Charge transport in a Tomonaga-Luttinger liquid: effects of pumping and bias

We study the current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, point-like impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the DC and AC components of the current have power law dependences on the bias and pumping frequencies with an exponent 2K - 1 for spinless electrons, where K is the interaction parameter. For K < 1/2, the current becomes large for special values of the bias. For non-interacting electrons with K = 1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons.Comment: 9 pages including 2 figures; this is the published versio

Gapless line for the anisotropic Heisenberg spin-1/2 chain in a magnetic field and the quantum axial next-nearest-neighbor Ising Chain

We study the anisotropic Heisenberg (XYZ) spin-1/2 chain placed in a magnetic field pointing along the x-axis. We use bosonization and a renormalization group analysis to show that the model has a non-trivial fixed point at a certain value of the XY anisotropy a and the magnetic field h. Hence, there is a line of critical points in the (a,h) plane on which the system is gapless, even though the Hamiltonian has no continuous symmetry. The quantum critical line corresponds to a spin-flop transition; it separates two gapped phases in one of which the Z_2 symmetry of the Hamiltonian is broken. Our study has a bearing on one of the transitions of the axial next-nearest neighbor Ising (ANNNI) chain in a transverse magnetic field. We also discuss the properties of the model when the magnetic field is increased further, in particular, the disorder line on which the ground state is a direct product of single spin states.Comment: Expanded version of cond-mat/0208216; Revtex, 7 pages, 2 eps figure

Further Evidence on the Dynamics of Unemployment by Gender

We present empirical evidence regarding differences in unemployment dynamics across gender for a group of twenty-three OECD countries. Our results indicate that there are substantial differences in the unemployment persistence for men and women across countries. Further, the female unemployment rates are relatively more persistent compared to the male unemployment rates.Unemployment Rate, Gender Gap, Persistence, Unit Root

Evidence Regarding Persistence in the Gender Unemployment Gap Based on the Ratio of Female to Male Unemployment Rate

We examine the level of persistence in the gender unemployment gap in eight OECD countries: Australia, Canada, Finland, France, Germany, Italy, Japan, and the United States. We use a new measure for the gender unemployment gap, namely, the ratio of the female to male unemployment rate. Our empirical evidence shows that the gender unemployment gap is not persistent given that we reject the unit root null hypothesis for all countries in our sample except Australia.

Fidelity susceptibility of one-dimensional models with twisted boundary conditions

Recently it has been shown that the fidelity of the ground state of a quantum many-body system can be used to detect its quantum critical points (QCPs). If g denotes the parameter in the Hamiltonian with respect to which the fidelity is computed, we find that for one-dimensional models with large but finite size, the fidelity susceptibility \chi_F can detect a QCP provided that the correlation length exponent satisfies \nu < 2. We then show that \chi_F can be used to locate a QCP even if \nu \ge 2 if we introduce boundary conditions labeled by a twist angle N\theta, where N is the system size. If the QCP lies at g = 0, we find that if N is kept constant, \chi_F has a scaling form given by \chi_F \sim \theta^{-2/\nu} f(g/\theta^{1/\nu}) if \theta \ll 2\pi/N. We illustrate this both in a tight-binding model of fermions with a spatially varying chemical potential with amplitude h and period 2q in which \nu = q, and in a XY spin-1/2 chain in which \nu = 2. Finally we show that when q is very large, the model has two additional QCPs at h = \pm 2 which cannot be detected by studying the energy spectrum but are clearly detected by \chi_F. The peak value and width of \chi_F seem to scale as non-trivial powers of q at these QCPs. We argue that these QCPs mark a transition between extended and localized states at the Fermi energy.Comment: 12 pages, 10 figures; made some changes in response to referees; this is the published versio

Local Quantum Uncertainty in Two-Qubit Separable States: A Case Study

Recent findings suggest, separable states, which are otherwise of no use in entanglement dependent tasks, can also be used in information processing tasks that depend upon the discord type general non classical correlations. In this work, we explore the nature of uncertainty in separable states as measured by local quantum uncertainty. Particularly in two-qubit system, we find separable X-state which has maximum local quantum uncertainty. Interestingly, this separable state coincides with the separable state, having maximum geometric discord. We also search for the maximum amount of local quantum uncertainty in separable Bell diagonal states. We indicate an interesting connection to the tightness of entropic uncertainty with the state of maximum uncertainty.Comment: 11 pages, 2 figures, latex2e, comments welcome, to appear in qi

Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential

We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low frequency limit we use adiabatic theory, while in the high frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an "engineered" initial state where the particles (taken to be hard core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light cone like spreading of the particles in real space.Comment: 8 pages, 5 figures; this is the final published versio

New Evidence on the Convergence of International Income from a Group of 29 Countries

This paper updates and extends the time-series evidence on the convergence of international incomes using a set of 29 countries over the period 1900-2001. Time-series tests for stochastic convergence are supplemented with tests which provide evidence on the notion of "Beta-convergence" predicted by the Solow model. The evidence indicates that the relative income series of 21 countries are consistent with stochastic convergence, and that Beta-convergence has occurred in at least 17 countries at some point over the 1900-2001 period. Further examination of the properties of the Beta- convergence test provides anecdotal evidence of conditional convergence during the post-war period in seven countries for which the convergence hypothesis was initially rejected. Analysis of the cross-country dispersion of incomes over time also suggests that convergence has occurred over the 1900-2001 period, with structural breaks associated with World War II in many countries causing a break in the convergence process.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity ($F$) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of $F$ for an anisotropic quantum critical point for both thermodynamic and non-thermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of $F$ inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate $F$ through the overlap between the ground states for angle of rotation $\eta$ and $\eta+d\eta$, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.Comment: 10 pages, 8 figure