A homomorphism theorem and a Trotter product formula for quantum stochastic flows with unbounded coefficients

We give a new method for proving the homomorphic property of a quantum stochastic ow satisfying a quantum stochastic differential equation with unbounded coefficients, under some further hypotheses. As an application, we prove a Trotter product formula for quantum stochastic ows and obtain quantum stochastic dilations of a class of quantum dynamical semigroups generalizing results of [5

On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg-picture dynamics of "observables", thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a "semi-classical" limit.Comment: Corrected typos and included an elementary proof of the Kato smoothing estimate (Lemma 6.1

X-ray measurement of residual stresses in laser surface melted Ti-6Al-4V alloy

In this paper, we report on the residual stresses in laser surface melted Ti-6Al-4V, determined using X-ray diffraction methods. The principal result is that there is an increase in the transverse residual stress with each successive, overlapping laser track. The result can be used to explain the observation of crack formation in overlapping tracks but not necessarily in single tracks produced under identical processing conditions.

Complexity of diatom response to Lateglacial and Holocene climate and environmental change in ancient, deep, and oligotrophic Lake Ohrid (Macedonia/Albania)

Lake Ohrid (Macedonia/Albania) is a rare example of a deep, ancient Mediterranean lake and is a key site for palaeoclimate research in the northeastern Mediterranean region. This study conducts the first high-resolution diatom analysis during the Lateglacial and Holocene in Lake Ohrid. It demonstrates a complex diatom response to temperature change, with a direct response to temperature-induced productivity and an indirect response to temperature-related stratification/mixing regime and epilimnetic nutrient availability. During the Lateglacial (ca. 12 300–11 800 cal yr BP), the low-diversity dominance of hypolimnetic Cyclotella fottii indicates low temperature-dependent lake productivity. During the earliest Holocene (ca. 11 800–10 600 cal yr BP), although the slight increase in small, epilimnetic C. minuscula suggests climate warming and enhanced thermal stratification, diatom concentration remains very low as during the Lateglacial, indicating that temperature increase was muted. The early Holocene (ca. 10 600–8200 cal yr BP) marked a sustained increase in epilimnetic taxa, with mesotrophic C. ocellata indicating high temperature-induced lake productivity between ca. 10 600–10 200 cal yr BP and between ca. 9500–8200 cal yr BP, and with C. minuscula in response to low nutrient availability in the epilimnion between ca. 10 200–9500 cal yr BP. During the mid Holocene (ca. 8200–2600 cal yr BP), when sedimentological and geochemical proxies provide evidence for high temperature, anomalously low C. ocellata abundance is probably a response to epilimnetic nutrient limitation, almost mimicking the Lateglacial flora apart from mesotrophic Stephanodiscus transylvanicus indicative of high temperature-induced productivity in the hypolimnion. During the late Holocene (ca. 2600–0 cal yr BP), high abundance and fluctuating composition of epilimnetic taxa is largely a response to enhanced anthropogenic nutrient input. In this deep, oligotrophic lake, this study demonstrates the strong influence of lake physical and chemical processes in mediating the complex response of diatoms to climate change with particular respect to temperature

On Blowup for time-dependent generalized Hartree-Fock equations

We prove finite-time blowup for spherically symmetric and negative energy solutions of Hartree-Fock and Hartree-Fock-Bogoliubov type equations, which describe the evolution of attractive fermionic systems (e. g. white dwarfs). Our main results are twofold: First, we extend the recent blowup result of [Hainzl and Schlein, Comm. Math. Phys. \textbf{287} (2009), 705--714] to Hartree-Fock equations with infinite rank solutions and a general class of Newtonian type interactions. Second, we show the existence of finite-time blowup for spherically symmetric solutions of a Hartree-Fock-Bogoliubov model, where an angular momentum cutoff is introduced. We also explain the key difficulties encountered in the full Hartree-Fock-Bogoliubov theory.Comment: 24 page

Complexity of diatom response to Lateglacial and Holocene climate and environmental change in ancient, deep and oligotrophic Lake Ohrid (Macedonia and Albania)

