Why Study History? On Its Epistemic Benefits and Its Relation to the Sciences

I try to return the focus of the philosophy of history to the nature of understanding, with a particular emphasis on Louis Mink’s project of exploring how historical understanding compares to the understanding we find in the natural sciences. On the whole, I come to a conclusion that Mink almost certainly would not have liked: that the understanding offered by history has a very similar epistemic profile to the understanding offered by the sciences, a similarity that stems from the fact that both are concerned with grasping how the objects of their study are structured, or how the various elements of the things they study depend upon and relate to one another. At the same time, however, I claim that historical inquiry naturally puts us in a position to acquire further epistemic goods, including the old-fashioned epistemic good of wisdom, which is plausibly constituted by knowledge of how to live well. This is something the natural sciences cannot offer, and it is part of the reason why history is such an important form of inquiry

Zero curvature conditions and conformal covariance

Two-dimensional zero curvature conditions with special emphasis on conformal properties are investigated in detail and the appearance of covariant higher order differential operators constructed in terms of a projective connection is elucidated. The analysis is based on the Kostant decomposition of simple Lie algebras in terms of representations with respect to their ``principal'' SL(2) subalgebra. Journal of Mathematical Physics is copyrighted by The American Institute of Physics

Noncollinear magnetic order in quasicrystals

Based on Monte-Carlo simulations, the stable magnetization configurations of an antiferromagnet on a quasiperiodic tiling are derived theoretically. The exchange coupling is assumed to decrease exponentially with the distance between magnetic moments. It is demonstrated that the superposition of geometric frustration with the quasiperiodic ordering leads to a three-dimensional noncollinear antiferromagnetic spin structure. The structure can be divided into several ordered interpenetrating magnetic supertilings of different energy and characteristic wave vector. The number and the symmetry of subtilings depend on the quasiperiodic ordering of atoms.Comment: RevTeX, 4 pages, 5 low-resolution color figures (due to size restrictions); to appear in Physical Review Letter

Lx-SFR relation in star forming galaxies

We compare the results of Grimm et al. (2003) and Ranalli et al. (2003) on the Lx-SFR relation in normal galaxies. Based on the Lx-stellar mass dependence for LMXBs, we show, that low SFR (SFR<1 Msun/year) galaxies in the Ranalli et al. sample are contaminated by the X-ray emission from low mass X-ray binaries, unrelated to the current star formation activity. The most important conclusion from our comparison is, however, that after the data are corrected for the ``LMXB contamination'', the two datasets become consistent with each other, despite of their different content, variability effects, difference in the adopted source distances, X-ray flux and star formation rate determination and in the cosmological parameters used in interpreting the HDF-N data. They also agree well, both in the low and high SFR regimes, with the predicted Lx-SFR dependence derived from the parameters of the ``universal'' HMXB luminosity function. This encouraging result emphasizes the potential of the X-ray luminosity as an independent star formation rate indicator for normal galaxies.Comment: revised, accepted for publication in MNRAS Letter

Scale invariant thermodynamics of a toroidally trapped Bose gas

We consider a system of bosonic atoms in an axially symmetric harmonic trap augmented with a two dimensional repulsive Gaussian optical potential. We find an expression for the grand free energy of the system for configurations ranging from the harmonic trap to the toroidal regime. For large tori we identify an accessible regime where the ideal gas thermodynamics of the system are found to be independent of toroidal radius. This property is a consequence of an invariant extensive volume of the system that we identify analytically in the regime where the toroidal potential is radially harmonic. In considering corrections to the scale invariant transition temperature, we find that the first order interaction shift is the dominant effect in the thermodynamic limit, and is also scale invariant. We also consider adiabatic loading from the harmonic to toroidal trap configuration, which we show to have only a small effect on the condensate fraction of the ideal gas, indicating that loading into the scale invariant regime may be experimentally practical.Comment: 10 pages, 3 figures, to appear in Phys. Rev. A, typos corrected, references added, rewritten to emphasize generalized volume. Results unchange

Exciting a d-density wave in an optical lattice with driven tunneling

Quantum phases with unusual symmetries may play a key role for the understanding of solid state systems at low temperatures. We propose a realistic scenario, well in reach of present experimental techniques, which should permit to produce a stationary quantum state with $d_{x^2-y^2}$-symmetry in a two-dimensional bosonic optical square lattice. This state, characterized by alternating rotational flux in each plaquette, arises from driven tunneling implemented by a stimulated Raman scattering process. We discuss bosons in a square lattice, however, more complex systems involving other lattice geometries appear possible.Comment: 4 pages, 3 figure

Statistical properties of the combined emission of a population of discrete sources: astrophysical implications

We study the statistical properties of the combined emission of a population of discrete sources (e.g. X-ray emission of a galaxy due to its X-ray binaries population). Namely, we consider the dependence of their total luminosity L_tot=SUM(L_k) and of fractional rms_tot of their variability on the number of sources N or, equivalently, on the normalization of the luminosity function. We show that due to small number statistics a regime exists, in which L_tot grows non-linearly with N, in an apparent contradiction with the seemingly obvious prediction =integral(dN/dL*L*dL) ~ N. In this non-linear regime, the rms_tot decreases with N significantly more slowly than expected from the rms ~ 1/sqrt(N) averaging law. For example, for a power law luminosity function with a slope of a=3/2, in the non-linear regime, L_tot ~ N^2 and the rms_tot does not depend at all on the number of sources N. Only in the limit of N>>1 do these quantities behave as intuitively expected, L_tot ~ N and rms_tot ~ 1/sqrt(N). We give exact solutions and derive convenient analytical approximations for L_tot and rms_tot. Using the total X-ray luminosity of a galaxy due to its X-ray binary population as an example, we show that the Lx-SFR and Lx-M* relations predicted from the respective ``universal'' luminosity functions of high and low mass X-ray binaries are in a good agreement with observations. Although caused by small number statistics the non-linear regime in these examples extends as far as SFR<4-5 Msun/yr and log(M*/Msun)<10.0-10.5, respectively.Comment: MNRAS, accepted for publicatio

Spectrum of a duality-twisted Ising quantum chain

The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which becomes a symmetry of the model at the critical point. Thus, at the critical point, the Ising quantum chain with the duality-twisted boundary is translationally invariant, similar as in the case of the usual periodic or antiperiodic boundary conditions. The complete energy spectrum of the Ising quantum chain is calculated analytically for finite systems, and the conformal properties of the scaling limit are investigated. This provides an explicit example of a conformal twisted boundary condition and a corresponding generalised twisted partition function.Comment: LaTeX, 7 pages, using IOP style

A critical Ising model on the Labyrinth

A zero-field Ising model with ferromagnetic coupling constants on the so-called Labyrinth tiling is investigated. Alternatively, this can be regarded as an Ising model on a square lattice with a quasi-periodic distribution of up to eight different coupling constants. The duality transformation on this tiling is considered and the self-dual couplings are determined. Furthermore, we analyze the subclass of exactly solvable models in detail parametrizing the coupling constants in terms of four rapidity parameters. For those, the self-dual couplings correspond to the critical points which, as expected, belong to the Onsager universality class.Comment: 25 pages, 6 figure