A Matlab Implementation of a Flat Norm Motivated Polygonal Edge Matching Method using a Decomposition of Boundary into Four 1-Dimensional Currents

We describe and provide code and examples for a polygonal edge matching method.Comment: Contains Matlab code and 4 figure

FRW and domain walls in higher spin gravity

We present exact solutions to Vasiliev's bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are infinite dimensional higher-spin extensions of spacetime isometries generated by six Killing vectors. The solutions presented are obtained by using a method of holomorphic factorization in noncommutative twistor space and gauge functions. In interpreting the solutions in terms of Fronsdal-type fields in spacetime, a field-dependent higher spin transformation is required, which is implemented at leading order. To this order, the scalar field solves Klein-Gordon equation with conformal mass in (anti) de Sitter space. We interpret the FRW solution with de Sitter asymptotics in the context of inflationary cosmology and we expect that the domain wall and FRW solutions are associated with spontaneously broken scaling symmetries in their holographic description. We observe that the factorization method provides a convenient framework for setting up a perturbation theory around the exact solutions, and we propose that the nonlinear completion of particle excitations over FRW and domain wall solutions requires black hole-like states.Comment: 63 page

Effective renormalized multi-body interactions of harmonically confined ultracold neutral bosons

We calculate the renormalized effective 2-, 3-, and 4-body interactions for N neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming 2-body interactions modeled with the combination of a zero-range and energy-dependent pseudopotential. We work to third-order in the scattering length a defined at zero collision energy, which is necessary to obtain both the leading-order effective 4-body interaction and consistently include finite-range corrections for realistic 2-body interactions. The leading-order, effective 3- and 4-body interaction energies are U3 = -(0.85576...)(a/l)^2 + 2.7921(1)(a/l)^3 + O[(a/l)^4] and U4 = +(2.43317...)(a/l)^3 + O[(a\l)^4], where w and l are the harmonic oscillator frequency and length, respectively, and energies are in units of hbar*w. The one-standard deviation error 0.0001 for the third-order coefficient in U3 is due to numerical uncertainty in estimating a slowly converging sum; the other two coefficients are either analytically or numerically exact. The effective 3- and 4-body interactions can play an important role in the dynamics of tightly confined and strongly correlated systems. We also performed numerical simulations for a finite-range boson-boson potential, and it was comparison to the zero-range predictions which revealed that finite-range effects must be taken into account for a realistic third-order treatment. In particular, we show that the energy-dependent pseudopotential accurately captures, through third order, the finite-range physics, and in combination with the multi-body effective interactions gives excellent agreement with the numerical simulations, validating our theoretical analysis and predictions.Comment: Updated introduction, correction of a few typos and sign error

Majorana fermions in ferromagnetic chains on the surface of bulk spin-orbit coupled ss-wave superconductors

Majorana fermion (MF) excitations in solid state system have non-Abelian statistics which is essential for topological quantum computation. Previous proposals to realize MF, however, generally requires fine-tuning of parameters. Here we explore a platform which avoids the fine-tuning problem, namely a ferromagnetic chain deposited on the surface of a spin-orbit coupled $s$-wave superconductor. We show that it generically supports zero-energy topological MF excitations near the two ends of the chain with minimal fine-tuning. Depending on the strength of the ferromagnetic moment in the chain, the number of MFs at each end, $n$, can be either one or two, and should be revealed by a robust zero-bias peak (ZBP) of height $2ne^2/h$ in scanning tunneling microscopy (STM) measurements which would show strong (weak) signals at the ends (middle) of the chain. The role of an approximate chiral symmetry which gives an integer topological invariant to the system is discussed.Comment: 9 pages, 4 figure

Potential Models and Lattice Gauge Current-Current Correlators

We compare current-current correlators in lattice gauge calculations with correlators in different potential models, for a pseudoscalar charmonium in the quark-gluon plasma. An important ingredient in the evaluation of the current-current correlator in the potential model is the basic principle that out of the set of continuum states, only resonance states and Gamow states with lifetimes of sufficient magnitudes can propagate as composite objects and can contribute to the current-current correlator. When the contributions from the bound states and continuum states are properly treated, the potential model current-current correlators obtained with the potential proposed in Ref. [11] are consistent with the lattice gauge correlators. The proposed potential model thus gains support to be a useful tool to complement lattice gauge calculations for the study of $Q\bar Q$ states at high temperatures.Comment: 18 pages, 4 figures, to be published in Physcial Review