Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation

In this article we apply the technique proposed in Deng-Hou-Yu (Comm. PDE, 2005) to study the level set dynamics of the 2D quasi-geostrophic equation. Under certain assumptions on the local geometric regularity of the level sets of $\theta$, we obtain global regularity results with improved growth estimate on $| \nabla^{\bot} \theta |$. We further perform numerical simulations to study the local geometric properties of the level sets near the region of maximum $| \nabla^{\bot} \theta |$. The numerical results indicate that the assumptions on the local geometric regularity of the level sets of $\theta$ in our theorems are satisfied. Therefore these theorems provide a good explanation of the double exponential growth of $| \nabla^{\bot} \theta |$ observed in this and past numerical simulations.Comment: 25 pages, 10 figures. Corrected a few typo

Deterministic spin-wave interferometer based on Rydberg blockade

The spin-wave (SW) NOON state is an $N$-particle Fock state with two atomic spin-wave modes maximally entangled. Attributed to the property that the phase is sensitive to collective atomic motion, the SW NOON state can be utilized as a novel atomic interferometer and has promising application in quantum enhanced measurement. In this paper we propose an efficient protocol to deterministically produce the atomic SW NOON state by employing Rydberg blockade. Possible errors in practical manipulations are analyzed. A feasible experimental scheme is suggested. Our scheme is far more efficient than the recent experimentally demonstrated one, which only creates a heralded second-order SW NOON state.Comment: 5 pages, 2 figure

Remote information concentration and multipartite entanglement in multilevel systems

Remote information concentration (RIC) in $d$-level systems (qudits) is studied. It is shown that the quantum information initially distributed in three spatially separated qudits can be remotely and deterministically concentrated to a single qudit via an entangled channel without performing any global operations. The entangled channel can be different types of genuine multipartite pure entangled states which are inequivalent under local operations and classical communication. The entangled channel can also be a mixed entangled state, even a bound entangled state which has a similar form to the Smolin state, but has different features from the Smolin state. A common feature of all these pure and mixed entangled states is found, i.e., they have $d^2$ common commuting stabilizers. The differences of qudit-RIC and qubit-RIC ($d=2$) are also analyzed.Comment: 10 pages, 3 figure

(1H-Benzimidazole-5-carb­oxy­lic acid-κN 3)(1H-benzimidazole-6-carb­oxy­lic acid-κN 3)silver(I) perchlorate

The reaction of 1H-benzimidazole-5-carb­oxy­lic acid with silver nitrate in the presence of perchloric acid under hydro­thermal conditions yielded the title complex, [Ag(C8H6N2O2)2]ClO4, which comprises of an [Ag(C8H6N2O2)2] mononuclear cation and a perchlorate anion. The AgI ion is coordinated by two N atoms from two different neutral 1H-benzimidazole-5-carb­oxy­lic acid ligands with an N—Ag—N bond angle of 163.21 (14)°, forming an [Ag(C8H6N2O2)2] mononuclear cation. Although both ligands in the mononuclear cation are monodentate with one N atom coordinated to the metal ion, they are different: one is N3 coordinated to the Ag I ion and the N1 atom protonated, the other with the N1 coordinated to the Ag I ion and the N3 atom protonated (and thus formally a 1H-benzimidazole-6-carb­oxy­lic acid rather than a 1H-benzimidazole-5-carb­oxy­lic acid ligand). The planes of the two planar ligands are roughly perpendicular, making a dihedral angle of 84.97 (2)°. The packing of the ions is stablized by extensive O—H⋯O, N—H⋯O and C—H⋯O hydrogen bonds, and by remote Ag⋯O inter­actions [3.002 (3), 3.581 (5) and 3.674 (5) Å]

Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases

From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.Comment: 5 pages, 2 figures; published versio