Towards an analytical theory for charged hard spheres

Ion mixtures require an exclusion core to avoid collapse. The Debye Hueckel theory, where ions are point charges, is accurate only in the limit of infinite dilution. The MSA is the embedding of hard cores into DH, is valid for higher densities. In the MSA the properties of any ionic mixture can be represented by a single screening parameter $\Gamma$. For equal ionic size restricted model is obtained from the Debye parameter $\kappa$. This one parameter representation (BIMSA) is valid for complex and associating systems, such as the general n-polyelectrolytes. The BIMSA is the only theory that satisfies the infinite dilution limit of the DH theory for any chain length. The contact pair distribution function of hard ions mixture is a functional of $\Gamma$ and a small mean field parameter. This yields good agreement with the Monte Carlo (Bresme et al. Phys. Rev. E {\textbf 51} 289 (1995)) .Comment: 6 pages, 1 figur

Optimal Competitive Auctions

We study the design of truthful auctions for selling identical items in unlimited supply (e.g., digital goods) to n unit demand buyers. This classic problem stands out from profit-maximizing auction design literature as it requires no probabilistic assumptions on buyers' valuations and employs the framework of competitive analysis. Our objective is to optimize the worst-case performance of an auction, measured by the ratio between a given benchmark and revenue generated by the auction. We establish a sufficient and necessary condition that characterizes competitive ratios for all monotone benchmarks. The characterization identifies the worst-case distribution of instances and reveals intrinsic relations between competitive ratios and benchmarks in the competitive analysis. With the characterization at hand, we show optimal competitive auctions for two natural benchmarks. The most well-studied benchmark $\mathcal{F}^{(2)}(\cdot)$ measures the envy-free optimal revenue where at least two buyers win. Goldberg et al. [13] showed a sequence of lower bounds on the competitive ratio for each number of buyers n. They conjectured that all these bounds are tight. We show that optimal competitive auctions match these bounds. Thus, we confirm the conjecture and settle a central open problem in the design of digital goods auctions. As one more application we examine another economically meaningful benchmark, which measures the optimal revenue across all limited-supply Vickrey auctions. We identify the optimal competitive ratios to be $(\frac{n}{n-1})^{n-1}-1$ for each number of buyers n, that is $e-1$ as $n$ approaches infinity

Improving the sign problem in QCD at finite density

If the fermion mass is large enough, the phase of the fermion determinant of QCD at finite density is strongly correlated with the imaginary part of the Polyakov loop. This fact can be exploited to reduce the fluctuations of the phase significantly, making numerical simulations feasible in regions of parameters where the naive brute force method does not work.Comment: LATTICE99 (Finite Temperature and Density II

Spin relaxation and decoherence of holes in quantum dots

We investigate heavy-hole spin relaxation and decoherence in quantum dots in perpendicular magnetic fields. We show that at low temperatures the spin decoherence time is two times longer than the spin relaxation time. We find that the spin relaxation time for heavy holes can be comparable to or even longer than that for electrons in strongly two-dimensional quantum dots. We discuss the difference in the magnetic-field dependence of the spin relaxation rate due to Rashba or Dresselhaus spin-orbit coupling for systems with positive (i.e., GaAs quantum dots) or negative (i.e., InAs quantum dots) $g$-factor.Comment: 5 pages, 1 figur

Real time plasma equilibrium reconstruction in a Tokamak

The problem of equilibrium of a plasma in a Tokamak is a free boundary problemdescribed by the Grad-Shafranov equation in axisymmetric configurations. The right hand side of this equation is a non linear source, which represents the toroidal component of the plasma current density. This paper deals with the real time identification of this non linear source from experimental measurements. The proposed method is based on a fixed point algorithm, a finite element resolution, a reduced basis method and a least-square optimization formulation

Macroscopic Resonant Tunneling in the Presence of Low Frequency Noise

We develop a theory of macroscopic resonant tunneling of flux in a double-well potential in the presence of realistic flux noise with significant low-frequency component. The rate of incoherent flux tunneling between the wells exhibits resonant peaks, the shape and position of which reflect qualitative features of the noise, and can thus serve as a diagnostic tool for studying the low-frequency flux noise in SQUID qubits. We show, in particular, that the noise-induced renormalization of the first resonant peak provides direct information on the temperature of the noise source and the strength of its quantum component.Comment: 4 pages, 1 figur

The role of the Polyakov loop in finite density QCD

We study the behavior of the fermion determinant at finite temperature and chemical potential, as a function of the Polyakov loop. The phase of the determinant is correlated with the imaginary part of the Polyakov loop. This correlation and its consequences are considered in static QCD, in a toy model of free quarks in a constant $A_0$ background, and in simulations constraining the imaginary part of the Polyakov loop to zero.Comment: 11 pages, 8 Postscript figures, Minor changes, quality of figures improve