Strongly Focused Gravitational Waves

This paper contains a new proof of the formation of trapped spheres, in vacuum spacetimes, by the focusing of gravitational waves, from generic data. The first such result was obtained by Christodoulou (Zurich: Eur Math Soc, 2009). We exploit the same physical mechanism, but give a logically independent construction of these spacetimes.     

Relaxation of fermionic excitations in a strongly attractive Fermi gas in an optical lattice

We theoretically study the relaxation of high energy single particle excitations into molecules in a system of attractive fermions in an optical lattice, both in the superfluid and the normal phase. In a system characterized by an interaction scale U and a tunneling rate t, we show that the relaxation rate scales as ～Ctexp[-αU(2)/t(2)ln(U/t)] in the large U/t limit. We obtain explicit expressions for the temperature and density dependent exponent α, both in the low temperature superfluid phase and the high temperature phase with pairing but no coherence between the molecules. We find that the relaxation rate decreases both with temperature and deviation of the fermion density from half filling. We show that quasiparticle and phase degrees of freedom are effectively decoupled within experimental time scales allowing for observation of ordered states even at high total energy of the system.     

Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.     

Synthesis, characterization, and controlled aggregation of biotemplated polystyrene nanodisks

Cross-linked polystyrene nanodisks were prepared by controlled polymerization of styrene and divinylbenzene in the interior of bicelles, discoidal lipid aggregates. Aggregation behavior of polymer nanodisks was studied in water, organic solvents, and solid phase. Nanodisks form stable dispersions in aqueous solutions of surfactants, such as sodium dodecyl sulfate (SDS). Varying SDS/nanodisk ratio allowed us to control the size of nanodisk aggregates. Nanodisks are readily solubilized in nonpolar organic solvents, such as toluene and carbon tetrachloride, to yield stable monodisperse suspensions. These findings open opportunities for creating nanodisk-based nanocomposite materials. Stable nanodisk suspension in toluene enabled small angle neutron scattering (SANS) measurements. SANS data confirmed the nanodisk diameter and allowed accurate measurement of nanodisk thickness (19.5 ± 1.0 Å). In solid phase, nanodisks aggregate in sub-micron platelets.     

Entanglement generated by dissipation and steady state entanglement of two macroscopic objects

Entanglement is a striking feature of quantum mechanics and an essential ingredient in most applications in quantum information. Typically, coupling of a system to an environment inhibits entanglement, particularly in macroscopic systems. Here we report on an experiment where dissipation continuously generates entanglement between two macroscopic objects. This is achieved by engineering the dissipation using laser and magnetic fields, and leads to robust event-ready entanglement maintained for 0.04 s at room temperature. Our system consists of two ensembles containing about 10(12) atoms and separated by 0.5 m coupled to the environment composed of the vacuum modes of the electromagnetic field. By combining the dissipative mechanism with a continuous measurement, steady state entanglement is continuously generated and observed for up to 1 h.     

On the nuclear modification factor at RHIC and LHC

We show that pQCD factorization incorporated with pre-hadronization energy-loss effect naturally leads to flatness of the nuclear modification factor RAA$R_{\mathit{AA}}$ for produced hadrons at high transverse momentum pT$p_T$. We consider two possible scenarios for the pre-hadronization: In scenario 1, the produced gluon propagates through dense QCD medium and loses energy. In scenario 2, all gluons first decay to quark–antiquark pairs and then each pair loses energy as propagating through the medium. We show that the estimates of the energy-loss in these two different models lead to very close values and is able to explain the suppression of high-pT$p_T$ hadrons in nucleus–nucleus collisions at RHIC. We show that the onset of the flatness of RAA$R_{\mathit{AA}}$ for the produced hadron in central collisions at midrapidity is about pT≈15$p_T\approx 15$ and 25 GeV at RHIC and the LHC energies, respectively. We show that the smallness (RAA<0.5$R_{\mathit{AA}}<0.5$ ) and the high-pT$p_T$ flatness of RAA$R_{\mathit{AA}}$ obtained from the kT$k_T$ factorization supplemented with the Balitsky–Kovchegov (BK) equation is rather generic and it does not strongly depend on the details of the BK solutions. We show that energy-loss effect reduces the nuclear modification factor obtained from the kT$k_T$ factorization about 30–50% at moderate pT$p_T$.     

An intelligent decomposition of pairwise comparison matrices for large-scale decisions

A Pairwise Comparison Matrix (PCM) has been used to compute for relative priorities of elements and are integral components in widely applied decision making tools: the Analytic Hierarchy Process (AHP) and its generalized form, the Analytic Network Process (ANP). However, PCMs suffer from several issues limiting their applications to large-scale decision problems. These limitations can be attributed to the curse of dimensionality, that is, a large number of pairwise comparisons need to be elicited from a decision maker. This issue results to inconsistent preferences due to the limited cognitive powers of decision makers. To address these limitations, this research proposes a PCM decomposition methodology that reduces the elicited pairwise comparisons. A binary integer program is proposed to intelligently decompose a PCM into several smaller subsets using interdependence scores among elements. Since the subsets are disjoint, the most independent pivot element is identified to connect all subsets to derive the global weights of the elements from the original PCM. As a result, the number of pairwise comparison is reduced and consistency is of the comparisons is improved. The proposed decomposition methodology is applied to both AHP and ANP to demonstrate its advantages.     

Phase-sensitive measurements of order parameters for ultracold atoms through two-particle interferometry

Nontrivial symmetry of order parameters is crucial in some of the most interesting quantum many-body states of ultracold atoms as well as condensed matter systems. Examples in cold atoms include p-wave Feshbach molecules and d-wave paired states of fermions that could be realized in optical lattices in the Hubbard regime. Identifying these states in experiments requires measurements of the relative phase of different components of the entangled pair wave function. We propose and discuss two schemes for such phase-sensitive measurements, based on two-particle interference revealed in atom-atom or atomic density correlations. Our schemes can also be used for relative phase measurements for nontrivial particle-hole order parameters, such as d-density wave order.     

Estimation of the absolute internal-rotation entropy of molecules with two torsional degrees of freedom from stochastic simulations

A method of statistical estimation is applied to the problem of evaluating the absolute entropy of internal rotation in a molecule with two torsional degrees of freedom. The configurational part of the entropy is obtained as that of the joint probability density of an arbitrary form represented by a two-dimensional Fourier series, the coefficients of which are statistically estimated using a sample of the torsional angles of the molecule obtained by a stochastic simulation. The internal rotors in the molecule are assumed to be attached to a common frame, and their reduced moments of inertia are initially calculated as functions of the two torsional angles, but averaged over all the remaining internal degrees of freedom using the stochastic-simulation sample of the atomic configurations of the molecule. The torsional-angle dependence of the reduced moments of inertia can be also averaged out, and the absolute internal-rotation entropy of the molecule is obtained in a good approximation as the sum of the configurational entropy and a kinetic contribution fully determined by the averaged reduced moments of inertia. The method is illustrated using Monte Carlo simulations of isomers of stilbene and halogenated derivatives of propane. The two torsional angles in cis-stilbene are found to be much more strongly correlated than those in trans-stilbene, while the degree of the angular correlation in propane increases strongly on substitution of hydrogen atoms with chlorine.