New spin squeezing and other entanglement tests for two mode systems of identical bosons

For any quantum state representing a physical system of identical particles, the density operator must satisfy the symmetrization principle (SP) and conform to super-selection rules (SSR) that prohibit coherences between differing total particle numbers. Here we consider bi-partitite states for massive bosons, where both the system and sub-systems are modes (or sets of modes) and particle numbers for quantum states are determined from the mode occupancies. Defining non-entangled or separable states as those prepared via local operations (on the sub-systems) and classical communication processes, the sub-system density operators are also required to satisfy the SP and conform to the SSR, in contrast to some other approaches. Whilst in the presence of this additional constraint the previously obtained sufficiency criteria for entanglement, such as the sum of the ˆSx and ˆSy variances for the Schwinger spin components being less than half the mean boson number, and the strong correlation test of |haˆm (bˆ†)ni|2 being greater than h(aˆ†)maˆm (bˆ†)nbˆni(m, n = 1, 2, . . .) are still valid, new tests are obtained in our work. We show that the presence of spin squeezing in at least one of the spin components ˆSx , ˆSy and ˆSz is a sufficient criterion for the presence of entanglement and a simple correlation test can be constructed of |haˆm (bˆ†)ni|2 merely being greater than zero.We show that for the case of relative phase eigenstates, the new spin squeezing test for entanglement is satisfied (for the principle spin operators), whilst the test involving the sum of the ˆSx and ˆSy variances is not. However, another spin squeezing entanglement test for Bose–Einstein condensates involving the variance in ˆSz being less than the sum of the squared mean values for ˆSx and ˆSy divided by the boson number was based on a concept of entanglement inconsistent with the SP, and here we present a revised treatment which again leads to spin squeezing as an entanglement test

Approximations of Sobolev norms in Carnot groups

This paper deals with a notion of Sobolev space $W^{1,p}$ introduced by J.Bourgain, H.Brezis and P.Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by A.Ponce to obtain a Poincar\'e-type inequality. The main results that we present are a generalization of these two works to a non-Euclidean setting, namely that of Carnot groups. We show that the seminorm expressd in terms of the intrinsic distance is equivalent to the $L^p$ norm of the intrinsic gradient, and provide a Poincar\'e-type inequality on Carnot groups by means of a constructive approach which relies on one-dimensional estimates. Self-improving properties are also studied for some cases of interest

Local structural studies of Ba1−x_{1-x}Kx_xFe2_2As2_2 using atomic pair distribution function analysis

Systematic local structural studies of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ system are undertaken at room temperature using atomic pair distribution function (PDF) analysis. The local structure of the Ba$_{1-x}$K$_x$Fe$_2$As$_2$ is found to be well described by the long-range structure extracted from the diffraction experiments, but with anisotropic atomic vibrations of the constituent atoms ($U_{11}$ = $U_{22} \ne U_{33}$). The crystal unit cell parameters, the FeAs$_4$ tetrahedral angle and the pnictogen height above the Fe-plane are seen to show systematic evolution with K doping, underlining the importance of the structural changes, in addition to the charge doping, in determining the properties of Ba$_{1-x}$K$_x$Fe$_2$As$_2$

On testing the violation of the Clausius inequality in nanoscale electric circuits

The Clausius inequality, one of the classical formulations of the second law, was recently found to be violated in the quantum regime. Here this result is formulated in the context of a mesoscopic or nanoscale linear RLC circuit interacting with a thermal bath. Previous experiments in this and related fields are analyzed and possibilities of experimental detection of the violation are pointed out. It is discussed that recent experiments reached the range of temperatures, where the effect should be visible, and that a part of the proposal was already confirmed.Comment: 5 pages revtex 4. No figure

Isotropic three-dimensional left-handed meta-materials

We investigate three-dimensional left-handed and related meta-materials based on a fully symmetric multi-gap single-ring SRR design and crossing continuous wires. We demonstrate isotropic transmission properties of a SRR-only meta-material and the corresponding left-handed material which possesses a negative effective index of refraction due to simultaneously negative effective permeability and permittivity. Minor deviations from complete isotropy are due to the finite thickness of the meta-material.Comment: 4 pages, 6 figure

