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

This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

/pdf/many-body-physics-with-ultracold-gases-552s10zfdn.pdf

Many-Body Physics with Ultracold Gases

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary Dirac-Born-Infeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its T-duality, and Morita equivalence. We also discuss the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory.

https://iopscience.iop.org/article/10.1088/1126-6708/1999/09/032/pdf

String theory and noncommutative geometry

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Non-Abelian Anyons and Topological Quantum Computation

Anyons in an exactly solved model and beyond

We prove a limiting absorption principle for the standard model of non-relativistic quantum electrodynamics (QED) and for Nelson's model describing interactions of electrons with phonons. To this end, we use the spectral renormalization group technique on the continuous spectrum in conjunction with Mourre theory.

Spectral Renormalization Group and Local Decay in the Standard Model of Non-Relativistic Quantum Electrodynamics

Topological anomalies in the n dependence of the n-states Potts lattice gauge theory

The quantum theory of indirect measurements in physical systems is studied. The example of an indirect measurement of an observable represented by a self-adjoint operator $${\mathcal {N}}$$
 with finite spectrum is analyzed in detail. The Hamiltonian generating the time evolution of the system in the absence of direct measurements is assumed to be given by the sum of a term commuting with $${\mathcal {N}}$$
 and a small perturbation not commuting with $${\mathcal {N}}$$
 . The system is subject to repeated direct (projective) measurements using a single instrument whose action on the state of the system commutes with $${\mathcal {N}}$$
 . If the Hamiltonian commutes with the observable $${\mathcal {N}}$$
 (i.e., if the perturbation vanishes), the state of the system approaches an eigenstate of $${\mathcal {N}}$$
 , as the number of direct measurements tends to $$\infty $$
 . If the perturbation term in the Hamiltonian does not commute with $${\mathcal {N}}$$
 , the system exhibits “jumps” between different eigenstates of $${\mathcal {N}}$$
 . We determine the rate of these jumps to leading order in the strength of the perturbation and show that if time is rescaled appropriately a maximum likelihood estimate of $${\mathcal {N}}$$
 approaches a Markovian jump process on the spectrum of $${\mathcal {N}}$$
 , as the strength of the perturbation tends to 0.

Perturbation Theory for Weak Measurements in Quantum Mechanics, Systems with Finite-Dimensional State Space

A variety of problems in quantum physics and classical statistical mechanics, in particular the quantization of topological solitons and the statistical mechanics of defects in ordered media, are described. These problems can be studied within a semi-classical approximation, or with the help of low-temperature expansions, respectively. The calculation of the leading term in such expansions gives rise to variational problems for sections of vector bundles characterized by certain topological constraints. Examples of such problems are the quantization of kinks in the two-dimensional λϕ4-theory and the analysis of Bloch walls in a Landau-Ginzburg model of a threedimensional anisotropic ferromagnet. We state a general existence result for variational problems of this kind and develop regularity and decay estimates for solutions of the Landau-Ginzburg model describing Bloch walls with prescribed boundaries. For certain boundary configurations stability results are established. The relation between the minimizers of the Landau-Ginzburg model in a certain strong-coupling limit and minimal surfaces is pursued in some detail. An open question is whether, asymptotically, the stability of the limit (minimal) surface will imply the stability of the minimizers of the Landau-Ginzburg model.

/pdf/variational-problems-on-vector-bundles-3wxoerfl4m.pdf

Variational problems on vector bundles

We study a system consisting of a heavy quantum particle, called the tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density ${\to \infty}$). Our estimates allow us to interchange the thermodynamic with the mean-field limit.

Jürg Fröhlich

Papers

Spectral Renormalization Group and Local Decay in the Standard Model of Non-Relativistic Quantum Electrodynamics

Topological anomalies in the n dependence of the n-states Potts lattice gauge theory

Perturbation Theory for Weak Measurements in Quantum Mechanics, Systems with Finite-Dimensional State Space

Variational problems on vector bundles

Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas