Active-space N-representability constraints for variational two-particle reduced density matrix calculations

The ground-state energy of a system of fermions can be calculated by minimizing a linear functional of the two-particle reduced density matrix (2-RDM) if an accurate set of N-representability conditions is applied. In this Letter we introduce a class of linear N-representability conditions based on exact calculations on a reduced active space. Unlike wave-function-based approaches, the 2-RDM methodology allows us to combine information from calculations on different active spaces. By adding active-space constraints, we can iteratively improve our estimate for the ground-state energy. Applying our methodology to a 1D Hubbard model yields a significant improvement over traditional 2-positivity constraints with the same computational scaling.     

Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases

We report on the observation of many-body spin dynamics of interacting, one-dimensional (1D) ultracold bosonic gases with two spin states. By controlling the nonlinear atomic interactions close to a Feshbach resonance we are able to induce a phase diffusive many-body spin dynamics of the relative phase between the two components. We monitor this dynamical evolution by Ramsey interferometry, supplemented by a novel, many-body echo technique, which unveils the role of quantum fluctuations in 1D. We find that the time evolution of the system is well described by a Luttinger liquid initially prepared in a multimode squeezed state. Our approach allows us to probe the nonequilibrium evolution of one-dimensional many-body quantum systems.     

Spinodal instabilities of asymmetric nuclear matter within the Brueckner–Hartree–Fock approach

We study the spinodal instabilities of asymmetric nuclear matter at finite temperature within the microscopic Brueckner–Hartree–Fock (BHF) approximation using the realistic Argonne V18 nucleon–nucleon potential plus a three-body force of Urbana type. Our results are compared with those obtained with the Skyrme force SLy230a and the relativistic mean field models NL3 and TW. We find that BHF predicts a larger spinodal region. This result is a direct consequence of the fact that our Brueckner calculation predicts a larger critical temperature and saturation density of symmetric nuclear matter than the Skyrme and relativistic mean field ones. We find that the instability is always dominated by total density fluctuations, in agreement with previous results of other authors. We study also the restoration of the isospin symmetry in the liquid phase, i.e., the so-called isospin distillation or fragmentation effect, finding that its efficiency increases with increasing proton fraction and decreases as temperature and density increase. In general, we find that the Brueckner results are comparable to those obtained with the Skyrme and the relativistic mean field models, although the restoration of isospin symmetry is not so efficient in this case.     

The Higher Frequency of Free Vibrations of Thin Annular Plates Made of Functionally Graded Material

Subject of this paper is a thin plate with a characteristic geometry: periodic in one direction and smoothly varying along the other. The aim of the contribution is to formulate and apply the averaged model which can describe higher frequencies of free vibrations. Problem of finding frequencies of free vibrations is very important. It could be applied to many engineering problems such as resonance phenomena, wave propagation, absorption of vibrations and many others. When the considered plate is made of an isotropic material, we can find the first, the second and the others frequencies in simply way. But if we consider plate made of a functionally graded material [1], which have varying properties and which is made of two components, this problem is more complicated. In this cause, apart from family of the base frequencies (first, second, etc), which depend on macroscopic properties of the plate, we have the higher frequency, which depends on a microscopic structure. We can find many papers describing the base frequencies of free vibrations for many different types of structures (for example [2] for considered type of plate). In this paper, we find the higher frequency. For solving this problem, we use the tolerance averaging technique described in [3]. This theory allows to take into account the microstructure size and to find the higher frequency of free vibrations. The equations have smooth coefficients. They can be solved numerically with help of the finite difference method, in polar coordinates for an annular plate. Next, we use special procedure for selecting of the higher frequencies of free vibrations, which depend on the microstructure size, from the list of all frequencies. After that we analyze an influence of ratios of material properties and the microstructure size on the higher frequency of free vibrations. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudocompact group topology, Forum Math. 6 (3) (1994) 323–337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm–Kaplansky invariants.We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan, M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811–837], and Dikranjan and Shakhmatov [D. Dikranjan, D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1–3) (2005) 2–54] showed this equivalence for groups of cardinality not greater than .We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality κ^ω, for any infinite cardinal κ. In particular, it is consistent that for every cardinal κ there are countably compact groups without non-trivial convergent sequences whose weight λ has countable cofinality and λ>κ.     

