Weak Pair Research Articles

On nonergodic property of Bose gas with weak pair interaction

In this paper we prove that Bose gas with weak pair interaction is non ergodic system. In order to prove this fact we consider the divergences in some nonequilibrium diagram technique. These divergences are analogous to the divergences in the kinetic equations discovered by Cohen and Dorfman. We develop the general theory of renormalization of such divergences and illustrate it with some simple examples. The fact that the system is non ergodic leads to the following consequence: to prove that the system tends to the thermal equilibrium we should take into account its behavior on its boundary. In this paper we illustrate this thesis with the Bogoliubov derivation of the kinetic equations.

Force-induced misfolding in RNA

RNA folding is a kinetic process governed by the competition of a large number of structures stabilized by the transient formation of base pairs that may induce complex folding pathways and the formation of misfolded structures. Despite its importance in modern biophysics, the current understanding of RNA folding kinetics is limited by the complex interplay between the weak base pair interactions that stabilize the native structure and the disordering effect of thermal forces. The possibility of mechanically pulling individual molecules offers a new perspective to understand the folding of nucleic acids. Here we investigate the folding and misfolding mechanism in RNA secondary structures pulled by mechanical forces. We introduce a model based on the identification of the minimal set of structures that reproduce the patterns of force-extension curves obtained in single molecule experiments. The model requires only two fitting parameters: the attempt frequency at the level of individual base pairs and a parameter associated to a free-energy correction that accounts for the configurational entropy of an exponentially large number of neglected secondary structures. We apply the model to interpret results recently obtained in pulling experiments in the three-helix junction S15 RNA molecule (RNAS15). We show that RNAS15 undergoes force-induced misfolding where force favors the formation of a stable non-native hairpin. The model reproduces the pattern of unfolding and refolding force-extension curves, the distribution of breakage forces, and the misfolding probability obtained in the experiments.

Classification of topological insulators and superconductors in three spatial dimensions

We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial insulators or superconductors in five out of ten symmetry classes introduced in seminal work by Altland and Zirnbauer within the context of random matrix theory, more than a decade ago. One of these is the recently introduced ${\mathbb{Z}}_{2}$ topological insulator in the symplectic (or spin-orbit) symmetry class. We show that there exist precisely four more topological insulators. For these systems, all of which are time-reversal invariant in three dimensions, the space of insulating ground states satisfying certain discrete symmetry properties is partitioned into topological sectors that are separated by quantum phase transitions. Three of the above five topologically nontrivial phases can be realized as time-reversal invariant superconductors. In these the different topological sectors are characterized by an integer winding number defined in momentum space. When such 3D topological insulators are terminated by a two-dimensional surface, they support a number (which may be an arbitrary nonvanishing even number for singlet pairing) of Dirac fermion (Majorana fermion when spin-rotation symmetry is completely broken) surface modes which remain gapless under arbitrary perturbations of the Hamiltonian that preserve the characteristic discrete symmetries, including disorder. In particular, these surface modes completely evade Anderson localization from random impurities. These topological phases can be thought of as three-dimensional analogs of well-known paired topological phases in two spatial dimensions such as the spinless chiral $({p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y})$-wave superconductor (or Moore-Read Pfaffian state). In the corresponding topologically nontrivial (analogous to ``weak pairing'') and topologically trivial (analogous to ``strong pairing'') 3D phases, the wave functions exhibit markedly distinct behavior. When an electromagnetic U(1) gauge field and fluctuations of the gap functions are included in the dynamics, the superconducting phases with nonvanishing winding number possess nontrivial topological ground-state degeneracies.

Symmetry of superconducting states with two orbitals on a tetragonal lattice: Application toLaFeAsO1−xFx

We use group theory to classify the superconducting states of systems with two orbitals on a tetragonal lattice. The orbital part of the superconducting gap function can be either symmetric or antisymmetric. For the orbital symmetric state, the parity is even for spin singlet and odd for spin triplet; for the orbital antisymmetric state, the parity is odd for spin singlet and even for spin triplet. The gap basis functions are obtained with the use of the group chain scheme by taking into account the spin-orbit coupling. In the weak pairing limit, the orbital antisymmetric state is only stable for the degenerate orbitals. Possible application to iron-based superconductivity is discussed.

Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds

We construct an exactly soluble spin- 1 2 model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free states. Basically, there are two phases, A phase and B phase. The behaviors of both A and B phases may be studied by mapping the ground state sector into a general p-wave paired states of spinless fermions with tunable pairing parameters on a square lattice. In this p-wave paired state theory, the A phase is shown to be the strong paired phase, an insulating phase. The B phase may be either gapped or gapless determined by the generalized inversion symmetry is broken or not. The gapped B is the weak pairing phase described by either the Moore–Read Pfaffian state of the spinless fermions or anti-Pfaffian state of holes depending on the sign of the next nearest neighbor hopping amplitude. A phase transition between Pfaffian and anti-Pfaffian states are found in the gapped B phase. Furthermore, we show that there is a hidden SU(2) gauge symmetry in our model. In the gapped B phase, the ground state has a non-trivial topological number, the spectral first Chern number or the chiral central charge, which reflects the chiral anomaly of the edge state. We proved that the topological number is identified to the reduced eta-invariant and this anomaly may be cancelled by a bulk Wess–Zumino term of SO(3) group through an index theorem in 2 + 1 dimensions.

Projection techniques as methods of particle-number symmetry restoration

The accuracy of the variation before (VBP) and after (VAP) particle-number projection methods, the Lipkin-Nogami (LN) prescription, and the projected Lipkin-Nogami (PLN) method have been studied using two exactly solvable models. It is shown that the VBP and the LN methods are rather dubious not only in a weak pairing regime, but also in strong pairing for the evaluation of quantities other than the ground state energy. The PLN method provides good results for the ground and the excited state energies, but it must be used with caution for the occupation probabilities and the observables that strongly depend on it. It seems that the VAP is the only suitable method for a global description of the nuclear properties.

Ground-state properties of even-evenN=Znuclei within the Hartree-Fock-BCS and higher Tamm–Dancoff approaches

We calculate the ground-state properties of well deformed, even-even $N=Z$ nuclei in the region between $^{56}\mathrm{Ni}$ and $^{100}\mathrm{Sn}$ within two different approaches, focusing on the binding energy and deformation and pairing properties. First, we employ the Hartree-Fock-BCS (HFBCS) approximation with the Skyrme effective nucleon-nucleon interaction and discuss how the results depend on the parametrization of the interaction and on the pairing force parameters adjusted in various schemes to reproduce the experimental odd-even mass differences. Then, within the Higher Tamm-Dancoff Approximation (HTDA), which explicitly conserves the particle number, we calculate the same properties starting from the HFBCS solutions. The HTDA treatment of the ground-state correlations is converged within a $n$-particle-$n$-hole expansion using up to $n=4$ particle-hole excitations of the pair type (in the sense of Cooper pairs). We compare the ground-state properties calculated in these two descriptions of pairing correlations and deduce the importance of the particle-number conservation in weak pairing regimes. Finally, we extend the HTDA calculations so as to include the proton-neutron residual interaction and investigate the role of proton-neutron pairing on the above ground-state properties.

Parallel Calculation of Coupled Cluster Singles and Doubles Wave Functions Using Array Files.

A new parallel implementation of the Coupled Cluster Singles and Doubles (CCSD) and related wave functions (e.g Quadratic Configuration Interaction, QCI, and Coupled Electron Pair, CEPA) is described, based on the Array Files middleware. The program can handle large basis sets, even without utilizing symmetry, on modest distributed memory workstation clusters. High computational efficiency is achieved by formulating all major operations in terms of matrix multiplications. Timings are provided for systems with 50-228 valence electrons and up to 1144 basis functions, with little or no symmetry. Our largest calculation (QCISD/aug-cc-pVQZ for the parallel displaced benzene dimer) uses 1512 basis functions. Calculations on the benzene dimer show that the usual procedure of estimating the effect of basis set enlargement from second-order Møller-Plesset (MP2) calculations is less reliable than previously assumed. Replacing the weak pair amplitudes in CCSD/QCISD calculations by MP2 amplitudes affects the calculated energy only slightly.

