Bilayer membrane in confined geometry: Interlayer slide and entropic repulsion

We derive the free energy functional of a bilayer lipid membrane from the first principles of elasticity theory. The model explicitly includes position-dependent mutual slide of monolayers and bending deformation. Our free energy functional of a liquid-crystal membrane allows for incompressibility of the membrane and vanishing of the in-plane shear modulus and obeys reflectional and rotational symmetries of the flat bilayer. Interlayer slide at the midplane of the membrane results in local difference of surface densities of the monolayers. The slide amplitude directly enters the free energy via the strain tensor. For small bending deformations, the ratio between the bending modulus and the area compression coefficient, K _b /K _A , is proportional to the square of monolayer thickness h. Using the functional, we perform self-consistent calculation of the entropic potential acting on a bilayer between parallel confining walls separated by distance 2d. We find that at the minimum of the confining potential, the temperature-dependent curvature α ∝ T ² /K _b d⁴ is enhanced four times for a bilayer with slide as compared with a unit bilayer. We also calculate viscous modes of a bilayer membrane between confining walls. Pure bending of the membrane is investigated, which is decoupled from area dilation at small amplitudes. Three sources of viscous dissipation are considered: water and membrane viscosities and interlayer drag. The dispersion relation gives two branches ω_{1, 2} (q).     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique

The Bethe-Salpeter equations for the quark-antiquark composite systems, q\(\bar q\), are written in terms of spectral integrals. For the q\(\bar q\) mesons characterized by the mass M, spin J, and radial quantum number n, the equations are presented for the following (n, M²) trajectories: π _J , η _J , a _J , f _J , ρ _J , ω _J , h _J , and b _J .     

Low-energy singlet sector in the spin-1/2 <Emphasis Type="Italic">J</Emphasis><Subscript>1</Subscript>–<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> Heisenberg model on a square lattice

Based on a special variant of the plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of a spin-\(\frac{1}{2}\) Heisenberg antiferromagnet on a square lattice with nearest-heighbor and frustrating next-nearest-neighbor exchange couplings J ₁ and J ₂. It is well known that a nonmagnetic phase arises in this model for 0.4 ? J ₂/J ₁ ? 0.6, sandwiched by two Néel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J ₂ ≈ 0.64 J ₁ from the non-magnetic phase to the Néel one. A large gap (? 0.4J ₁) is found in the singlet spectrum for J ₂ < 0.64J ₁, which excludes a gapless spin-liquid state for 0.4 ? J ₂/J ₁ ? 0.6 and the deconfined quantum criticality scenario for the QPT to another Néel phase. We observe a first-order QPT at J ₂ ≈ 0.55J ₁, presumably between two nonmagnetic phases.     

Depolarizing collisions in ytterbium vapor: Isotropic and anisotropic relaxation

Isotropic depolarizing collisions are studied using a stimulated photon echo with a specific polarization of the excitation radiation pulses in a mixture of ytterbium with krypton for the J = 1 ? J = 0 transition of ¹⁷⁴Yb. The difference between the relaxation rates of orientation and alignment γ _b ⁽²⁾ ? γ _b ⁽¹⁾ of the ³ P ₁(6s6p) ¹⁷⁴Yb level is measured as a function of the krypton pressure. The collision photon echo at the J = 1 ? J = 0 transition induced by the anisotropic relaxation is studied for the Yb + Xe mixture. The power of the collision echo increases from zero with the addition of a buffer gas to ytterbium, reaches an optimal level, and decreases with an increase in the buffer gas pressure. The polarization of this collision-induced echo differs from the polarization of the conventional echo. The experimental results are in qualitative agreement with theoretical predictions.     

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

In this short review, we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn–Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin–Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T_C of the order of 100 K) we should proceed to the t–J model with the van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we note that to describe superconductivity in metallic hydrogen alloys under pressure (with T_C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron–phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal–Eliashberg strong coupling theory or even Fermi–Bose mixture theory of Ranninger et al. and its generalizations.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

The analysis of the densities of <Emphasis Type="Italic">s</Emphasis>-wave neutron resonances separated with respect to spin

The density ratio of s-wave neutron resonances z=ρ(J₁)/ρ(J₂) was analyzed on the basis of the experimental data for 22 atomic nuclei and the Gilbert-Cameron formula for ρ(J). Here, J₁=I_x—1/2 and J₂=I_x+1/2, where I_x denotes the spin of the target nucleus in the ground state. Our aim was to verify whether the factor η(I_x), as a multiplier, can be applied in the expression describing ρ(J₁), with the assumption that ρ(J₂) values remain unchanged, or whether the factor 1η(I_x) can be applied, as a multiplier with ρ(J₂), while the ρ(J₁) values remain unchanged. The final conclusions, e.g., the confirmation or the negation of the fact that it may be necessary to apply the η(I_x) factor, depend on the values of “real” errors Δz of the z variable, which can be calculated if the optimal values of Δρ(J₁) and Δρ(J₂) are known.     

