Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice

We experimentally investigate diffraction of a Rb-87 Bose-Einstein condensate from a 1D optical lattice. We use a range of lattice periods and timescales, including those beyond the Raman-Nath limit. We compare the results to quantum mechanical and classical simulations, with quantitative and qualitative agreement, respectively. The classical simulation predicts that the envelope of the time-evolving diffraction pattern is shaped by caustics: singularities in the phase space density of classical trajectories. This behavior becomes increasingly clear as the lattice period grows.Comment: 7 pages, 6 figure

The eigenspectra of Indian musical drums

In a family of drums used in the Indian subcontinent, the circular drum head is made of material of non-uniform density. Remarkably, and in contrast to a circular membrane of uniform density, the low eigenmodes of the non-uniform membrane are harmonic. In this work we model the drum head by a non-uniform membrane whose density varies smoothly between two prescribed values. Using a Fourier-Chebyshev spectral collocation method we obtain the eigenmodes and eigenvalues of the drum head. For a suitable choice of parameters, which we find by optimising a cost function, the eigenspectra obtained from our model are in excellent agreement with experimental values. Our model and the numerical method should find application in numerical sound synthesis

Sensitivity of monsoon circulation and precipitation over India to model horizontal resolution and orographic effects

A triple-nested regional weather prediction model was used to investigate the effects of the model horizontal resolution and orography on southwest monsoon precipitation over India. Numerical experiments with different resolution topography and different horizontal resolution model domains were conducted. Simulation results indicate that both the distribution and intensity of simulated southwest monsoon precipitation over India is highly sensitive to model horizontal resolution and topography. The model with a finer resolution is able to predict mesoscale organization of rainfall over the land mass. Rainfall predicted over the coarse domain is much less than that observed owing to its unrealistic representation of orographic effects and mesoscale forcings. Simulated wind speed, surface pressure, and latent and sensible heat flux distributions are also sensitive to the model resolution. Larger values and more detailed structure of the distribution of the wind speed and latent and sensible heat fluxes are simulated in the finer domains

Extended Quantum Dimer Model and novel valence-bond phases

We extend the quantum dimer model (QDM) introduced by Rokhsar and Kivelson so as to construct a concrete example of the model which exhibits the first-order phase transition between different valence-bond solids suggested recently by Batista and Trugman and look for the possibility of other exotic dimer states. We show that our model contains three exotic valence-bond phases (herringbone, checkerboard and dimer smectic) in the ground-state phase diagram and that it realizes the phase transition from the staggered valence-bond solid to the herringbone one. The checkerboard phase has four-fold rotational symmetry, while the dimer smectic, in the absence of quantum fluctuations, has massive degeneracy originating from partial ordering only in one of the two spatial directions. A resonance process involving three dimers resolves this massive degeneracy and dimer smectic gets ordered (order from disorder).Comment: 20 pages, 13 figures, accepted for publication in J. Stat. Mec

Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions

Eigenvalues and eigenfunctions of Mathieu's equation are found in the short wavelength limit using a uniform approximation (method of comparison with a `known' equation having the same classical turning point structure) applied in Fourier space. The uniform approximation used here relies upon the fact that by passing into Fourier space the Mathieu equation can be mapped onto the simpler problem of a double well potential. The resulting eigenfunctions (Bloch waves), which are uniformly valid for all angles, are then used to describe the semiclassical scattering of waves by potentials varying sinusoidally in one direction. In such situations, for instance in the diffraction of atoms by gratings made of light, it is common to make the Raman-Nath approximation which ignores the motion of the atoms inside the grating. When using the eigenfunctions no such approximation is made so that the dynamical diffraction regime (long interaction time) can be explored.Comment: 36 pages, 16 figures. This updated version includes important references to existing work on uniform approximations, such as Olver's method applied to the modified Mathieu equation. It is emphasised that the paper presented here pertains to Fourier space uniform approximation

Quantum thermodynamics at critical points during melting and solidification processes

