Even-Odd and Super-Even Effects in the Attractive Hubbard Model

The canonical BCS wave function is tested for the attractive Hubbard model. Results are presented for one dimension, and are compared with the exact solutions by the Bethe ansatz and the results from the conventional grand canonical BCS approximation, for various chain lengths, electron densities, and coupling strengths. While the exact ground state energies are reproduced very well both by the canonical and grand canonical BCS approximations, the canonical method significantly improves the energy gaps for small systems and weak coupling. The ``parity'' effect due to the number of electrons being even or odd naturally emerges in our canonical results. Furthermore, we find a ``super-even'' effect: the energy gap oscillates as a function of even electron number, depending on whether the number of electrons is $4 m$ or $4 m + 2$ (m integer). Such oscillations as a function of electron number should be observable with tunneling measurements in ultrasmall metallic grains.Comment: 20 pages, 9 figure

Fixed Number and Quantum Size Effects in Nanoscale Superconductors

In recent experiments on nanoscale Al particles, whose electron number was fixed by charging effects, a ``negative gap'' was observed in particles with an odd number of electrons. This observation has called into question the use of a grand canonical ensemble in describing superconductivity in such ultrasmall particles. We have studied the effects of fixed electron number and finite size in nanoscale superconductors, by applying the canonical BCS theory for the attractive Hubbard model. The ground state energy and the energy gap are compared with the conventional and parity-projected grand canonical BCS results, and in one dimension also with the exact solutions by the Bethe ansatz. The crossover from the bulk to quantum limit is studied for various regimes of electron density and coupling strength. The effects of boundary conditions and different lattice structures are also examined. A ``negative gap'' for odd electron number emerges most naturally in the canonical scheme. For even electron number, the gap is particularly large for ``magic numbers'' of electrons for a given system size or of atoms for a fixed electron density. These features are in accordance with the exact solutions, but are essentially missed in the grand canonical results.Comment: 2 pages, 4 figures, submitted to Physica C for M2S-HTSC-VI Proceeding

Measuring Norms of Income Transfers: Trust Experiments and Survey Data from Vietnam

This paper compares the patterns of income transfers within village communities in the north and south of Vietnam by analyzing household survey and experimental data. The results of household data analysis show private transfers flow from high-income households to low-income households in the south where social safety net is limited. In contrast, private transfers do not correlate with pre-transfer income in the north where public transfers are more widespread. In addition, public transfers crowd out private transfers in the north. We conducted a trust game in both regions and found consistent results. People in the south are more altruistic toward the poor: they send more to the poor without expecting higher repayment. This pattern is consistent with the idea that private norms of redistribution from rich to poor are active in the south, but are crowded out in the north, possibly by communist public institutions, although we observe higher levels of trust and reciprocity in the north

Poverty, politics, and preferences: Field experiments and survey data from Vietnam

We conducted field experiments to investigate how wealth, political history, occupation, and other demographic variables (from a comprehensive earlier household survey) are correlated with risk, time discounting and trust in Vietnam. Our experiments suggest risk and time preferences depend on the stage of economic development. In wealthier villages, people are less loss-averse and more patient. Our research also shows people who participate in ROSCAs (rotating credit associations) are more patient than non-participant, but those who participate in bidding ROSCAs are less patient and more risk averse than those who participate in fixed ROSCAs. Results from a trust game demonstrate both positive and negative effects of communism. Villagers in the South tend to invest more in low-income partners without expecting repayment. On the other hand, people in the north are more trustworthy but do not pass on more money to the poor. Our findings also suggest market activities, like starting a small trade business, are correlated with trust and trustworthiness. We also contribute to experimental methodology by using choices that separate different aspects of risk aversion and time preferences in behavioral economics specifications

Risk and Time Preferences: Linking Experimental and Household Survey Data from Vietnam

We conducted experiments in Vietnamese villages to determine the predictors of risk and time preferences. In villages with higher mean income, people are less loss-averse and more patient. Household income is correlated with patience but not with risk. We expand measurements of risk and time preferences beyond expected utility and exponential discounting, replacing those models with prospect theory and a three-parameter hyperbolic discounting model. Comparable risk parameter estimates have been found for Chinese farmers, using our method

Microscopic study of inhomogeneous superconductors

We study various inhomogeneity effects on superconductivity as due to quantum confinement, surfaces and impurities, using the self-consistent Bogoliubov-de Gennes formalism on the attractive Hubbard model. The results are also compared with those obtained from the Anderson prescription, a BCS formalism for incorporating spatial inhomogeneity.Comment: 4 pages, 6 figure

Escape of black holes from the brane

TeV-scale gravity theories allow the possibility of producing small black holes at energies that soon will be explored at the LHC or at the Auger observatory. One of the expected signatures is the detection of Hawking radiation, that might eventually terminate if the black hole, once perturbed, leaves the brane. Here, we study how the `black hole plus brane' system evolves once the black hole is given an initial velocity, that mimics, for instance, the recoil due to the emission of a graviton. The results of our dynamical analysis show that the brane bends around the black hole, suggesting that the black hole eventually escapes into the extra dimensions once two portions of the brane come in contact and reconnect. This gives a dynamical mechanism for the creation of baby branes.Comment: 4 pages, 6 figure

Single-cycle THz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3

Using the tilted-pulse-intensity-front scheme, we generate single-cycle terahertz (THz) pulses by optical rectification of femtosecond laser pulses in LiNbO3. In the THz generation setup, the condition that the image of the grating coincides with the tilted-optical-pulse front is fulfilled to obtain optimal THz beam characteristics and pump-to-THz conversion efficiency. The designed focusing geometry enables tight focus of the collimated THz beam with a spot size close to the diffraction limit, and the maximum THz electric field of 1.2 MV/cm is obtained