Heat-kernel approach for scattering

An approach for solving scattering problems, based on two quantum field theory methods, the heat kernel method and the scattering spectral method, is constructed. This approach converts a method of calculating heat kernels into a method of solving scattering problems. This allows us to establish a method of scattering problems from a method of heat kernels. As an application, we construct an approach for solving scattering problems based on the covariant perturbation theory of heat-kernel expansions. In order to apply the heat-kernel method to scattering problems, we first calculate the off-diagonal heat-kernel expansion in the frame of the covariant perturbation theory. Moreover, as an alternative application of the relation between heat kernels and partial-wave phase shifts presented in this paper, we give an example of how to calculate a global heat kernel from a known scattering phase shift

Intertemporal Risk Management Decisions of Farmers under Preference, Market, and Policy Dynamics

This paper adapts a generalized expected utility (GEU) maximization model (Epstein and Zin, 1989 and 1991) to examine the intertemporal risk management of wheat producers in the Pacific Northwest. Optimization results based on simulated data indicate the feasibility of the GEU optimization as a modeling framework. It further extends the GEU model by incorporating a welfare measure, the certainty equivalent, to investigate the impacts of U.S. government programs and market institutions on farmers' risk management decisions and welfare. A comparison between the GEU and other expected utility models further implies GEU has the advantage of specifying farmers' intertemporal preferences separately and completely. Impact analysis results imply that farmers' optimal hedging is sensitive to changes in the preferences and the effects of these preference changes are intertwined. Target price and loan rate levels, offered by certain government payment programs, can lead to the substitution of government programs for hedging. The evaluation of current risk management tools shows both crop insurance and government payments can improve farmers' welfare significantly. Government payment programs have a greater effect on farmers' welfare than crop insurance and crop insurance outperforms hedging.generalized expected utility, risk management, multi-period production, dynamic optimization, intertemporal preference, market institution, government payments, Risk and Uncertainty, Q14, D9, C61,

Scattering theory without large-distance asymptotics

In conventional scattering theory, to obtain an explicit result, one imposes a precondition that the distance between target and observer is infinite. With the help of this precondition, one can asymptotically replace the Hankel function and the Bessel function with the sine functions so that one can achieve an explicit result. Nevertheless, after such a treatment, the information of the distance between target and observer is inevitably lost. In this paper, we show that such a precondition is not necessary: without losing any information of distance, one can still obtain an explicit result of a scattering rigorously. In other words, we give an rigorous explicit scattering result which contains the information of distance between target and observer. We show that at a finite distance, a modification factor --- the Bessel polynomial --- appears in the scattering amplitude, and, consequently, the cross section depends on the distance, the outgoing wave-front surface is no longer a sphere, and, besides the phase shift, there is an additional phase (the argument of the Bessel polynomial) appears in the scattering wave function