Systematic multivariate analysis (sMVA) strategy for improved process unerstanding of inustrial biorefinery processes with applications in fatty acid production

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Quantum harmonic oscillator systems with disorder

We study many-body properties of quantum harmonic oscillator lattices with disorder. A sufficient condition for dynamical localization, expressed as a zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the eigenfunction correlators for an effective one-particle Hamiltonian. We show how state-of-the-art techniques for proving Anderson localization can be used to prove that these properties hold in a number of standard models. We also derive bounds on the static and dynamic correlation functions at both zero and positive temperature in terms of one-particle eigenfunction correlators. In particular, we show that static correlations decay exponentially fast if the corresponding effective one-particle Hamiltonian exhibits localization at low energies, regardless of whether there is a gap in the spectrum above the ground state or not. Our results apply to finite as well as to infinite oscillator systems. The eigenfunction correlators that appear are more general than those previously studied in the literature. In particular, we must allow for functions of the Hamiltonian that have a singularity at the bottom of the spectrum. We prove exponential bounds for such correlators for some of the standard models

Transport of interface states in the Heisenberg chain

We demonstrate the transport of interface states in the one-dimensional ferromagnetic Heisenberg model by a time dependent magnetic field. Our analysis is based on the standard Adiabatic Theorem. This is supplemented by a numerical analysis via the recently developed time dependent DMRG method, where we calculate the adiabatic constant as a function of the strength of the magnetic field and the anisotropy of the interaction.Comment: minor revision, final version; 13 pages, 4 figure

Non-equilibrium states of a photon cavity pumped by an atomic beam

We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking into account leaking of the cavity, we prove that the mean photon number in the cavity stabilizes in time. The limiting state of the cavity in this case exists and it is independent of the initial state. We calculate the characteristic functional of this non-quasi-free non-equilibrium state. We also calculate the energy flux in both the ideal and open cavity and the entropy production for the ideal cavity.Comment: Corrected energy production calculations and made some changes to ease the readin

A model with simultaneous first and second order phase transitions

We introduce a two dimensional nonlinear XY model with a second order phase transition driven by spin waves, together with a first order phase transition in the bond variables between two bond ordered phases, one with local ferromagnetic order and another with local antiferromagnetic order. We also prove that at the transition temperature the bond-ordered phases coexist with a disordered phase as predicted by Domany, Schick and Swendsen. This last result generalizes the result of Shlosman and van Enter (cond-mat/0205455). We argue that these phenomena are quite general and should occur for a large class of potentials.Comment: 7 pages, 7 figures using pstricks and pst-coi

The spectral gap for some spin chains with discrete symmetry breaking

We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics. This general scheme is interesting in its own right and therefore, although the basic idea is not new, we present it in a system-independent setting. The results are illustrated with an number of examples.Comment: 48 pages, Plain TeX, BN26/Oct/9

The Loop Algorithm

A review of the Loop Algorithm, its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a Quantum Monte Carlo procedure which employs nonlocal changes of worldline configurations, determined by local stochastic decisions. It is based on a formulation of quantum models of any dimension in an extended ensemble of worldlines and graphs, and is related to Swendsen-Wang algorithms. It can be represented directly on an operator level, both with a continuous imaginary time path integral and with the stochastic series expansion (SSE). It overcomes many of the difficulties of traditional worldline simulations. Autocorrelations are reduced by orders of magnitude. Grand-canonical ensembles, off-diagonal operators, and variance reduced estimators are accessible. In some cases, infinite systems can be simulated. For a restricted class of models, the fermion sign problem can be overcome. Transverse magnetic fields are handled efficiently, in contrast to strong diagonal ones. The method has been applied successfully to a variety of models for spin and charge degrees of freedom, including Heisenberg and XYZ spin models, hard-core bosons, Hubbard, and tJ-models. Due to the improved efficiency, precise calculations of asymptotic behavior and of quantum critical exponents have been possible.Comment: Third Edition, July 2002. (78 pages, 11 figures). To appear in Adv.Phys. Updated. New chapter on Operator Formulation, with continuous time and with SS

Refining soil organic carbon stock estimates for China’s palustrine wetlands

Palustrine wetlands include all bogs, fens, swamps and marshes that are non-saline and which are not lakes or rivers. They therefore form a highly important group of wetlands which hold large carbon stocks. If these wetlands are not protected properly they could become a net carbon source in the future. Compilation of spatially explicit wetland databases, national inventory data and in-situ measurement of soil organic carbon (SOC) could be useful to better quantify SOC and formulate long-term strategies for mitigating global climate change. In this study, a synergistic mapping approach was used to create a hybrid map for palustrine wetlands for China and to estimate their SOC content. Total SOC storage in palustrine wetlands was estimated to be 4.3±1.4 Pg C, with a SOC density of 31.17 (±10.55) kg C m-2 in the upper 1 m of the soil layer. This carbon stock is concentrated in Northeast China (49%) and the Qinghai-Tibet Plateau (41%). Given the large pool of carbon stored in palustrine wetlands compared to other soil types, we suggest that urgent monitoring programmes on SOC should be established in regions with very few datasets, but where palustrine wetlands appear to be common such as the Tibet region and Northwest China