Temperature dependent fluctuations in the two-dimensional XY model

We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite two-dimensional XY (2dXY) model. In the low temperature critical phase of this model, the PDF approaches a universal non-Gaussian limit distribution in the limit T-->0. Our analysis resolves the question of temperature dependence of the PDF in this regime, for which conflicting results have been reported. We show analytically that a weak temperature dependence results from the inclusion of multiple loop graphs in a previously-derived graphical expansion. This is confirmed by numerical simulations on two controlled approximations to the 2dXY model: the Harmonic and ``Harmonic XY'' models. The Harmonic model has no Kosterlitz-Thouless-Berezinskii (KTB) transition and the PDF becomes progressively less skewed with increasing temperature until it closely approximates a Gaussian function above T ~ 4\pi. Near to that temperature we find some evidence of a phase transition, although our observations appear to exclude a thermodynamic singularity.Comment: 15 pages, 5 figures and 1 tabl

Parameterizing the interstellar dust temperature

The temperature of interstellar dust particles is of great importance to astronomers. It plays a crucial role in the thermodynamics of interstellar clouds, because of the gas-dust collisional coupling. It is also a key parameter in astrochemical studies that governs the rate at which molecules form on dust. In 3D (magneto)hydrodynamic simulations often a simple expression for the dust temperature is adopted, because of computational constraints, while astrochemical modelers tend to keep the dust temperature constant over a large range of parameter space. Our aim is to provide an easy-to-use parametric expression for the dust temperature as a function of visual extinction ($A_{\rm V}$) and to shed light on the critical dependencies of the dust temperature on the grain composition. We obtain an expression for the dust temperature by semi-analytically solving the dust thermal balance for different types of grains and compare to a collection of recent observational measurements. We also explore the effect of ices on the dust temperature. Our results show that a mixed carbonaceous-silicate type dust with a high carbon volume fraction matches the observations best. We find that ice formation allows the dust to be warmer by up to 15% at high optical depths ($A_{\rm V}> 20$ mag) in the interstellar medium. Our parametric expression for the dust temperature is presented as $T_{\rm d} = \left[ 11 + 5.7\times \tanh\bigl( 0.61 - \log_{10}(A_{\rm V})\bigr) \right] \, \chi_{\rm uv}^{1/5.9}$, where $\chi_{\rm uv}$ is in units of the Draine (1978) UV fieldComment: 16 pages, 17 figures, 4 tables. Accepted for publication in A&A. Version 2: the omission of factor 0.921 in equation 4 is correcte

Finite temperature bosonization

Finite temperature properties of a non-Fermi liquid system is one of the most challenging probelms in current understanding of strongly correlated electron systems. The paradigmatic arena for studying non-Fermi liquids is in one dimension, where the concept of a Luttinger liquid has arisen. The existence of a critical point at zero temperature in one dimensional systems, and the fact that experiments are all undertaken at finite temperature, implies a need for these one dimensional systems to be examined at finite temperature. Accordingly, we extended the well-known bosonization method of one dimensional electron systems to finite temperatures. We have used this new bosonization method to calculate finite temperature asymptotic correlation functions for linear fermions, the Tomonaga-Luttinger model, and the Hubbard model.Comment: REVTex, 48 page

On the Second Law of thermodynamics and the piston problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio $m/M$ is a very small parameter, where $m$ is the mass of one particle of the gaz and $M$ is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.Comment: 29 pages, 9 figures submitted to Journal of Statistical Physics (2003

Laboratory and tentative interstellar detection of trans-methyl formate using the publicly available Green Bank Telescope PRIMOS survey

The rotational spectrum of the higher-energy trans conformational isomer of methyl formate has been assigned for the first time using several pulsed-jet Fourier transform microwave spectrometers in the 6-60 GHz frequency range. This species has also been sought toward the Sagittarius B2(N) molecular cloud using the publicly available PRIMOS survey from the Green Bank Telescope. We detect seven absorption features in the survey that coincide with laboratory transitions of trans-methyl formate, from which we derive a column density of 3.1 (+2.6, -1.2) \times 10^13 cm-2 and a rotational temperature of 7.6 \pm 1.5 K. This excitation temperature is significantly lower than that of the more stable cis conformer in the same source but is consistent with that of other complex molecular species recently detected in Sgr B2(N). The difference in the rotational temperatures of the two conformers suggests that they have different spatial distributions in this source. As the abundance of trans-methyl formate is far higher than would be expected if the cis and trans conformers are in thermodynamic equilibrium, processes that could preferentially form trans-methyl formate in this region are discussed. We also discuss measurements that could be performed to make this detection more certain. This manuscript demonstrates how publicly available broadband radio astronomical surveys of chemically rich molecular clouds can be used in conjunction with laboratory rotational spectroscopy to search for new molecules in the interstellar medium.Comment: 40 pages, 7 figures, 4 tables; accepted for publication in Ap

