There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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.

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Many-Body Physics with Ultracold Gases

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Table Of Integrals Series And Products

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

This Colloquium examines the field of the Einstein, Podolsky, and Rosen (EPR) gedanken experiment, from the original paper of Einstein, Podolsky, and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. The relationship with entanglement and Bell's theorem are analyzed, and the progress to date towards experimental confirmation of the EPR paradox is summarized, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fiber quantum soliton experiments. Current proposals for extending EPR experiments to massive-particle systems are discussed, including spin squeezing, atomic position entanglement, and quadrature entanglement in ultracold atoms. Finally, applications of this technology to quantum key distribution, quantum teleportation, and entanglement swapping are examined.

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Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications

The capacity C of a communication channel is the maximum rate at which information can be transmitted without error from the channel's input to its output. The authors review quantum limits on the capacity that can be achieved with linear bosonic communication channels that have input power P. The limits arise ultimately from the Einstein relation that a field quantum at frequency f has energy E=hf. A single linear bosonic channel corresponds to a single transverse mode of the bosonic field i.e., to a particular spatial dependence in the plane orthogonal to the propagation direction and to a particular spin state or polarization. For a single channel the maximum communication rate is CWB=( ln 2)2P3h bits/s. This maximum rate can be achieved by a "number-state channel," in which information is encoded in the number of quanta in the bosonic field and in which this information is recovered at the output by counting quanta. Derivations of the optimum capacity CWB are reviewed. Until quite recently all derivations assumed, explicitly or implicitly, a number-state channel. They thus left open the possibility that other techniques for encoding information on the bosonic field, together with other ways of detecting the field at the output, might lead to a greater communication rate. The authors present their own general derivation of the single-channel capacity upper bound, which applies to any physically realizable technique for encoding information on the bosonic field and to any physically realizable detection scheme at the output. They also review the capacities of coherent communication channels that encode information in coherent states and in quadrature-squeezed states. A three-dimensional bosonic channel can employ many transverse modes as parallel single channels. An upper bound on the information flux that can be transferred down parallel bosonic channels is derived.

Quantum limits on bosonic communication rates

The squeezing spectrum for nondegenerate parametric oscillation above threshold is calculated, including phase diffusion. A nonclassical correlation in phase and intensity occurs which is an example of the Einstein-Podolsky-Rosen paradox, even in fields of large photon number.

Quantum correlations of phase in nondegenerate parametric oscillation.

Time reversed acoustics

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial stare for the condensate and compare results to those for single-mode models. [S1050-2947(98)06612-8].

/pdf/dynamical-quantum-noise-in-trapped-bose-einstein-condensates-nmg93pj18e.pdf

Peter D. Drummond

Papers

Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications

Quantum limits on bosonic communication rates

Quantum correlations of phase in nondegenerate parametric oscillation.

Time reversed acoustics

Dynamical quantum noise in trapped bose-einstein condensates