Entropy, chaos and excited-state quantum phase transitions in the Dicke model

We study non-equilibrium processes in an isolated quantum system ---the Dicke model--- focusing on the role played by the transition from integrability to chaos and the presence of excited-state quantum phase transitions. We show that both diagonal and entanglement entropies are abruptly increased by the onset of chaos. Also, this increase ends in both cases just after the system crosses the critical energy of the excited-state quantum phase transition. The link between entropy production, the development of chaos and the excited-state quantum phase transition is more clear for the entanglement entropy. On the contrary, the heat dissipated by the process is affected neither by the onset of chaos, nor by the excited-state quantum phase transition.Comment: 12 pages, 9 figures, RevTex 4.

A one-parameter family of interpolating kernels for Smoothed Particle Hydrodynamics studies

A set of interpolating functions of the type f(v)={(sin[v pi/2])/(v pi/2)}^n is analyzed in the context of the smoothed-particle hydrodynamics (SPH) technique. The behaviour of these kernels for several values of the parameter n has been studied either analytically as well as numerically in connection with several tests carried out in two dimensions. The main advantage of this kernel relies in its flexibility because for n=3 it is similar to the standard widely used cubic-spline, whereas for n>3 the interpolating function becomes more centrally condensed, being well suited to track discontinuities such as shock fronts and thermal waves.Comment: 36 pages, 12 figures (low-resolution), published in J.C.

Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential

The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: i) an interacting atomic Bose gas, and ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition (QPT) is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground-state is degenerate. For repulsive and small attractive interaction, the ground-state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition (ESQPT). For the mixed atom-molecule system the critical point of the ESQPT displays a discontinuity in the first derivative of the density of states.Comment: 25 pages, 18 figures. RevTex 4.1 (version to appear in Phys. Rev. E

Approximated integrability of the Dicke model

A very approximate second integral of motion of the Dicke model is identified within a broad region above the ground state, and for a wide range of values of the external parameters. This second integral, obtained from a Born Oppenheimer approximation, classifies the whole regular part of the spectrum in bands labelled by its corresponding eigenvalues. Results obtained from this approximation are compared with exact numerical diagonalization for finite systems in the superradiant phase, obtaining a remarkable accord. The region of validity of our approach in the parameter space, which includes the resonant case, is unveiled. The energy range of validity goes from the ground state up to a certain upper energy where chaos sets in, and extends far beyond the range of applicability of a simple harmonic approximation around the minimal energy configuration. The upper energy validity limit increases for larger values of the coupling constant and the ratio between the level splitting and the frequency of the field. These results show that the Dicke model behaves like a two-degree of freedom integrable model for a wide range of energies and values of the external parameters.Comment: 6 pages, 3 figures. Second version with added text, references and some new figure

Quantum quenches in disordered systems: Approach to thermal equilibrium without a typical relaxation time

We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.Comment: 5 pages, 5 figure

Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians

Using a new 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 cases, 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 to the work of the Berry and Tabor in the semiclassical limit.Comment: 5 pages, 4 figures, LaTeX (RevTeX 4) Content changed, References added Accepted for publication in PR

Decoherence induced by an interacting spin environment in the transition from integrability to chaos

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 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 depend on the dynamical regime of the bath. We interpret the latter results as due to a comparable complexity of the Hamiltonian for both the integrable and the fully chaotic limits.Comment: Submitted to Phys. Rev.

Through U.S. Eyes: Examining Spanish Multilingual Education Policies

This article offers an overview of the main language education policies aimed at addressing the needs of immigrant background students currently implemented in Spain's multilingual schools. In particular, the article examines the politics of segregation of language immersion programs for newcomers in the Spanish State, as well as their relationship with other language learning programs implemented as part of European initiatives to promote the use of Global English. This study is based on long-term ethnographic research conducted in different schools in Madrid. Adopting a comparative perspective, we also discuss different language programs in U.S. public schools: e.g., English as a Second Language (ESL) programs, bilingual education initiatives, Transitional and Dual Immersion programs. We examine how different educational policies for English language learners in the U.S. might be able to inform Spanish language education policies, forcing us to rethink the current school integration of immigrant origin students in Spain. We conclude with a critical discussion of the lessons we can draw from both casesEste artículo revisa las principales políticas lingüísticas dirigidas a los estudiantes de origen inmigrante en los centros educativos españoles con una amplia población multilingüe. Adoptando una perspectiva comparativa, el artículo parte de las últimas investigaciones sobre política lingüística desarrolladas en EEUU. Tomando como punto de partida el trabajo etnográfico llevado a cabo en diferentes escuelas de Madrid, se analizan los resultados de las políticas segregadoras que imponen algunos programas de inmersión lingüística para recién llegados en el Estado español. Igualmente, se analiza la relación de estas políticas con otros programas lingüísticos implementados en Madrid como parte de determinadas iniciativas europeas centradas en la promoción del uso del inglés como lengua global. El objetivo es estudiar estas cuestiones desde la perspectiva estadounidense y, por lo tanto, desde el análisis de las diferentes orientaciones en cuanto a planificación de la política lingüística en sus escuelas públicas (entre otros, se parte de los programas de inglés como segunda lengua (ESL) o de las diversas iniciativas de educación bilingüe, como los programas de transición y de doble inmersión lingüística). Por lo tanto, el artículo analiza cómo las diferentes políticas educativas dirigidas a los aprendices de inglés en EEUU pueden arrojar alguna luz sobre el sentido de las políticas lingüísticas implementadas en los centros educativos españoles y, sobre todo, ayudarnos a reflexionar sobre la influencia de dichas políticas lingüísticas en la integración del alumnado de origen inmigrante. Se concluye con una reflexión crítica sobre las lecciones que pueden extraerse del análisis de ambos casos

High resolution simulations of the head-on collision of white dwarfs

The direct impact of white dwarfs has been suggested as a plausible channel for type Ia supernovae. In spite of their (a priori) rareness, in highly populated globular clusters and in galactic centers, where the amount of white dwarfs is considerable, the rate of violent collisions between two of them might be non-negligible. Even more, there are indications that binary white dwarf systems orbited by a third stellar-mass body have an important chance to induce a clean head-on collision. Therefore, this scenario represents a source of contamination for the supernova light-curves sample that it is used as standard candles in cosmology, and it deserves further investigation. Some groups have conducted numerical simulations of this scenario, but their results show several differences. In this paper we address some of the possible sources of these differences, presenting the results of high resolution hydrodynamical simulations jointly with a detailed nuclear post-processing of the nuclear abundances, to check the viability of white dwarf collisions to produce significant amounts of 56Ni. To that purpose, we use a 2D-axial symmetric smoothed particle hydrodynamic code to obtain a resolution considerably higher than in previous studies. In this work, we also study how the initial mass and nuclear composition affect the results. The gravitational wave emission is also calculated, as this is a unique signature of this kind of events. All calculated models produce a significant amount of 56Ni, ranging from 0.1 Msun to 1.1 Msun, compatible not only with normal-Branch type Ia supernova but also with the subluminous and super-Chandrasekhar subset. Nevertheless, the distribution mass-function of white dwarfs favors collisions among 0.6-0.7 Msun objects, leading to subluminous events.Comment: 24 pages, 12 figures, accepted for publication in MNRA