaya \cite{Senjaya}., Comment: 3 pages. Comment on "Exact massless spinor quasibound states of Schwarzschild black hole'' (DOI: 10.1016/j.physletb.2024.138714)

The generation of propagating acoustic waves is essential for telecommunication applications, quantum technologies, and sensing. Up to now, the electrical generation has been at the core of most implementations, but is technologically limited to a few gigahertz. Overcoming this frequency limit holds the prospect of faster modulators, quantum acoustics at higher working temperatures, nanoacoustic sensing from smaller volumes. Alternatively, the optical excitation of acoustic resonators has unlocked frequencies up to 1 THz, but in most cases, the acoustic energy cannot be efficiently extracted from the resonator into a propagating wave. Here, we demonstrate a quasi-continuous and coherent source of 20 GHz acoustic phonons, based on a ridge waveguide, structured in the vertical direction as a high-Q acousto-optic resonator. The high frequency phonons propagate up to 20 $\mu$m away from the source, with a decay rate of $\sim$1.14 dB/$\mu$m. We demonstrate the coherence between acoustic phonons generated from two distant sources through spatio-temporal interference. This concept could be scaled up to a larger number of sources, which enable a new generation of optically programmed, reconfigurable nanoacoustic devices and applications.

We investigate the set of invariant idempotent probabilities for countable idempotent iterated function systems (IFS) defined in compact metric spaces. We demonstrate that, with constant weights, there exists a unique invariant idempotent probability. Utilizing Secelean's approach to countable IFSs, we introduce partially finite idempotent IFSs and prove that the sequence of invariant idempotent measures for these systems converges to the invariant measure of the original countable IFS. We then apply these results to approximate such measures with discrete systems, producing, in the one-dimensional case, data series whose Higuchi fractal dimension can be calculated. Finally, we provide numerical approximations for two-dimensional cases and discuss the application of generalized Higuchi dimensions in these scenarios.

We will consider a family of cellular automata $\Phi: \{1,2,...,r\}^\mathbb{N}\circlearrowright$ that are not of algebraic type. Our first goal is to determine conditions that result in the identification of probabilities that are at the same time $\sigma$-invariant and $\Phi$-invariant, where $\sigma$ is the full shift. Via the use of versions of the Ruelle operator $\mathcal{L}_{A,\sigma}$ and $\mathcal{L}_{B,\Phi}$ we will show that there is an abundant set of measures with this property; they will be equilibrium probabilities for different Lispchitz potentials $A,B$ and for the corresponding dynamics $\sigma$ and $\Phi$. Via the use of a version of the involution kernel $W$ for a $(\sigma,\Phi)$-mixed skew product $\hat{\Phi}: \{1,2,...,r\}^\mathbb{Z}\circlearrowright$, given $A$ one can determine $B$, in such way that the integral kernel $e^W$ produce a duality between eigenprobabilities $\rho_A$ for $(\mathcal{L}_{A,\sigma})^*$ and eigenfunctions $\psi_B$ for $\mathcal{L}_{B,\Phi}$. In another direction, considering the non-mixed extension $\hat{\Phi}_n : \{1,2,...,r\}^\mathbb{Z}\circlearrowright$ of $\Phi$, given a Lispchitz potential $\hat{A} : \{1,2,...,r\}^\mathbb{Z}\to \mathbb{R}$, we can identify a Lipschitz potential $A:\{1,2,...,r\}^\mathbb{N} \to \mathbb{R} $, in such away that relates the variational problem of $\hat{\Phi}_n$-Topological Pressure for $\hat{A}$ with the $\Phi$-Topological Pressure for $A$. We also present a version of Livsic's Theorem. Whether or not $\Phi$ (or $\hat{\Phi})$ can eventually be conjugated with another shift of finite type is irrelevant in our context.

