1.

Estudo de conceitos da termodinâmica no ensino médio por meio de UEPS
- Pradella, Marcos
Esta dissertação é o relato da aplicação de quatro Unidades de Ensino Potencialmente Significativas (UEPS) voltadas ao ensino de conceitos de Termodinâmica em uma escola pública de Ensino Médio. Nas unidades de ensino são abordados conceitos de temperatura, sua relação com a estrutura da matéria, dilatação, energia interna, calor, comportamento dos gases e a Primeira Lei da Termodinâmica, enfatizando especialmente as relações entre estes conceitos. As situações-problema abordadas são contextualizadas no dia-a-dia do estudante, com situações e perguntas instigantes e cativantes para o estudo do conteúdo proposto. Nesta aplicação, são utilizadas estratégias didáticas como a utilização de simulações interativas pertinentes...

2.

Misleading signatures of quantum chaos
- Relaño Pérez, Armando; Gómez Gómez, José María; Molina, R. A.; Retamosa Granado, Joaquín
The main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest-neighbor spacing distribution P(s) and the spectral rigidity given by the Delta(3)(L) statistic. It is shown that some standard unfolding procedures, such as local unfolding and Gaussian broadening, lead to a spurious saturation of Delta(3)(L) that spoils the relationship of this statistic with the regular or chaotic motion of the system. This effect can also be misinterpreted as Berry's saturation.

3.

Quantum chaos and 1/f noise
- Relaño Pérez, Armando; Gómez Gómez, José María; Molina, R. A.; Retamosa Granado, Joaquín; Faleiro, E.
The main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest-neighbor spacing distribution P(s) and the spectral rigidity given by the Delta(3)(L) statistic. It is shown that some standard unfolding procedures, such as local unfolding and Gaussian broadening, lead to a spurious saturation of Delta(3)(L) that spoils the relationship of this statistic with the regular or chaotic motion of the system. This effect can also be misinterpreted as Berry's saturation.

4.

1/f noise in the two-body random ensemble
- Relaño Pérez, Armando; Molina, R. A.; Retamosa Granado, Joaquín
We show that the spectral fluctuations of the two-body random ensemble exhibit 1/f noise. This result supports a recent conjecture stating that chaotic quantum systems are characterized by 1/f noise in their energy level fluctuations. After suitable individual averaging, we also study the distribution of the exponent alpha in the 1/f(alpha) noise for the individual members of the ensemble. Almost all the exponents lie inside a narrow interval around alpha=1, suggesting that also individual members exhibit 1/f noise, provided they are individually unfolded.

5.

Stringent numerical test of the Poisson distribution for finite quantum integrable Hamiltonians
- Relaño Pérez, Armando; Dukelsky, J.; Gómez Gómez, José María; Retamosa Granado, Joaquín
Using a class of exactly solvable models based on the pairing interaction, we show that it is possible to construct integrable Hamiltonians with a Wigner distribution of nearest-neighbor level spacings. However, these Hamiltonians involve many-body interactions and the addition of a small integrable perturbation very quickly leads the system to a Poisson distribution. Besides this exceptional case, we show that the accumulated distribution of an ensemble of random integrable two-body pairing Hamiltonians is in perfect agreement with the Poisson limit. These numerical results for quantum integrable Hamiltonians provide a further empirical confirmation of the work of Berry and Tabor in...

6.

Principal components analysis of extensive air showers applied to the identification of cosmic TeV gamma-rays
- Relaño Pérez, Armando; Faleiro, E.; Gómez Gómez, José María; Muñoz, L.; Retamosa Granado, Joaquín
We apply a principal components analysis (PCA) to the secondary particle density distributions at ground level produced by cosmic gamma-rays and protons. For this purpose, high-energy interactions of cosmic rays with Earth's atmosphere and the resulting extensive air showers have been simulated by means of the CORSIKA Monte Carlo code. We show that a PCA of the two-dimensional particle density fluctuations provides a decreasing sequence of covariance matrix eigenvalues that have typical features of a polynomial law, which are different for different primary cosmic rays. This property is applied to the separation of electromagnetic showers from proton simulated extensive air...

7.

