Decoherence in Phase Space

Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schr\"{o}dinger "cat" state) corresponding to two widely separated wave packets. Decoherence refers to the destruction of the interference term in the quantum probability function. Here, we stress that a quantitative measure of decoherence depends not only on the specific system being studied but also on whether one is considering coordinate, momentum or phase space. We show that this is best illustrated by considering Wigner phase space where the measure is again different. Analytic results for the time development of the Wigner distribution function for a two-Gaussian Schrodinger "cat" state have been obtained in the high-temperature limit (where decoherence can occur even for negligible dissipation) which facilitates a simple demonstration of our remarks.Comment: in press in Laser Phys.13(2003

Note on the derivative of the hyperbolic cotangent

In a letter to Nature (Ford G W and O'Connell R F 1996 Nature 380 113) we presented a formula for the derivative of the hyperbolic cotangent that differs from the standard one in the literature by an additional term proportional to the Dirac delta function. Since our letter was necessarily brief, shortly after its appearance we prepared a more extensive unpublished note giving a detailed explanation of our argument. Since this note has been referenced in a recent article (Estrada R and Fulling S A 2002 J. Phys. A: Math. Gen. 35 3079) we think it appropriate that it now appear in print. We have made no alteration to the original note

Self reported aggravating activities do not demonstrate a consistent directional pattern in chronic non specific low back pain patients: An observational study

Question: Do the self-reported aggravating activities of chronic non-specific low back pain patients demonstrate a consistent directional pattern? Design: Cross-sectional observational study. Participants: 240 chronic non specific low back pain patients. Outcome measure: We invited experienced clinicians to classify each of the three self-nominated aggravating activities from the Patient Specific Functional Scale by the direction of lumbar spine movement. Patients were described as demonstrating a directional pattern if all nominated activities moved the spine into the same direction. Analyses were undertaken to determine if the proportion of patients demonstrating a directional pattern was greater than would be expected by chance. Results: In some patients, all tasks did move the spine into the same direction, but this proportion did not differ from chance (p = 0.328). There were no clinical or demographic differences between those who displayed a directional pattern and those who did not (all p > 0.05). Conclusion: Using patient self-reported aggravating activities we were unable to demonstrate the existence of a consistent pattern of adverse movement in patients with chronic non-specific low back pain

Ownership of Intellectual Property and Corporate Taxation

AbstractIntellectual property accounts for a growing share of firms' assets. It is more mobile than other forms of capital, and could be used by firms to shift income offshore and to reduce their corporate income tax liability. We consider how influential corporate income taxes are in determining where firms choose to legally own intellectual property. We estimate a mixed (or random coefficients) logit model that incorporates important observed and unobserved heterogeneity in firms' location choices. We obtain estimates of the full set of location specific tax elasticities and conduct ex ante analysis of how the location of ownership of intellectual property will respond to changes in tax policy. We find that recent reforms that give preferential tax treatment to income arising from patents are likely to have significant effects on the location of ownership of new intellectual property, and could lead to substantial reductions in tax revenue

Laplace transform of spherical Bessel functions

We provide a simple analytic formula in terms of elementary functions for the Laplace transform j_{l}(p) of the spherical Bessel function than that appearing in the literature, and we show that any such integral transform is a polynomial of order l in the variable p with constant coefficients for the first l-1 powers, and with an inverse tangent function of argument 1/p as the coefficient of the power l. We apply this formula for the Laplace transform of the memory function related to the Langevin equation in a one-dimensional Debye model.Comment: 5 pages LATEX, no figures. Accepted 2002, Physica Script