Unconventional spin-charge phase separation in a model 2D cuprate

In this work, we address a challenging problem of a competition of charge and spin orders for high-T _c cuprates within a simplified 2D spin-pseudospin model which takes into account both conventional Heisenberg Cu²⁺?Cu²⁺ antiferromagnetic spin exchange coupling (J) and the on-site (U) and intersite (V) charge correlations in the CuO₂ planes with the on-site Hilbert space reduced to only three effective charge states (nominally Cu^1+;2+;3+). We performed classical Monte Carlo calculations for large square lattices implying the mobile doped charges and focusing on a case of a small intersite repulsion V ? J. The on-site attraction (U < 0) does suppress the antiferromagnetic ordering and gives rise to a checkerboard charge order with the doped charge distributed randomly over a system in the whole temperature range. However, under the on-site repulsion (U > 0) the homogeneous ground state antiferromagnetic solutions of the doped system found in a mean-field approximation are shown to be unstable with respect to a phase separation with the charge and spin subsystems behaving like immiscible quantum liquids. Puzzlingly, with lowering the temperature one can observe two sequential phase transitions: first, an antiferromagnetic ordering in the spin subsystem diluted by randomly distributed charges, then, a charge condensation in the charge droplets. The effects are illustrated by the Monte Carlo calculations of the specific heat and longitudinal magnetic susceptibility.     

The effective Hamiltonian for copper oxides

The concentration dependence of the exchange integral for the subsystem of spin moments of copper ions J(h) = J ? J ₁ × h ? J ₂ × h ² has been calculated for the Emery model within the effective Hamiltonian obtained with due regard to intersite interactions and oxygen configurations with different numbers of holes. It is shown that allowance for the oxygen single-hole states occurring upon doping leads to additional contributions to J(h), whose intensities depend on the intersite correlations of the nearest environment of exchange-coupled copper ions.     

Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy

The low-energy constants, namely the spin stiffness ρ _s , the staggered magnetization density ? _s per area, and the spinwave velocity c of the two-dimensional (2D) spin-1 Heisenberg model on the square and rectangular lattices are determined using the first principles Monte Carlo method. In particular, the studied models have different antiferromagnetic couplings J ₁ and J ₂ in the spatial 1- and 2-directions, respectively. For each considered J ₂∕J ₁, the aspect ratio of the corresponding linear box sizes L ₂∕L ₁ used in the simulations is adjusted so that the squares of the two spatial winding numbers take the same values. In addition, the relevant finite-volume and -temperature predictions from magnon chiral perturbation theory are employed in extracting the numerical values of these low-energy constants. Our results of ρ _s1 are in quantitative agreement with those obtained by the series expansion method over a broad range of J ₂∕J ₁. This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The ? _s and c presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.     

Dependence of the Curie temperature on the effective de Gennes factor in ferromagnets with exchange frustration

Considering the magneto-diluted gadolinium-containing Adamian alloys, it is shown that the dependence of the Curie temperature on the de Gennes factor ξ = c(g ? 1)2J(J + 1) can be expanded for ferromagnets with the exchange frustration. It is shown that in this case it is necessary to replace J by S _eff and that the linear dependence of T _C on ξ_eff remains up to the pure spin-glass state with S _eff = 0.     

Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J₁ and J₂, respectively. PTs in these models are analyzed for the ratio r = J₂/J₁ of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J₁ < 0 and J₂ < 0 exhibits a first-order PT in the range of 0 ? r < 0.2, whereas, in the interval 0.2 ? r ? 1.0, frustrations arise in the system. At the same time, for J₁ > 0 and J₂ < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ? |r| ? 1/3, the model exhibits a second-order PT.     

Inflation of the early cold Universe filled with a nonlinear scalar field and a nonideal relativistic Fermi gas

We consider a possible scenario for the evolution of the early cold Universe born from a fairly large quantum fluctuation in a vacuum with a size a ₀ ? l _P (where l _P is the Planck length) and filled with both a nonlinear scalar field φ, whose potential energy density U(φ) determines the vacuum energy density λ, and a nonideal Fermi gas with short-range repulsion between particles, whose equation of state is characterized by the ratio of pressure P(n _F ) to energy density ε(n _F ) dependent on the number density of fermions n _F . As the early Universe expands, the dimensionless quantity ν(n _F ) = P(n _F )/ε(n _F ) decreases with decreasing n _F from its maximum value ν_max = 1 for n _F → ∞ to zero for n _F → 0. The interaction of the scalar and gravitational fields, which is characterized by a dimensionless constant ξ, is proportional to the scalar curvature of four-dimensional space R = κ[3P(n _F )–ε(n _F )–4λ] (where κ is Einstein’s gravitational constant), and contains terms both quadratic and linear in φ. As a result, the expanding early Universe reaches the point of first-order phase transition in a finite time interval at critical values of the scalar curvature R = R _c =–μ²/ξ and radius a _c ? a ₀. Thereafter, the early closed Universe “rolls down” from the flat inflection point of the potential U(φ) to the zero potential minimum in a finite time. The release of the total potential energy of the scalar field in the entire volume of the expanding Universe as it “rolls down” must be accompanied by the production of a large number of massive particles and antiparticles of various kinds, whose annihilation plays the role of the Big Bang. We also discuss the fundamental nature of Newton’ gravitational constant G _N .     

Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket

The anisotropic antiferromagnetic Ising model on the fractal Sierpiński gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with 0 ≤ J_b/J_a< 1, and an interesting crossover behavior between different phases at J_b/J_a = 1 is unveiled, whose dynamics can be described by the J_b/J_a-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpiński gasket are obtained in both the 1 / 3 plateau disordered phase and the 5/9 plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpiński gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.     

Periodic Striped Ground States in Ising Models with Competing Interactions

We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value J_c(p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2d and J in a left neighborhood of J_c(p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.     

The effect of high pressure on the structure and on the magnetic and electronic properties of nickel monoxide

A diamond anvil cell is used to investigate the effect of high pressure (up to 37.5 GPa) on the optical absorption spectra of a single crystal of nickel oxide (NiO). In addition, strain-gage measurements are used to experimentally investigate the V(P) equation of state at a hydrostatic pressure of up to 8.5 GPa in a high-pressure chamber of the “toroid” type. Measurements are performed at room temperature. Absorption bands are observed, which correspond to optical d-d transitions of Ni²⁺ ion in the crystal field of ligands ³A_2g → ³T_2g, ³A_2g → {au1}E_1g, ³A_2g → ³T_1g(F), and ³A_2g → ¹T_2g. The values of energy of these transitions increase linearly with pressure, and their pressure coefficients are 7.3 ± 0.2, 2.87 ± 0.9, 9.7 ± 0.5, and 8.9 ± 0.3 meV/GPa, respectively. The pressure derivative of the crystal field parameter 10Dq corresponding to the ³A_2g → ³T_2g transition gives the pressure dependence of the magnitude of exchange integral J in the Anderson hybridization model. It is found that, in the pressure range from zero to 37.5 GPa, the behavior of the exchange integral J is largely defined by the hybridization parameter b = (10Dq/3). At the same time, the Coulomb interaction parameter U_eff is independent of pressure and, therefore, has no effect on the variation of J. The Coulomb interaction U_eff ≈ 7.47 ± 0.005 eV is determined. The experimental data on the equation of state are used to derive the \(J \propto V^\varepsilon \) correlation, where ε = ?2.99 ± 0.15, which is in good agreement with the predictions of Bloch’s theory (ε = ?10/3).     

Entropic pressure between fluctuating membranes in multilayer systems

Gaining insights into the fluctuation-induced entropic pressure between membranes that mediates cell adhesion and signal transduction is of great significance for understanding numerous physiological processes driven by intercellular communication. Although much effort has been directed toward investigating this entropic pressure, there still exists tremendous controversy regarding its quantitative nature, which is of primary interest in biophysics, since Freund challenged the Helfrich’s well-accepted results on the distance dependence. In this paper, we have investigated the entropic pressure between fluctuating membranes in multilayer systems under pressure and tension through theoretical analysis and Monte Carlo simulations. We find that the scaling relations associated with entropic pressure depend strongly on the magnitude of the external pressures in both bending rigidityand surface tension-dominated regimes. In particular, both theoretical and computational results consistently demonstrate that, in agreement with Helfrich, the entropic pressure p decays with inter-membrane separations c as p~c^–3 for the tensionless multilayer systems confined by small external pressures. However, our results suggest that the entropic pressure law follows to be p~c^–1 and p~c^–3, respectively, in the limit of large and small thermal wavelengths for bending fluctuations of the membranes in a tension-independent manner for the case of large external pressures.     

Electronic structures of ternary iron arsenides <Emphasis Type="Italic">A</Emphasis>Fe<Subscript>2</Subscript>As<Subscript>2</Subscript> (<Emphasis Type="Italic">A</Emphasis> = Ba,Ca, or Sr)

We have studied the electronic and magnetic structures of the ternary iron arsenides AFe₂As₂ (A = Ba, Ca, or Sr) using the first-principles density functional theory. The ground states of these compounds are in a collinear antiferromagnetic order, resulting from the interplay between the nearest and the next-nearest neighbor superexchange antiferromagnetic interactions bridged by As 4p orbitals. The correction from the spin-orbit interaction to the electronic band structure is given. The pressure can reduce dramatically the magnetic moment and diminish the collinear antiferromagnetic order. Based on the calculations, we propose that the low energy dynamics of these materials can be described effectively by a t-J _H -J ₁-J ₂-type model [2008, arXiv: 0806.3526v2].