Rapid quantum approaches for combinatorial optimisation inspired by optimal state-transfer

We propose a new design heuristic to tackle combinatorial optimisation problems, inspired by Hamiltonians for optimal state-transfer. The result is a rapid approximate optimisation algorithm. We provide numerical evidence of the success of this new design heuristic. We find this approach results in a better approximation ratio than the Quantum Approximate Optimisation Algorithm at lowest depth for the majority of problem instances considered, while utilising comparable resources. This opens the door to investigating new approaches for tackling combinatorial optimisation problems, distinct from adiabatic-influenced approaches

A Circulating Hydrogen Ultra-High Purification System for the MuCap Experiment

The MuCap experiment is a high-precision measurement of the rate for the basic electroweak process of muon capture, mu- + p -> n + nu . The experimental approach is based on an active target consisting of a time projection chamber (TPC) operating with pure hydrogen gas. The hydrogen has to be kept extremely pure and at a stable pressure. A Circulating Hydrogen Ultrahigh Purification System was designed at the Petersburg Nuclear Physics Institute (PNPI) to continuously clean the hydrogen from impurities. The system is based on an adsorption cryopump to stimulate the hydrogen flow and on a cold adsorbent for the hydrogen cleaning. It was installed at the Paul Scherrer Institute (PSI) in 2004 and performed reliably during three experiment runs. During several months long operating periods the system maintained the hydrogen purity in the detector on the level of 20 ppb for moisture, which is the main contaminant, and of better than 7 ppb and 5 ppb for nitrogen and oxygen, respectively. The pressure inside the TPC was stabilized to within 0.024% of 10 bar at a hydrogen flow rate of 3 standard liters per minute.Comment: submitted to Nucl. Instr. Methods Phys. Res.

Path Integral Monte Carlo Approach to the U(1) Lattice Gauge Theory in (2+1) Dimensions

Path Integral Monte Carlo simulations have been performed for U(1) lattice gauge theory in (2+1) dimensions on anisotropic lattices. We extractthe static quark potential, the string tension and the low-lying "glueball" spectrum.The Euclidean string tension and mass gap decrease exponentially at weakcoupling in excellent agreement with the predictions of Polyakov and G{\" o}pfert and Mack, but their magnitudes are five times bigger than predicted. Extrapolations are made to the extreme anisotropic or Hamiltonian limit, and comparisons are made with previous estimates obtained in the Hamiltonian formulation.Comment: 12 pages, 16 figure

Magnetism in the dilute Kondo lattice model

The one dimensional dilute Kondo lattice model is investigated by means of bosonization for different dilution patterns of the array of impurity spins. The physical picture is very different if a commensurate or incommensurate doping of the impurity spins is considered. For the commensurate case, the obtained phase diagram is verified using a non-Abelian density-matrix renormalization-group algorithm. The paramagnetic phase widens at the expense of the ferromagnetic phase as the $f$-spins are diluted. For the incommensurate case, antiferromagnetism is found at low doping, which distinguishes the dilute Kondo lattice model from the standard Kondo lattice model.Comment: 11 pages, 2 figure

Brane Decay of a (4+n)-Dimensional Rotating Black Hole. III: spin-1/2 particles

In this work, we have continued the study of the Hawking radiation on the brane from a higher-dimensional rotating black hole by investigating the emission of fermionic modes. A comprehensive analysis is performed that leads to the particle, power and angular momentum emission rates, and sheds light on their dependence on fundamental parameters of the theory, such as the spacetime dimension and angular momentum of the black hole. In addition, the angular distribution of the emitted modes, in terms of the number of particles and energy, is thoroughly studied. Our results are valid for arbitrary values of the energy of the emitted particles, dimension of spacetime and angular momentum of the black hole, and complement previous results on the emission of brane-localised scalars and gauge bosons.Comment: Latex file, JHEP style, 34 pages, 16 figures Energy range in plots increased, minor changes, version published in JHE

A Mathematical Model of Liver Cell Aggregation In Vitro

The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work

Confinement and Chiral Symmetry Breaking via Domain-Like Structures in the QCD Vacuum

A qualitative mechanism for the emergence of domain structured background gluon fields due to singularities in gauge field configurations is considered, and a model displaying a type of mean field approximation to the QCD partition function based on this mechanism is formulated. Estimation of the vacuum parameters (gluon condensate, topological susceptibility, string constant and quark condensate) indicates that domain-like structures lead to an area law for the Wilson loop, nonzero topological susceptibility and spontaneous breakdown of chiral symmetry. Gluon and ghost propagators in the presence of domains are calculated explicitly and their analytical properties are discussed. The Fourier transforms of the propagators are entire functions and thus describe confined dynamical fields.Comment: RevTeX, 48 pages (32 pages + Appendices A-E), new references added [1,2,4,5] and minor formulae corrected for typographical error

Superstrings on NS5 backgrounds, deformed AdS3 and holography

We study a non-standard decoupling limit of the D1/D5-brane system, which interpolates between the near-horizon geometry of the D1/D5 background and the near-horizon limit of the pure D5-brane geometry. The S-dual description of this background is actually an exactly solvable two-dimensional (worldsheet) conformal field theory: {null-deformed SL(2,R)} x SU(2) x T^4 or K3. This model is free of strong-coupling singularities. By a careful treatment of the SL(2,R), based on the better-understood SL(2,R) / U(1) coset, we obtain the full partition function for superstrings on SL(2,R) x SU(2) x K3. This allows us to compute the partition functions for the J^3 and J^2 current-current deformations, as well as the full line of supersymmetric null deformations, which links the SL(2,R) conformal field theory with linear dilaton theory. The holographic interpretation of this setup is a renormalization-group flow between the decoupled NS5-brane world-volume theory in the ultraviolet (Little String Theory), and the low-energy dynamics of super Yang--Mills string-like instantons in six dimensions.Comment: JHEP style, 59 pages, 1 figure; v2: minor changes, to appear in JHE

Supersymmetric string model with 30 kappa--symmetries in an extended D=11 superspace and 30/ 32 BPS states

A supersymmetric string model in the D=11 superspace maximally extended by antisymmetric tensor bosonic coordinates, $\Sigma^{(528|32)}$, is proposed. It possesses 30 $\kappa$-symmetries and 32 target space supersymmetries. The usual preserved supersymmetry-$\kappa$-symmetry correspondence suggests that it describes the excitations of a BPS state preserving all but two supersymmetries. The model can also be formulated in any $\Sigma^{({n(n+1)\over 2}|n)}$ superspace, n=32 corresponding to D=11. It may also be treated as a `higher--spin generalization' of the usual Green--Schwarz superstring. Although the global symmetry of the model is a generalization of the super--Poincar\'e group, ${\Sigma}^{({n(n+1)\over 2}|n)}\times\supset Sp(n)$, it may be formulated in terms of constrained OSp(2n|1) orthosymplectic supertwistors. We work out this supertwistor realization and its Hamiltonian dynamics. We also give the supersymmetric p-brane generalization of the model. In particular, the $\Sigma^{(528|32)}$ supersymmetric membrane model describes excitations of a 30/32 BPS state, as the $\Sigma^{(528|32)}$ supersymmetric string does, while the supersymmetric 3-brane and 5-brane correspond, respectively, to 28/32 and 24/32 BPS states.Comment: 23 pages, RevTex4. V2: minor corrections in title and terminology, some references and comments adde