Biogeochemical modeling at mass extinction boundaries

The causes of major mass extinctions is a subject of considerable interest to those concerned with the history and evolution of life on earth. The primary objectives of the proposed plan of research are: (1) to develop quantitative time-dependent biogeochemical cycle models, coupled with an ocean atmosphere in order to improve the understanding of global scale physical, chemical, and biological processes that control the distribution of elements important for life at times of mass extinctions; and (2) to develop a comprehensive data base of the best available geochemical, isotopic, and other relevant geologic data from sections across mass extinction boundaries. These data will be used to constrain and test the biogeochemical model. These modeling experiments should prove useful in: (1) determining the possible cause(s) of the environmental changes seen at bio-event boundaries; (2) identifying and quantifying little-known feedbacks among the oceans, atmosphere, and biosphere; and (3) providing additional insights into the possible responses of the earth system to perturbations of various timescales. One of the best known mass extinction events marks the Cretaceous/Tertiary (K/T) boundary (66 Myr ago). Data from the K/T boundary are used here to constrain a newly developed time-dependent biogeochemical cycle model that is designed to study transient behavior of the earth system. Model results predict significant fluctuations in ocean alkalinity, atmospheric CO2, and global temperatures caused by extinction of calcareous plankton and reduction in the sedimentation rates of pelagic carbonates and organic carbon. Oxygen-isotome and other paleoclimatic data from K/T time provide some evidence that such climatic fluctuations may have occurred, but stabilizing feedbacks may have acted to reduce the ocean alkalinity and carbon dioxide fluctuations

Ocean alkalinity and the Cretaceous/Tertiary boundary

A biogeochemical cycle model resolving ocean carbon and alkalinity content is applied to the Maestrichtian and Danian. The model computes oceanic concentrations and distributions of Ca(2+), Mg(2+), and Sigma-CO2. From these values an atmospheric pCO2 value is calculated, which is used to estimate rates of terrestrial weathering of calcite, dolomite, and calcium and magnesium silicates. Metamorphism of carbonate rocks and the subsequent outgassing of CO2 to the atmosphere are parameterized in terms of carbonate rock reservoir sizes, total land area, and a measure of overall tectonic activity, the sea-floor generation rate. The ocean carbon reservoir computed by the model is used with Deep Sea Drilling Project (DSDP) C-13 data to estimate organic detrital fluxes under a variety of ocean mixing rate assumptions. Using Redfield ratios, the biogenic detrital flux estimate is used to partition the ocean carbon and alkalinity reservoirs between the mixed layer and deep ocean. The calcite flux estimate and carbonate ion concentrations are used to determine the rate of biologically mediated CaCO3 titration. Oceanic productivity was severely limited for approximately 500 kyr following the K/T boundary resulting in significant increases in total ocean alkalinity. As productivity returned to the ocean, excess carbon and alkalinity was removed from the ocean as CaCO3. Model runs indicate that this resulted in a transient imbalance in the other direction. Ocean chemistry returned to near-equilibrium by about 64 mybp

Single-Spin Measurement and Decoherence in Magnetic Resonance Force Microscopy

We consider a simple version of a cyclic adiabatic inversion (CAI) technique in magnetic resonance force microscopy (MRFM). We study the problem: What component of the spin is measured in the CAI MRFM? We show that the non-destructive detection of the cantilever vibrations provides a measurement of the spin component along the effective magnetic field. This result is based on numerical simulations of the Hamiltonian dynamics (the Schrodinger equation) and the numerical solution of the master equation.Comment: 5 pages + 5 figures (PNG format

Multiplicative Noise: Applications in Cosmology and Field Theory

Physical situations involving multiplicative noise arise generically in cosmology and field theory. In this paper, the focus is first on exact nonlinear Langevin equations, appropriate in a cosmologica setting, for a system with one degree of freedom. The Langevin equations are derived using an appropriate time-dependent generalization of a model due to Zwanzig. These models are then extended to field theories and the generation of multiplicative noise in such a context is discussed. Important issues in both the cosmological and field theoretic cases are the fluctuation-dissipation relations and the relaxation time scale. Of some importance in cosmology is the fact that multiplicative noise can substantially reduce the relaxation time. In the field theoretic context such a noise can lead to a significant enhancement in the nucleation rate of topological defects.Comment: 21 pages, LaTex, LA-UR-93-210

Fluctuation-dissipation theorem and quantum tunneling with dissipation

We suggest to take the fluctuation-dissipation theorem of Callen and Welton as a basis to study quantum dissipative phenomena (such as macroscopic quantum tunneling) in a manner analogous to the Nambu-Goldstone theorem for spontaneous symmetry breakdown. It is shown that the essential physical contents of the Caldeira-Leggett model such as the suppression of quantum coherence by Ohmic dissipation are derived from general principles only, namely, the fluctuation-dissipation theorem and unitarity and causality (i.e., dispersion relations), without referring to an explicit form of the Lagrangian. An interesting connection between quantum tunneling with Ohmic dissipation and the Anderson's orthogonality theorem is also noted.Comment: To appear in Phys. Rev.