Algorithms for the generalized quadratic assignment problem combining Lagrangean decomposition and the Reformulation-Linearization Technique

In this paper, we propose two exact algorithms for the GQAP (generalized quadratic assignment problem). In this problem, given M facilities and N locations, the facility space requirements, the location available space, the facility installation costs, the flows between facilities, and the distance costs between locations, one must assign each facility to exactly one location so that each location has sufficient space for all facilities assigned to it and the sum of the products of the facility flows by the corresponding distance costs plus the sum of the installation costs is minimized. This problem generalizes the well-known quadratic assignment problem (QAP). Both exact algorithms combine a previously proposed branch-and-bound scheme with a new Lagrangean relaxation procedure over a known RLT (Reformulation-Linearization Technique) formulation. We also apply transformational lower bounding techniques to improve the performance of the new procedure. We report detailed experimental results where 19 out of 21 instances with up to 35 facilities are solved in up to a few days of running time. Six of these instances were open.     

Recent applications of magnesium- and Zinc-TMP amides in the synthesis of bioactive targets

Magnesium- and zinc-TMP amides have come out from relative obscurity to be recognized as important tools in modern synthetic chemistry. Development of LiCl-activated metal amides like TMPMgCl·LiCl and TMP₂Zn·2MgCl₂·2LiCl has been important to obtain new organometallic reagents through highly chemo- and regioselective reactions. Herein, we review how these reagents are applied in the synthesis of important bioactive targets such as natural products and drugs.     

2‐Ethyl­phenyl acridine‐9‐carboxyl­ate and 2,5‐dimethyl­phenyl acridine‐9‐carboxyl­ate

The title compounds, 2‐ethyl­phenyl acridine‐9‐carboxyl­ate, C₂₂H₁₇NO₂, (I), and 2,5‐dimethyl­phenyl acridine‐9‐carboxyl­ate, C₂₂H₁₇NO₂, (II), form triclinic and monoclinic crystals, respectively. Related by a centre of symmetry, adjacent molecules of (I) are linked in the lattice via a network of C—H·π and non‐specific dispersive interactions. As a result, acridine moieties and independent phenyl moieties of (I) are parallel in the lattice. The molecules of (II), arranged in a `head‐to‐tail' manner and related by a centre of symmetry, form pairs stabilized via C—H·π interactions. These are linked in the crystal via dispersive interactions. Acridine and independent phenyl moieties lie parallel within the pairs, while adjacent pairs are perpendicular, forming a herring‐bone pattern.     

Photoluminescent layered lanthanide silicates

The hydrothermal synthesis and structural characterization of layered lanthanide silicates, K(3)[M(1-a)Ln(a)Si(3)O(8)(OH)(2)] (M = Y(3+), Tb(3+); Ln = Eu(3+), Er(3+), Tb(3+), and Gd(3+)), named AV-22 materials, are reported. The structure of these solids was elucidated by single-crystal (180 K) and powder X-ray diffraction and further characterized by chemical analysis, thermogravimetry, scanning electron microscopy, (29)Si MAS NMR, and photoluminescence spectroscopy. The Er-AV-22 material is a room-temperature infrared phosphor, while Tb- and Eu-AV-22 are visible emitters with output efficiencies comparable to standards used in commercial lamps. The structure of these materials allows the inclusion of a second (or even a third) type of Ln(3+) ion in the framework and, therefore, the fine-tuning of their photoluminescent properties. For the mixed Tb(3+)/Eu(3+) materials, evidence has been found of the inclusion of Eu(3+) ions in the interlayer space by replacing K+ ions, further allowing the activation of Tb(3+)-to-Eu(3+) energy transfer mechanisms. The occurrence probability of such mechanisms ranges from 0.62 (a = 0.05) to 1.20 ms(-1) (a = 0.1) with a high energy transfer efficiency (0.73 and 0.84, respectively).