Calculating and visualizing the density of states for simple quantum mechanical systems

We present a graphical approach to understanding the degeneracy, density of states, and cumulative state number for some simple quantum systems. By taking advantage of basic computing operations, we define a straightforward procedure for determining the relationship between discrete quantum energy levels and the corresponding density of states and cumulative level number. The density of states for a particle in a rigid box of various shapes and dimensions is examined and graphed. It is seen that the dimension of the box, rather than its shape, is the most important feature. In addition, we look at the density of states for a multi-particle system of identical bosons built on the single-particle spectra of those boxes. A simple model is used to explain how the N-particle density of states arises from the single particle system it is based on

The abundance of C18O and HDO in the envelope and hot core of the intermediate mass protostar NGC 7129 FIRS 2

NGC 7129 FIRS 2 is a young intermediate-mass (IM) protostar, which is associated with two energetic bipolar outflows and displays clear signs of the presence of a hot core. It has been extensively observed with ground based telescopes and within the WISH Guaranteed Time Herschel Key Program. We present new observations of the C18O 3-2 and the HDO 3_{12}-2_{21} lines towards NGC 7129 FIRS 2. Combining these observations with Herschel data and modeling their emissions, we constrain the C18O and HDO abundance profiles across the protostellar envelope. In particular, we derive the abundance of C18O and HDO in the hot core. The intensities of the C18O lines are well reproduced assuming that the C18O abundance decreases through the protostellar envelope from the outer edge towards the centre until the point where the gas and dust reach the CO evaporation temperature (~20-25 K) where the C18O is released back to the gas phase. Once the C18O is released to the gas phase, the modelled C18O abundance is found to be ~1.6x10^{-8}, which is a factor of 10 lower than the reference abundance. This result is supported by the non-detection of C18O 9-8, which proves that even in the hot core (T_k>100 K) the CO abundance must be 10 times lower than the reference value. Several scenarios are discussed to explain this C18O deficiency. One possible explanation is that during the pre-stellar and protostellar phase, the CO is removed from the grain mantles by reactions to form more complex molecules. Our HDO modeling shows that the emission of HDO 3_{12}-2_{21} line is maser and comes from the hot core (T_k>100 K). Assuming the physical structure derived by Crimier et al. (2010), we determine a HDO abundance of ~0.4 - 1x10^{-7} in the hot core of this IM protostar, similar to that found in the hot corinos NGC 1333 IRAS 2A and IRAS 16293-2422.Comment: 10 pages, 7 figure

Introducing willingness-to-pay for noise changes into transport appraisal: an application of benefit transfer.

Numerous research studies have elicited willingness-to-pay values for transport-related noise, however, in many industrialised countries including the UK, noise costs and benefits are still not incorporated into appraisals for most transport projects and policy changes (Odgaard et al, 2005; Grant-Muller et al, 2001). This paper describes the actions recently taken in the UK to address this issue, comprising: primary research based on the city of Birmingham; an international review of willingness-to-pay evidence; development of values using benefit transfers over time and locations; and integration with appraisal methods. Amongst the main findings are: that the willingness-to-pay estimates derived for the UK are broadly comparable with those used in appraisal elsewhere in Europe; that there is a case for a lower threshold at 1 45dB(A)Leq,18hr1 rather than the more conventional 55dB(A); and that values per dB(A) increase with the noise level above this threshold. There are significant issues over the valuation of rail versus road noise, the neglect of non-residential noise and the valuation of high noise levels in different countries. Conclusions are drawn regarding the feasibility of noise valuation based on benefit transfers in the UK and elsewhere, and future research needs in this field are discussed