Theoretical derivation of 1/ƒ noise in quantum chaos
- Relaño Pérez, Armando; Faleiro, E.; Gómez Gómez, José María; Molina, R. A.; Muñoz, L.; Retamosa Granado, Joaquín
It was recently conjectured that 1/ƒ noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the power spectrum behavior of the excitation energy fluctuations, which is different for chaotic and integrable systems. Using random matrix theory, we derive theoretical expressions that explain without free parameters the universal behavior of the excitation energy fluctuations power spectrum. The theory gives excellent agreement with numerical calculations and reproduces to a good approximation the 1/ƒ (1/ƒ^(2)) power law characteristic of chaotic (integrable) systems. Moreover, the theoretical results are valid for semiclassical systems as well.

8.

1/ƒ^(α) noise in spectral fluctuations of quantum systems
- Relaño Pérez, Armando; Gómez Gómez, José María; Retamosa Granado, Joaquín; Faleiro, E.; Salasnich, L.; Vranicar, M.; Robnik, M.
The power law 1/ƒ^(α) in the power spectrum characterizes the fluctuating observables of many complex natural systems. Considering the energy levels of a quantum system as a discrete time series where the energy plays the role of time, the level fluctuations can be characterized by the power spectrum. Using a family of quantum billiards, we analyze the order-to-chaos transition in terms of this power spectrum. A power law 1/ƒ^(α) is found at all the transition stages, and it is shown that the exponent alpha is related to the chaotic component of the classical phase space of the quantum system.

9.

Fluctuations in the level density of a fermi gas
- Relaño Pérez, Armando; Leboeuf, P.; Monastra, A. G.
We present a theory that accurately describes the counting of excited states of a noninteracting fermionic gas. At high excitation energies the results reproduce Bethe's theory. At low energies oscillatory corrections to the many-body density of states, related to shell effects, are obtained. The fluctuations depend nontrivially on energy and particle number. Universality and connections with Poisson statistics and random matrix theory are established for regular and chaotic single-particle motion.

10.

Spectral statistics of Hamiltonian matrices in tridiagonal form
- Relaño Pérez, Armando; Molina, R. A.; Zuker, A. P.; Retamosa Granado, Joaquín
When a matrix is reduced to Lanczos tridiagonal form, its matrix elements can be divided into an analytic smooth mean value and a fluctuating part. The next-neighbor spacing distribution P(s) and the spectral rigidity Delta _(3) are shown to be universal functions of the average value of the fluctuating part. It is explained why the behavior of these quantities suggested by random matrix theory is valid in far more general cases.

11.

Correlation structure of the δ_(n) statistic for chaotic quantum systems
- Relaño Pérez, Armando; Retamosa Granado, Joaquín; Faleiro, E.; Gómez Gómez, José María
The existence of a formal analogy between quantum energy spectra and discrete time series has been recently pointed out. When the energy level fluctuations are described by means of the δ_(n) statistic, it is found that chaotic quantum systems are characterized by 1/f noise, while regular systems are characterized by 1/f(2). In order to investigate the correlation structure of the δ_(n) statistic, we study the qth-order height-height correlation function C-q(tau), which measures the momentum of order q, i.e., the average qth power of the signal change after a time delay tau. It is shown that this function has a logarithmic...

12.

1/f noise and very high spectral rigidity
- Relaño Pérez, Armando; Retamosa Granado, Joaquín; Faleiro, E.; Molina, R. A.; Zuker, A. P.
It was recently pointed out that the spectral fluctuations of quantum systems are formally analogous to discrete time series, and therefore their structure can be characterized by the power spectrum of the signal. Moreover, it is found that the power spectrum of chaotic spectra displays a 1/f behavior, while that of regular systems follows a 1/f(2) law. This analogy provides a link between the concepts of spectral rigidity and antipersistence. Trying to get a deeper understanding of this relationship, we have studied the correlation structure of spectra with high spectral rigidity. Using an appropriate family of random Hamiltonians, we increase...

13.

Spectral statistics in noninteracting many-particle systems
- Relaño Pérez, Armando; Muñoz, L.; Faleiro, E.; Molina, R. A.; Retamosa Granado, Joaquín
It is widely accepted that the statistical properties of energy level spectra provide an essential characterization of quantum chaos. Indeed, the spectral fluctuations of many different systems like quantum billiards, atoms, or atomic nuclei have been studied. However, noninteracting many-body systems have received little attention, since it is assumed that they must exhibit Poisson-like fluctuations. Apart from a heuristic argument of Bloch, there are neither systematic numerical calculations nor a rigorous derivation of this fact. Here we present a rigorous study of the spectral fluctuations of noninteracting identical particles moving freely in a mean field emphasizing the evolution with the...

