Homer and Oral Tradition: The Formula, Part I

Processing note: review needed on strange symbol in abstract.This survey of the formula in Homer is divided into ten sections; the first five follow, the remainder will appear in a later issue of Oral Tradition. The sections are arranged as follows: Bibliographies and surveys ; The structure of the Homeric hexameter ; The formula and the hexameter ; The history of Homeric formulae: Homer, Hesiod, the Homeric Hymns and later poetry ; Enjambement ; Studies of specifi c formulae ; Formulae and meaning ; Analyses of formulae and tests for orality ; Homer and the criticism of oral poetry ; Future directions. Each of the first nine sections is followed by a list of references; a few items appear in more than one list. I have commented on most of the items, but for reasons of space a few are merely listed. Reviews are normally not included, and my knowledge of dissertations is usually limited to the synopses in Dissertation Abstracts. There must be omissions, for which I apologize; I will try to refer to them in later updates.--Page 171.Mark W. Edwards (Stanford University) is well known for his analyses of Homer's traditional style, having published papers that continue the kind of close philological scrutiny associated with Milman Parry's original work. He has written on aspects of phraseology, type-scenes, and the tension between convention and individuality in the Iliad

Homer and the oral tradition

Work done recently in the fields of linguistics (grammar of speech) and cognitive science (on memorization, etc.) has already been applied to Homeric studies and is producing exciting new understanding.Not

Tunneling phase gate for neutral atoms in a double-well lattice

We propose a new two--qubit phase gate for ultra--cold atoms confined in an experimentally realized tilted double--well optical lattice [Sebby--Strabley et al., Phys. Rev. A {\bf 73} 033605 (2006)]. Such a lattice is capable of confining pairs of atoms in a two--dimensional array of double--well potentials where control can be exercised over the barrier height and the energy difference of the minima of the two wells (known as the ``tilt''). The four lowest single--particle motional states consist of two pairs of motional states in which each pair is localized on one side of the central barrier, allowing for two atoms confined in such a lattice to be spatially separated qubits. We present a time--dependent scheme to manipulate the tilt to induce tunneling oscillations which produce a collisional phase gate. Numerical simulations demonstrate that this gate can be performed with high fidelity.Comment: 5 pages, 4 figure

Collective excitations of atomic Bose-Einstein condensates

We apply linear-response analysis of the Gross-Pitaevskii equation to obtain the excitation frequencies of a Bose-Einstein condensate confined in a time-averaged orbiting potential trap. Our calculated values are in excellent agreement with those observed in a recent experiment.Comment: 11 pages, 2 Postscript figures, uses psbox.tex for automatic figure inclusion. More info at http://amo.phy.gasou.edu/bec.htm

Momentum-space engineering of gaseous Bose-Einstein condensates

We show how the momentum distribution of gaseous Bose--Einstein condensates can be shaped by applying a sequence of standing-wave laser pulses. We present a theory, whose validity for was demonstrated in an earlier experiment [L.\ Deng, et al., \prl {\bf 83}, 5407 (1999)], of the effect of a two-pulse sequence on the condensate wavefunction in momentum space. We generalize the previous result to the case of $N$ pulses of arbitrary intensity separated by arbitrary intervals and show how these parameters can be engineered to produce a desired final momentum distribution. We find that several momentum distributions, important in atom-interferometry applications, can be engineered with high fidelity with two or three pulses.Comment: 13 pages, 4 figure

Probing the circulation of ring-shaped Bose-Einstein condensates

This paper reports the results of a theoretical and experimental study of how the initial circulation of ring-shaped Bose-Einstein condensates (BECs) can be probed by time-of-flight (TOF) images. We have studied theoretically the dynamics of a BEC after release from a toroidal trap potential by solving the 3D Gross-Pitaevskii (GP) equation. The trap and condensate characteristics matched those of a recent experiment. The circulation, experimentally imparted to the condensate by stirring, was simulated theoretically by imprinting a linear azimuthal phase on the initial condensate wave function. The theoretical TOF images were in good agreement with the experimental data. We find that upon release the dynamics of the ring--shaped condensate proceeds in two distinct phases. First, the condensate expands rapidly inward, filling in the initial hole until it reaches a minimum radius that depends on the initial circulation. In the second phase, the density at the inner radius increases to a maximum after which the hole radius begins slowly to expand. During this second phase a series of concentric rings appears due to the interference of ingoing and outgoing matter waves from the inner radius. The results of the GP equation predict that the hole area is a quadratic function of the initial circulation when the condensate is released directly from the trap in which it was stirred and is a linear function of the circulation if the trap is relaxed before release. These scalings matched the data. Thus, hole size after TOF can be used as a reliable probe of initial condensate circulation. This connection between circulation and hole size after TOF will facilitate future studies of atomtronic systems that are implemented in ultracold quantum gases.Comment: 9 pages, 9 figure

Symmetry-Breaking and Symmetry-Restoring Dynamics of a Mixture of Bose-Einstein Condensates in a Double Well

We study the coherent nonlinear tunneling dynamics of a binary mixture of Bose-Einstein condensates in a double-well potential. We demonstrate the existence of a new type of mode associated with the "swapping" of the two species in the two wells of the potential. In contrast to the symmetry breaking macroscopic quantum self-trapping (MQST) solutions, the swapping modes correspond to the tunneling dynamics that preserves the symmetry of the double well potential. As a consequence of two distinct types of broken symmetry MQST phases where the two species localize in the different potential welils or coexist in the same well, the corresponding symmetry restoring swapping modes result in dynamics where the the two species either avoid or chase each other. In view of the possibility to control the interaction between the species, the binary mixture offers a very robust system to observe these novel effects as well as the phenomena of Josephson oscillations and pi-mode