A General qq-Oscillator Algebra

It is well-known that the Macfarlane-Biedenharn $q$-oscillator and its generalization has no Hopf structure, whereas the Hong Yan $q$-oscillator can be endowed with a Hopf structure. In this letter, we demonstrate that it is possible to construct a general $q$-oscillator algebra which includes the Macfarlane-Biedenharn oscillator algebra and the Hong Yan oscillator algebra as special cases.Comment: Needs subeqnarray.sty and epsf.sty (contains 2 figures

Superstrings, Gauge Fields and Black Holes

There has been spectacular progress in the development of string and superstring theories since its inception thirty years ago. Development in this area has never been impeded by the lack of experimental confirmation. Indeed, numerous bold and imaginative strides have been taken and the sheer elegance and logical consistency of the arguments have served as a primary motivation for string theorists to push their formulations ahead. In fact the development in this area has been so rapid that new ideas quickly become obsolete. On the other hand, this rapid development has proved to be the greatest hindrance for novices interested in this area. These notes serve as a gentle introduction to this topic. In these elementary notes, we briefly review the RNS formulation of superstring theory, GSO projection, $D$-branes, bosonic strings, dualities, dynamics of $D$-branes and the microscopic description of Bekenstein entropy of a black hole.Comment: Lecture notes for talk delivered at NUS in 1997-1998. Some recent updates added. The material may be somewhat outdated but it could still be useful for physicists new to the fiel

Symmetric Multiplets in Quantum Algebras

We consider a modified version of the coproduct for \U(\su_q(2)) and show that in the limit when $q \rightarrow 1$, there exists an essentially non-cocommutative coproduct. We study the implications of this non-cocommutativity for a system of two spin-$1/2$ particles. Here it is shown that, unlike the usual case, this non-trivial coproduct allows for symmetric and anti-symmetric states to be present in the multiplet. We surmise that our analysis could be related to the ferromagnetic and antiferromagnetic cases of the Heisenberg magnets.Comment: Needs subeqnarray.sty. To be published in Mod Phys Lett.

Monitoring currents in cold-atom circuits

Complex circuits of cold atoms can be exploited to devise new protocols for the diagnostics of cold-atoms systems. Specifically, we study the quench dynamics of a condensate confined in a ring-shaped potential coupled with a rectilinear guide of finite size. We find that the dynamics of the atoms inside the guide is distinctive of the states with different winding numbers in the ring condensate. We also observe that the depletion of the density, localized around the tunneling region of the ring condensate, can decay in a pair of excitations experiencing a Sagnac effect. In our approach, the current states of the condensate in the ring can be read out by inspection of the rectilinear guide only, leaving the ring condensate minimally affected by the measurement. We believe that our results set the basis for definition of new quantum rotation sensors. At the same time, our scheme can be employed to explore fundamental questions involving dynamics of bosonic condensates.Comment: Figures are enlarged. Section IV is added. Journal reference adde

Quantum nonlocality of four-qubit entangled states

Quantum nonlocality of several four-qubit states is investigated by constructing a new Bell inequality. These include the Greenberger-Zeilinger-Horne (GHZ) state, W state, cluster state, and the state $|\chi>$ that has been recently proposed in [PRL, {\bf 96}, 060502 (2006)]. The Bell inequality is optimally violated by $|\chi>$ but not violated by the GHZ state. The cluster state also violates the Bell inequality though not optimally. The state $|\chi>$ can thus be discriminated from the cluster state by using the inequality. Different aspects of four-partite entanglement are also studied by considering the usefulness of a family of four-qubit mixed states as resources for two-qubit teleportation. Our results generalize those in [PRL, {\bf 72}, 797 (1994)].Comment: 13 pages, 1 figur

Analytic Expression for Exact Ground State Energy Based on an Operator Method for a Class of Anharmonic Potentials

A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic expressions for the exact ground state energy have also been derived specifically for a large class of the one-dimensional oscillator with cubic-quartic anharmonic terms. Our analytical results can be used to check the accuracy of existing numerical methods, for instance the method of state-dependent diagonalization. Our results also agree with the asymptotic behavior in the divergent pertubative expansion of quartic harmonic oscillator.Comment: LaTeX with six figure (gif) files; Submitted to Phys. Rev.