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Lattice vs. continuum theory of the periodic Heisenberg chain

We consider the detailed structure of low energy excitations in the periodic spin-1/2 XXZ Heisenberg chain. By performing a perturbative calculation of the non-linear corrections to the Gaussian model, we determine the exact coefficients of asymptotic expansions in inverse powers of the system length N for a large number of low-lying excited energy levels. This allows us to calculate eigenenergies of the lattice model up to order order N^-4, without having to solve the Bethe Ansatz equations. At the same time, it is possible to express the exact eigenstates of the lattice model in terms of bosonic modes.Comment: 17 pages, 8 Figures. The latest version can be found at http://www.physik.uni-kl.de/eggert/papers/index.htm

Wigner crystal vs. Friedel oscillations in the 1D Hubbard model

We analyze the fermion density of the one-dimensional Hubbard model using bosonization and numerical DMRG calculations. For finite systems we find a relatively sharp crossover even for moderate short range interactions into a region with $4k_F$ density waves as a function of density. The results show that the unstable fixed point of a spin-incoherent state can dominate the physical behavior in a large region of parameter space in finite systems. The crossover may be observable in ultra cold fermionic gases in optical lattices and in finite quantum wires.Comment: 6 pages, 6 figures. Published version. The most recent file can be found at http://www.physik.uni-kl.de/eggert/papers/index.htm

Thinking Ahead: Protecting the Environment in the 21st Century

The United States has made notable progress in cleaning up the environment over the last 30 years. Our nation\u27s air, land and water are, in almost all cases, significantly cleaner than they were only a few decades ago.\u27 Before declaring victory though, we must acknowledge that some environmental problems are getting worse, and the nature of our environmental problems has changed. Many environmental problems are now global problems, as opposed to problems that could be dealt with at the national or state level. Problems have become diffuse, with no clearly identifiable source and with a lengthy delay between cause and effect, whereas before problems were immediately obvious with distinct sources. Finally, environmental problems have become very complex, changing from the relatively simple problems such as thinning eggshells due to pesticide abuse . Government agencies continue to address this new generation of problems with tools designed for a generation of problems now largely behind us. The time has come to develop complementary tools designed for these new problems. As environmental regulatory agencies investigate new approaches to environmental protection, the way questions are phrased has a profound impact on the answers generated. If the question concerns how an environmental agency can do a better job working with businesses to ensure that they act in an environmentally responsible manner, then the nswer must involve some type of cooperative effort between the environmental agency and the relevant businesses. If, however, the question concerns how an environmental agency can best use its resources to protect the environment, then the answer may require the agency to work with many different groups. It is my belief that environmental regulatory agencies should be asking the second question. Further, one possible answer to the question of how to develop effective, supplemental approaches to protecting and enhancing the environment lies in educating and influencing the public, specifically with respect to consumer purchasing decisions

Thinking Ahead: Protecting the Environment in the 21st Century

The United States has made notable progress in cleaning up the environment over the last 30 years. Our nation\u27s air, land and water are, in almost all cases, significantly cleaner than they were only a few decades ago.\u27 Before declaring victory though, we must acknowledge that some environmental problems are getting worse, and the nature of our environmental problems has changed. Many environmental problems are now global problems, as opposed to problems that could be dealt with at the national or state level. Problems have become diffuse, with no clearly identifiable source and with a lengthy delay between cause and effect, whereas before problems were immediately obvious with distinct sources. Finally, environmental problems have become very complex, changing from the relatively simple problems such as thinning eggshells due to pesticide abuse . Government agencies continue to address this new generation of problems with tools designed for a generation of problems now largely behind us. The time has come to develop complementary tools designed for these new problems. As environmental regulatory agencies investigate new approaches to environmental protection, the way questions are phrased has a profound impact on the answers generated. If the question concerns how an environmental agency can do a better job working with businesses to ensure that they act in an environmentally responsible manner, then the nswer must involve some type of cooperative effort between the environmental agency and the relevant businesses. If, however, the question concerns how an environmental agency can best use its resources to protect the environment, then the answer may require the agency to work with many different groups. It is my belief that environmental regulatory agencies should be asking the second question. Further, one possible answer to the question of how to develop effective, supplemental approaches to protecting and enhancing the environment lies in educating and influencing the public, specifically with respect to consumer purchasing decisions

Precision orbit computations for an operational environment

Taking advantage of the improvements to the Earth's gravitation field and tracking station coordinates, an orbital computational consistency of the order of 5 meters was achieved for total position differences between orbital solutions for the Seasat and GEOS-3. The main source of error in these solutions was in the mathematical models that are required to generate these results, i.e., gravitation, atmospheric drag, etc. Different Earth gravitation fields and tracking coordinates were analyzed and evaluated in obtaining these computational results. Comparisons and evaluations of the Seasat results were obtained in terms of different solution types such as the Doppler only, Laser only, Doppler and Laser, etc. Other investigation using the Seasat data were made in order to determine their effect on the computational results at this particular level of consistency

Universal cross-over behavior of a magnetic impurity and consequences for doping in spin-1/2 chains

We consider a magnetic impurity in the antiferromagnetic spin-1/2 chain which is equivalent to the two-channel Kondo problem in terms of the field theoretical description. Using a modification of the transfer-matrix density matrix renormalization group (DMRG) we are able to determine local and global properties in the thermodynamic limit. The cross-over function for the impurity susceptibility is calculated over a large temperature range, which exhibits universal data-collapse. We are also able to determine the local susceptibilities near the impurity, which show an interesting competition of boundary effects. This results in quantitative predictions for experiments on doped spin-1/2 chains, which could observe two-channel Kondo physics directly.Comment: 5 pages in revtex format including 3 embedded figures (using epsf). The latest version in PDF format is available from http://fy.chalmers.se/~eggert/papers/crossover.pdf . Accepted by PR

Impurity corrections to the thermodynamics in spin chains using a transfer-matrix DMRG method

We use the density matrix renormalization group (DMRG) for transfer matrices to numerically calculate impurity corrections to thermodynamic properties. The method is applied to two impurity models in the spin-1/2 chain, namely a weak link in the chain and an external impurity spin. The numerical analysis confirms the field theory calculations and gives new results for the crossover behavior.Comment: 9 pages in revtex format including 5 embedded figures (using epsf). To appear in PRB. The latest version in PDF format can be found at http://fy.chalmers.se/~eggert/papers/DMRGimp.pd

Neel order in doped quasi one-dimensional antiferromagnets

We study the Neel temperature of quasi one-dimensional S=1/2 antiferromagnets containing non-magnetic impurities. We first consider the temperature dependence of the staggered susceptibility of finite chains with open boundary conditions, which shows an interesting difference for even and odd length chains. We then use a mean field theory treatment to incorporate the three dimensional inter-chain couplings. The resulting Neel temperature shows a pronounced drop as a function of doping by up to a factor of 5.Comment: 4 pages in revtex4 format including 2 epsf-embedded figures. The latest version in PDF format is available from http://fy.chalmers.se/~eggert/papers/staggered.pd