Precise Control of Molecular Dynamics with a Femtosecond Frequency Comb

We present a general and highly efficient scheme for performing narrow-band Raman transitions between molecular vibrational levels using a coherent train of weak pump-dump pairs of shaped ultrashort pulses. The use of weak pulses permits an analytic description within the framework of coherent control in the perturbative regime, while coherent accumulation of many pulse pairs enables near unity transfer efficiency with a high spectral selectivity, thus forming a powerful combination of pump-dump control schemes and the precision of the frequency comb. Simulations verify the feasibility and robustness of this concept, with the aim to form deeply bound, ultracold molecules.

Theoretical investigation of bulk ordering and surface segregation in Ag-Pd and other isoelectornic alloys

Bulk ordering in Ag-Pd and other isoelectronic alloys is investigated theoretically by a number of first-principles techniques. The electronic structure and total energy have been calculated by the Green's function Korringa-Kohn-Rostocker and full-potential plane wave methods. The effective cluster interactions of the Ising-type Hamiltonian have been obtained by the screened generalized perturbation method. They reveal a complex concentration-dependent ordering behavior in these alloys due to band filling and Fermi surface effects. In particular we show that long-period superstructures are gradually stabilized by a great number of relatively weak long-range effective pair- and three-site interactions, which can be seen as ``collective'' effect. A similar complex concentration dependence is also found for surfaces of Ag-Pd alloys. The surface composition of the (111) and (100) surface of ${\mathrm{Ag}}_{75}{\mathrm{Pd}}_{25}$, ${\mathrm{Ag}}_{50}{\mathrm{Pd}}_{50}$, and ${\mathrm{Ag}}_{33}{\mathrm{Pd}}_{67}$ alloys have been then investigated by the surface Green's function technique and the screened generalized perturbation method for the effective interactions of the Ising-type Hamiltonian and the grand canonical Monte Carlo method for statistical thermodynamic simulations at finite temperatures. We compare our results with experimental data and other theoretical calculations.

The role of retrieval inhibition in the associative memory impairment of schizophrenia

To examine retrieval-induced forgetting (RIF) in schizophrenia, subjects studied category–exemplar words taken from either strong or weak categories, and then practiced retrieval by completing category word-stems on half of the word pairs. Patients had reduced recall and recognition, but showed the expected RIF effect of better recall of unpracticed items from unpracticed categories than for unpracticed items from practiced categories. By contrast, patients and controls showed differing RIF for recognition as a function of categorical dominance: whereas controls showed RIF only for dominant category exemplar word pairs, patients showed RIF for both dominant and weak categories. Different patterns of baseline practiced retrieval for weak associate pairs in schizophrenia may explain this finding. The results failed to support faulty RIF in the associative memory impairment of schizophrenia.

Thermally Stable Amorphous Mesoporous Aluminophosphates with Controllable P/Al Ratio: Synthesis, Characterization, and Catalytic Performance for Selective O-Methylation of Catechol

Amorphous mesoporous aluminophosphates (AlPO) with P/Al molar ratio in the range 0.8-1.15 are synthesized by using the citric acid (CA) route and are systematically characterized using N(2)-adsorption, XRD, SEM, solid-state CP-MAS NMR, FT-IR, TG-DTA, CO(2)-TPD, and NH(3)-TPD. The characterization studies show that the change in P/Al ratio could affect the structure, texture, thermal stability, and surface acid-base properties of AlPO. Samples with a relatively low P/Al ratio (< or =1.0) exhibit uniform amorphous mesoporous character and high thermal stability (up to 1173 K). Partial crystallization of the AlPO framework easily occurred on the sample with higher P/Al ratio (> or =1.1), thus leading to significant decrease of surface area and formation of particle pile mesopores. Both weak acid and weak base sites are observed over AlPO materials, and the amounts of acid-base sites can be effectively controlled by adjusting the P/Al ratio. The presence of suitable interaction between citric acid and AlPO framework is critical for the formation of mesoporous structures. Both CA and PO(4) units are considered to be ligands to coordinate with aluminum ions, forming relative uniform complexes (such as CA-Al-PO(4)) in the as-synthesized AlPO materials. The mesoporous structure of AlPO materials is obtained after the rapid decomposition of citric acid. Vapor phase selective O-methylation of catechol with methanol reaction is carried out to investigate the catalytic performances of AlPO materials with different P/Al ratios. Among them, AlP(1.1)O shows the highest activity (88.4% conversion of catechol) and the highest yield of guaiacol (74.3%). The presence of suitable weak acid-base pairs may play an important role on the title reaction.

