Classification of linear differential operators with an invariant subspace of monomials

A complete classification of linear differential operators possessing finite-dimensional invariant subspace with a basis of monomials is presented.Comment: 10 p

Group Identity and Discrimination in Small Markets: Asymmetry of In-Group Favors

We experimentally study the inuence of induced group identity on the determination of prices and beliefs in a small market game. We create group identity through a focal point coordination game. Subjects play a three-person bargaining game where one seller can sell an indivisible good to one of two competing buyers under four different treatments varying the buyer-seller constellation. We find evidence of in group favoritism on the buyer side. However we do not detect a lower ask prices for in-group sellers for in-group buyers, indicating that in-group favoritism is in favor of the more powerful market participant.Group identity, Experiments, Markets, Bargaining

Ceteris Paribus Laws

Laws of nature take center stage in philosophy of science. Laws are usually believed to stand in a tight conceptual relation to many important key concepts such as causation, explanation, confirmation, determinism, counterfactuals etc. Traditionally, philosophers of science have focused on physical laws, which were taken to be at least true, universal statements that support counterfactual claims. But, although this claim about laws might be true with respect to physics, laws in the special sciences (such as biology, psychology, economics etc.) appear to have—maybe not surprisingly—different features than the laws of physics. Special science laws—for instance, the economic law “Under the condition of perfect competition, an increase of demand of a commodity leads to an increase of price, given that the quantity of the supplied commodity remains constant” and, in biology, Mendel's Laws—are usually taken to “have exceptions”, to be “non-universal” or “to be ceteris paribus laws”. How and whether the laws of physics and the laws of the special sciences differ is one of the crucial questions motivating the debate on ceteris paribus laws. Another major, controversial question concerns the determination of the precise meaning of “ceteris paribus”. Philosophers have attempted to explicate the meaning of ceteris paribus clauses in different ways. The question of meaning is connected to the problem of empirical content, i.e., the question whether ceteris paribus laws have non-trivial and empirically testable content. Since many philosophers have argued that ceteris paribus laws lack empirically testable content, this problem constitutes a major challenge to a theory of ceteris paribus laws

The Kernel Polynomial Method

Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of Chebyshev expansion based algorithms and the Kernel Polynomial Method. Characterized by a resource consumption that scales linearly with the problem dimension these methods enjoyed growing popularity over the last decade and found broad application not only in physics. Representative examples from the fields of disordered systems, strongly correlated electrons, electron-phonon interaction, and quantum spin systems we discuss in detail. In addition, we illustrate how the Kernel Polynomial Method is successfully embedded into other numerical techniques, such as Cluster Perturbation Theory or Monte Carlo simulation.Comment: 32 pages, 17 figs; revised versio

Fast, precise, and widely tunable frequency control of an optical parametric oscillator referenced to a frequency comb

Optical frequency combs (OFC) provide a convenient reference for the frequency stabilization of continuous-wave lasers. We demonstrate a frequency control method relying on tracking over a wide range and stabilizing the beat note between the laser and the OFC. The approach combines fast frequency ramps on a millisecond timescale in the entire mode-hop free tuning range of the laser and precise stabilization to single frequencies. We apply it to a commercially available optical parametric oscillator (OPO) and demonstrate tuning over more than 60 GHz with a ramping speed up to 3 GHz/ms. Frequency ramps spanning 15 GHz are performed in less than 10 ms, with the OPO instantly relocked to the OFC after the ramp at any desired frequency. The developed control hardware and software is able to stabilize the OPO to sub-MHz precision and to perform sequences of fast frequency ramps automatically.Comment: 8 pages, 7 figures, accepted for publication in Review of Scientific Instrument

Delbrück scattering in a strong external field

We evaluate the Delbrück scattering amplitude to all orders of the interaction with the external field of a nucleus employing nonperturbative electron Green's functions. The results are given analytically in form of a multipole expansion