Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

MuSR method and tomographic probability representation of spin states

Muon spin rotation/relaxation/resonance (MuSR) technique for studying matter structures is considered by means of a recently introduced probability representation of quantum spin states. A relation between experimental MuSR histograms and muon spin tomograms is established. Time evolution of muonium, anomalous muonium, and a muonium-like system is studied in the tomographic representation. Entanglement phenomenon of a bipartite muon-electron system is investigated via tomographic analogues of Bell number and positive partial transpose (PPT) criterion. Reconstruction of the muon-electron spin state as well as the total spin tomography of composed system is discussed.Comment: 20 pages, 4 figures, LaTeX, submitted to Journal of Russian Laser Researc

Measurement of the 1s-2s energy interval in muonium

The 1s-2s interval has been measured in the muonium ({$\mu^+e^-$}) atom by Doppler-free two-photon laser spectroscopy. The frequency separation of the states was determined to be 2 455 528 941.0(9.8)~MHz in good agreement with quantum electrodynamics. The muon-electron mass ratio can be extracted and is found to be 206.768 38(17). The result may be interpreted as measurement of the muon-electron charge ratio as $-1- 1.1(2.1)\cdot 10^{-9}$

Remotely induced magnetism in a normal metal using a superconducting spin-valve

Superconducting spintronics has emerged in the past decade as a promising new field that seeks to open a new dimension for nanoelectronics by utilizing the internal spin structure of the superconducting Cooper pair as a new degree of freedom1, 2. Its basic building blocks are spin-triplet Cooper pairs with equally aligned spins, which are promoted by proximity of a conventional superconductor to a ferromagnetic material with inhomogeneous macroscopic magnetization3. Using low-energy muon spin-rotation experiments we find an unanticipated effect, in contradiction with the existing theoretical models of superconductivity and ferromagnetism: the appearance of a magnetization in a thin layer of a non-magnetic metal (gold), separated from a ferromagnetic double layer by a 50-nm-thick superconducting layer of Nb. The effect can be controlled either by temperature or by using a magnetic field to control the state of the remote ferromagnetic elements, and may act as a basic building block for a new generation of quantum interference devices based on the spin of a Cooper pair

A solid state laser system for Doppler-free spectroscopy of muonium

to 1MHz, was found to be of the order of 80-120 MHz for a 30-40 mJ output. This chirp was shown to be the result of a fast change of the refractive index in the alexandrite rods, and was found to be directly proportional to the population inversion change during the Q-switched pulse. A method of chirp compensation was developed leading to a reduction of the chirp by an order of magnitude i.e. to the level of 5-15 MHz. The alexandrite output was frequency tripled using LBO and BBO crystals with a conversion efficiency in excess of 10 %, yielding UV pulse energies of 3 to 6 mJ. The 1S-2S transition frequency has been measured to be 2,455,528,940.99 (9.75)(3.5) MHz which is in agreement with the theoretical value of 2,455,528,934.61 (3.44) MHz. Measurement of 1S-2S interval in deuterium, performed primarily to study systematic errors, represents the best pulsed measurement to date and is in an agreement with values obtained with cw lasers. The thesis describes a new high precision measurement of the 1S-2S transition frequency in muonium, carried out at the ISIS facility at the Rutherford Appleton Laboratory, using a solid-state laser system. The focus of the thesis is mainly the work carried out on the pulsed part of the laser system. The transition frequency is measured by the Doppler-free spectroscopy. The two-photon 1S-2S transition is detected by observing the positive muon released after subsequent photo-ionisation from the 2S state by a third photon from the same laser field. An accurate frequency standard for the experiment was provided by a Doppler-free transition in molecular iodine. A cw Ti:sapphire laser operating around 732 nm locked to this reference transition provided a stable output for injection seeding the pulsed alexandrite laser. This has been optimised and modified to achieve a stable operation in a single transverse and longitudinal mode. There were stringent requirements on the laser pulse timing relative to an external trigger in order to synchronise the laser pulse with the muon pulse from the ISIS facility. A method of cavity length stabilisation, which reduced the jitter of the laser from approximately 20 mu s to 100ns and allowed us to trigger the laser externally, is described. This was performed in two stages using an intracavity, piezo-mounted, quartz plate and two fast, electro-optic modulators. The frequency chirp of the laser output, measured using a heterodyne techniqu