14.

Power spectrum of nuclear spectra with missing levels and mixed symmetries
- Relaño Pérez, Armando; Molina, R. A.; Retamosa Granado, Joaquín; Muñoz, L.; Faleiro, E.
Sequences of energy levels in nuclei are often plagued with missing levels whose number and position are unknown. It is also quite usual that all the quantum numbers of certain levels cannot be experimentally determined, and thus levels of different symmetries are mixed in the same sequence. The analysis of these imperfect spectra (from the point of view of spectral statistics) is unavoidable if one wants to extract some statistical information. The power spectrum of the delta(q) statistic has emerged in recent years as an important tool for the study of quantum chaos and spectral statistics. We derive analytical expressions...

15.

Spectral-fluctuations test of the quark-model baryon spectrum
- Relaño Pérez, Armando; Fernández Ramírez, C.
We study the low-lying baryon spectrum (up to 2.2 GeV) provided by experiments and different quark models using statistical tools which allow us to postulate the existence of missing levels in spectra. We confirm that the experimental spectrum is compatible with random matrix theory, the paradigmatic model of quantum chaos, and we find that the quark models are more similar to a Poisson distribution, which is not compatible with what should be expected in a correlated spectrum. From our analysis it stems that the spectral fluctuation properties of quark-model spectra are incompatible with experimental data. This result can be used...

16.

Decoherence induced by an interacting spin environment in the transition from integrability to chaos
- Relaño Pérez, Armando; Dukelsky, J.; Molina, R. A.
We investigate the decoherence properties of a central system composed of two spins 1/2 in contact with a spin bath. The dynamical regime of the bath ranges from a fully integrable limit to complete chaoticity. We show that the dynamical regime of the bath determines the efficiency of the decoherence process. For perturbative regimes, the integrable limit provides stronger decoherence, while in the strong coupling regime the chaotic limit becomes more efficient. We also show that the decoherence time behaves in a similar way. On the contrary, the rate of decay of magnitudes like linear entropy or fidelity does not...

17.

Power-spectrum characterization of the continuous Gaussian ensemble
- Relaño Pérez, Armando; Muñoz, L.; Retamosa Granado, Joaquín; Faleiro, E.; Molina, R. A.
The continuous Gaussian ensemble, also known as the nu-Gaussian or nu-Hermite ensemble, is a natural extension of the classical Gaussian ensembles of real (nu= 1), complex (nu= 2), or quaternion (nu=4) matrices, where nu is allowed to take any positive value. From a physical point of view, this ensemble may be useful to describe transitions between different symmetries or to describe the terrace-width distributions of vicinal surfaces. Moreover, its simple form allows one to speed up and increase the efficiency of numerical simulations dealing with large matrix dimensions. We analyze the long-range spectral correlations of this ensemble by means of...

18.

Chaos-assisted tunneling and 1/ƒ^(α) spectral fluctuations in the order-chaos transition
- Relaño Pérez, Armando
It has been shown that the spectral fluctuations of different quantum systems are characterized by 1/ƒ^(α) noise, with 1

19.

Decoherence as a signature of an excited-state quantum phase transition
- Relaño Pérez, Armando; Arias, J. M.; Dukelsky, J.; García Ramos, J. E.; Pérez Fernández, P.
We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment. We conclude that the dynamics of the qubit changes dramatically when the environment passes through a continuous excited state quantum phase transition. If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power law.

20.

Decoherence due to an excited-state quantum phase transition in a two-level boson model
- Relaño Pérez, Armando; Pérez Fernández, P.; Arias, J. M.; Dukelsky, J.; García Ramos, J. E.
The decoherence induced on a single qubit by its interaction with the environment is studied. The environment is modeled as a scalar two-level boson system that can go through either first-order or continuous-excited-state quantum phase transitions, depending on the values of the control parameters. A mean-field method based on the Tamm-Damkoff approximation is worked out in order to understand the observed behavior of the decoherence. Only the continuous-excited-state phase transition produces a noticeable effect in the decoherence of the qubit. This is maximal when the system-environment coupling brings the environment to the critical point for the continuous phase transition. In...