Quantum Stochastic Processes: A Case Study

We present a detailed study of a simple quantum stochastic process, the quantum phase space Brownian motion, which we obtain as the Markovian limit of a simple model of open quantum system. We show that this physical description of the process allows us to specify and to construct the dilation of the quantum dynamical maps, including conditional quantum expectations. The quantum phase space Brownian motion possesses many properties similar to that of the classical Brownian motion, notably its increments are independent and identically distributed. Possible applications to dissipative phenomena in the quantum Hall effect are suggested.Comment: 35 pages, 1 figure

Discrete approximation of the free Fock space

International audienceWe prove that the free Fock space {\F}(\R^+;\C), which is very commonly used in Free Probability Theory, is the continuous free product of copies of the space \C^2. We describe an explicit embeding and approximation of this continuous free product structure by means of a discrete-time approximation: the free toy Fock space, a countable free product of copies of \C^2. We show that the basic creation, annihilation and gauge operators of the free Fock space are also limit of elementary operators on the free toy Fock space. When applying these constructions and results to the probabilistic interpretations of these spaces, we recover some discrete approximations of the semi-circular Brownian motion and of the free Poisson process. All these results are also extended to the higher multiplicity case, that is, {\F}(\R^+;\C^N) is the continuous free product of copies of the space \C^{N+1}

Hillslopes record the growth and decay of landscapes

Earth's surface archives the combined history of tectonics and erosion, which tend to roughen landscapes, and sediment transport and deposition, which smooth them. We analyzed hillslope morphology in the tectonically active Dragon’s Back Pressure Ridge in California, United States, to assess whether tectonic uplift history can be reconstructed using measurable attributes of hillslope features within landscapes. Hilltop curvature and hillslope relief mirror measured rates of vertical displacement caused by tectonic forcing, and their relationships are consistent with those expected when idealizing hillslope transport as a nonlinear diffusion process. Hilltop curvature lags behind relief in its response to changing erosion rates, allowing growing landscapes to be distinguished from decaying landscapes. Numerical modeling demonstrates that hillslope morphology may be used to infer changes in tectonic rates

Temporal variability in detrital 10Be concentrations in large Himalayan catchments

Accurately quantifying sediment fluxes in large rivers draining tectonically active landscapes is complicated by the stochastic nature of sediment inputs. Cosmogenic 10Be concentrations measured in modern river sands have been used to estimate 102- to 104-year sediment fluxes in these types of catchments, where upstream drainage areas are often in excess of 10 000 km2. It is commonly assumed that within large catchments, the effects of stochastic sediment inputs are buffered such that 10Be concentrations at the catchment outlet are relatively stable in time. We present 18 new 10Be concentrations of modern river and dated Holocene terrace and floodplain deposits from the Ganga River near to the Himalayan mountain front (or outlet). We demonstrate that 10Be concentrations measured in modern Ganga River sediments display a notable degree of variability, with concentrations ranging between ∼9000 and 19 000 atoms g−1. We propose that this observed variability is driven by two factors. Firstly, by the nature of stochastic inputs of sediment (e.g. the dominant erosional process, surface production rates, depth of landsliding, degree of mixing) and, secondly, by the evacuation timescale of individual sediment deposits which buffer their impact on catchment-averaged concentrations. Despite intensification of the Indian Summer Monsoon and subsequent doubling of sediment delivery to the Bay of Bengal between ∼11 and 7 ka, we also find that Holocene sediment 10Be concentrations documented at the Ganga outlet have remained within the variability of modern river concentrations. We demonstrate that, in certain systems, sediment flux cannot be simply approximated by converting detrital concentration into mean erosion rates and multiplying by catchment area as it is possible to generate larger volumetric sediment fluxes whilst maintaining comparable average 10Be concentrations

A partition-free approach to transient and steady-state charge currents

We construct a non-equilibrium steady state and calculate the corresponding current for a mesoscopic Fermi system in the partition-free setting. To this end we study a small sample coupled to a finite number of semi-infinite leads. Initially, the whole system of quasi-free fermions is in a grand canonical equilibrium state. At t = 0 we turn on a potential bias on the leads and let the system evolve. We study how the charge current behaves in time and how it stabilizes itself around a steady state value, which is given by a Landauer-type formula.Comment: 14 pages, submitte

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

Impact of recycling and lateral sediment input on grain size fining trends – implications for reconstructing tectonic and climate forcings in ancient sedimentary systems

Grain size trends in basin stratigraphy are thought to preserve a rich record of the climatic and tectonic controls on landscape evolution. Stratigraphic models assume that over geological timescales, the downstream profile of sediment deposition is in dynamic equilibrium with the spatial distribution of tectonic subsidence in the basin, sea level and the flux and calibre of sediment supplied from mountain catchments. Here, we demonstrate that this approach in modelling stratigraphic responses to environmental change is missing a key ingredient: the dynamic geomorphology of the sediment routing system. For three large alluvial fans in the Iglesia basin, Argentine Andes we measured the grain size of modern river sediment from fan apex to toe and characterise the spatial distribution of differential subsidence for each fan by constructing a 3D model of basin stratigraphy from seismic data. We find, using a self-similar grain size fining model, that the profile of grain size fining on all three fans cannot be reproduced given the subsidence profile measured and for any sediment supply scenario. However, by adapting the self-similar model, we demonstrate that the grain size trends on each fan can be effectively reproduced when sediment is not only sourced from a single catchment at the apex of the system, but also laterally, from tributary catchments and through fan surface recycling. Without constraint on the dynamic geomorphology of these large alluvial systems, signals of tectonic and climate forcing in grain size data are masked and would be indecipherable in the geological record. This has significant implications for our ability to make sensitive, quantitative reconstructions of external boundary conditions from the sedimentary record