The circumstellar envelope of AFGL 4106

We present new imaging and spectroscopy of the post-red supergiant binary AFGL 4106. Coronographic imaging in H-alpha reveals the shape and extent of the ionized region in the circumstellar envelope (CSE). Echelle spectroscopy with the slit covering almost the entire extent of the CSE is used to derive the physical conditions in the ionized region and the optical depth of the dust contained within the CSE. The dust shell around AFGL 4106 is clumpy and mixed with ionized gas. H-alpha and [N II] emission is brightest from a thin bow-shaped layer just outside of the detached dust shell. On-going mass loss is traced by [Ca II] emission and blue-shifted absorption in lines of low-ionization species. A simple model is used to interpret the spatial distribution of the circumstellar extinction and the dust emission in a consistent way.Comment: 10 pages, 11 figures. Accepted for publication in Astronomy & Astrophysics Main Journa

Negative curves on algebraic surfaces

We study curves of negative self-intersection on algebraic surfaces. We obtain results for smooth complex projective surfaces X on the number of reduced, irreducible curves C of negative self-intersection C^2. The only known examples of surfaces for which C^2 is not bounded below are in positive characteristic, and the general expectation is that no examples can arise over the complex numbers. Indeed, we show that the idea underlying the examples in positive characteristic cannot produce examples over the complex number field. The previous version of this paper claimed to give a counterexample to the Bounded Negativity Conjecture. The idea of the counterexample was to use Hecke translates of a smooth Shimura curve in order to create an infinite sequence of curves violating the Bounded Negativity Conjecture. To this end we applied Hirzebruch Proportionality to all Hecke translates, simultaneously desingularized by a version of Jaffee's Lemma which exists in the literature but which turns out to be false. Indeed, in the new version of the paper, we show that only finitely many Hecke translates of a special subvariety of a Hilbert modular surface remain smooth. This new result is based on work done jointly with Xavier Roulleau, who has been added as an author. The other results in the original posting of this paper remain unchanged.Comment: 14 pages, X. Roulleau added as author, counterexample to Bounded Negativity Conjecture withdrawn and replaced by a proof that there are only finitely many smooth Shimura curves on a compact Hilbert modular surface; the other results in the original posting of this paper remain unchange

Cysteine proteases: The S2P2 hydrogen bond is more important for catalysis than is the analogous S1P1 bond

AbstractHigh hydrophobicity of the second amino acid N-terminal to the scissile bond (P2 residue) is generally considered to be the major factor in the specificity of the substrates for cysteine proteases of the papain family. To examine the catalytic contribution of the S2P2 hydrogen bond apparent from X-ray crystallographic studies, the kinetics of Z-Phe-Gly-OEt and its thiono derivative were compared. The thiono compound contains a sulfur atom in place of the carbonyl oxygen of the phenylalanine residue. It was found that the specificity rate constants for the reactions of the thiono substrate with various cysteine proteases are lower by 2–3 orders of magnitude as compared to the corresponding rate constants for the oxo substrate. This remarkable effect is not expected in the light of previous studies indicating that the change from oxygen to sulfur in the P1 residue was without an appreciable effect. The results are interpreted in terms of a distorted binding of the thiono substrate

The structure of disks around intermediate-mass young stars from mid-infrared interferometry. Evidence for a population of group II disks with gaps

The disks around Herbig Ae/Be stars are commonly divided into group I and group II based on their far-infrared spectral energy distribution, and the common interpretation for that is flared and flat disks. Recent observations suggest that many flaring disks have gaps, whereas flat disks are thought to be gapless. The different groups of objects can be expected to have different structural signatures in high-angular-resolution data. Over the past 10 years, the MIDI instrument on the Very Large Telescope Interferometer has collected observations of several tens of protoplanetary disks. We model the large set of observations with simple geometric models. A population of radiative-transfer models is synthesized for interpreting the mid-infrared signatures. Objects with similar luminosities show very different disk sizes in the mid-infrared. Restricting to the young objects of intermediate mass, we confirm that most group I disks are in agreement with being transitional. We find that several group II objects have mid-infrared sizes and colors overlapping with sources classified as group I, transition disks. This suggests that these sources have gaps, which has been demonstrated for a subset of them. This may point to an intermediate population between gapless and transition disks. Flat disks with gaps are most likely descendants of flat disks without gaps. Gaps, potentially related to the formation of massive bodies, may therefore even develop in disks in a far stage of grain growth and settling. The evolutionary implications of this new population could be twofold. Either gapped flat disks form a separate population of evolved disks, or some of them may further evolve into flaring disks with large gaps. The latter transformation may be governed by the interaction with a massive planet, carving a large gap and dynamically exciting the grain population in the disk.Comment: 24 pages, 11 figures, A&A in pres