A Topological Study of the Geometry of AF6E Molecules: Weak and Inactive Lone Pairs

The geometries of AF6E molecules, which may have either an O(h) or a C(3v) geometry, have been studied by means of the electron localization function. Our results show that when the molecule has a C(3v) geometry, there is a valence-shell monosynaptic V(A) basin corresponding to the presence of a lone pair in the valence shell of the central atom A. The population of this basin is, however, extensively delocalized so that the electron density has a core-valence basin character, which is consistent with an earlier suggestion of a weakly active lone pair that gives a C(3v) distorted octahedral molecule rather than the valence-shell electron-pair repulsion predicted pentagonal-pyramid geometry. In contrast, the molecules with O(h) geometry do not have a monosynaptic valence-shell basin, but they have a larger core. These results provide confirmation of a previous suggestion that in AX6E (X = Cl, Br, I) molecules with the O(h) geometry the ligands X are sufficiently closely packed around the central atom A so as to leave no space in the valence shell for the lone pair E, which remains part of the core. Among the corresponding fluorides, only BrF6- has the O(h) geometry, while the others have the C(3v) geometry because there is sufficient space in the valence shell to accommodate the lone pair, the presence of which distorts the O(h) geometry to C(3v). The energies of the O(h) and C(3v) geometries have been shown to be very similar so the observed geometries are a consequence of a very fine balance between ligand-ligand repulsions and the energy gained by the expansion of the two nonbonding electrons into the valence shell.

Pairing correlations in mesoscopic systems

The particle number projected generator coordinate method is applied to the study of generalized pairing Hamiltonians. The calculations reproduce the exact solution where available in the weak, crossover and strong pairing regimes. The behaviour of the wave functions is analysed showing large mixtures in the weak and smaller ones in the strong pairing regime. The physical insight of the ansatz and its numerical simplicity make this theory an excellent tool to study pairing correlations in complex situations and/or involved Hamiltonians.

Classification of the possible pairs between the first anticodon and the third codon positions based on a simple model assuming two geometries with which the pairing effectively potentiates the decoding complex

Crick's wobble theory states that some specific pairs between the bases at the first position of the anticodon (position 34) and the third position of the codon (position III) are allowed and the others are disallowed during the correct codon recognition. However, later researches have shown that the pairing rule, or the wobble rule, is different from the supposed one. Despite the continuing efforts including computer-aided model building studies and analyses of three-dimensional structures in the crystals of the ribosomes, the structural backgrounds of the wobble rule are still unclear. Here, I classify the possible pairs into 6 classes according to the increases accompanying the formation of the pairs in the potential productivity of the decoding complex on the basis of a simple model that was originally proposed previously and is refined here. In the model, the conformation with the base at position 34 displaced toward the minor groove side from the position for the Watson–Crick pairs is supposed to be equivalent to the conformation with the Watson–Crick pairs. It is also reasoned and supposed that some weak pairs may sometimes be allowed depending on the structural context. It is demonstrated that most of the experimental results reported so far are consistent with the model. I discuss on which experimental facts can be reasoned with the model and which need further explanations. I expect that the model will be a good basis for further understanding of the wobble rule and its structural backgrounds.

Social structure of the bushveld sengi (Elephantulus intufi) in Namibia and the evolution of monogamy in the Macroscelidea

AbstractThe elephant‐shrews or sengis (order Macroscelidea) represent a monophyletic radiation endemic to Africa with 15 extant species in four genera. Field studies of representatives from all four genera indicate that all are socially monogamous. Resource and female dispersion, indirect paternal investment and male mate guarding have been proposed as factors contributing to sengi monogamy. To better understand sengi social organization, we studied the behavioural ecology of the bushveld sengi Elephantulus intufi in Namibia. Radio‐tags and direct observation were used to gather spatial and behavioural data during 5 months in 2000–2002. Bushveld sengis were distributed as monogamous pairs on exclusive territories, similar to other sengis. Maternal care was characterized by an ‘absentee’ strategy and there was no evidence of direct or indirect paternal care. Sengis share many life‐history traits with small antelopes, including uni‐parental monogamy. Unlike the antelopes, which exhibit strong pair bonds, bushveld sengi pairs spend little time in coordinated activities. Male mate guarding best explains why sengis are socially monogamous – a model largely developed from studies of small antelopes. The similarity in morphology, life history and behaviour among sengi species results in a distinctive adaptive syndrome, which explains the consistency of their social structure, even in the extremes of terrestrial habitats that they occupy. The degree of sengi social monogamy is labile, which is related to their weak pair bond, same‐sex aggression and variable densities.

