Linear Continuum Mechanics for Quantum Many-Body Systems

We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the time-dependent wave function in a locally co-moving reference frame can be described as a geometric deformation of the ground-state wave function. We show that this equation of motion is exact for systems consisting of a single particle, and for all systems at sufficiently high frequency, and that it leads to an excitation spectrum that has the correct integrated strength. The theory is illustrated by simple model applications to one- and two-electron systems.Comment: 4 pages, 1 figure, 1 tabl

Continuum Mechanics for Quantum Many-Body Systems: The Linear Response Regime

We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-particle orbitals. We refer to our approach as continuum mechanics for quantum many-body systems. In the linear response regime, the equation of motion for the displacement field becomes a linear fourth-order integro-differential equation, whose only inputs are the one-particle density matrix and the pair correlation function of the ground-state. The complexity of this equation remains essentially unchanged as the number of particles increases. We show that our equation of motion is a hermitian eigenvalue problem, which admits a complete set of orthonormal eigenfunctions under a scalar product that involves the ground-state density. Further, we show that the excitation energies derived from this approach satisfy a sum rule which guarantees the exactness of the integrated spectral strength. Our formulation becomes exact for systems consisting of a single particle, and for any many-body system in the high-frequency limit. The theory is illustrated by explicit calculations for simple one- and two-particle systems.Comment: 23 pages, 4 figures, 1 table, 6 Appendices This paper is a follow-up to PRL 103, 086401 (2009

Pion and Eta Strings

In this paper we construct a string-like classical solution, the pion-string, in the linear sigma model. We then study the stability of the pion-string, and find that it is unstable in the parameter space allowed experimentally. We also speculate on the existance of an unstable eta-string, associated with spontaneous breakdown of the anomalous $U_A(1)$ symmetry in QCD at high temperatures. The implications of the pion and eta strings for cosmology and heavy ion collisions are briefly mentioned.Comment: 5 pages, LATE

Experimental measurement-based quantum computing beyond the cluster-state model

The paradigm of measurement-based quantum computation opens new experimental avenues to realize a quantum computer and deepens our understanding of quantum physics. Measurement-based quantum computation starts from a highly entangled universal resource state. For years, clusters states have been the only known universal resources. Surprisingly, a novel framework namely quantum computation in correlation space has opened new routes to implement measurement-based quantum computation based on quantum states possessing entanglement properties different from cluster states. Here we report an experimental demonstration of every building block of such a model. With a four-qubit and a six-qubit state as distinct from cluster states, we have realized a universal set of single-qubit rotations, two-qubit entangling gates and further Deutsch's algorithm. Besides being of fundamental interest, our experiment proves in-principle the feasibility of universal measurement-based quantum computation without using cluster states, which represents a new approach towards the realization of a quantum computer.Comment: 26 pages, final version, comments welcom

Effects of Shielding on Properties of Eddy Current Probes with Ferrite Cup Cores

In eddy current inspection the ability to detect small defects depends on the sensitivity of the system and on the relative sizes of the probe and the defect. To detect defects on the opposite surface the probe radius should be at least as great as the thickness of the material. This limits the sensitivity to small defects that can be achieved by decreasing the probe size. Assuming the instrumentation is a given, further sensitivity can be achieved by improving the sensitivity of the probe itself.</p

Combined Effect of IL-12Rβ2 and IL-23R Expression on Prognosis of Patients with Laryngeal Cancer

