Condensate deformation and quantum depletion of Bose-Einstein condensates in external potentials

The one-body density matrix of weakly interacting, condensed bosons in external potentials is calculated using inhomogeneous Bogoliubov theory. We determine the condensate deformation caused by weak external potentials on the mean-field level. The momentum distribution of quantum fluctuations around the deformed ground state is obtained analytically, and finally the resulting quantum depletion is calculated. The depletion due to the external potential, or potential depletion for short, is a small correction to the homogeneous depletion, validating our inhomogeneous Bogoliubov theory. Analytical results are derived for weak lattices and spatially correlated random potentials, with simple, universal results in the Thomas-Fermi limit of very smooth potentials.Comment: 17 pages, 4 figures. v2: published version, minor change

Feshbach-type resonances for two-particle scattering in graphene

Two-particle scattering in graphene is a multichannel problem, where the energies of the identical or opposite-helicity channels lie in disjoint energy segments. Due to the absence of Galilean invariance, these segments depend on the total momentum $Q$. The dispersion relations for the two opposite-helicity scattering channels are analogous to those of two one-dimensional tight-binding lattices with opposite dispersion relations, which are known to easily bind states at their edges. When an $s$-wave separable interaction potential is assumed, those bound states reveal themselves as three Feshbach resonances in the identical-helicity channel. In the limit $Q \rightarrow 0$, one of the resonances survives and the opposite-helicity scattering amplitudes vanish.Comment: 8 pages, 2 figure

Spin-dependent THz oscillator based on hybrid graphene superlattices

We theoretically study the occurrence of Bloch oscillations in biased hybrid graphene systems with spin-dependent superlattices. The spin-dependent potential is realized by a set of ferromagnetic insulator strips deposited on top of a gapped graphene nanoribbon, which induce a proximity exchange splitting of the electronic states in the graphene monolayer. We numerically solve the Dirac equation and study Bloch oscillations in the lowest conduction band of the spin-dependent superlattice. While the Bloch frequency is the same for both spins, we find the Bloch amplitude to be spin dependent. This difference results in a spin-polarized ac electric current in the THz range.Comment: 4 pages, 6 figure

\u3ci\u3eFoster v. Carson\u3c/i\u3e: The Ninth Circuit Misapplies the Capable-of-Retention-Yet-Evading-Review Exception to the Mootness Doctrine and Lends a Free Hand to Budget-Cutting State Officials

In Foster v. Carson, public defender organizations and indigent defendants sued the chief justice of the Oregon Supreme Court for suspending appointments of indigent defense counsel. Before the parties could fully litigate the case, the chief justice reinstated appointments. Subsequently, the United States Court of Appeals for the Ninth Circuit dismissed the case as moot and held that the exception to the mootness doctrine for cases capable-of-repetition-yet-evading-review did not apply. A case falls under that exception when the party resisting mootness demonstrates that it was not possible to fully litigate the action before it ceased and there is a reasonable expectation that the party will be subjected to the same action in the future. Because the court concluded that it was not possible to fully litigate the case before the chief justice reinstated appointments, applicability of the capable-of-repetition-yet-evading-review exception depended only on whether there was a reasonable expectation that the injury would recur. When evaluated in light of U.S. Supreme Court and Ninth Circuit precedent, the facts in Foster support a finding that there was a reasonable expectation that the chief justice would again suspend funding for indigent defense counsel. The public interest in deciding the constitutionality of the chief justice\u27s action further supports application of the exception

Exploring multivariate data structures with local principal curves.

A new approach to find the underlying structure of a multidimensional data cloud is proposed, which is based on a localized version of principal components analysis. More specifically, we calculate a series of local centers of mass and move through the data in directions given by the first local principal axis. One obtains a smooth ``local principal curve'' passing through the "middle" of a multivariate data cloud. The concept adopts to branched curves by considering the second local principal axis. Since the algorithm is based on a simple eigendecomposition, computation is fast and easy

Spin foam model from canonical quantization

We suggest a modification of the Barrett-Crane spin foam model of 4-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found as a space of the so-called projected spin networks. These spin networks are identified with the boundary states of a spin foam model and provide a generalization of the unique Barrette-Crane intertwiner. We propose a way to modify the Barrett-Crane quantization procedure to arrive at this generalization: the B field (bi-vectors) should be promoted not to generators of the gauge algebra, but to their certain projection. The modification is also justified by the canonical analysis of Plebanski formulation. Finally, we compare our construction with other proposals to modify the Barret-Crane model.Comment: 26 pages; presentation improved, important changes concerning the closure constraint and the vertex amplitude; minor correctio

On the Universality of the Entropy-Area Relation

We present an argument that, for a large class of possible dynamics, a canonical quantization of gravity will satisfy the Bekenstein-Hawking entropy-area relation. This result holds for temperatures low compared to the Planck temperature and for boundaries with areas large compared to Planck area. We also relate our description, in terms of a grand canonical ensemble, to previous geometric entropy calculations using area ensembles.Comment: 6 page

Dynamics and stability of Bose-Einstein solitons in tilted optical lattices

Bloch oscillations of Bose-Einstein condensates realize sensitive matter-wave interferometers. We investigate the dynamics and stability of bright-soliton wave packets in one-dimensional tilted optical lattices with a modulated mean-field interaction $g(t)$. By means of a time-reversal argument, we prove the stability of Bloch oscillations of breathing solitons that would be quasistatically unstable. Floquet theory shows that these breathing solitons can be more stable against certain experimental perturbations than rigid solitons or even non-interacting wave packets.Comment: final, published versio