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This paper explores as didactically as possible the fundamental principles of both classical and quantum metrology, focusing on the Cram\'er-Rao Bound and how it defines the maximum precision in parameter estimation, taking into account noise and the information extracted from the data. We also conduct a detailed study of Fisher Information (both classical and quantum), showing the physical significance of this important figure of merit in metrology. We further discuss how quantum states can surpass classical limits, providing much greater precision. Examples of technological applications include the development of quantum sensors, quantum thermometers, and phase parameter estimation. Finally, we review our results on the estimation of the unknown compression parameter applied to a mode of a quantum Gaussian state., Comment: This article aims to detail and contextualize part of the authors' presentations at the 20th Matogrossense School of Physics (EMF), held in October 2024. In Portuguese. Accepted in "Jornal Mato-Grossense de F\'isica"

This work explores the use of Role Playing Games (RPG) as an active methodology in teaching Modern Physics, focusing on a game called Newton's Revenge. The game was developed with the aim of engaging students in collaborative and investigative learning processes, using gamification elements to increase motivation and involvement. Based on the constructivist theories of Piaget and Vygotsky, the RPG stimu-\newline lates cognitive and social development by placing students in the roles of historical science figures. Through contextualized physical challenges, such as understanding the Photoelectric Effect, participants actively construct knowledge. This study presents preliminary learning data obtained through pre- and post-tests, as well as evaluates students' perceptions of using educational games in science education. The results indicate that the use of RPG can be an effective tool for teaching Modern Physics, promoting greater engagement and understanding of scientific concepts., Comment: This article aims to detail and contextualize part of one of the authors' presentations at the 20th Matogrossense School of Physics, held in October 2024. In Portuguese. Accepted in "Jornal Mato-Grossense de F\'isica"

The study of open system dynamics is of paramount importance both from its fundamental aspects as well as from its potential applications in quantum technologies. In the simpler and most commonly studied case, the dynamics of the system can be described by a Lindblad master equation. However, identifying the Lindbladian that leads to general non-equilibrium steady states (NESS) is usually a non-trivial and challenging task. Here we introduce a method for reconstructing the corresponding Lindbaldian master equation given any target NESS, i.e., a Lindbladian Reverse Engineering ($\mathcal{L}$RE) approach. The method maps the reconstruction task to a simple linear problem. Specifically, to the diagonalization of a correlation matrix whose elements are NESS observables and whose size scales linearly (at most quadratically) with the number of terms in the Hamiltonian (Lindblad jump operator) ansatz. The kernel (null-space) of the correlation matrix corresponds to Lindbladian solutions. Moreover, the map defines an iff condition for $\mathcal{L}$RE, which works as both a necessary and a sufficient condition; thus, it not only defines, if possible, Lindbaldian evolutions leading to the target NESS, but also determines the feasibility of such evolutions in a proposed setup. We illustrate the method in different systems, ranging from bosonic Gaussian to dissipative-driven collective spins. We also discuss non-Markovian effects and possible forms to recover Markovianity in the reconstructed Lindbaldian., Comment: 11 pages, 7 figures

We investigate the transport of particles in the chaotic component of phase space for a two-dimensional, area-preserving nontwist map. The survival probability for particles within the chaotic sea is described by an exponential decay for regions in phase space predominantly chaotic and it is scaling invariant in this case. Alternatively, when considering mixed chaotic and regular regions, there is a deviation from the exponential decay, characterized by a power law tail for long times, a signature of the stickiness effect. Furthermore, due to the asymmetry of the chaotic component of phase space with respect to the line $I = 0$, there is an unbalanced stickiness which generates a ratchet current in phase space. Finally, we perform a phenomenological description of the diffusion of chaotic particles by identifying three scaling hypotheses, and obtaining the critical exponents via extensive numerical simulations.

This study explores a detailed examination of various classes of single- and two-mode Gaussian states as key elements for an estimation process, specifically targeting the evaluation of an unknown squeezing parameter encoded in one mode. To quantify the efficacy of each probe, we employ the concept of Average Quantum Fisher Information (AvQFI) as a robust metric to quantify the optimal performance associated with specific classes of Gaussian states as input. For single-mode probes, we identify pure squeezed single-mode states as the optimal choice and we explore the correlation between Coherence and AvQFI. Also, we show that pure two-mode squeezed states exhibit behavior resembling their single-mode counterparts for estimating the encoded squeezing parameter, and we studied the interplay between entanglement and AvQFI. This paper presents both analytical and numerical results that encompass all the studied classes, offering valuable insights for quantum estimation processes., Comment: 26 pages, 9 figures, comments are welcome

The ${\bf E}\times{\bf B}$ drift motion of particles in tokamaks provides valuable information on the turbulence-driven anomalous transport. One of the characteristic features of the drift motion dynamics is the presence of chaotic orbits for which the guiding center can experience large-scale drifts. If one or more exits are placed within that chaotic orbit, the corresponding escape basins structure is complicated and, indeed, exhibits fractal structures. We investigate those structures through a number of numerical diagnostics, tailored to quantify the final-state uncertainty related to the fractal escape basins. We estimate the escape basin boundary dimension through the uncertainty exponent method, and quantify final-state uncertainty by the basin entropy and the basin boundary entropy. Finally, we describe the so-called Wada property, for the case of three or more escape basins. This property is verified both qualitatively and quantitatively, using a grid approach., Comment: 15 pages, 10 figures

