46,997 research outputs found

    Integrity bases for local invariants of composite quantum systems

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    Unitary group branchings appropriate to the calculation of local invariants of density matrices of composite quantum systems are formulated using the method of SS-function plethysms. From this, the generating function for the number of invariants at each degree in the density matrix can be computed. For the case of two two-level systems the generating function is F(q)=1+q+4q2+6q3+16q4+23q5+52q6+77q7+150q8+224q9+396q10+583q11+O(q12)F(q) = 1 + q + 4q^{2} + 6 q^{3} + 16 q^{4} + 23 q^{5} + 52 q^{6} + 77 q^{7} + 150 q^{8} + 224 q^{9} + 396 q^{10} + 583 q^{11}+ O(q^{12}). Factorisation of such series leads in principle to the identification of an integrity basis of algebraically independent invariants. This note replaces Appendix B of our paper\cite{us} J Phys {\bf A33} (2000) 1895-1914 (\texttt{quant-ph/0001076}) which is incorrect.Comment: Latex, 4 pages, correcting Appendix B of quant-ph/0001076 Error in F(q)F(q) corrected and conclusions modified accordingl

    How idiosyncratic are banking crises in OECD countries?

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    Low levels of bank capital and liquidity in combination with ongoing crises in other countries are shown to increase the probability of banking crises in OECD countries. Hence global coordination of regulatory reform is vital for reducing crisis risks.Funding was received from the ESRC for this work

    Vacuum Decay on a Brane World

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    The bubble nucleation rate for a first order phase transition occurring on a brane world is calculated. Both the Coleman-de Luccia thin wall instanton and the Hawking-Moss instanton are considered. The results are compared with the corresponding nucleation rates for standard four-dimensional gravity.Comment: 5 page

    The Quantum Cosmological Wavefunction at Very Early Times for a Quadratic Gravity Theory

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    The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, the wavefunction would satisfy a third-order differential equation near the inflationary epoch which has a solution that is singular in the scale factor limit a(t)0a(t)\to 0. When scalar field derivatives are included, a sixth-order differential equation is obtained for the wavefunction and the solution by Mellin transform is regular in the a0a\to 0 limit. It follows that inclusion of the scalar field in the quadratic gravity action is necessary for consistency of the quantum cosmology of the theory at very early times.Comment: Tex, 13 page

    Sewing sound quantum flesh onto classical bones

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    Semiclassical transformation theory implies an integral representation for stationary-state wave functions ψm(q)\psi_m(q) in terms of angle-action variables (θ,J\theta,J). It is a particular solution of Schr\"{o}dinger's time-independent equation when terms of order 2\hbar^2 and higher are omitted, but the pre-exponential factor A(q,θ)A(q,\theta) in the integrand of this integral representation does not possess the correct dependence on qq. The origin of the problem is identified: the standard unitarity condition invoked in semiclassical transformation theory does not fix adequately in A(q,θ)A(q,\theta) a factor which is a function of the action JJ written in terms of qq and θ\theta. A prescription for an improved choice of this factor, based on succesfully reproducing the leading behaviour of wave functions in the vicinity of potential minima, is outlined. Exact evaluation of the modified integral representation via the Residue Theorem is possible. It yields wave functions which are not, in general, orthogonal. However, closed-form results obtained after Gram-Schmidt orthogonalization bear a striking resemblance to the exact analytical expressions for the stationary-state wave functions of the various potential models considered (namely, a P\"{o}schl-Teller oscillator and the Morse oscillator).Comment: RevTeX4, 6 page
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