Obtaining Breathers in Nonlinear Hamiltonian Lattices

We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamiltonian lattice. We compare these results with analytical considerations of the spatial decay. We show that nonlinear contributions have to be considered, and obtain very good agreement between the latter and the numerical results. We discuss further applications of the method and results.Comment: 21 pages (LaTeX), 8 figures in ps-files, tar-compressed uuencoded file, Physical Review E, in pres

Quantum localized modes in capacitively coupled Josephson junctions

We consider the quantum dynamics of excitations in a system of two capacitively coupled Josephson junctions. Quantum breather states are found in the middle of the energy spectrum of the confined nonescaping states of the system. They are characterized by a strong excitation of one junction. These states perform slow tunneling motion from one junction to the other, while keeping their coherent nature. The tunneling time sensitively depends on the initial excitation energy. By using an external bias as a control parameter, the tunneling time can be varied with respect to the escape time and the experimentally limited coherence time. Thus one can control the flow of quantum excitations between the two junctions.Comment: 5 pages, 3 figures. Improved version, title was slightly changed. Accepted in Europhysics Letters (http://www.iop.org/EJ/journal/EPL

Quantum breathers in capacitively coupled Josephson junctions: Correlations, number conservation, and entanglement

We consider the classical and quantum dynamics of excitations in a system of two capacitively coupled Josephson junctions. In the classical case the equations of motion admit discrete breather solutions, which are time periodic and localized predominantly on one of the junctions. In the quantum case breather states are found in the central part of the energy spectrum of the confined nonescaping states of the system. We perform a systematic analysis of their tunneling frequency, site correlations, fluctuations of the number of quanta, and entanglement. Quantum breather states show strong site correlation of quanta and are characterized by a strong excitation of quanta on one junction which perform slow coherent tunneling motion from one junction to the other. They suppress fluctuations of the total number of excited quanta. Quantum breather states are the least entangled states among the group of eigenstates in the same range of the energy spectrum. We describe how quantum breather excitations could be experimentally observed by employing the already developed techniques for quantum information processing using Josephson junctions.Comment: 10 pages, 9 figures. Improved version with further discussions. Accepted in Physical Review

Breathers on lattices with long range interaction

We analyze the properties of breathers (time periodic spatially localized solutions) on chains in the presence of algebraically decaying interactions $1/r^s$. We find that the spatial decay of a breather shows a crossover from exponential (short distances) to algebraic (large distances) decay. We calculate the crossover distance as a function of $s$ and the energy of the breather. Next we show that the results on energy thresholds obtained for short range interactions remain valid for $s>3$ and that for $s < 3$ (anomalous dispersion at the band edge) nonzero thresholds occur for cases where the short range interaction system would yield zero threshold values.Comment: 4 pages, 2 figures, PRB Rapid Comm. October 199

Acoustic breathers in two-dimensional lattices

The existence of breathers (time-periodic and spatially localized lattice vibrations) is well established for i) systems without acoustic phonon branches and ii) systems with acoustic phonons, but also with additional symmetries preventing the occurence of strains (dc terms) in the breather solution. The case of coexistence of strains and acoustic phonon branches is solved (for simple models) only for one-dimensional lattices. We calculate breather solutions for a two-dimensional lattice with one acoustic phonon branch. We start from the easy-to-handle case of a system with homogeneous (anharmonic) interaction potentials. We then easily continue the zero-strain breather solution into the model sector with additional quadratic and cubic potential terms with the help of a generalized Newton method. The lattice size is $70\times 70$. The breather continues to exist, but is dressed with a strain field. In contrast to the ac breather components, which decay exponentially in space, the strain field (which has dipole symmetry) should decay like $1/r^a, a=2$. On our rather small lattice we find an exponent $a\approx 1.85$

Quantum q-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

We study the spectrum and eigenstates of the quantum discrete Bose-Hubbard Hamiltonian in a finite one-dimensional lattice containing two bosons. The interaction between the bosons leads to an algebraic localization of the modified extended states in the normal mode space of the noninteracting system. Weight functions of the eigenstates in the space of normal modes are computed by using numerical diagonalization and perturbation theory. We find that staggered states do not compactify in the dilute limit for large chains.Comment: 7 pages, 7 figures. Minor changes and additional comments. Acepted in Physical Review

Slow Relaxation and Phase Space Properties of a Conservative System with Many Degrees of Freedom

We study the one-dimensional discrete $\Phi^4$ model. We compare two equilibrium properties by use of molecular dynamics simulations: the Lyapunov spectrum and the time dependence of local correlation functions. Both properties imply the existence of a dynamical crossover of the system at the same temperature. This correlation holds for two rather different regimes of the system - the displacive and intermediate coupling regimes. Our results imply a deep connection between slowing down of relaxations and phase space properties of complex systems.Comment: 14 pages, LaTeX, 10 Figures available upon request (SF), Phys. Rev. E, accepted for publicatio

On the interactions between land and water use in Brazilian rainfed agriculture

In the coming decades, one of humankind’s main challenges will be to guarantee food supply for a growing population while managing ever more scarce resources, and safeguarding the availability of water and land for natural ecosystems. Brazil is a country with abundance of water and land resources, and has recently become one of the world’s main exporters of agricultural commodities. The Brazilian agricultural sector recently went through unprecedented intensification and extensification processes, which include the expansion of cropland and pasture areas into vulnerable ecosystems. This PhD thesis advances the research field on water and land resources assessment by investigating the following processes: i) changes in green water use by major rainfed crops in Brazil during recent decades ii) potential improvements of land and green water productivity for Brazilian rainfed crops, with and without implementation of supplemental irrigation, iii) influences of intensification and expansion of soybean production in Brazil on green water use, and iv) impacts of double-cropping on water use intensity. The process-based biogeophysical crop model EPIC was chosen and applied to simulate water use and crop growth for Brazilian rainfed crops, under diverse management conditions. In Chapter 2, I simulated yields, water use and water productivity for soybeans, maize, cotton and wheat under different scenarios of agricultural management, for rainfed and irrigated conditions. Chapter 3 focuses on soybean and maize, and analyzes water use for the production of these crops under single and double-cropping conditions. The results show an increase in green water use for the production of maize, cotton, soybeans and wheat from 145 to 263 km3 per year between 1990 and 2013. This increase is in large part due to the expansion of harvested area for soybean production. The analysis of management scenarios shows that improving nutrient management has a larger potential to improve land and water productivity compared to supplemental irrigation. Furthermore, supplemental irrigation would lead to a reduction in water productivity despite marginal improvements in land productivity. The analysis of double-cropping practices for soybean and maize production systems finds a greater water appropriation of these systems avoiding cropland expansion and improving overall water productivity. This thesis improves the understanding of current and future use of land and water, the role of intensification and expansion processes, and interactions between land and water use. The results lead to the main conclusion that harvested area expansion has been a major driving force in the increase of green water appropriation in Brazil in the last decades, but that different intensification processes have led to a more productive use of water and land over time. More importantly, the growth of double-cropping has allowed a decoupling between the appropriation of water and land, allowing a great increase of agricultural water use without further expansion of cropland