We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems and permutationally invariant systems. The condition relates a nonzero macroscopic cumulant correlation in the steady state to the presence of gapless modes in the Lindbladian. In phases arising from competing coherent and dissipative Lindbladian terms, we argue that such gapless modes, concomitant with angular momentum conservation, can lead to persistent dynamics in the spin observables with the possible formation of dissipative time-crystals. We study different models within this perspective, from Lindbladians with Hermitian jump operators, to non-Hermitian ones composed by collective spins and Floquet spin-boson systems. We also provide a simple analytical proof for the exactness of mean-field semiclassical approach in such systems based on a cumulant expansion., Comment: 18 pages, 7 figures

Two-dimensional materials (2DM) have attracted much interest due to their distinct optical, electronic, and catalytic properties. These properties can be by tuned a range of methods including substitutional doping or, as recently demonstrated, by surface functionalization with single atoms, increasing even further 2DM portfolio. Here we theoretically and experimentally describe the coordination reaction between MoS$_2$ monolayers with 3d transition metals (TMs), exploring the nature and the trend of MoS$_2$-TMs interaction. Density Functional Theory calculations, X-Ray Photoelectron Spectroscopy (XPS), and Photoluminescence (PL) point to the formation of MoS$_2$-TM coordination complexes, where the adsorption energy trend for 3d TM resembles the crystal-field (CF) stabilization energy for weak-field complexes. Pearson's theory for hard-soft acid-base and Ligand-field theory were applied to discuss the periodic trends on 3d TM coordination on the MoS$_2$ surface. We found that softer acids with higher ligand field stabilization energy, such as Ni$^{2+}$, tend to form bonds with more covalent character with MoS$_2$, which can be considered a soft base. On the other hand, harder acids, such as Cr$^{3+}$, tend to form bonds with more ionic character. Additionally, we studied the trends in charge transfer and doping observed in the XPS and PL results, where metals such as Ni led to an n-type of doping, while Cu functionalization results in p-type doping. Therefore, the formation of coordination complexes on TMD's surface is demonstrated to be a promising and effective way to control and to understand the nature of the single-atom functionalization of TMD., Comment: 27 pages, 8 figures, Support Information after references section

Recent predictions for quantum-mechanical enhancements in the operation of small heat engines have raised renewed interest in their study from both a fundamental perspective and in view of applications. One essential question is whether collective effects may help to carry enhancements over larger scales, when increasing the number of systems composing the working substance of the engine. Such enhancements may consider not only power and efficiency, that is its performance, but, additionally, its constancy, i.e. the stability of the engine with respect to unavoidable environmental fluctuations. We explore this issue by introducing a many-body quantum heat engine model composed by spin pairs working in continuous operation. We study how power, efficiency and constancy scale with the number of spins composing the engine and introduce a well-defined macroscopic limit where analytical expressions are obtained. Our results predict power enhancements, both in finite-size and macroscopic cases, for a broad range of system parameters and temperatures, without compromising the engine efficiency, accompanied by coherence-enhanced constancy for finite sizes. We discuss these quantities in connection to Thermodynamic Uncertainty Relations (TUR)., Comment: 20 pages, 10 figures

Inertia amplification is a mechanism coupling degrees of freedom within a vibrating structure. Its goal is to achieve an apparent high dynamic mass and, accordingly, a low resonance frequency. Such structures have been described for use in locally resonant metamaterials and phononic crystals to lower the starting frequency of a band gap without adding mass to the system. This study shows that any non-linear kinematic coupling between translational or rotational vibrations leads to the appearance of amplitude-dependent damping. The analytical derivation of the equation of motion of a resonator with inertia amplification creates insight in the damping process, and shows that the vibration damping increases with its amplitude. The theoretical study is validated by experimental evidence from two types of inertia-amplification resonators. Finally, the importance of amplitude-dependent damping is illustrated when the structure is used as a tuned mass damper for a cantilever beam.

Boundary time crystals (BTC's) are non-equilibrium phases of matter occurring in quantum systems in contact to an environment, for which a macroscopic fraction of the many body system breaks time translation symmetry. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$. We find that BTC's appear in different forms for the different cases. We first consider the model with collective $d=2$-level systems [presented in Phys. Rev. Lett. $121$, $035301$ ($2018$)], whose dynamics is described by a Lindblad master equation, and perform a throughout analysis of its phase diagram and Jacobian stability for different interacting terms in the coherent Hamiltonian. In particular, using perturbation theory for general (non Hermitian) matrices we obtain analytically how a specific $\mathbb{Z}_2$ symmetry breaking Hamiltonian term destroys the BTC phase in the model. Based on these results we define a $d=4$ model composed of a pair of collective $2$-level systems interacting with each other. We show that this model support richer dynamical phases, ranging from limit-cycles, period-doubling bifurcations and a route to chaotic dynamics. The BTC phase is more robust in this case, not annihilated by the former symmetry breaking Hamiltonian terms. The model with collective $d=3$-level systems is defined similarly, as competing pairs of levels, but sharing a common collective level. The dynamics can deviate significantly from the previous cases, supporting phases with the coexistence of multiple limit-cycles, closed orbits and a full degeneracy of zero Lyapunov exponents., Comment: 18 pages, 12 figures