Dissipative superfluid mass flux through solid 4He

The thermo-mechanical effect in superfluid helium is used to create an initial chemical potential difference, $\Delta \mu_0$, across a solid $^4$He sample. This $\Delta \mu_0$ causes a flow of helium atoms from one reservoir filled with superfluid helium, through a sample cell filled with solid helium, to another superfluid-filled reservoir until chemical potential equilibrium is restored. The solid helium sample is separated from each of the reservoirs by Vycor rods that allow only the superfluid component to flow. With an improved technique, measurements of the flow, $F$, at several fixed solid helium temperatures, $T$, have been made as function of $\Delta \mu$ in the pressure range 25.5 - 26.1 bar. And, measurements of $F$ have been made as a function of temperature in the range $180 < T < 545$~mK for several fixed values of $\Delta \mu$. The temperature dependence of the flow above $100$~mK shows a reduction of the flux with an increase in temperature that is well described by $F = F_0^*[1 - a\exp(-E/T)]$. The non-linear functional dependence $F \sim (\Delta \mu)^b$, with $b < 0.5$ independent of temperature but dependent on pressure, documents in some detail the dissipative nature of the flow and suggests that this system demonstrates Luttinger liquid-like one-dimensional behavior. The mechanism that causes this flow behavior is not certain, but is consistent with superflow on the cores of edge dislocations.Comment: 11 pages, 14 figure

Mass flux characteristics in solid 4He for T> 100 mK: Evidence for Bosonic Luttinger Liquid behavior

At pressure $\sim$ 25.7 bar the flux, $F$, carried by solid \4he for $T >$ 100 mK depends on the net chemical potential difference between two reservoirs in series with the solid, $\Delta \mu$, and obeys $F \sim (\Delta \mu)^b$, where $b \approx 0.3$ is independent of temperature. At fixed $\Delta \mu$ the temperature dependence of the flux, $F$, can be adequately represented by $F \sim - \ln(T/\tau)$, $\tau \approx 0.6$ K, for $0.1 \leq T \leq 0.5$ K. A single function $F = F_0(\Delta \mu)^b\ln(T/\tau)$ fits all of the available data sets in the range 25.6 - 25.8 bar reasonably well. We suggest that the mass flux in solid \4he for $T > 100$ mK may have a Luttinger liquid-like behavior in this bosonic system.Comment: 4 pages, 5 figure

On gauge-invariant Green function in 2+1 dimensional QED

Both the gauge-invariant fermion Green function and gauge-dependent conventional Green function in $2+1$ dimensional QED are studied in the large $N$ limit. In temporal gauge, the infra-red divergence of gauge-dependent Green function is found to be regulariable, the anomalous dimension is found to be $\eta= \frac{64}{3 \pi^{2} N}$. This anomalous dimension was argued to be the same as that of gauge-invariant Green function. However, in Coulomb gauge, the infra-red divergence of the gauge-dependent Green function is found to be un-regulariable, anomalous dimension is even not defined, but the infra-red divergence is shown to be cancelled in any gauge-invariant physical quantities. The gauge-invariant Green function is also studied directly in Lorentz covariant gauge and the anomalous dimension is found to be the same as that calculated in temporal gauge.Comment: 8 pages, 6 figures, to appear in Phys. Rev.

Market Equilibrium with Transaction Costs

Identical products being sold at different prices in different locations is a common phenomenon. Price differences might occur due to various reasons such as shipping costs, trade restrictions and price discrimination. To model such scenarios, we supplement the classical Fisher model of a market by introducing {\em transaction costs}. For every buyer $i$ and every good $j$, there is a transaction cost of \cij; if the price of good $j$ is $p_j$, then the cost to the buyer $i$ {\em per unit} of $j$ is p_j + \cij. This allows the same good to be sold at different (effective) prices to different buyers. We provide a combinatorial algorithm that computes $\epsilon$-approximate equilibrium prices and allocations in $O\left(\frac{1}{\epsilon}(n+\log{m})mn\log(B/\epsilon)\right)$ operations - where $m$ is the number goods, $n$ is the number of buyers and $B$ is the sum of the budgets of all the buyers