Scaling limit of virtual states of triatomic systems

For a system with three identical atoms, the dependence of the $s-$wave virtual state energy on the weakly bound dimer and trimer binding energies is calculated in a form of a universal scaling function. The scaling function is obtained from a renormalizable three-body model with a pairwise Dirac-delta interaction. It was also discussed the threshold condition for the appearance of the trimer virtual state.Comment: 9 pages, 3 figure

Correlated N-boson systems for arbitrary scattering length

We investigate systems of identical bosons with the focus on two-body correlations and attractive finite-range potentials. We use a hyperspherical adiabatic method and apply a Faddeev type of decomposition of the wave function. We discuss the structure of a condensate as function of particle number and scattering length. We establish universal scaling relations for the critical effective radial potentials for distances where the average distance between particle pairs is larger than the interaction range. The correlations in the wave function restore the large distance mean-field behaviour with the correct two-body interaction. We discuss various processes limiting the stability of condensates. With correlations we confirm that macroscopic tunneling dominates when the trap length is about half of the particle number times the scattering length.Comment: 15 pages (RevTeX4), 11 figures (LaTeX), submitted to Phys. Rev. A. Second version includes an explicit comparison to N=3, a restructured manuscript, and updated figure

Instability of a Bose-Einstein Condensate with Attractive Interaction

We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically lithium 7. Our method is to solve the time-dependent nonlinear Schrodinger equation numerically. For an isolated condensate, with no gain or loss, we find that the system is stable (apart from quantum tunneling) if the particle number N is less than a critical number N_c. For N > N_c, the system collapses to high-density clumps in a region near the center of the trap. The time for the onset of collapse is on the order of 1 trap period. Within numerical uncertainty, the results are consistent with the formation of a "black hole" of infinite density fluctuations, as predicted by Ueda and Huang. We obtain numerically N_c approximately 1251. We then include gain-loss mechanisms, i.e., the gain of atoms from a surrounding "thermal cloud", and the loss due to two- and three-body collisions. The number N now oscillates in a steady state, with a period of about 145 trap periods. We obtain N_c approximately 1260 as the maximum value in the oscillations.Comment: Email correspondence to [email protected] ; 18 pages and 9 EPS figures, using REVTeX and BoxedEPS macro

Dynamics with Infinitely Many Derivatives: The Initial Value Problem

Differential equations of infinite order are an increasingly important class of equations in theoretical physics. Such equations are ubiquitous in string field theory and have recently attracted considerable interest also from cosmologists. Though these equations have been studied in the classical mathematical literature, it appears that the physics community is largely unaware of the relevant formalism. Of particular importance is the fate of the initial value problem. Under what circumstances do infinite order differential equations possess a well-defined initial value problem and how many initial data are required? In this paper we study the initial value problem for infinite order differential equations in the mathematical framework of the formal operator calculus, with analytic initial data. This formalism allows us to handle simultaneously a wide array of different nonlocal equations within a single framework and also admits a transparent physical interpretation. We show that differential equations of infinite order do not generically admit infinitely many initial data. Rather, each pole of the propagator contributes two initial data to the final solution. Though it is possible to find differential equations of infinite order which admit well-defined initial value problem with only two initial data, neither the dynamical equations of p-adic string theory nor string field theory seem to belong to this class. However, both theories can be rendered ghost-free by suitable definition of the action of the formal pseudo-differential operator. This prescription restricts the theory to frequencies within some contour in the complex plane and hence may be thought of as a sort of ultra-violet cut-off.Comment: 40 pages, no figures. Added comments concerning fractional operators and the implications of restricting the contour of integration. Typos correcte

The bio refinery; producing feed and fuel from grain

It is both possible and practicable to produce feed and fuel from grain. Using the value of grain to produce renewable energy for transport, while using the remaining protein content of the grain as a valuable protein source for livestock and for fish, can be seen as a complimentary and optimal use of all the grain constituents. Consideration must be given to maximise the value of the yeast components, as substantial yeast is generated during the fermentation of the grain starch to produce ethanol. Yeast is a nutritionally rich feed ingredient, with potential for use both as feed protein and as a feed supplement with possible immunity and gut health enhancing properties. Bioprocessing, with the consequent economies of scale, is a process whereby the value of grain can be optimised in a way that is traditional, natural and sustainable for primarily producing protein and oil for feed with a co-product ethanol as a renewable fuel

Quantum Kinetic Theory V: Quantum kinetic master equation for mutual interaction of condensate and noncondensate

A detailed quantum kinetic master equation is developed which couples the kinetics of a trapped condensate to the vapor of non-condensed particles. This generalizes previous work which treated the vapor as being undepleted.Comment: RevTeX, 26 pages and 5 eps figure

Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy

We present three holographic constructions of fractional quantum Hall effect (FQHE) via string theory. The first model studies edge states in FQHE using supersymmetric domain walls in N=6 Chern-Simons theory. We show that D4-branes wrapped on CP^1 or D8-branes wrapped on CP^3 create edge states that shift the rank or the level of the gauge group, respectively. These holographic edge states correctly reproduce the Hall conductivity. The second model presents a holographic dual to the pure U(N)_k (Yang-Mills-)Chern-Simons theory based on a D3-D7 system. Its holography is equivalent to the level-rank duality, which enables us to compute the Hall conductivity and the topological entanglement entropy. The third model introduces the first string theory embedding of hierarchical FQHEs, using IIA string on C^2/Z_n.Comment: 36 pages, 6 figures; v2: with an improved derivation of Hall conductivity in section 3.2, typo corrections, and additional references; v3: explanations and comments adde

Quantum Kinetic Theory III: Quantum kinetic master equation for strongly condensed trapped systems

We extend quantum kinetic theory to deal with a strongly Bose-condensed atomic vapor in a trap. The method assumes that the majority of the vapor is not condensed, and acts as a bath of heat and atoms for the condensate. The condensate is described by the particle number conserving Bogoliubov method developed by one of the authors. We derive equations which describe the fluctuations of particle number and phase, and the growth of the Bose-Einstein condensate. The equilibrium state of the condensate is a mixture of states with different numbers of particles and quasiparticles. It is not a quantum superposition of states with different numbers of particles---nevertheless, the stationary state exhibits the property of off-diagonal long range order, to the extent that this concept makes sense in a tightly trapped condensate.Comment: 3 figures submitted to Physical Review