Lake Ohrid (Macedonia and Albania) is a rare example of a deep, ancient Mediterranean lake and is a key site for palaeoclimate research in the northeastern Mediterranean region. This study conducts the analysis of diatoms as a proxy for Lateglacial and Holocene climate and environmental change in Lake Ohrid at a higher resolution than in previous studies. While Lake Ohrid has the potential to be sensitive to water temperature change, the data demonstrate a highly complex diatom response, probably comprising a direct response to temperature-induced lake productivity in some phases and an indirect response to temperature-related lake stratification or mixing and epilimnetic nutrient availability in others. The data also demonstrate the possible influence of physical limnological (e.g. the influence of wind stress on stratification or mixing) and chemical processes (e.g. the influence of catchment dynamics on nutrient input) in mediating the complex response of diatoms. During the Lateglacial (ca. 12 300–11 800 cal yr BP), the low-diversity dominance of hypolimnetic Cyclotella fottii indicates low lake productivity, linked to low water temperature. Although the subsequent slight increase in small, epilimnetic C. minuscula during the earliest Holocene (ca. 11 800–10 600 cal yr BP) suggests climate warming and enhanced stratification, diatom concentration remains as low as during the Lateglacial, suggesting that water temperature increase was muted across this major transition. The early Holocene (ca. 10 600–8200 cal yr BP) is characterised by a sustained increase in epilimnetic taxa, with mesotrophic C. ocellata indicating high water-temperature-induced productivity between ca. 10 600–10 200 cal yr BP and between ca. 9500–8200 cal yr BP and with C. minuscula in response to low nutrient availability in the epilimnion between ca. 10 200–9500 cal yr BP. During the middle Holocene (ca. 8200–2600 cal yr BP), when sedimentological and geochemical proxies provide evidence for maximum Holocene water temperature, anomalously low C. ocellata abundance is probably a response to epilimnetic nutrient limitation, almost mimicking the Lateglacial flora apart from the occurrence of mesotrophic Stephanodiscus transylvanicus in the hypolimnion. During the late Holocene (ca. 2600 cal yr BP–present), high abundance and fluctuating composition of epilimnetic taxa are probably a response more to enhanced anthropogenic nutrient input, particularly nitrogen enrichment, than to climate. Overall, the data indicate that previous assumptions concerning the linearity of diatom response in this deep, ancient lake are invalid, and multi-proxy analysis is essential to improve understanding of palaeolimnological dynamics in future research on the long, Quaternary sequence

String Theory on Lorentzian AdS_3 in Minisuperspace

We investigate string theory on Lorentzian AdS_3 in the minisuperspace approximation. The minisuperspace model reduces to the worldline theory of a scalar particle in the Lorentzian AdS_3. The Hilbert space consists of normalizable wave functions, and we see that the unitarity of the theory (or the self-adjointness of the Hamiltonian) restricts the possible sets of wave functions. The restricted wave functions have the property of probability conservation (or current conservation) across the horizons. Two and three point functions are also computed. In the Euclidean model functional forms of these quantities are restricted by the SL(2,R) symmetry almost uniquely, however, in the Lorentzian model there are several ambiguities left. The ambiguities are fixed by the direct computation of overlaps of wave functions.Comment: 32 pages, no figures, minor changes, references adde

Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering

The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts by a Moyal-deformed multiplication with respect to the spatial variables. The Moyal-deformed multiplication corresponds to the product of the algebra of a Moyal plane described in the setting of spectral geometry. It will be explained how this leads to an interpretation of the Dirac field as a quantum field theory on Moyal-deformed Minkowski spacetime (with commutative time) in a setting of Lorentzian spectral geometries of which some basic aspects will be sketched. The scattering transformation will be shown to be unitarily implementable in the canonical vacuum representation of the Dirac field. Furthermore, it will be indicated how the functional derivatives of the ensuing unitary scattering operators with respect to the strength of the non-commutative potential induce, in the spirit of Bogoliubov's formula, quantum field operators (corresponding to observables) depending on the elements of the non-commutative algebra of Moyal-Minkowski spacetime.Comment: 60 pages, 1 figur

Local states of free bose fields

These notes contain an extended version of lectures given at the ``Summer School on Large Coulomb Systems'' in Nordfjordeid, Norway, in august 2003. They furnish a short introduction to the theory of quantum harmonic systems, or free bose fields. The main issue addressed is the one of local states. I will adopt the definition of Knight of ``strictly local excitation of the vacuum'' and will then state and prove a generalization of Knight's Theorem which asserts that finite particle states cannot be perfectly localized. It will furthermore be explained how Knight's a priori counterintuitive result can be readily understood if one remembers the analogy between finite and infinite dimensional harmonic systems alluded to above. I will also discuss the link between the above result and the so-called Newton-Wigner position operator thereby illuminating, I believe, the difficulties associated with the latter. I will in particular argue that those difficulties do not find their origin in special relativity or in any form of causality violation, as is usually claimed