Supremum distribution of Bessel process of drifting Brownian motion

Let (B^{(1)}_t ;B^{(2)}_t ;B^{(3)}_t + \mu t) be a three-dimensional Brownian motion with drift \mu, starting at the origin. Then X_t = ||(B^{(1)}_t ;B^{(2)}_t ;B^{(3)}_t +\mu t)||, its distance from the starting point, is a diffusion with many applications. We investigate the distribution of the supremum of (X_t), give an infinite-series formula for its density and an exact estimate by elementary functions

Spin susceptibility of two-dimensional electron systems

A quantum computer, in contrast to traditional computers based on transistors, is a device that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform computation. One of possible realizations is a so-called spin-qubit quantum computer which uses the intrinsic spin degree of freedom of an electron confined to a quantum dot as a qubit (a unit of quantum information that can be in a linear superposition of the basis states). Electron spins in semiconductor quantum dots, e.g., in GaAs, are inevitably coupled via hyperfine interaction to the surrounding environment of nuclear spins. This coupling results in decoherence, which is the process leading to the loss of information stored in a qubit. Spontaneous polarization of nuclear spins should suppress decoherence in single-electron spin qubits and ultimately facilitate quantum computing in these systems. The main focus of this thesis is to study nonanalytic properties of electron spin susceptibility, which was shown to effectively describe the coupling strength between nuclear spins embedded in a two dimensional electron gas (2DEG), and give detailed insights into the issue of spontaneous polarization of nuclear spins. In the first part we consider the effect of rescattering of pairs of quasiparticles in the Cooper channel resulting in the strong renormalization of second-order corrections to the spin susceptibility in a 2DEG. We use the Fourier expansion of the scattering potential in the vicinity of the Fermi surface to find that each harmonic becomes renormalized independently. Since some of those harmonics are negative, the first derivative of the spin susceptibility is bound to be negative at small momenta, in contrast to the lowest order perturbation theory result, which predicts a positive slope. We present in detail an effective method to calculate diagrammatically corrections to the spin susceptibility to infinite order. The second part deals with the effect of the Rashba spin-orbit interaction (SOI) on the nonanalytic behavior of the spin susceptibility for a two-dimensional electron liquid. A long-range interaction via virtual particle-hole pairs between Fermi-liquid quasiparticles leads to the nonanalytic behavior of the spin susceptibility as a function of the temperature, magnetic field, and wavenumber . Although the SOI breaks the SU(2) symmetry, it does not eliminate nonanalyticity but rather makes it anisotropic: while the linear scaling of the out-of-plane spin susceptibility with temperature and the magnetic field saturates at the energy scale set by the SOI, that of the in-plane spin susceptibility continues through this energy scale, until renormalization of the electron-electron interaction in the Cooper channel becomes important. We show that the Renormalization Group flow in the Cooper channel has a non-trivial fixed point, and study the consequences of this fixed point for the nonanalytic behavior of the spin susceptibility. In the third part we analyze the ordered state of nuclear spins embedded in an interacting 2DEG with Rashba SOI. Stability of the ferromagnetic nuclear-spin phase is governed by nonanalytic dependences of the electron spin susceptibility tensor on the momentum and on the SOI coupling constant. The uniform (zero-momentum) spin susceptibility is anisotropic (with the out-of-plane component being larger than the in-plane one by a term proportional to the SOI coupling to second order in electron-electron interaction). For momenta larger than the SOI coupling, corrections to the leading, linear-in-SOI-coupling term scale linearly with momentum for the in-plane component and are absent for the out-of plane component of the spin susceptibility. This anisotropy has important consequences for the ferromagnetic nuclear-spin phase: (i) the ordered state, if achieved, is of an Ising type and (ii) the spin-wave dispersion is gapped at the vanishing momentum. To second order in electron-electron interaction, the dispersion is a decreasing function of the momentum, and the anisotropy is not sufficient to stabilize long-range order. However, we show that renormalization in the Cooper channel for momenta much larger than the SOI coupling is capable of reversing the sign of the momentum-dependence of the in-plane spin susceptibility and thus stabilizing the ordered state, if the system is sufficiently close to (but not necessarily in the immediate vicinity of) the Kohn-Luttinger instability

Quantum Computing with Electron Spins in Quantum Dots

Several topics on the implementation of spin qubits in quantum dots are reviewed. We first provide an introduction to the standard model of quantum computing and the basic criteria for its realization. Other alternative formulations such as measurement-based and adiabatic quantum computing are briefly discussed. We then focus on spin qubits in single and double GaAs electron quantum dots and review recent experimental achievements with respect to initialization, coherent manipulation and readout of the spin states. We extensively discuss the problem of decoherence in this system, with particular emphasis on its theoretical treatment and possible ways to overcome it.Comment: Lecture notes for Course CLXXI "Quantum Coherence in Solid State Systems" Int. School of Physics "Enrico Fermi", Varenna, July 2008, 61 pages, 20 figure

O pewnym szczególe z wilamowskiej fonetyki – próba analizy w kontekście arealnym

On a Certain Phonetic Feature of Wymysorys: An Analysis of Areal AspectsIn Wymysorys, also known as Vilamovicean (a Germanic language spoken in Wilamowice, a small town in the south of Poland), velarized laterals [ɫ] have turned into [w]. This shift is characteristic of some Polish and German dialects, although in the latter it only occurs under certain conditions. Since Wymysorys displays a strong influence of Polish in many other respects, this change is more likely to have stemmed from contact with Polish. O pewnym szczególe z wilamowskiej fonetyki – próba analizy w kontekście arealnymW wilamowskim welaryzowane [ɫ] (kontynuant średnio-wysoko-niemieckiego l) przeszło w glajd [w]. Zmiana ta charakterystyczna jest dla różnych języków Europy, w tym dla polszczyzny i niektórych dialektów niemieckich (w tych ostatnich jednak zachodzi jedynie w pewnych warunkach). Silny wpływ polskiego na wilamowski (obserwowany nie tylko w fonetyce) uprawnia do stwierdzenia, iż omawiana zmiana jest wynikiem oddziaływania polszczyzny i dokonała się w ostatnim pokoleniu użytkowników wilamowszczyzny