Exact C=1 Boundary Conformal Field Theories

We present a solution of the problem of a free massless scalar field on the half line interacting through a periodic potential on the boundary. For a critical value of the period, this system is a conformal field theory with a non-trivial and explicitly calculable S-matrix for scattering from the boundary. Unlike all other exactly solvable conformal field theories, it is non-rational ({\it i.e.} has infinitely many primary fields). It describes the critical behavior of a number of condensed matter systems, including dissipative quantum mechanics and of barriers in ``quantum wires''.Comment: harvmac, 10 pages, PUPT-1432/IASSNS-HEP-93/7

Non-additivity of decoherence rates in superconducting qubits

We show that the relaxation and decoherence rates 1/T_1 and 1/T_2 of a qubit coupled to several noise sources are in general not additive, i.e., that the total rates are not the sums of the rates due to each individual noise source. To demonstrate this, we calculate the relaxation and pure dephasing rates 1/T_1 and 1/T_\phi of a superconducting (SC) flux qubit in the Born-Markov approximation in the presence of several circuit impedances Z_i using network graph theory and determine their deviation from additivity (the mixing term). We find that there is no mixing term in 1/T_\phi and that the mixing terms in 1/T_1 and 1/T_2 can be positive or negative, leading to reduced or enhanced relaxation and decoherence times T_1 and T_2. The mixing term due to the circuit inductance L at the qubit transition frequency \omega_{01} is generally of second order in \omega_{01}L/Z_i, but of third order if all impedances Z_i are pure resistances. We calculate T_{1,2} for an example of a SC flux qubit coupled to two impedances.Comment: 5 pages, 2 figure

Fluctuation-dissipation theorem and quantum tunneling with dissipation at finite temperature

A reformulation of the fluctuation-dissipation theorem of Callen and Welton is presented in such a manner that the basic idea of Feynman-Vernon and Caldeira -Leggett of using an infinite number of oscillators to simulate the dissipative medium is realized manifestly without actually introducing oscillators. If one assumes the existence of a well defined dissipative coefficient $R(\omega)$ which little depends on the temperature in the energy region we are interested in, the spontanous and induced emissions as well as induced absorption of these effective oscillators with correct Bose distribution automatically appears. Combined with a dispersion relation, we reproduce the tunneling formula in the presence of dissipation at finite temperature without referring to an explicit model Lagrangian. The fluctuation-dissipation theorem of Callen-Welton is also generalized to the fermionic dissipation (or fluctuation) which allows a transparent physical interpretation in terms of second quantized fermionic oscillators. This fermionic version of fluctuation-dissipation theorem may become relevant in the analyses of, for example, fermion radiation from a black hole and also supersymmetry at the early universe.Comment: 19 pages. Phys. Rev. E (in press

Theory of Two-Dimensional Josephson Arrays in a Resonant Cavity

We consider the dynamics of a two-dimensional array of underdamped Josephson junctions placed in a single-mode resonant cavity. Starting from a well-defined model Hamiltonian, which includes the effects of driving current and dissipative coupling to a heat bath, we write down the Heisenberg equations of motion for the variables of the Josephson junction and the cavity mode, extending our previous one-dimensional model. In the limit of large numbers of photons, these equations can be expressed as coupled differential equations and can be solved numerically. The numerical results show many features similar to experiment. These include (i) self-induced resonant steps (SIRS's) at voltages V = (n hbar Omega)/(2e), where Omega is the cavity frequency, and n is generally an integer; (ii) a threshold number N_c of active rows of junctions above which the array is coherent; and (iii) a time-averaged cavity energy which is quadratic in the number of active junctions, when the array is above threshold. Some differences between the observed and calculated threshold behavior are also observed in the simulations and discussed. In two dimensions, we find a conspicuous polarization effect: if the cavity mode is polarized perpendicular to the direction of current injection in a square array, it does not couple to the array and there is no power radiated into the cavity. We speculate that the perpendicular polarization would couple to the array, in the presence of magnetic-field-induced frustration. Finally, when the array is biased on a SIRS, then, for given junction parameters, the power radiated into the array is found to vary as the square of the number of active junctions, consistent with expectations for a coherent radiation.Comment: 11 pages, 8 eps figures, submitted to Phys. Rev

Dynamics of a Simple Quantum System in a Complex Environment

We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective stochastic models which emerge from random matrix theory. Using the Feynman-Vernon path integral formalism, we derive the influence functional and obtain either analytical or numerical solutions for the time evolution of the entire quantum system. We discuss thoroughly the structure of the solutions for some representative cases and make connections to well known limiting results, particularly to Brownian motion, Kramers classical limit and the Caldeira-Leggett approach.Comment: 41 pages and 12 figures in revte