Incompleteness of Representation Theory: Hidden symmetries and Quantum Non-Integrability

Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of these hidden symmetries depends upon the realization of the Hamiltonian.Comment: 4 pages, Revtex, Phys. Rev. Lett. , July 27 (1997), in pres

Evolution of magnetic properties in the vicinity of the Verwey transition in Fe3O4 thin films

We have systematically studied the evolution of magnetic properties, especially the coercivity and the remanence ratio in the vicinity of the Verwey transition temperature (TV ), of high-quality epitaxial Fe3O4 thin films grown on MgO (001), MgAl2O4 (MAO) (001), and SrTiO3 (STO) (001) substrates. We observed rapid change of magnetization, coercivity, and remanence ratio at TV , which are consistent with the behaviors of resistivity versus temperature [\r{ho}(T )] curves for the different thin films. In particular, we found quite different magnetic behaviors for the thin films onMgOfrom those onMAOand STO, inwhich the domain size and the strain state play very important roles. The coercivity is mainly determined by the domain size but the demagnetization process is mainly dependent on the strain state. Furthermore, we observed a reversal of remanence ratio at TV with thickness for the thin films grown on MgO: from a rapid enhancement for 40-nm- to a sharp drop for 200-nm-thick film, and the critical thickness is about 80 nm. Finally, we found an obvious hysteretic loop of coercivity (or remanence ratio) with temperature around TV , corresponding to the hysteretic loop of the \r{ho}(T ) curve, in Fe3O4 thin film grown on MgO

Remark on approximation in the calculation of the primordial spectrum generated during inflation

We re-examine approximations in the analytical calculation of the primordial spectrum of cosmological perturbation produced during inflation. Taking two inflation models (chaotic inflation and natural inflation) as examples, we numerically verify the accuracy of these approximations.Comment: 10 pages, 6 figures, to appear in PR

Estimating statistical distributions using an integral identity

We present an identity for an unbiased estimate of a general statistical distribution. The identity computes the distribution density from dividing a histogram sum over a local window by a correction factor from a mean-force integral, and the mean force can be evaluated as a configuration average. We show that the optimal window size is roughly the inverse of the local mean-force fluctuation. The new identity offers a more robust and precise estimate than a previous one by Adib and Jarzynski [J. Chem. Phys. 122, 014114, (2005)]. It also allows a straightforward generalization to an arbitrary ensemble and a joint distribution of multiple variables. Particularly we derive a mean-force enhanced version of the weighted histogram analysis method (WHAM). The method can be used to improve distributions computed from molecular simulations. We illustrate the use in computing a potential energy distribution, a volume distribution in a constant-pressure ensemble, a radial distribution function and a joint distribution of amino acid backbone dihedral angles.Comment: 45 pages, 7 figures, simplified derivation, a more general mean-force formula, add discussions to the window size, add extensions to WHAM, and 2d distribution