Adaptive propagation of quantum few-body systems with time-dependent Hamiltonians

In this study, a variety of methods are tested and compared for the numerical solution of the Schr\"odinger equation for few-body systems with explicitely time-dependent Hamiltonians, with the aim to find the optimal one. The configuration interaction method, generally applied to find stationary eigenstates accurately and without approximations to the wavefunction's structure, may also be used for the time-evolution, which results in a large linear system of ordinary differential equations. The large basis sizes typically present when the configuration interaction method is used calls for efficient methods for the time evolution. Apart from efficiency, adaptivity (in the time domain) is the other main focus in this study, such that the time step is adjusted automatically given some requested accuracy. A method is suggested here, based on an exponential integrator approach, combined with different ways to implement the adaptivity, which was found to be faster than a broad variety of other methods that were also considered.Comment: 16 pages, 1 figure (4 panels

Vortices in Bose-Einstein condensates - finite-size effects and the thermodynamic limit

For a weakly-interacting Bose gas rotating in a harmonic trap we relate the yrast states of small systems (that can be treated exactly) to the thermodynamic limit (derived within the mean-field approximation). For a few dozens of atoms, the yrast line shows distinct quasi-periodic oscillations with increasing angular momentum that originate from the internal structure of the exact many-body states. These finite-size effects disappear in the thermodynamic limit, where the Gross-Pitaevskii approximation provides the exact energy to leading order in the number of particles N. However, the exact yrast states reveal significant structure not captured by the mean-field approximation: Even in the limit of large N, the corresponding mean-field solution accounts for only a fraction of the total weight of the exact quantum state.Comment: Phys Rev A, in pres

Tunable Wigner States with Dipolar Atoms and Molecules

We study the few-body physics of trapped atoms or molecules with electric or magnetic dipole moments aligned by an external field. Using exact numerical diagonalization appropriate for the strongly correlated regime, as well as a classical analysis, we show how Wigner localization emerges with increasing coupling strength. The Wigner states exhibit non-trivial geometries due to the anisotropy of the interaction. This leads to transitions between different Wigner states as the tilt angle of the dipoles with the confining plane is changed. Intriguingly, while the individual Wigner states are well described by a classical analysis, the transitions between different Wigner states are strongly affected by quantum statistics. This can be understood by considering the interplay between quantum-mechanical and spatial symmetry properties. Finally, we demonstrate that our results are relevant to experimentally realistic systems.Comment: 4 pages, 6 figure

Mixtures of Bose gases under rotation

We examine the rotational properties of a mixture of two Bose gases. Considering the limit of weak interactions between the atoms, we investigate the behavior of the system under a fixed angular momentum. We demonstrate a number of exact results in this many-body system.Comment: 4 pages, RevTex, 6 figure

Vortices in fermion droplets with repulsive dipole-dipole interactions

Vortices are found in a fermion system with repulsive dipole-dipole interactions, trapped by a rotating quasi-two-dimensional harmonic oscillator potential. Such systems have much in common with electrons in quantum dots, where rotation is induced via an external magnetic field. In contrast to the Coulomb interactions between electrons, the (externally tunable) anisotropy of the dipole-dipole interaction breaks the rotational symmetry of the Hamiltonian. This may cause the otherwise rotationally symmetric exact wavefunction to reveal its internal structure more directly.Comment: 5 pages, 5 figure

Transport and interaction blockade of cold bosonic atoms in a triple-well potential

We theoretically investigate the transport properties of cold bosonic atoms in a quasi one-dimensional triple-well potential that consists of two large outer wells, which act as microscopic source and drain reservoirs, and a small inner well, which represents a quantum-dot-like scattering region. Bias and gate "voltages" introduce a time-dependent tilt of the triple-well configuration, and are used to shift the energetic level of the inner well with respect to the outer ones. By means of exact diagonalization considering a total number of six atoms in the triple-well potential, we find diamond-like structures for the occurrence of single-atom transport in the parameter space spanned by the bias and gate voltages. We discuss the analogy with Coulomb blockade in electronic quantum dots, and point out how one can infer the interaction energy in the central well from the distance between the diamonds.Comment: 18 pages, 6 figure

Signatures of Wigner Localization in Epitaxially Grown Nanowires

It was predicted by Wigner in 1934 that the electron gas will undergo a transition to a crystallized state when its density is very low. Whereas significant progress has been made towards the detection of electronic Wigner states, their clear and direct experimental verification still remains a challenge. Here we address signatures of Wigner molecule formation in the transport properties of InSb nanowire quantum dot systems, where a few electrons may form localized states depending on the size of the dot (i.e. the electron density). By a configuration interaction approach combined with an appropriate transport formalism, we are able to predict the transport properties of these systems, in excellent agreement with experimental data. We identify specific signatures of Wigner state formation, such as the strong suppression of the antiferromagnetic coupling, and are able to detect the onset of Wigner localization, both experimentally and theoretically, by studying different dot sizes.Comment: 4 pages, 4 figure

Chuvas intensas no Estado de Mato Grosso.

O objetivo deste trabalho foi determinar a probabilidade de ocorrência de chuvas intensas no Estado de Mato Grosso. Séries com os valores máximos anuais da precipitação de um dia de 151 postos pluviométricos de Mato Grosso foram ajustadas à Distribuição de Gumbel. Os parâmetros da distribuição foram estimados pelo método de máxima verossimilhança. Houve ajuste de todas as séries de intensidade máxima anual à distribuição Gumbel, de acordo com o teste Kolmogorov-Smirnov. Através das distribuições ajustadas foram calculados os valores de precipitação máxima de 1 dia para períodos de retorno de 2, 3, 4, 5, 10, 15, 20 e 50 anos. Utilizando o método de desagregação de chuvas, estimou-se a precipitação máxima com duração de 5, 10, 15, 20, 25, 30 minutos e 1, 6, 8, 10, 12 e 24 horas. Foram confeccionados mapas de isolinhas com os dados de chuvas intensas, com duração de 10, 15 e 30 minutos e 1 e 6 horas, para períodos de retorno de 4, 10, 15 e 20 anos.bitstream/item/23529/1/DOC2010104.pd

Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions

When a Bose-Einstein condensed cloud of atoms is given some angular momentum, it forms vortices arranged in structures with a discrete rotational symmetry. For these vortex states, the Hilbert space of the exact solution separates into a "primary" space related to the mean-field Gross-Pitaevskii solution and a "complementary" space including the corrections beyond mean-field. Considering a weakly-interacting Bose-Einstein condensate of harmonically-trapped atoms, we demonstrate how this separation can be used to close the conceptual gap between exact solutions for systems with only a few atoms and the thermodynamic limit for which the mean-field is the correct leading-order approximation. Although we illustrate this approach for the case of weak interactions, it is expected to be more generally valid.Comment: 8 pages, 5 figure