In this work, we investigate the massive Kane-Mele model for graphene in the presence of disclination and an external magnetic field, where graphene behaviors as a topological insulator. In the low-energy limit, the effective field equation for graphene is described by a Dirac equation with three different degrees of freedom. We succeed to decouple the set of eight components of the Dirac equation by using the spin projector \hat{C} in the disclinated geometry. As consequence, we obtain the Landau levels in this framework, in which we note the emergence of zero modes as edge states due to the inversion symmetry breaking. We also note that for different sites in sublattices \mathcal{A/B}, one can have different values of gap width., Comment: 12 pages and 8 figures

In this comment, we showed that the line element ("metric'') worked by Jusufi (Eur. Phys. J. C 76: 332, 2016) is incorrect since he worked with a spinning cosmic string with torsion in $(2+1)$-dimensions (and in polar coordinates), which cannot happen. Indeed, as in $(2+1)$-dimensions there are no screw dislocations or screw torsion (a consequence of the absence of the third spatial dimension, i.e., of the $z$-axis), and being a cosmic string with torsion a type of screw dislocation, but of cosmic origin (i.e., are cosmic dislocations), implies that a $(2+1)$-dimensional cosmic string does not have/carry torsion (since $dz=0$). Therefore, the line element worked by Jusufi is physically incoherent/unacceptable and inappropriate for the research/study., Comment: Comment on arXiv:1605.02781

The fast-growing development of optomechanical applications has motivated advancements in Brillouin scattering research. In particular, the study of high frequency acoustic phonons at the nanoscale is interesting due to large range of interactions with other excitations in matter. However, standard Brillouin spectroscopy schemes rely on fixed wavelength filtering, which limits the usefulness for the study of tunable optophononic resonators. It has been recently demonstrated that elliptical optophononic micropillar resonators induce different energy-dependent polarization states for the Brillouin and the elastic Rayleigh scattering, and that a polarization filtering setup could be implemented to increase the contrast between the inelastic and elastic scattering of the light. An optimal filtering configuration can be reached when the polarization states of the laser and the Brillouin signal are orthogonal from each other. In this work, we theoretically investigate the parameters of such polarization-based filtering technique to enhance the efficiency of Brillouin scattering detection. For the filtering optimization, we explore the initial wavelength and polarization state of the incident laser, as well as in the ellipticity of the micropillars, and reach an almost optimal configuration for nearly background-free Brillouin detection. Our findings are one step forward on the efficient detection of Brillouin scattering in nanostructures for potential applications in fields such as optomechanics and quantum communication.

A finitely generated group is said to be an automata group if it admits a faithful self-similar finite-state representation on some regular $m$-tree. We prove that if $G$ is a subgroup of an automata group, then for each finitely generated abelian group $A$, the wreath product $A \wr G$ is a subgroup of an automata group. We obtain, for example, that $C_2 \wr (C_{2} \wr \mathbb{Z})$, $\mathbb{Z} \wr (C_2 \wr \mathbb{Z})$, $C_2 \wr (\mathbb{Z} \wr \mathbb{Z})$, and $\mathbb{Z} \wr (\mathbb{Z} \wr \mathbb{Z})$ are subgroups of automata groups. In the particular case $\mathbb{Z} \wr (\mathbb{Z} \wr \mathbb{Z})$, we prove that it is a subgroup of a two-letters automata group; this solves Problem 15.19 - (b) of the Kourovka Notebook proposed by A. M. Brunner and S. Sidki in 2000 [8, 17].

In this paper, we determine the bound-state solutions for Dirac fermions with electric dipole moment (EDM) and position-dependent mass (PDM) in the presence of a radial magnetic field generated by magnetic monopoles. To achieve this, we work with the (2+1)-dimensional (DE) Dirac equation with nonminimal coupling in polar coordinates. Posteriorly, we obtain a second-order differential equation via quadratic DE (simplified by a similarity transformation). Solving this differential equation through a change of variable and the asymptotic behavior, we obtain a generalized Laguerre equation. From this, we obtain the bound-state solutions of the system, given by the two-component Dirac spinor and by the relativistic energy spectrum. So, we note that such spinor is written in terms of the generalized Laguerre polynomials, and such spectrum (for a fermion and an antifermion) is quantized in terms of the radial and total magnetic quantum numbers $n$ and $m_j$, and explicitly depends on the EDM $d$, PDM parameter $\kappa$, magnetic charge density $\lambda_m$, and on the spinorial parameter $s$. In particular, the quantization is a direct result of the existence of $\kappa$ (i.e., $\kappa$ acts as a kind of ``external field or potential''). Besides, we discuss in detail the characteristics of the spectrum as well as graphically analyze the behavior of the spectrum as a function of $\kappa$ and $\lambda_m$ for three different values of $n$ (ground state and the first two excited states)., Comment: 12 pages, 2 figures

