'New' sources for the study of migration in early nineteenth-century Germany

Der Mangel an verläßlichen direkten Messungen über den Grad der Wanderungsbewegungen in Deutschland vor Ende des 19. Jahrhunderts haben zu ungestützten Verallgemeinerungen über Mobilitätsbewegungen vor der Industrialisierung geführt. Wir schreiben eine praktisch ungenutzte Quelle von demographischen Aufzeichnungen aus dem Regierungsbezirk Düsseldorf, die Wanderungsbewegungen auf der Gemeinde-Ebene zwischen 1812 und 1865 zusammenfaßt. Die Daten und ihre Sammlung werden beschrieben, ihre Genauigkeit wird einer Prüfung unterzogen und die bekannten Aufbewahrungsstellen aufgeführt. (KWübers.)'The lack of reliable direct measurements of migration in Germany before the late nineteenth century has led to unsupported generalizations about mobility trends before industrialization. We describe a virtually unused source of demographic records from the Regierungsbezirk Düsseldorf which aggregated yearly migrations at their collection are described, their accuracy is evaluated, and their known locations listed.' (author's abstract

Fermions on one or fewer Kinks

We find the full spectrum of fermion bound states on a Z_2 kink. In addition to the zero mode, there are int[2 m_f/m_s] bound states, where m_f is the fermion and m_s the scalar mass. We also study fermion modes on the background of a well-separated kink-antikink pair. Using a variational argument, we prove that there is at least one bound state in this background, and that the energy of this bound state goes to zero with increasing kink-antikink separation, 2L, and faster than e^{-a2L} where a = min(m_s, 2 m_f). By numerical evaluation, we find some of the low lying bound states explicitly.Comment: 7 pages, 4 figure

Reconstructing Jacobi Matrices from Three Spectra

Cut a Jacobi matrix into two pieces by removing the n-th column and n-th row. We give neccessary and sufficient conditions for the spectra of the original matrix plus the spectra of the two submatrices to uniqely determine the original matrix. Our result contains Hostadt's original result as a special case

Orthosymplectically invariant functions in superspace

The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically symmetric functions can be used to solve orthosymplectically invariant Schroedinger equations in superspace, such as the (an)harmonic oscillator or the Kepler problem. Finally the obtained machinery is used to prove the Funk-Hecke theorem and Bochner's relations in superspace.Comment: J. Math. Phy

Scattering and delay time for 1D asymmetric potentials: the step-linear and the step-exponential cases

We analyze the quantum-mechanical behavior of a system described by a one-dimensional asymmetric potential constituted by a step plus (i) a linear barrier or (ii) an exponential barrier. We solve the energy eigenvalue equation by means of the integral representation method, classifying the independent solutions as equivalence classes of homotopic paths in the complex plane. We discuss the structure of the bound states as function of the height U_0 of the step and we study the propagation of a sharp-peaked wave packet reflected by the barrier. For both the linear and the exponential barrier we provide an explicit formula for the delay time \tau(E) as a function of the peak energy E. We display the resonant behavior of \tau(E) at energies close to U_0. By analyzing the asymptotic behavior for large energies of the eigenfunctions of the continuous spectrum we also show that, as expected, \tau(E) approaches the classical value for E -> \infty, thus diverging for the step-linear case and vanishing for the step-exponential one.Comment: 14 pages, 10 figure

Spectroscopy of a Cooper-Pair box in the Autler-Townes configuration

A theoretical spectroscopic analysis of a microwave driven superconducting charge qubit (Cooper-pair box coupled) to an RLC oscillator model is performed. By treating the oscillator as a probe through the backreaction effect of the qubit on the oscillator circuit, we extract frequency splitting features analogous to the Autler-Townes effect from quantum optics, thereby extending the analogies between superconducting and quantum optical phenomenology. These features are found in a frequency band that avoids the need for high frequency measurement systems and therefore may be of use in qubit characterization and coupling schemes. In addition we find this frequency band can be adjusted to suit an experimental frequency regime by changing the oscillator frequency.Comment: 13 pages, 7 figures. v2: Revised version after referee comments. Accepted for publication by Physical Review

Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited

We derive expansions of the resolvent Rn(x;y;t)=(Qn(x;t)Pn(y;t)-Qn(y;t)Pn(x;t))/(x-y) of the Hermite kernel Kn at the edge of the spectrum of the finite n Gaussian Unitary Ensemble (GUEn) and the finite n expansion of Qn(x;t) and Pn(x;t). Using these large n expansions, we give another proof of the derivation of an Edgeworth type theorem for the largest eigenvalue distribution function of GUEn. We conclude with a brief discussion on the derivation of the probability distribution function of the corresponding largest eigenvalue in the Gaussian Orthogonal Ensemble (GOEn) and Gaussian Symplectic Ensembles (GSEn)

Spherical harmonics and integration in superspace

In this paper the classical theory of spherical harmonics in R^m is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic properties of polynomial null-solutions of this operator, a new type of integration over the supersphere is introduced by exploiting the formal equivalence with an old result of Pizzetti. This integral is then used to prove orthogonality of spherical harmonics of different degree, Green-like theorems and also an extension of the important Funk-Hecke theorem to superspace. Finally, this integration over the supersphere is used to define an integral over the whole superspace and it is proven that this is equivalent with the Berezin integral, thus providing a more sound definition of the Berezin integral.Comment: 22 pages, accepted for publication in J. Phys.

Necessary conditions for the emergence of homochirality via autocatalytic self-replication

We analyze a recent proposal for spontaneous mirror symmetry breaking based on the coupling of first-order enantioselective autocatalysis and direct production of the enantiomers that invokes a critical role for intrinsic reaction noise. For isolated systems, the racemic state is the unique stable outcome for both stochastic and deterministic dynamics when the system is in compliance with the constraints dictated by the thermodynamics of chemical reaction processes. In open systems, the racemic outcome also results for both stochastic and deterministic dynamics when driving the auto-catalysis unidirectionally by external reagents. Nonracemic states can result in the latter only if the reverse reactions are strictly zero: these are kinetically controlled outcomes for small populations and volumes, and can be simulated by stochastic dynamics. However, the stability of the thermodynamic limit proves that the racemic outcome is the unique stable state for strictly irreversible externally driven autocatalysis. These findings contradict the suggestion that the inhibition requirement of the Frank autocatalytic model for the emergence of homochirality may be relaxed in a noise-induced mechanism

The Coulomb phase shift revisited

We investigate the Coulomb phase shift, and derive and analyze new and more precise analytical formulae. We consider next to leading order terms to the Stirling approximation, and show that they are important at small values of the angular momentum $l$ and other regimes. We employ the uniform approximation. The use of our expressions in low energy scattering of charged particles is discussed and some comparisons are made with other approximation methods.Comment: 13 pages, 5 figures, 1 tabl