Time-dependent currents of 1D bosons in an optical lattice

We analyse the time-dependence of currents in a 1D Bose gas in an optical lattice. For a 1D system, the stability of currents induced by accelerating the lattice exhibits a broad crossover as a function of the magnitude of the acceleration, and the strength of the inter-particle interactions. This differs markedly from mean-field results in higher dimensions. Using the infinite Time Evolving Block Decimation algorithm, we characterise this crossover by making quantitative predictions for the time-dependent behaviour of the currents and their decay rate. We also compute the time-dependence of quasi-condensate fractions which can be measured directly in experiments. We compare our results to calculations based on phase-slip methods, finding agreement with the scaling as the particle density increases, but with significant deviations near unit filling.Comment: 19 pages, 10 figure

First year student experience

The application was made on behalf of the undergraduate courses team who sought to enhance the first year experience by engaging students in the practice of business. The intention was to develop and signpost enterprising qualities and characteristics in first year learners and develop confidence as well as competence. The undergraduate review for FBL commenced in September 2009. This offered an opportunity to innovate and build good practice in enterprise learning as a pilot to inform the undergraduate review. The team sought to provide a coherent and relevant set of learning experiences that could be achieved outside structured curriculum that would enable learning through live projects

The error of representation: basic understanding

Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor) and the forecast climatology (forecast attractor) leads to the error of representation. A new gain matrix for the data assimilation problem is derived that illustrates the proper approaches one may take to perform Bayesian data assimilation when the observations are of states on one attractor but the forecast model resides on another. This new data assimilation algorithm is the optimal scheme for the situation where the distributions on the true attractor and the forecast attractors are separately Gaussian and there exists a linear map between them. The results of this theory are illustrated in a simple Gaussian multivariate model

Dissipative dynamics and cooling rates of trapped impurity atoms immersed in a reservoir gas

We study the dissipative dynamics of neutral atoms in anisotropic harmonic potentials, immersed in a reservoir species that is not trapped by the harmonic potential. Considering initial motional excitation of the atoms along one direction, we explore the resulting spontaneous emission of reservoir excitations, across a range of trap parameters from strong to weak radial confinement. In different limits these processes are useful as a basis for analogies to laser cooling, or as a means to introduce controlled dissipation to many-body dynamics. For realistic experimental parameters, we analyze the distribution of the atoms during the decay and determine the effects of heating arising from a finite temperature reservoir

Bounds and comparisons of the loss ratio in queues driven by an M/M/∞ source.

We obtain upper bounds for the loss probability in a queue driven by an M/M/∞ source. The bound is compared with exact numerical results, and with bounds for two related arrivals models: superposed two state Markov fluids, and the Ornstein—Uhlenbeck process. The bounds are shown to behave continuously through approximation procedures relating the models

Classical simulation of quantum many-body systems with a tree tensor network

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement is bounded for any bipartite split along an edge of the tree. This is achieved by expanding the {\em time-evolving block decimation} simulation algorithm for time evolution from a one dimensional lattice to a tree graph, while replacing a {\em matrix product state} with a {\em tree tensor network}. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.Comment: 4 pages,7 figure

High order non-unitary split-step decomposition of unitary operators

We propose a high order numerical decomposition of exponentials of hermitean operators in terms of a product of exponentials of simple terms, following an idea which has been pioneered by M. Suzuki, however implementing it for complex coefficients. We outline a convenient fourth order formula which can be written compactly for arbitrary number of noncommuting terms in the Hamiltonian and which is superiour to the optimal formula with real coefficients, both in complexity and accuracy. We show asymptotic stability of our method for sufficiently small time step and demonstrate its efficiency and accuracy in different numerical models.Comment: 10 pages, 4 figures (5 eps files) Submitted to J. of Phys. A: Math. Ge

Is efficiency of classical simulations of quantum dynamics related to integrability?

Efficiency of time-evolution of quantum observables, and thermal states of quenched hamiltonians, is studied using time-dependent density matrix renormalization group method in a family of generic quantum spin chains which undergo a transition from integrable to non-integrable - quantum chaotic case as control parameters are varied. Quantum states (observables) are represented in terms of matrix-product-operators with rank D_\epsilon(t), such that evolution of a long chain is accurate within fidelity error \epsilon up to time t. We find that rank generally increases exponentially, D_\epsilon(t) \propto \exp(const t), unless the system is integrable in which case we find polynomial increase.Comment: 4 pages; v2. added paragraph discussing pure state

Tooth Enamel Structure in the Koala, Phascolarctos cinereus: - Some Functional Interpretations

The purpose of this study is to determine whether the structural organization of Pattern 2 marsupial enamel in the Koala is disposed to resist wear on the sectorial crests of the molar teeth. The orientation of wear on the crests is uniformly delineated by parallel scratches on their polished surfaces. Twin blades, a leading and a trailing edge of enamel are formed on each crest by wear into dentine on which the differential wear at enamel to dentine interfaces indicates that the direction of wear is labial to lingual. 96 leading and trailing edges from 12 koala molars were examined by light and scanning electron microscopy as ground sections, polished and etched surfaces or polished and etched whole mount preparations sputter coated with gold. The results showed that the leading and trailing enamel edges are different in their thicknesses, and in the course of their rods. The rods in the thinner leading edge are angled at 25° to the long axis of the tooth and cross the worn surface al 60-70°. Trailing rods run at 5° to the long axis to cross the worn surface at 90°. The inter-rod sheets run parallel to the wear striations and thus hold the rods in palisades angled in the leading edge particularly to resist the vector of the occlusal forces in the direction of wear. Crystals in the rods emerge roughly perpendicular onto the worn surface which makes them more resistant to abrasion than those in the inter-rod substance which lie parallel to the worn surface and are more readily removed. Koala enamel on the sectorial crests is thus a simple Pattern 2 rod packing pattern but the angles of the rods and the alignment of the inter-rod substance appear to be adapted to resist occlusal forces and abrasion

Preparation and spectroscopy of a metastable Mott insulator state with attractive interactions

We prepare and study a metastable attractive Mott insulator state formed with bosonic atoms in a three-dimensional optical lattice. Starting from a Mott insulator with Cs atoms at weak repulsive interactions, we use a magnetic Feshbach resonance to tune the interactions to large attractive values and produce a metastable state pinned by attractive interactions with a lifetime on the order of 10 seconds. We probe the (de-)excitation spectrum via lattice modulation spectroscopy, measuring the interaction dependence of two- and three-body bound state energies. As a result of increased on-site three-body loss we observe resonance broadening and suppression of tunneling processes that produce three-body occupation.Comment: 7 pages, 6 figure