We consider two compact metric spaces $J$ and $X$ and a uniform contractible iterated function system $\{\phi_j: X \to X \, | \, j \in J \}$. For a Lipschitz continuous function $A$ on $J \times X$ and for each $\beta>0$ we consider the Gibbs probability $\rho_{_{\beta A}}$. Our goal is to study a large deviation principle for such family of probabilities as $\beta \to +\infty$ and its connections with idempotent probabilities. In the non-place dependent case ($A(j,x)=A_j,\,\forall x\in X$) we will prove that $(\rho_{_{\beta A}})$ satisfy a LDP and $-I$ (where $I$ is the deviation function) is the density of the unique invariant idempotent probability for a mpIFS associated to $A$. In the place dependent case, we prove that, if $(\rho_{_{\beta A}})$ satisfy a LDP, then $-I$ is the density of an invariant idempotent probability. Such idempotent probabilities were recently characterized through the Ma\~{n}\'{e} potential and Aubry set, therefore we will obtain an identical characterization for $-I$., Comment: 24 pages

In this paper, we study the relativistic energy spectrum for Dirac fermions under rainbow gravity effects in the $(3+1)$-dimensional Bonnor-Melvin-Lambda spacetime, where we work with the curved Dirac equation in cylindrical coordinates. Using the tetrads formalism of General Relativity and considering a first-order approximation for the trigonometric functions, we obtain a Bessel equation. To solve this differential equation, we also consider a region where a hard-wall confining potential is present (i.e., some finite distance where the radial wave function is null). In other words, we define a second boundary condition (Dirichlet boundary condition) to achieve the quantization of the energy. Consequently, we obtain the spectrum for a fermion/antifermion, which is quantized in terms of quantum numbers $n$, $m_j$ and $m_s$, where $n$ is the radial quantum number, $m_j$ is the total magnetic quantum number, $m_s$ is the spin magnetic quantum number, and explicitly depends on the rainbow functions $F(\xi)$ and $G(\xi)$, curvature parameter $\alpha$, cosmological constant $\Lambda$, fixed radius $r_0$, and on the rest energy $m_0$, and $z$-momentum $p_z$. So, analyzing this spectrum according to the values of $m_j$ and $m_s$, we see that for $m_j>0$ with $m_s=-1/2$ (positive angular momentum and spin down), and for $m_j<0$ with $m_s=+1/2$ (negative angular momentum and spin up), the spectrum is the same. Besides, we graphically analyze in detail the behavior of the spectrum for the three scenarios of rainbow gravity as a function of $\Lambda$, $r_0$, and $\alpha$ for three different values of $n$ (ground state and the first two excited states)., Comment: 12 pages, 3 figures, 2 tables. arXiv admin note: text overlap with arXiv:2403.01366