Background/Aims: This study aimed to pathologically elucidate the roles of interleukin-12 receptor (IL-12R) β2 and interleukin-23 receptor (IL-23R) expression in tumor cells and tumor-infiltrating lymphocytes (TILs) in the tumor microenvironment and to determine their combined effect on prognosis of laryngeal cancer (LC). Methods: The tumor-cell expression scores and TIL positivity ratiosof IL-12Rβ2 and IL-23R in matched LC and normal laryngeal tissue samples from 61 LC patients were measured via immunohistochemistry (IHC). We adopted a linear regression model to analyze the correlation between IL-12Rβ2 and IL-23R expression in tumor cells and TIL ratios. TheKaplan-Meier log-rank test and Cox regression hazard ratios were used to analyze survival. Results: LC tumor cells had a higher IL-12Rβ2 expression and TIL ratio than IL-23R expression and TIL ratio. The significant correlations between IL-12Rβ2 and IL-23R expression and TIL ratios were identified in LC tissues, particularly in well-differentiated LC. Furthermore, either high tumor cell IL-12Rβ2 or low IL-23R expression had better survival than its corresponding low or high expression, respectively. Similar results did for IL-12Rβ2 ratio and IL-23R ratio. Finally, patients with both high IL-12Rβ2 and low IL-23R had the best prognosis among any other combined groups with both gene expression (HR, 0.1; 95% CI, 0.0-0.8). Likewise, patients with positive ratios of high IL-12Rβ2 and low IL-23R TILs had the best survival (HR, 0.1; 95% CI, 0.0-0.4). Conclusion: IL-12Rβ2 and IL-23R create a homeostasis within the tumor cells and TILs, and this homeostasis affects prognosis. While the intrinsic mechanisms of epigenetic immunoediting for IL-12Rβ2 and IL-23R remain unknown, additional larger and functional studies are warranted for validation

Power corrections in the longitudinal and transverse structure functions of proton and deuteron

Power corrections to the Q**2 behaviour of the low-order moments of both the longitudinal and transverse structure functions of proton and deuteron have been investigated using available phenomenological fits of existing data in the Q**2 range between 1 and 20 (GeV/c)**2. The Natchmann definition of the moments has been adopted for disentangling properly target-mass and dynamical higher-twist effects in the data. The leading twist has been treated at next-to-leading order in the strong coupling constant and the effects of higher orders of the perturbative series have been estimated using a renormalon-inspired model. The contributions of (target-dependent) multiparton correlations to both 1/Q**2 and 1/Q**4 power terms have been determined in the transverse channel, while the longitudinal one appears to be consistent with a pure infrared renormalon picture in the whole Q**2-range between 1 and 20 (GeV/c)**2. Finally, the extracted twist-2 contribution in the deuteron turns out to be compatible with the hypothesis of an enhanced d-quark parton distribution at large x.Comment: revised version with only minor changes, to appear in Nuclear Physics

Twisting K3 x T^2 Orbifolds

We construct a class of geometric twists of Calabi-Yau manifolds of Voisin-Borcea type (K3 x T^2)/Z_2 and study the superpotential in a type IIA orientifold based on this geometry. The twists modify the direct product by fibering the K3 over T^2 while preserving the Z_2 involution. As an important application, the Voisin-Borcea class contains T^6/(Z_2 x Z_2), the usual setting for intersecting D6 brane model building. Past work in this context considered only those twists inherited from T^6, but our work extends these twists to a subset of the blow-up modes. Our work naturally generalizes to arbitrary K3 fibered Calabi-Yau manifolds and to nongeometric constructions.Comment: 57 pages, 4 figures; uses harvmac.tex, amssym.tex; v3: minor corrections, references adde

On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy

In this paper, we present a uniqueness result for solutions to the Gross-Pitaevskii hierarchy on the three-dimensional torus, under the assumption of an a priori spacetime bound. We show that this a priori bound is satisfied for factorized solutions to the hierarchy which come from solutions of the nonlinear Schr\"{o}dinger equation. In this way, we obtain a periodic analogue of the uniqueness result on $\mathbb{R}^3$ previously proved by Klainerman and Machedon, except that, in the periodic setting, we need to assume additional regularity. In particular, we need to work in the Sobolev class $H^{\alpha}$ for $\alpha>1$. By constructing a specific counterexample, we show that, on $\mathbb{T}^3$, the existing techniques don't apply in the endpoint case $\alpha=1$. This is in contrast to the known results in the non-periodic setting, where the these techniques are known to hold for all $\alpha \geq 1$. In our analysis, we give a detailed study of the crucial spacetime estimate associated to the free evolution operator. In this step of the proof, our methods rely on lattice point counting techniques based on the concept of the determinant of a lattice. This method allows us to obtain improved bounds on the number of lattice points which lie in the intersection of a plane and a set of radius $R$, depending on the number-theoretic properties of the normal vector to the plane. We are hence able to obtain a sharp range of admissible Sobolev exponents for which the spacetime estimate holds.Comment: 42 page