On the intersection of free subgroups in free products of groups

Let (G_i | i in I) be a family of groups, let F be a free group, and let G = F *(*I G_i), the free product of F and all the G_i. Let FF denote the set of all finitely generated subgroups H of G which have the property that, for each g in G and each i in I, H \cap G_i^{g} = {1}. By the Kurosh Subgroup Theorem, every element of FF is a free group. For each free group H, the reduced rank of H is defined as r(H) = max{rank(H) -1, 0} in \naturals \cup {\infty} \subseteq [0,\infty]. To avoid the vacuous case, we make the additional assumption that FF contains a non-cyclic group, and we define sigma := sup{r(H\cap K)/(r(H)r(K)) : H, K in FF and r(H)r(K) \ne 0}, sigma in [1,\infty]. We are interested in precise bounds for sigma. In the special case where I is empty, Hanna Neumann proved that sigma in [1,2], and conjectured that sigma = 1; almost fifty years later, this interval has not been reduced. With the understanding that \infty/(\infty -2) = 1, we define theta := max{|L|/(|L|-2) : L is a subgroup of G and |L| > 2}, theta in [1,3]. Generalizing Hanna Neumann's theorem, we prove that sigma in [theta, 2 theta], and, moreover, sigma = 2 theta if G has 2-torsion. Since sigma is finite, FF is closed under finite intersections. Generalizing Hanna Neumann's conjecture, we conjecture that sigma = theta whenever G does not have 2-torsion.Comment: 28 pages, no figure

Proof of the Standard Quantum Limit for Monitoring Free-Mass Position

The measurement result of the moved distance for a free mass m during the time t between two position measurements cannot be predicted with uncertainty smaller than sqrt{hbar t/2m}. This is formulated as a standard quantum limit (SQL) and it has been proven to always hold for the following position measurement: a probe is set in a prescribed position before the measurement. Just after the interaction of the mass with the probe, the probe position is measured, and using this value, the measurement results of the pre-measurement and post-measurement positions are estimated.Comment: 4 pages, no figur

The Lueders Postulate and the Distinguishability of Observables

The Lueders postulate is reviewed and implications for the distinguishability of observables are discussed. As an example the distinguishability of two similar observables for spin-1/2 particles is described. Implementation issues are briefly analyzed.Comment: Submitted to the proceedings of ICFNCS, Hong Kong, 200

Properties of the first excited state of 9Be derived from (gamma,n) and (e,e') reactions

Properties of the first excited state of the nucleus 9Be are discussed based on recent (e,e') and (gamma,n) experiments. The parameters of an R-matrix analysis of different data sets are consistent with a resonance rather than a virtual state predicted by some model calculations. The energy and the width of the resonance are deduced. Their values are rather similar for all data sets, and the energy proves to be negative. It is argued that the disagreement between the extracted B(E1) values may stem from different ways of integration of the resonance. If corrected, fair agreement between the (e,e') and one of the (gamma,n) data sets is found. A recent (gamma,n) experiment at the HIgS facility exhibits larger cross sections close to the neutron threshold which remain to be explained.Comment: 5 pages, accepted fro publication in Phys. Rev.

Quantum Control Landscapes

Numerous lines of experimental, numerical and analytical evidence indicate that it is surprisingly easy to locate optimal controls steering quantum dynamical systems to desired objectives. This has enabled the control of complex quantum systems despite the expense of solving the Schrodinger equation in simulations and the complicating effects of environmental decoherence in the laboratory. Recent work indicates that this simplicity originates in universal properties of the solution sets to quantum control problems that are fundamentally different from their classical counterparts. Here, we review studies that aim to systematically characterize these properties, enabling the classification of quantum control mechanisms and the design of globally efficient quantum control algorithms.Comment: 45 pages, 15 figures; International Reviews in Physical Chemistry, Vol. 26, Iss. 4, pp. 671-735 (2007

Generation of pulse trains by current-controlled magnetic mirrors

The evolution of a spin-wave packet trapped between two direct current-carrying wires placed on the surface of a ferrite film is observed by Brillouin light scattering. The wires act as semi-transparent mirrors confining the packet. Because the spin-wave energy partially passes through these mirrors, trains of spin-wave packets are generated outside the trap. A numerical model of this process is presented and applied to the case when the current in the wires is dynamically controlled. This dynamical control of the mirror reflectivity provides new functionalities interesting for the field of spin-wave logic like that of a spin-wave memory cell.Comment: 4 pages, 3 figure

The Dynamics of Relief Spending and the Private Urban Labor Market During the New Deal

During the New Deal the Roosevelt Administration dramatically expanded relief spending to combat extraordinarily high rates of unemployment. We examine the dynamic relationships between relief spending and local private labor markets using a new panel data set of monthly relief, private employment and private earnings for major U.S. cities in the 1930s. Impulse response functions derived from a panel VAR model that controls for time and city fixed effects show that a work relief shock in period t-1 led to a decline in private employment and a rise in private monthly earnings. The finding offers evidence consistent with contemporary employers' complaints that work relief made it more difficult to hire, even though work relief officials followed their stated policies to avoid affecting private labor markets directly. Meanwhile, negative shocks to private employment led to increases in work relief, consistent with Roosevelt's stated goal of using relief to promote relief and recovery.

Reduction of Effective Terahertz Focal Spot Size By Means Of Nested Concentric Parabolic Reflectors

An ongoing limitation of terahertz spectroscopy is that the technique is generally limited to the study of relatively large samples of order 4 mm across due to the generally large size of the focal beam spot. We present a nested concentric parabolic reflector design which can reduce the terahertz focal spot size. This parabolic reflector design takes advantage of the feature that reflected rays experience a relative time delay which is the same for all paths. The increase in effective optical path for reflected light is equivalent to the aperture diameter itself. We have shown that the light throughput of an aperture of 2 mm can be increased by a factor 15 as compared to a regular aperture of the same size at low frequencies. This technique can potentially be used to reduce the focal spot size in terahertz spectroscopy and enable the study of smaller samples