Use of Weakly Coordinating Anions to Develop an Integrated Approach to the Tuning of ΔE1/2Values by Medium Effects

An integrated approach to the control of deltaE(1/2) values, and therefore comproportionation equilibria, through medium effects was delineated for multi-step redox reactions involving cationic products. deltaE(1/2) values (defined as E(1/2)(2+/1+) - E(1/2)(1+/0)) of the two one-electron oxidations of bis(fulvalene)dinickel, 1, were measured under 45 different conditions of solvent and supporting electrolyte. The smallest value, 212 mV, was found in anisole/0.1 M [NBu4]Cl and the largest, 850 mV, in CH2Cl2/0.02 M Na[B(C6H3(CF3)2)4]. By systematically changing the solvent properties, the degree of ion-pairing strengths of the supporting electrolyte ions, and the concentration of the electrolytes, a set of ideal properties was found for maximizing deltaE(1/2) values involving positively charged electrode products. Most importantly (i) the solvent must be of lower polarity and low donor strength and (ii) the supporting electrolyte must have a weakly coordinating anion (WCA). The contrast in ion-pairing tendencies of 1(2+) with WCAs (on the weak side) and halides (on the strong side) mimics that of dianions in THF, where longer chain tetraalkylammonium ions (weak ion pairing) contrast with alkali metal ions (strong ion pairing). The broad picture of medium effects is that of a "mirror image" of solvent and electrolyte properties that influence the tuning of deltaE(1/2) values for multi-electron systems. Application was made both to the four-step oxidation process and to the two-step reduction process of the tetraferrocenyl complex Ni(S2C2Fc2)2, Fc = Fe(C5H5)(C5H4), 2. The two-electron process 2(0/2-) is observed either as a single two-electron voltammetric wave or as two well-separated one-electron waves, depending on the medium. The consequences of the present model for the interpretation of deltaE(1/2) values in mixed-valence chemistry are discussed.

Explicitly correlated second-order perturbation theory using density fitting and local approximations

Three major obstacles in electronic structure theory are the steep scalings of computer time with respect to system size and basis size and the slow convergence of correlation energies in orbital basis sets. Three solutions to these are, respectively, local methods, density fitting, and explicit correlation; in this work, we combine all three to produce a low-order scaling method that can achieve accurate MP2 energies for large systems. The errors introduced by the local approximations into the R12 treatment are analyzed for 16 chemical reactions involving 21 molecules. Weak pair approximations, as well as local resolution of the identity approximations, are tested for molecules with up to 49 atoms, over 100 correlated electrons, and over 1000 basis functions.

Spectral Properties of Four-Dimensional Compact Flat Manifolds

We study the spectral properties of a large class of compact flat Riemannian manifolds of dimension 4, namely, those whose corresponding Bieberbach groups have the canonical lattice as translation lattice. By using the explicit expression of the heat trace of the Laplacian acting on p-forms, we determine all p-isospectral and L-isospectral pairs and we show that in this class of manifolds, isospectrality on functions and isospectrality on p-forms for all values of p are equivalent to each other. The list shows for any p, 1 ≤ p ≤ 3, many p-isospectral pairs that are not isospectral on functions and have different lengths of closed geodesics. We also determine all length isospectral pairs (i.e. with the same length multiplicities), showing that there are two weak length isospectral pairs that are not length isospectral, and many pairs, p-isospectral for all p and not length isospectral.

Pairing correlations in finite systems: from the weak to the strong fluctuations regime

The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the generator coordinate is analyzed performing numerical applications for the most relevant collective coordinates. The calculations reproduce the exact solution in the weak, crossover and strong pairing regimes. The physical insight of the Ansatz and its numerical simplicity make this theory an excellent tool to study pairing correlations in complex situations and/or involved Hamiltonians.