245 research outputs found

### '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

### 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

### 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

### 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.

### 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

### Uniqueness of the potential function for the vectorial Sturm-Liouville equation on a finite interval

[[abstract]]In this paper, the vectorial Sturm-Liouville operator L Q =−d 2 dx 2 +Q(x) is considered, where Q(x) is an integrable m×m matrix-valued function defined on the interval [0,π] . The authors prove that m 2 +1 characteristic functions can determine the potential function of a vectorial Sturm-Liouville operator uniquely. In particular, if Q(x) is real symmetric, then m(m+1) 2 +1 characteristic functions can determine the potential function uniquely. Moreover, if only the spectral data of self-adjoint problems are considered, then m 2 +1 spectral data can determine Q(x) uniquely.[[notice]]補正完畢[[incitationindex]]SCI[[cooperationtype]]國外[[booktype]]電子

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