Analysis of the A~−X~\tilde{A}-\tilde{X} bands of the Ethynyl Radical near 1.48μ\mum and Re-evaluation of X~\tilde{X} State Energies

We report the observation and analysis of spectra in part of the near-infrared spectrum of C$_2$H, originating in rotational levels in the ground and lowest two excited bending vibrational levels of the ground $\tilde{X}\,^2\Sigma^+$ state. In the analysis, we have combined present and previously reported high resolution spectroscopic data for the lower levels involved in the transitions to determine significantly improved molecular constants to describe the fine and hyperfine split rotational levels of the radical in the zero point, $v_2=1$ and the $^2\Sigma^+$ component of $v_2=2$. Two of the upper state vibronic levels involved had not been observed previously. The data and analysis indicate the electronic wavefunction character changes with bending vibrational excitation in the ground state and provide avenues for future measurements of reactivity of the radical as a function of vibrational excitation.Comment: 16 pages including references, 2 figures and 2 table

How important is the credit channel? An empirical study of the US banking crisis

We examine whether by adding a credit channel to the standard New Keynesian model we can account better for the behaviour of US macroeconomic data up to and including the banking crisis. We use the method of indirect inference which evaluates statistically how far a model's simulated behaviour mimics the behaviour of the data. We find that the model with credit dominates the standard model by a substantial margin. Credit shocks are the main contributor to the variation in the output gap during the crisis

High-precision simulation of the height distribution for the KPZ equation

The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as 10^{-1000} in the tails. Both short and long times are investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations. At short times the agreement with the analytical expression is spectacular. We observe that the far left and right tails, with exponents 5/2 and 3/2 respectively, are preserved until large time. We present some evidence for the predicted non-trivial crossover in the left tail from the 5/2 tail exponent to the cubic tail of Tracy-Widom, although the details of the full scaling form remains beyond reach.Comment: 6 pages, 5 figure

Non-crossing Brownian paths and Dyson Brownian motion under a moving boundary

We compute analytically the probability $S(t)$ that a set of $N$ Brownian paths do not cross each other and stay below a moving boundary $g(\tau)= W \sqrt{\tau}$ up to time $t$. We show that for large $t$ it decays as a power law $S(t) \sim t^{- \beta(N,W)}$. The decay exponent $\beta(N,W)$ is obtained as the ground state energy of a quantum system of $N$ non-interacting fermions in a harmonic well in the presence of an infinite hard wall at position $W$. Explicit expressions for $\beta(N,W)$ are obtained in various limits of $N$ and $W$, in particular for large $N$ and large $W$. We obtain the joint distribution of the positions of the walkers in the presence of the moving barrier $g(\tau) =W \sqrt{\tau}$ at large time. We extend our results to the case of $N$ Dyson Brownian motions (corresponding to the Gaussian Unitary Ensemble) in the presence of the same moving boundary $g(\tau)=W\sqrt{\tau}$. For $W=0$ we show that the system provides a realization of a Laguerre biorthogonal ensemble in random matrix theory. We obtain explicitly the average density near the barrier, as well as in the bulk far away from the barrier. Finally we apply our results to $N$ non-crossing Brownian bridges on the interval $[0,T]$ under a time-dependent barrier $g_B(\tau)= W \sqrt{\tau(1- \frac{\tau}{T})}$.Comment: 44 pages, 13 figure

Wigner function of noninteracting trapped fermions

We study analytically the Wigner function $W_N({\bf x},{\bf p})$ of $N$ noninteracting fermions trapped in a smooth confining potential $V({\bf x})$ in $d$ dimensions. At zero temperature, $W_N({\bf x},{\bf p})$ is constant over a finite support in the phase space $({\bf x},{\bf p})$ and vanishes outside. Near the edge of this support, we find a universal scaling behavior of $W_N({\bf x},{\bf p})$ for large $N$. The associated scaling function is independent of the precise shape of the potential as well as the spatial dimension $d$. We further generalize our results to finite temperature $T>0$. We show that there exists a low temperature regime $T \sim e_N/b$ where $e_N$ is an energy scale that depends on $N$ and the confining potential $V({\bf x})$, where the Wigner function at the edge again takes a universal scaling form with a $b$-dependent scaling function. This temperature dependent scaling function is also independent of the potential as well as the dimension $d$. Our results generalize to any $d\geq 1$ and $T \geq 0$ the $d=1$ and $T=0$ results obtained by Bettelheim and Wiegman [Phys. Rev. B ${\bf 84}$, 085102 (2011)].Comment: 16 pages, 4 figure

Why Use a Hamilton Approach in QCD?

We discuss $QCD$ in the Hamiltonian frame work. We treat finite density $QCD$ in the strong coupling regime. We present a parton-model inspired regularisation scheme to treat the spectrum ($\theta$-angles) and distribution functions in $QED_{1+1}$. We suggest a Monte Carlo method to construct low-dimensionasl effective Hamiltonians. Finally, we discuss improvement in Hamiltonian $QCD$.Comment: Proceedings of Hadrons and Strings, invited talk given by H. Kr\"{o}ger; Text (LaTeX file), 3 Figures (ps file