We systematically explore and show the existence of finite-temperature continuous quantum phase transition (CTQPT) at a critical point, namely, during solidification or melting such that the first-order thermal phase transition is a special case within CTQPT. Infact, CTQPT is related to chemical reaction where quantum fluctuation (due to wavefunction transformation) is caused by thermal energy and it can occur maximally for temperatures much higher than zero Kelvin. To extract the quantity related to CTQPT, we use the ionization energy theory and the energy-level spacing renormalization group method to derive the energy-level spacing entropy, renormalized Bose-Einstein distribution and the time-dependent specific heat capacity. This work unambiguously shows that the quantum phase transition applies for any finite temperatures.Comment: To be published in Indian Journal of Physics (Kolkata

The role of radiative transfer in maintaining the Indian summer monsoon circulation

The radiative-convective feedback and land-sea thermal forcing play significant roles in maintenance of the summer monsoon circulation over the Indian sub-continent. In this study, the role of radiative transfer in maintaining the monsoon circulation is examined with numerical sensitivity experiments. For this purpose, a sixteen layer primitive equation limited area model is used to perform numerical simulations with and without atmospheric radiative transfer processes parameterized in the model. The initial values and boundary conditions for the numerical integrations of the model are derived from operational analyses of the ECMWF, UK. The results show that the radiative transfer is essential in maintaining the intensity of the low level Somali Jet as well as the upper level Tropical Easterly Jet (TEJ) over the Indian sub-continent and adjoining seas. The meridional circulation over the region is also well simulated. As a result, enough moisture transports from the warm equatorial region to simulate more realistic orographic precipitation in the windward side of the mountains along the West coast of India. Without radiative transfer processes in the model atmosphere the simulated monsoon circulation weakens, moisture transport decreases and the precipitation lessens

Numerical simulation of the sensitivity of summer monsoon circulation and rainfall over india to land surface processes

The influence of soil moisture and vegetation variation on simulation of monsoon circulation and rainfall is investigated. For this purpose a simple land surface parameterization scheme is incorporated in a three-dimensional regional high resolution nested grid atmospheric model. Based on the land surface parameterization scheme, latent heat and sensible heat fluxes are explicitly estimated over the entire domain of the model. Two sensitivity studies are conducted; one with bare dry soil conditions (no latent heat flux from land surface) and the other with realistic representation of the land surface parameters such as soil moisture, vegetation cover and landuse patterns in the numerical simulation. The sensitivity of main monsoon features such as Somali jet, monsoon trough and tropical easterly jet to land surface processes are discussed. Results suggest the necessity of including a detailed land surface parameterization in the realistic short-range weather numerical predictions. An enhanced short-range prediction of hydrological cycle including precipitation was produced by the model, with land surface processes parameterized. This parameterization appears to simulate all the main circulation features associated with the summer monsoon in a realistic manner

The Christiansen experiment

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TRATADOS INTERNACIONAIS DE DIREITOS HUMANOS NO DIREITO BRASILEIRO: REFLEXÕES SOBRE UMA POSSÍVEL REGULAMENTAÇÃO LEGISLATIVA

Trata-se de trabalho que visa refletir sobre uma provável regulamentação legislativa da incorporação do tratado de direitos humanos no direito brasileiro. Para tanto, faz-se um estudo preliminar acerca das principais discussões sobre a incorporação e a hierarquia dos tratados internacionais de direitos humanos no direito brasileiro, antes e depois da vigência da Emenda Constitucional nº 45/2004, que introduziu o § 3º ao artigo 5º da Constituição Federal. Em seguida, far-se-á uma análise crítica sobre três projetos legislativos, dois em trâmite na Câmara e um no Senado, que propõem a regulamentação do referido tema para, ao final, concluir-se de acordo com tudo o que foi exposto, no texto, apresentando impressões e sugestões sobre o assunto, esperando, assim, dar uma modesta contribuição a um tema tão importante e em destaque atualmente no cenário brasileiro