Solvable Hydrodynamics of Quantum Integrable Systems

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudo-momenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudo-momentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.Comment: 6+5 pages, published versio

Evidence for dependency of bacterial growth on enzymatic hydrolysis of particulate organic matter in the mesopelagic ocean

Organic material entering the oceanic mesopelagic zone may either reenter the euphotic zone or settle into deeper waters. Therefore it is important to know about mechanisms and efficiency of substrate conversion in this water layer. Bacterial biomass, bacteria secondary production (BSP). extra­cellular peptidase activity (EPA) and particulate organic nitrogen (PON) were measured in vertical pro­files of the North Atlantic (46° N 18° W; 57° N 23° W) during the Joint Global Ocean Flux Study (JGOFS) cruise in May 1989. The magnitude of these parameters decreased differently with depth. The strong­est decreases were observed for bacterial production (3H-thymidine incorporation) and peptide turn­over (using the substrate analog leucine-methylcoumarinylamide). Bacterial biomass and peptidase potential activity were not reduced as much in the mesopelagic zone. Peptidase potential per unit cell biomass of mesopelagic bacteria was 2 to 3 times higher than that of bacteria in surface water. Nevertheless bacterial growth at depth was slow, due to slow actual hydrolysis. Values of theoretical PON hydrolysis were calculated from PON measurements and protein hydrolysis rates. These corre­sponded well to bacterial production rates, and the degree of correspondence increased from a factor of 0.63 (PON hydrolysis/ESP) in the mixed surface layer to 0.87 in the mesopelagic zone. Thus we hypothesized an effective coupling between particle hydrolysis and uptake of hydrolysate by bacteria, which depletes the deeper water of easily degradable substrates as hydrolysates usually are. The low enzymatic PON turnover rate of 0.04 d- 1 in the subeuphotic zone suggests that residence time of parti­cles within a depth stratum may be important for its contribution to export. storage and recycling of organic matter

Superdiffusive transport of energy in generic Luttinger liquids

Metals in one spatial dimension are described at the lowest energy scales by the Luttinger liquid theory. It is well understood that this free theory, and even interacting integrable models, can support ballistic transport of conserved quantities including energy. In contrast, realistic Luttinger-liquid metals, even without disorder, contain integrability-breaking interactions that are expected to lead to thermalization and conventional diffusive linear response. We show that the expansion of energy when such a non-integrable Luttinger liquid is locally heated above its ground state shows superdiffusive behavior (i.e., spreading of energy that is intermediate between diffusion and ballistic propagation), by combining an analytical anomalous diffusion model with numerical matrix product state calculations.Comment: 5 pages, 3 figure

The role of mesoscale hydrography on microbial dynamics in the northeast Atlantic: Results of a spring bloom experiment

During RV Meteor cruise No. 10 from May to June 1989 (JGOFS pilot study) bacterial and picocyanobacterial abundance, biomass, and bacterial production were estimated at two drift stations close to 47N, 20W and 58N, 20W in the northeast Atlantic. At 47N two different mesoscale hydrographic structures were sampled which divided the drift experiment into a cyclonic and an anticyclonic circulation phase. Transition from one phase to the next was clearly reflected by changes of the biological structure in the upper water column. Phytoplankton stocks maintained during the cyclonic phase were about 1.8 times higher than those of the anticyclonic phase (1552 mg C m−2 and 880 mg C m−2, resp., integrated over the mixed layer, Deckers, 1991). Integrated stocks of bacteria showed an opposite pattern of distribution. Picocyanobacterial biomass (PCB) was 3.4 times higher during the anticyclonic phase than during the cyclonic phase (96 mg C m−2 and 28 mg C m−2, resp.), and the respective factor for total bacterial biomass (TBB) was 3.7 (830 mg C m−2 and 225 mg C m−2, resp.). Our analysis indicates that the combined bacterial biomass dominated within the mixed layer during the anticyclonic phase, while the cyclonic phase was clearly dominated by eucaryotic phytoplankton. Additional evidence for a shift of biology toward the microbial food web was indicated by a strong increase of bacteria during the anticyclonic phase. Thus, simultaneously and side by side, an autotrophic and a heterotrophic system were supported by the prevailing hydrographic conditions. At 58N within an anticyclonic mesoscale hydrographic structure the phytoplankton bloom was at a developing stage, characterized by low biomass (730 mg C m−2 in the mixed layer, Deckers, 1991) but relatively high primary production. In contrast, bacterial stocks were quite high, but bacterial production was low in comparison to the anticyclonic phase at 47N (90 mg C m−2 d−1 and 153 mg C m−2 d−1, resp., integrated from 0–300 m). It was calculated that bacterial gross production averaged 42% (47N, anticyclonic phase) and 25% (58N) of primary production. These results suggest that within a specific type of hydrographic structure either a heterotrophic or an autotrophic system can be established, depending on the stage of bloom development. In conclusion: Depending on their origin and age, mesoscale hydrographic structures can be correlated with different stages of biological development. This leads to the mesoscale patchiness of biological measurements, which is a characteristic feature of the northeast Atlantic

Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain

Quantum integrable systems, such as the interacting Bose gas in one dimension and the XXZ quantum spin chain, have an extensive number of local conserved quantities that endow them with exotic thermalization and transport properties. We discuss recently introduced hydrodynamic approaches for such integrable systems from the viewpoint of kinetic theory and extend the previous works by proposing a numerical scheme to solve the hydrodynamic equations for finite times and arbitrary locally equilibrated initial conditions. We then discuss how such methods can be applied to describe nonequilibrium steady states involving ballistic heat and spin currents. In particular, we show that the spin Drude weight in the XXZ chain, previously accessible only by rigorous techniques of limited scope or controversial thermodynamic Bethe ansatz arguments, may be evaluated from hydrodynamics in very good agreement with density-matrix renormalization group calculations

Level-occupation switching of the Quantum Dot, and phase anomalies in mesoscopic interferometry

For a variety of quantum dots, the widths of different single-particle levels may naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. We found that in this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation of the salient features of the behavior of the transmission phase in an interferometer with a QD. The theory of this effect will be reviewed with special emphasis on the role of the interactions. New results on the dot-charging measurements and the fine structure of occupation switchings will be presented, accompanied by the unified description of the whole series of CB peaks caused by a single broad level. We then discuss the case where the system approaches the Kondo regime.Comment: 30 pages in IOP format, 11 figure

Interaction quench dynamics in the Kondo model in presence of a local magnetic field

In this work we investigate the quench dynamics in the Kondo model on the Toulouse line in presence of a local magnetic field. It is shown that this setup can be realized by either applying the local magnetic field directly or by preparing the system in a macroscopically spin-polarized initial state. In the latter case, the magnetic field results from a subtlety in applying the bosonization technique where terms that are usually referred to as finite-size corrections become important in the present non-equilibrium setting. The transient dynamics is studied by analyzing exact analytical results for the local spin dynamics. The time scale for the relaxation of the local dynamical quantities turns out to be exclusively determined by the Kondo scale. In the transient regime, one observes damped oscillations in the local correlation functions with a frequency set by the magnetic field.Comment: 8 pages, 2 figures; minor changes, version as publishe