In this paper, we determine the relativistic and nonrelativistic energy levels for Dirac fermions in a spinning conical G\"odel-type spacetime in $(2+1)$-dimensions, where we work with the curved Dirac equation in polar coordinates and we use the tetrads formalism. Solving a second-order differential equation for the two components of the Dirac spinor, we obtain a generalized Laguerre equation, and the relativistic energy levels of the fermion and antifermion, where such levels are quantized in terms of the radial and total magnetic quantum numbers $n$ and $m_j$, and explicitly depends on the spin parameter $s$ (describes the ``spin''), spinorial parameter $u$ (describes the two components of the spinor), curvature and rotation parameters $\alpha$ and $\beta$ (describes the conical curvature and the angular momentum of the spinning cosmic string), and on the vorticity parameter $\Omega$ (describes the G\"odel-type spacetime). In particular, the quantization is a direct result of the existence of $\Omega$ (i.e. $\Omega$ acts as a kind of ``external field or potential''). We see that for $m_j>0$, the energy levels do not depend on $s$ and $u$; however, depend on $n$, $m_j$, $\alpha$, and $\beta$. In this case, $\alpha$ breaks the degeneracy of the energy levels and such levels can increase infinitely in the limit $\frac{4\Omega\beta}{\alpha}\to 1$. Already for $m_j<0$, we see that the energy levels depends on $s$, $u$ and $n$; however, it no longer depends on $m_j$, $\alpha$ and $\beta$. In this case, it is as if the fermion ``lives only in a flat G\"odel-type spacetime''. Besides, we also study the low-energy or nonrelativistic limit of the system. In both cases (relativistic and nonrelativistic), we graphically analyze the behavior of energy levels as a function of $\Omega$, $\alpha$, and $\beta$ for three different values of $n$ (ground state and the first two excited states)., Comment: 15 pages, 6 figures. arXiv admin note: text overlap with arXiv:2402.15720

We study limit points of the spectral radii of Laplacian matrices of graphs. We adapted the method used by J. B. Shearer in 1989, devised to prove the density of adjacency limit points of caterpillars, to Laplacian limit points. We show that this fails, in the sense that there is an interval for which the method produces no limit points. Then we generalize the method to Laplacian limit points of linear trees and prove that it generates a larger set of limit points. The results of this manuscript may provide important tools for proving the density of Laplacian limit points in $[4.38+, \infty)$.

We study limit points of the spectral radii of $A_{\alpha}$-matrices of graphs. Adapting a method used by J. B. Shearer in 1989, we prove a density property of $A_{\alpha}$-limit points of caterpillars for $\alpha$ close to zero. Precisely, we show that for $\alpha \in [0, 1/2)$ there exists a positive number $\tau_2(\alpha)>2$ such that any value $\lambda> \tau_2(\alpha)$ is an $A_{\alpha}$-limit point. We also determine the existence of other intervals for which all its points are $A_{\alpha}$-limit points., Comment: 22 pages

The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix of the linear programming problem includes dense columns. In this paper, we propose a preconditioner to handle linear programming problems with dense columns, and we prove theoretically that the final linear system to solve is uniformly bounded when the Interior-Point Method is converging to an optimal solution. This result is illustrated through computational experiments, which show that our proposed method is robust and competitive in terms of running time and/or number of iterations compared with existing methods.

We will denote by $\mathcal{M}$ the space of Borel probabilities on the symbolic space $\Omega=\{1,2...,m\}^\mathbb{N}$. $\mathcal{M}$ is equipped Monge-Kantorovich metric. We consider here the push-forward map $\mathfrak{T}:\mathcal{M} \to \mathcal{M}$ as a dynamical system. The space of Borel probabilities on $\mathcal{M}$ is denoted by $\mathfrak{M}$. Given a continuous function $A: \mathcal{M}\to \mathbb{R}$, an {\it a priori} probability $\Pi_0$ on $\mathcal{M}$, and a certain convolution operation acting on pairs of probabilities on $\mathcal{M}$, we define an associated Level-2 IFS Ruelle operator. We show the existence of an eigenfunction and an eigenprobability $\hat{\Pi}\in\mathfrak{M}$ for such an operator. Under a normalization condition for $A$, we show the existence of some $\mathfrak{T}$-invariant probabilities $\hat{\Pi}\in\mathfrak{M}.$ We are able to define the variational entropy of such $\hat{\Pi}$ and a related maximization pressure problem associated to $A$. In some particular examples, we show how to get eigenprobabilities solutions on $\mathfrak{M}$ for the Level-2 Thermodynamic Formalism problem from eigenprobabilities on $\mathcal{M}$ for the classical (Level-1) Thermodynamic Formalism. These examples highlight the fact that our approach is a natural generalization of the classic case.

