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

The notion of a quantum dynamical semigroup is defined using the concept of a completely positive map. An explicit form of a bounded generator of such a semigroup onB(ℋ) is derived. This is a quantum analogue of the Levy-Khinchin formula. As a result the general form of a large class of Markovian quantum-mechanical master equations is obtained.

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On the Generators of Quantum Dynamical Semigroups

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

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Decoherence, einselection, and the quantum origins of the classical

Preface. Part I: Gathering the Tools. 1. Introduction to Quantum Physics. 2. Quantum Tests. 3. Complex Vector Space. 4. Continuous Variables. Part II: Cryptodeterminism and Quantum Inseparability. 5. Composite Systems. 6. Bell's Theorem. 7. Contextuality. Part III: Quantum Dynamics and Information. 8. Spacetime Symmetries. 9. Information and Thermodynamics. 10. Semiclassical Methods. 11. Chaos and Irreversibility. 12. The Measuring Process. Author Index. Subject Index.

Quantum Theory: Concepts and Methods

The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2, 3). In order to reveal level repulsion under conditions of global classical chaos special care may be necessary: (i) subspectra referring to different values of the quantum numbers related to symmetries must be dealt with separately and (ii) for systems with quantum localization only levels whose wavefunctions have overlapping support must be admitted. A “level” may either be an energy eigenvalue E in the case of autonomous systems or, for periodically driven systems, a quasi-energy φ, i.e. an eigenphase of the unitary Floquet operator transporting the wavevector from period to period.

Quantum signatures of chaos

This paper deals with the dynamics of open systems (S) moving irreversibly under the influence of their surroundings (B). As a basis for the discussion of an open system S we use a complete microscopic description of the composite system S⊕B. By eliminating the coordinates of B we infer the behavior of S. The motivation for this investigation is that nature frequently confronts us with coupled systems S and B only one of which, say S, is of experimental relevance. It is then a dictate of economy to look for a “closed” description of the dynamics of S alone. Let us mention just three out of the countless examples.

Statistical treatment of open systems by generalized master equations

Strong damping and low-temperature anomalies for the harmonic oscillator.

Strong damping and low-temperature anomalies for the harmonic oscillator

Fully chaotic dynamics enjoy ergodicity and thus visit everywhere in the accessible space with uniform likeli- hood, over long periods of time. Even long periodic orbits bring about such uniform coverage. Moreover, classical ergodicity provides quantum chaos with universal char- acteristics. Given chaos, quantum energy levels are correlated within local few-level clusters but become statistically in- dependent as their distance grows much larger than the mean level spacing �. The decay of correlations on the scaleis empirically found system independent, within universality classes distinguished by presence or absence of time-reversal (T ) invariance (1, 2). The corresponding universal long-time characteristics act on the Heisenberg scale TH = 2π¯�, withPlanck's constant. Universal spectral fluctuations were conjectured as a manifestation of quantum chaos two decades ago (3). Now, the semiclassical core of a proof can be given. Based on Gutzwiller's periodic-orbit theory (4), our progress comes with two surprises: one lies in its simplicity, the other in the appearance of interesting mathematics (non- trivial properties of permutations). Moreover, the often disputed intimate relation between periodic orbits and quantum field theory is confirmed for good. We thus expect the underlying ideas to radiate beyond spectral fluctuations, like to transport and localization. Technically speaking, we want to show that each com- pletely hyberbolic classical dynamics has a quantum en- ergy spectrum with the same fluctuations as a random- matrix caricature HRMT of its Hamiltonian, even though that caricature has nothing in common with the Hamilto- nian but symmetry (absence or presence of T invariance). The theory of random matrices (RMT) (1, 2, 5), devel- oped by Wigner and Dyson to account for fluctuations in nuclear spectra yields analytic results for correlators of the level density ρ(E), by averaging over suitable ensem- bles of random matrices. Simplest is the two-point corre- lator ρ(E)ρ(E ' ) −ρ(E) ρ(E ' ), where the overlines denote ensemble average. Its Fourier transform with respect to the energy difference E − E ' , called spectral form factor K(τ), is predicted by RMT for systems without time re- versal invariance (unitary class) and with that symmetry (orthogonal class) as

Fritz Haake

Papers

Quantum signatures of chaos

Statistical treatment of open systems by generalized master equations

Strong damping and low-temperature anomalies for the harmonic oscillator.

Strong damping and low-temperature anomalies for the harmonic oscillator

Semiclassical Foundation of Universality in Quantum Chaos