Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

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Methods Of Modern Mathematical Physics

We prove the uniqueness and non-degeneracy of positive solutions to a cubic nonlinear Schrodinger (NLS) type equation that describes nucleons. The main difficulty stems from the fact that the mass depends on the solution itself. As an application, we construct solutions to the ${\sigma}$–${\omega}$ model, which consists of one Dirac equation coupled to two Klein–Gordon equations (one focusing and one defocusing).

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Uniqueness and non-degeneracy for a nuclear nonlinear Schrödinger equation

The method of choice for describing attractive quantum systems is Hartree-Fock-Bogoliubov (HFB) theory. This is a nonlinear model which allows for the description of pairing effects, the main explanation for the superconductivity of certain materials at very low temperature. This paper is the first study of Hartree-Fock-Bogoliubov theory from the point of view of numerical analysis. We start by discussing its proper discretization and then analyze the convergence of the simple fixed point (Roothaan) algorithm. Following works by Canc\`es, Le Bris and Levitt for electrons in atoms and molecules, we show that this algorithm either converges to a solution of the equation, or oscillates between two states, none of them being a solution to the HFB equations. We also adapt the Optimal Damping Algorithm of Canc\`es and Le Bris to the HFB setting and we analyze it. The last part of the paper is devoted to numerical experiments. We consider a purely gravitational system and numerically discover that pairing always occurs. We then examine a simplified model for nucleons, with an effective interaction similar to what is often used in nuclear physics. In both cases we discuss the importance of using a damping algorithm.

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A Numerical Perspective on Hartree-Fock-Bogoliubov Theory

We consider the nonlinear Hartree equation for an interacting gas containing infinitely many particles and we investigate the large-time stability of the stationary states of the form $f(-\Delta)$, describing an homogeneous Fermi gas. Under suitable assumptions on the interaction potential and on the momentum distribution $f$, we prove that the stationary state is asymptotically stable in dimension 2. More precisely, for any initial datum which is a small perturbation of $f(-\Delta)$ in a Schatten space, the system weakly converges to the stationary state for large times.

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The Hartree equation for infinitely many particles. II. Dispersion and scattering in 2D

We summarize recent results on positive temperature equilibrium states of large bosonic systems. The emphasis will be on the connection between bosonic grand-canonical thermal states and the (semi-) classical Gibbs measures on one-body quantum states built using the corresponding mean-field energy functionals. An illustrative comparison with the case of distinguishable " particles (boltzons) is provided."

Bose gases at positive temperature and non-linear gibbs measures

Consider an electron moving in the Coulomb potential −μ∗|x|−1−μ∗|x|−1 generated by any non-negative finite measure μμ. It is well known that the lowest eigenvalue of the corresponding Schrodinger operator −Δ/2−μ∗|x|−1−Δ/2−μ∗|x|−1 is minimized, at fixed mass μ(R3)=νμ(R3)=ν, when μμ is proportional to a delta. In this paper we investigate the conjecture that the same holds for the Dirac operator −iα⋅∇+β−μ∗|x|−1−iα⋅∇+β−μ∗|x|−1. In a previous work on the subject we proved that this operator is well defined and that its eigenvalues are given by min-max formulas. Here we show that there exists a critical number ν1ν1 below which the lowest eigenvalue does not dive into the lower continuum spectrum, for all μ≥0μ≥0 with μ(R3)<ν1μ(R3)<ν1. Our main result is that for all 0≤ν<ν10≤ν<ν1, there exists an optimal measure μ≥0 μ≥0 giving the lowest possible eigenvalue at fixed mass μ(R3)=νμ(R3)=ν, which concentrates on a compact set of Lebesgue measure zero. The last property is shown using a new unique continuation principle for Dirac operators.

Mathieu Lewin

Papers

Uniqueness and non-degeneracy for a nuclear nonlinear Schrödinger equation

A Numerical Perspective on Hartree-Fock-Bogoliubov Theory

The Hartree equation for infinitely many particles. II. Dispersion and scattering in 2D

Bose gases at positive temperature and non-linear gibbs measures

Dirac–Coulomb operators with general charge distribution II. The lowest eigenvalue