Investigation of A^＋c- and Ab-Hypernuclei in Relativistic Mean-Field Model

We investigate the properties of A^ c- and Ab-hypernuclei within the framework of the relativistic mean-field model (RMF). It is found that no A^ c bound states can exist if the A^ c potential well depth |UA^ c| in nuclear matter is less than 10 MeV. If |UA^ c|is less than 20 MeV, A^ c cannot bind to the heavier nuclei with atomic number larger than 100. We suggest it is preferable to search the A^ c-hypernuclei from medium-heavy nuclear systems in experiment. Very small spin-orbit splitting for the A^ c in hypernuclei is a/so observed, and for the Ab it is nearly zero.     

Periodic Ground States in the Neutral Falicov–Kimball Model in Two Dimensions

We consider the Falicov–Kimball model in two dimensions in the neutral case, i.e., the number of mobile electrons is equal to the number of ions. For rational densities between 1/3 and 2/5 we prove that the ground state is periodic if the strength of the attraction between the ions and electrons is large enough. The periodic ground state is given by taking the one dimensional periodic ground state found by Lemberger and then extending it into two dimensions in such a way that the configuration is constant along lines at a 45 degree angle to the lattice directions.     

Influence of Monomer Types on the Designability of a Protein—Model Chain

In a three-dimensional off-lattice model,the method of Shakhnovich and Gutin for minimizing the Hamiltonian is applied to the design of a protein-model chain.The effect of the number of hydrophobic and hydrophilic monomer types on the designability of a protein-model chain is investigated.The simulation results reveal that the number of hydrophobic monomer types is a much more important factor than that of the polar monomer types in the design of a protein-model chain.     

The Mixed Spin-1/2 and Spin-1 Ising–Heisenberg Model in the Mean-Field Approximation: a New Approach

Thermodynamic properties of the mixed spin-1 and spin-1/2 Ising–Heisenberg model are studied on a honeycomb lattice using a new approach in the mean-field approximation to analyze the effects of longitudinal D_z and transverse D_x crystal fields. The phase diagrams are calculated in detail by studying the thermal variations of the order parameters, i.e., magnetizations and quadrupole moments, and compared with the literature to assess the reliability of the new approach. It is found that the model yields both second-and first-order phase transitions, and tricritical points. The compensation behavior of the model is also investigated for the sublattice magnetizations, and longitudinal and transverse quadrupolar moments. The latter type of compensation is observed in the literature but its possible importance is overlooked.     

Structure‐Property Relationships for Model Heterocyclic Polymer Networks: Effect of Monomer Functionality

The effect of initial monomer functionality on the final properties of densely cross‐linked heterocyclic polymer networks (HPN) was evaluated from comparative studies of the viscoelastic behavior and enthalpy relaxation in the glass transition range of polyisocyanurates prepared from a bifunctional monomer D (1,6‐hexamethylene diisocyanate, HDI) and a trifunctional monomer T (the isocyanurate of HDI). Quantitative analysis of these data suggested that an HPN prepared from the monomer T was chemically more heterogeneous and possessed a lower effective network density (presumably, as a result of a lower mobility of the initial monomer T compared to monomer D).     

Codimension-Two Bifurcation Analysis in Hindmarsh-Rose Model with Two Parameters

Bifurcation phenomena in a Hindmarsh Rose neuron model are investigated. Special attention is paid to the bifurcation structures of two parameters, where codimension-two generalized-Hopf bifurcation and fold-Hopf bifurcation occur. The classification of firing patterns as well as the transition mechanism in different regions on the parameter plane are obtained.     

The Gor'kov and Melik-Barkhudarov Correction to the Mean-Field Critical Field Transition to Fulde–Ferrell–Larkin–Ovchinnikov States

The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) states, characterized by Cooper pairs condensed at finite-momentum are, at the same time, exotic and elusive. It is partially due to the fact that the FFLO states allow superconductivity to survive even in strong magnetic fields at the mean-field level. The effects of induced interactions at zero temperature are calculated in both clean and dirty cases, and it is found that the critical field at which the quantum phase transition to an FFLO state occurs at the mean-field level is strongly suppressed in imbalanced Fermi gases. This strongly shrinks the phase space region where the FFLO state is unstable and more exotic ground state is to be found. In the presence of high level impurities, this shrinkage may destroy the FFLO state completely.     

Dynamic Critical Behavior of the Chayes–Machta Algorithm for the Random-Cluster Model,I. Two Dimensions

We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes–Machta dynamics for the Fortuin–Kasteleyn random-cluster model, which generalizes the Swendsen–Wang dynamics for the q-state Potts ferromagnet to non-integer q≥1. We consider spatial dimension d=2 and 1.25≤q≤4 in steps of 0.25, on lattices up to 1024², and obtain estimates for the dynamic critical exponent z _CM. We present evidence that when 1≤q≲1.95 the Ossola–Sokal conjecture z _CM≥β/ν is violated, though we also present plausible fits compatible with this conjecture. We show that the Li–Sokal bound z _CM≥α/ν is close to being sharp over the entire range 1≤q≤4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.     

Rate of Convergence Towards the Hartree–von Neumann Limit in the Mean-Field Regime

In the mean-field regime we prove convergence, with explicit bounds, of N-particle density matrices satisfying the time-dependent von Neumann equation with factorized initial data to a product of one particle density matrices satisfying the Hartree–von Neumann equation. To prove explicit bounds we generalize techniques developed by Pickl (in A simple derivation of mean field limits for quantum systems. ArXiv:0907.4464, 2009) and Knowles–Pickl (in Commun. Math. Phys. 298(1):101–138, 2010).     

Ground State Properties of a Local Sine-Gordon Model with Two Scatters

We investigate the local sine-Gordon model with two scatters by a variational method. The renormalization mass is calculated. It is found that there is an Ising-like phase transition, which is analogous in the global sineGordon model with two frequencies. The renormalization mass can be modulated by the distance between the two scatters.     

Emission Spectrum of Two Atoms in Two-mode Multiphoton Raman Coupled Model

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