Phase-space distribution functions for photon propagation in waveguides coupled to a qubit

We investigate propagation of few-photon pulses in waveguides coupled to a two-level system by means of the method of distribution functions in coordinate-momentum space that provides a detailed description of photon systems. We find that the distribution function of the transmitted pulse can be negative for the nonclassical input (i.e., single-photon Fock state). This reveals the quasiprobability nature of photon distribution. Analytical expressions for photon densities in the momentum space as well as in the coordinate space are obtained for the mentioned single-photon Gaussian input. We also study evolution of the multimode coherent-state input for an arbitrary photon number. Time-dependent differential equations describing average densities and fluctuations of outgoing photons are derived and solved. Influence of the number of input photons, pulse width, and radiation-atom interaction strength on the statistical properties of the fluctuations is investigated.Comment: 22 pages, 6 figure

Obsolescence of Durable Goods and Optimal Consumption

We study a model with a durable good subject to abrupt, periodic obsolescence, and characterize the optimal purchasing policy. Consumers optimally synchronize new purchases with the arrival of new durable models. Hence, some agents use a "flexible" optimal replacement rule that switches between two adjacent replacement frequencies at irregular intervals. These agents react to wealth shocks by changing the timing of future purchases. The model has distinct comparative statics on obsolescence and durability and can explain how durables with high depreciation rates may have more volatile expenditure. The model also predicts how demand fluctuations respond to a change in product variety. These predictions match the observed changes in volatility of the US auto sales after the introduction of smaller foreign cars in the 1970sOptimal consumption, durable goods, volatility

Dimension of gradient measures

We prove that if pure derivatives with respect to all coordinates of a function on $\mathbb{R}^n$ are signed measures, then their lower Hausdorff dimension is at least $n-1$. The derivatives with respect to different coordinates may be of different order.Comment: 8 page

Technological Progress and Worker Productivity at Different Ages

Economists have long thought of technological progress as a primary determinant of rising living standards over time. One might think of technological progress as increasing the “effectiveness” of labor, thereby raising the amount of output that each unit of labor can produce. The purpose of this paper is to ask whether, as an empirical matter, technological progress increases the productivity of workers evenly, or whether it augments the effectiveness of young workers the most. As low birthrates and increases in longevity lead to an “aging” of the population, the productivity of older workers relative to younger workers is likely to become an ever more important issue. Analyzing data from the decennial Censuses and annual data from the Current Population Survey, this paper draws three tentative conclusions. First, we find that the “aging” of the U.S. work force seems more likely to increase aggregate productivity – by raising the proportion of laborers with sizable accumulations of human capital from experience – than to decrease it – by slowing the adoption rate for innovations. Our preliminary estimates imply that the latter effect is of modest magnitude. Second, since our preliminary estimates point to “general” rather than “specific” technological progress, each household faces a problem of having to predict the course of technological progress over its life span. This means that households face more risk than otherwise, and it complicates the specification of the life-cycle model that analysts should employ. Third, when we disaggregate across education groups, the groups show quite unequal benefits from technological progress after 1980, and this may lead to further challenges in modeling household behavior.