In this paper, we study the relativistic and nonrelativistic Landau levels for Dirac fermions in the cosmic string spacetime in the context of rainbow gravity in $(3+1)$-dimensions, where we work with the curved Dirac equation with minimal coupling in cylindrical coordinates. Using the tetrads formalism of General Relativity, we obtain a second-order differential equation. Solving this differential equation, we obtain a generalized Laguerre equation as well as the relativistic Landau levels for the fermion and antifermion, where such energy levels are quantized in terms of the quantum numbers $n$, $m_j$ and $m_s$, and explicitly depends on the rainbow functions $f(\varepsilon)$ and $g(\varepsilon)$, charge parameter $\sigma$, cyclotron frequency $\omega_c$, curvature parameter $\alpha$, and on the square rest energy $m^2_0$ and square $z$-momentum $k^2_z$, respectively. Posteriorly, we study the nonrelativistic limit of the system, where we obtain the nonrelativistic Landau levels. In both cases (relativistic and nonrelativistic), we graphically analyze the behavior of Landau levels for the three rainbow gravity scenarios as a function of the magnetic field $B$ and of the curvature parameter $\alpha$. In addition, we also compared our problem with other works, where we verified that our results generalize several particular cases in the literature., Comment: 17 pages, 4 figures

In this paper, we analyze the relativistic and nonrelativistic energy spectra (fermionic Landau levels) for the noncommutative quantum Hall effect with anomalous magnetic moment in the conical G\"odel-type spacetime in (2+1)-dimensions, where such spacetime is the combination of the flat G\"odel-type spacetime with a cosmic string (conical gravitational topological defect). To analyze these energy spectra, we start from the noncommutative Dirac equation with minimal and nonminimal couplings in polar coordinates. Using the tetrads formalism, we obtain a second-order differential equation. Next, we solve exactly this differential equation, where we obtain a generalized Laguerre equation, and also a quadratic polynomial equation for the total relativistic energy. By solving this polynomial equation, we obtain the relativistic energy spectrum of the fermion and antifermion. Besides, we also analyze the nonrelativistic limit of the system, where we obtain the nonrelativistic energy spectrum. In both cases (relativistic and nonrelativistic), we discuss in detail the characteristics of each spectrum as well as the influence of all parameters and physical quantities in such spectra. Comparing our problem with other works, we verified that our results generalize several particular cases in the literature., Comment: 15 pages, no figure

A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio. At each iteration, a smaller trace ratio problem is addressed in the search subspace. Additionally, the algorithm is endowed with a restarting strategy, that ensures the monotonicity of the trace ratio value throughout the iterations. The behavior of the approximate solution is investigated from a theoretical viewpoint, extending existing results on Ritz values and vectors, as the angle between the search subspace and the exact solution approaches zero. Numerical experiments in multigroup classification show that this new subspace method tends to be more efficient than iterative approaches relying on (partial) eigenvalue decompositions at each step.

In this comment, we showed that the Dirac equation in the screw dislocation space-time also carries a term that represents the torsion of such topological defect, given by $K_\mu$. Therefore, the Dirac equation worked by Wang et al. is incomplete since such a term was ignored in your equation (what cannot happen). In other words, it is only possible to work with the Dirac equation in the form presented by Wang et al. if the space-time is torsion-free, which is obviously not the case., Comment: 3 pages, no figure

We study the performance of a quantum Otto heat engine with two spins coupled by a Heisenberg interaction, taking into account not only the mean values of work and efficiency but also their fluctuations. We first show that, for this system, the output work and its fluctuations are directly related to the magnetization and magnetic susceptibility of the system at equilibrium with either heat bath. We analyze the regions where the work extraction can be done with low relative fluctuation for a given range of temperatures, while still achieving an efficiency higher than that of a single spin system heat engine. In particular, we find that, due to the presence of `idle' levels, an increase in the inter-spin coupling can either increase or decrease fluctuations, depending on the other parameters. In all cases, however, we find that the relative fluctuations in work or efficiency remain large, implying that this microscopic engine is not very reliable as a source of work., Comment: 13 pages, 11 figures

