Multilevel quantum Otto heat engines with identical particles

A quantum Otto heat engine is studied with multilevel identical particles trapped in one-dimensional box potential as working substance. The symmetrical wave function for Bosons and the anti-symmetrical wave function for Fermions are considered. In two-particle case, we focus on the ratios of $W^i$ ($i=B,F$) to $W_s$, where $W^B$ and $W^F$ are the work done by two Bosons and Fermions respectively, and $W_s$ is the work output of a single particle under the same conditions. Due to the symmetric of the wave functions, the ratios are not equal to $2$. Three different regimes, low temperature regime, high temperature regime, and intermediate temperature regime, are analyzed, and the effects of energy level number and the differences between the two baths are calculated. In the multiparticle case, we calculate the ratios of $W^i_M/M$ to $W_s$, where $W^i_M/M$ can be seen as the average work done by a single particle in multiparticle heat engine. For other working substances whose energy spectrum have the form of $E_n\sim n^2$, the results are similar. For the case $E_n\sim n$, two different conclusions are obtained

The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics

We consider the class of Levi nondegenerate hypersurfaces $M$ in \bC^{n+1} that admit a local (CR transversal) embedding, near a point $p\in M$, into a standard nondegenerate hyperquadric in $\Bbb C^{N+1}$ with codimension $k:=N-n$ small compared to the CR dimension $n$ of $M$. We show that, for hypersurfaces in this class, there is a normal form (which is closely related to the embedding) such that any local equivalence between two hypersurfaces in normal form must be an automorphism of the associated tangent hyperquadric. We also show that if the signature of $M$ and that of the standard hyperquadric in \bC^{N+1} are the same, then the embedding is rigid in the sense that any other embedding must be the original embedding composed with an automorphism of the quadric

Rotating Stellar Models Can Account for the Extended Main Sequence Turnoffs in Intermediate Age Clusters

We show that the extended main sequence turnoffs seen in intermediate age Large Magellanic Cloud (LMC) clusters, often attributed to age spreads of several hundred Myr, may be easily accounted for by variable stellar rotation in a coeval population. We compute synthetic photometry for grids of rotating stellar evolution models and interpolate them to produce isochrones at a variety of rotation rates and orientations. An extended main sequence turnoff naturally appears in color-magnitude diagrams at ages just under 1 Gyr, peaks in extent between ~1 and 1.5 Gyr, and gradually disappears by around 2 Gyr in age. We then fit our interpolated isochrones by eye to four LMC clusters with very extended main sequence turnoffs: NGC 1783, 1806, 1846, and 1987. In each case, stellar populations with a single age and metallicity can comfortably account for the observed extent of the turnoff region. The new stellar models predict almost no correlation of turnoff color with rotational vsini: the red edge of the turnoff is populated by a combination of slow rotators and edge-on rapid rotators.Comment: 7 pages, 4 figures, 1 table, ApJ accepted. Conclusions unchange

Production interdependence and welfare

The international welfare effects of a country's monetary policy shocks have been controversial in the new open economy macro (i.e., NOEM) literature. While a unilateral monetary expansion increases the production efficiency in each country, it affects the terms of trade in favor of one country against another depending on the currencies of price setting. In this paper, we incorporate multiple stages of production and trade into a standard NEOM model to capture world production interdependence, and show that increased world production interdependence tends to magnify the e±ciency-improvement effect while dampening the terms-of-trade effect. As a consequence, a unilateral monetary expansion can be mutually beneficial regardless of in which currency prices are set. In this sense, international monetary policy transmission may not be a source of potential conflict in a world with production interdependence. JEL Classification: E32, F31, F41Local currency pricing, Monopolistic competition, Stages of processing, Welfare

Inflation targeting: what inflation rate to target?

In an economy with nominal rigidities in both an intermediate good sector and a finished good sector, and thus with a natural distinction between CPI and PPI inflation rates, a benevolent central bank faces a tradeoff between stabilizing the two measures of inflation: a final output gap, and unique to our model, a real marginal cost gap in the intermediate sector, so that optimal monetary policy is second-best. We discuss how to implement the optimal policy with minimal information requirement and evaluate the robustness of these simple rules when the central bank may not know the exact sources of shocks or nominal rigidities. A main finding is that a simple hybrid rule under which the short-term interest rate responds to CPI inflation and PPI inflation results in a welfare level close to the optimum, whereas policy rules that ignore PPI inflation or PPI sector shocks can result in significant welfare losses.Inflation (Finance)

Overconfidence in financial markets and consumption over the life cycle

Overconfidence is a widely documented phenomenon. Empirical evidence reveal two types of overconfidence in financial markets: investors both overestimate the average rate of return to their assets and underestimate uncertainty associated with the return. This paper explores implications of overconfidence in financial markets for consumption over the life cycle. The authors obtain a closed-form solution to the time-inconsistent problem facing an overconfident investor/consumer who has a CRRA utility function. They use this solution to show that overestimation of the mean return gives rise to a hump in consumption during the work life if and only if the elasticity of intertemporal substitution in consumption is less than unit. They find that underestimation of uncertainty has little effect on the long-run average behavior of consumption over the work life. Their calibrated model produces a hump-shaped work-life consumption profile with both the age and the amplitude of peak consumption consistent with empirical observations.Consumption (Economics) ; Financial markets

Staggered Contracts and Business Cycle Persistence

Staggered price and staggered wage contracts are commonly viewed as similar mechanisms in generating persistent real effects of monetary shocks. In this paper, we distinguish the two mechanisms in a dynamic stochastic general equilibrium framework. We show that, although the dynamic price setting and wage setting equations are alike, a key parameter governing persistence is linked to the underlying preferences and technologies in different ways. Under the staggered wage mechanism, an intertemporal smoothing incentive in labor supply creates a real rigidity that is absent under the staggered price mechanism. Consequently, the two mechanisms have different implications on persistence. While the staggered price mechanism by itself does not contribute to, the staggered wage mechanism plays an important role in generating persistence.Staggered Contracts; Business Cycle Persistence; Monetary Policy

Multiple stages of processing and the quantity anomaly in international business cycle models.

We construct a two-country DSGE model with multiple stages of processing and local-currency staggered price-setting to study cross-country quantity correlations driven by monetary shocks. The model embodies a mechanism that propagates a monetary surprise in the home country to lower the foreign price level while restraining the home price level from rising too quickly. It does so through reducing material costs in terms of the foreign currency unit while dampening the upward movements in the costs in terms of the home currency unit, both in absolute terms and relative to the costs of primary factors. We show that, through this mechanism and a resulting factor substitution effect, the model is able to generate significant cross-country quantity correlations, with correlations in consumption considerably lower than correlations in output, as in the data.Business cycles

Specific factors meet intermediate inputs: implications for strategic complementarities and persistence.

A central challenge to monetary business-cycle theory is to find a solution to the problem of persistence and delay in the real effects of monetary shocks. Previous research has identified separately specific factors and intermediate inputs as two promising mechanisms for generating the persistence and delay in a staggered price-setting framework. Models based on either of these two mechanisms have also been used in the design of optimal monetary policy. ; By examining a staggered price model that features both specific factors and intermediate inputs, the author finds an offsetting interaction between the two individually promising mechanisms, which leads to a cancellation of much of the impact of each in propagating monetary shocks. This finding posits a challenge to the search for a robust monetary transmission mechanism and design of optimal monetary policy.Business cycles