Internal and External Fluctuation Activated Non-equilibrium Reactive Rate Process

The activated rate process for non-equilibrium open systems is studied taking into account both internal and external noise fluctuations in a unified way. The probability of a particle diffusing passing over the saddle point and the rate constant together with the effective transmission coefficient are calculated via the method of reactive flux. We find that the complexity of internal noise is always harmful to the diffusion of particles. However the external modulation may be beneficial to the rate process.Comment: 10 pages, 1 figure (containing 2 subgraphs). arXiv admin note: text overlap with arXiv:cond-mat/9911028 by other author

Accidental Peccei-Quinn Symmetry from Discrete Flavour Symmetry and Pati-Salam

We show how an accidental $U(1)$ Peccei-Quinn (PQ) symmetry can arise from a discrete $A_4$ family symmetry combined with a discrete flavour symmetry $\mathbb{Z}_3 \times \mathbb{Z}_5^2$, in a realistic Pati-Salam unified theory of flavour. Imposing only these discrete flavour symmetries, the axion solution to the strong $CP$ problem is protected from PQ-breaking operators to the required degree. A QCD axion arises from a linear combination of $A_4$ triplet flavons, which are also responsible for fermion flavour structures due to their vacuum alignments. We find that the requirement of an accidental PQ symmetry arising from a discrete flavour symmetry constrains the form of the Yukawa matrices, providing a link between flavour and the strong $CP$ problem. Our model predicts specific flavour-violating couplings of the flavourful axion and thus puts a strong limit on the axion scale from kaon decays.Comment: 14 pages, 2 figure

Experimental evidence for new symmetry axis of electromagnetic beams

The new symmetry axis of a well-behaved electromagnetic beam advanced in paper Physical Review A 78, 063831 (2008) is not purely a mathematical concept. The experimental result reported by Hosten and Kwiat in paper Science 319, 787 (2008) is shown to demonstrate the existence of this symmetry axis that is neither perpendicular nor parallel to the propagation axis.Comment: 10 pages and 3 figure

Leading-Order Auxiliary Field Theory of the Bose-Hubbard Model

We discuss the phase diagram of the Bose-Hubbard (BH) model in the leading-order auxiliary field (LOAF) theory. LOAF is a conserving non-perturbative approximation that treats on equal footing the normal and anomalous density condensates. The mean-field solutions in LOAF correspond to first-order and second-order phase transition solutions with two critical temperatures corresponding to a vanishing Bose-Einstein condensate, $T_c$, and a vanishing diatom condensate, $T^\star$. The \emph{second-order} phase transition solution predicts the correct order of the transition in continuum Bose gases. For either solution, the superfluid state is tied to the presence of the diatom condensate related to the anomalous density in the system. In ultracold Bose atomic gases confined on a three-dimensional lattice, the critical temperature $T_c$ exhibits a quantum phase transition, where $T_c$ goes to zero at a finite coupling. The BH phase diagram in LOAF features a line of first-order transitions ending in a critical point beyond which the transition is second order while approaching the quantum phase transition. We identify a region where a diatom condensate is expected for temperatures higher than $T_c$ and less than $T_0$, the critical temperature of the non-interacting system. The LOAF phase diagram for the BH model compares qualitatively well with existing experimental data and results of \emph{ab initio} Monte Carlo simulations.Comment: 10 pages, 6 figure

Theory for supersolid 4^4He

Although both vacancies and interstitial have relatively high activation energies in the normal solid, we propose that a lower energy bound state of a vacancy and an interstitial may facilitate vacancy condensation to give supersolidity in $^{4}$He . We use a phenomenological two-band boson lattice model to demonstrate this new mechanism and discuss the possible relevance to the recently observed superfluid-like, non-classical rotational inertial experiments of Kim and Chan in solid $^{4}$He. Some of our results may also be applicable to trapped bosons in optical lattices.Comment: 5 pages, 2 figure