Hamilton-chain saturated hypergraphs

AbstractWe say that a hypergraph H is hamiltonian path (cycle) saturated if H does not contain an open (closed) hamiltonian chain but by adding any new edge we create an open (closed) hamiltonian chain in H. In this paper we ask about the smallest size of an r-uniform hamiltonian path (cycle) saturated hypergraph, mainly for r=3. We present a construction of a family of 3-uniform path (cycle) saturated hamiltonian hypergraphs with O(n5/2) edges. On the other hand we prove that the number of edges in an r-uniform hamiltonian path (cycle) saturated hypergraph is at least Ω(nr−1)

Importance of Atomic Composition and Moisture Content of Cement based Composites in Neutron Radiation Shielding

AbstractMonte Carlo computer simulations confirmed that an increase in density has a minor effect on the weakening of neutron transport and, therefore, the optimum composition of a shielding concrete against gamma radiation is different than the one against neutron radiation. Neutron radiation shielding is a two-step process: slowing down of fast neutrons and absorption of thermal ones. Both result from the atomic composition of the barrier but their dependence on specified atomic compositions and moisture content is different. The aim of the presented research is to develop a high density concrete the composition of which would also assure good efficiency of neutron shielding. Neutron transport through standard cement mortar, PCC mortar, normal-weight concrete and magnetite heavy-weight concrete has been analyzed in the paper. The goal in research was to find an influence of the cement type, polymer addition, density and moisture content on the shielding properties against neutron. The research based on convergent results of MC computer simulations and real experiments confirmed the influence of the cement type on fast neutron attenuation. It was also found that each 1% of moisture content makes 10% increase of fast neutron thermalization effectiveness, what is a little less than it was estimated for cement based mortars. It was also proved that heavy-weight concrete is not proper solution for shielding against fast neutrons, but its efficiency is visible in the case of thermal neutrons absorption, probably due to increase of Fe content at the expense of Si and O in the atomic composition as well as water retained by magnetite aggregate

Coulomb Blockade of a Three-terminal Quantum Dot

We study an interacting single-level quantum dot weakly coupled to three electrodes. When two electrodes are biased by voltages with opposite polarities, while keeping the third lead (the stem) grounded, the current through the stem is a measure of electron-hole asymmetry of the dot. In this setup we calculate the stem current for both metallic and ferromagnetic (collinearly polarized) leads and discuss how the three-terminal device gives additional information compared to the usual two-terminal setup. We calculate both the sequential and cotunneling contribution for the currents. For the latter part we include a regularization procedure for the cotunneling current, which enables us to also describe the behavior at the charge degeneracy points.Comment: 9 pages, 7 figure

Evaluation of individual absolute fracture risk in obese perimenopausal women

Powszechnie uznaje się, że większa masa ciała wiąże się z większą gęstością mineralną kości oraz zmniejszonym tempem ubytku masy kostnej. Z drugiej strony, pojawiają się prace, w których autorzy donoszą, że nadmiar tkanki tłuszczowej nie wykazuje ochronnego wpływu na ubytek masy kostnej. Ponieważ wyniki dostępnych badań są rozbieżne i nie pozwalają na jednoznaczne wnioskowanie co do wpływu otyłości na tkankę kostną, autorzy pracy zdecydowali się ocenić 10-letnie bezwzględne ryzyko złamania u otyłych kobiet w wieku okołomenopauzalnym. Badaniem objęto grupę 60 otyłych kobiet. Grupę kontrolną stanowiło 15 zdrowych kobiet w porównywalnym wieku. Badanie gęstości mineralnej kości w obrębie szyjki kości udowej oraz odcinka lędźwiowego kręgosłupa wykonano metodą absorpcjometrii podwójnej energii promieniowania rentgenowskiego przy użyciu aparatu Lunar DPXL. Dziesięcioletnie bezwzględne ryzyko złamania obliczono zgodnie z zaleceniami Światowej Organizacji Zdrowia/ Polskiej Fundacji Osteoporozy. Otyłe kobiety charakteryzowały się większą gęstością mineralną kości w obrębie szyjki kości udowej oraz odcinka lędźwiowego kręgosłupa oraz mniejszym10-letnim bezwzględnym ryzykiem złamania w porównaniu z kobietami z prawidłową masą ciała.It is widely known that an elevated body weight correlates with increased bone mass and a lower rate of bone loss. However, some authors have suggested that excessive fat mass may not protect against a decrease in bone mass. As results of recent studies have diverged, and it is still unclear whether or not obesity has a beneficial effect on bone, we decided to evaluate the individual absolute fracture risk in obese perimenopausal women. Sixty obese perimenopausal women were enrolled into the study. The control group consisted of 15 healthy women of comparable age. Dual energy X-ray absorptiometry (DXA) of the lumbar spine and femoral neck to measure bone mineral density (BMD) was performed using the Lunar DPXL apparatus. Absolute 10-year fracture risk was calculated as a multiplication of relative risk, according to the guidelines of the WHO/Polish Foundation of Osteoporosis. Obese women have significantly a higher BMD both of the lumbar spine and the femoral neck and a significantly lower 10-year absolute fracture risk in comparison to healthy controls