The present article reports new data on the $^{48}$Ti($^{18}$O,$^{17}$O)$^{49}$Ti reaction at 275 MeV incident energy as part of the systematic research pursued within the NUMEN project. Supplementary measurements of the same reaction on $^{16}$O and $^{27}$Al targets were also performed in order to estimate the background arising from the use of a composite target (TiO$_{2}$ + $^{27}$Al). These data were analyzed under the same theoretical framework as those obtained with the titanium target in order to reinforce the conclusions of our analysis. Differential cross-section angular distribution measurements for the $^{17}$O$^{8+}$ ejectiles were performed in a wide angular range by using the MAGNEX large acceptance magnetic spectrometer. The experimental results were analyzed within the distorted-wave and coupled-channels Born Approximation frameworks. The optical potentials at the entrance and exit channels were calculated in a double folding approach adopting the S\~ao Paulo potential, and the spectroscopic amplitudes for the projectile and target overlaps were obtained from large-scale shell model calculations. The differential cross-sections are well-described by the theoretical calculations, where a weak coupling to collective excitations of projectile and target is inferred. The sensitivity of transfer cross-sections on different model spaces adopted in nuclear structure calculations, is also discussed.

It is usually expected and observed that non-integrable isolated quantum systems thermalize. However, for some non-integrable spin chain models, in a numerical study, initial states with oscillations that persisted for some time were found and the phenomenon was named weak thermalization. Later, it was argued that such oscillations will eventually decay suggesting that weak thermalization was about time scales and not the size of the fluctuations. Nevertheless, the analyses of the size of the fluctuations were more qualitative. Here, using exact diagonalization we analyze how the size of the typical fluctuation, after long enough time for equilibration to happen, scales with the system size. For that, we use rigorous mathematical upper bounds on the equilibration of isolated quantum systems. We show that weak thermalization can be understood to be due to the small effective dimension of the initial state. Furthermore, we show that the fluctuations decay exponentially with the system size for both weak and strong thermalization indicating no sharp transitions between these two regimes.

We study the set of invariant idempotent probabilities for place dependent idempotent iterated function systems defined in compact metric spaces. Using well-known ideas from dynamical systems, such as the Ma\~{n}\'{e} potential and the Aubry set, we provide a complete characterization of the densities of such idempotent probabilities. As an application, we provide an alternative formula for the attractor of a class of fuzzy iterated function systems., Comment: 34 pages

With the control of ever more complex quantum systems becoming a reality, new scenarios are emerging where generalizations of the most foundational aspects of statistical quantum mechanics are imperative. In such experimental scenarios the often natural correspondence between the particles that compose the system and the relevant degrees-of-freedom might not be observed. In the present work we employ quantum channels to define generalized subsystems, which should capture the pertinent degrees-of-freedom, and obtain their associated canonical state. Moreover, we show that generalized subsystems also display the phenomena of canonical typicality, i.e., the generalized subsystem description generated from almost any microscopic pure state of the whole system will behave similarly as the corresponding canonical state. In particular we demonstrate that the property regulating the emergence of the canonical typicality behavior is the entropy of the channel used to define the generalized subsystem., Comment: 5+8 pages, 2 figures. Comments are welcome

Gigahertz acoustic resonators have the potential to advance data processing and quantum communication. However, they are expensive and lack responsiveness to external stimuli, limiting their use in sensing applications. In contrast, low-cost nanoscale mesoporous materials, known for their high surface-to-volume ratio, have shown promise in various applications. We recently demonstrated that mesoporous silicon dioxide (SiO2) and titanium dioxide (TiO2) thin layers can support coherent acoustic modes in the 5 to 100 GHz range. In this study, we propose a new method for designing tunable acoustic resonators using mesoporous thin films on acoustic distributed Bragg reflectors. By infiltrating the pores with different chemicals, the material's properties could be altered and achieve tunability in the acoustic resonances. We present four device designs and use simulations to predict resonators with Q-factors up to 1000. We also observe that the resonant frequency and intensity show a linear response to relative humidity, with a tunability of up to 60 %. Our platform offers a unique opportunity to design cost-effective nanoacoustic sensing and reconfigurable optoacoustic nanodevices., Comment: 9 pages, 5 figures