Igor Travěnec

Thermodynamic Properties of the Two-Dimensional Two-Component Plasma

The model under consideration is a two-dimensional two-component plasma, stable against collapse for the dimensionless coupling constant β<2. The combination of a technique of renormalized Mayer expansion with the mapping onto the sine-Gordon theory provides the full thermodynamics of the plasma in the whole stability range of β. The explicit forms of the density–fugacity relationship and of the specific heat (at constant volume) per particle are presented.

The Sixth-Moment Sum Rule for the Pair Correlations of the Two-Dimensional One-Component Plasma: Exact Result

The system under consideration is a two-dimensional one-component plasma in the fluid regime, at density n and arbitrary coupling Γ=βe2 (e=unit charge, β=inverse temperature). The Helmholtz free energy of the model, as the generating functional for the direct pair correlation c, is treated in terms of a convergent renormalized Mayer diagrammatic expansion in density. Using specific topological transformations within the bond-renormalized Mayer expansion, we prove that the nonzero contributions to the regular part of the Fourier component of c up to the k2-term originate exclusively from the ring diagrams (unable to undertake the bond-renormalization procedure) of the Helmholtz free energy. In particular, ĉ(k)=−Γ/k2+Γ/(8πn)−k2/[96(πn)2]+O(k4). This result fixes via the Ornstein–Zernike relation, besides the well-known zeroth-, second-, and fourth-moment sum rules, the new sixth-moment condition for the truncated pair correlation h, n(πΓn/2)3 ∫ r6h(r) dr=3(Γ−6)(8−3Γ)/4.

The influence of tungsten on the oxygen sublattice in yttria-stabilized zirconia (YSZ)

Abstract The study of electrical conductivity, Raman and IR spectra, and microhardness of both polycrystalline and single crystalline forms of samples has proved that the kind of incorporation of tungsten into the YSZ lattice is a function of its concentration. However, the influence of tungsten impurity on the investigated physical properties of YSZ is rather weak. The electrical conductivity does not change markedly its character with an exception of an anomaly at 0.1–0.2 wt% WO 3 . The observed decrease of the intensities of the defect-induced Raman bands can be caused by the strong electronic influence of W 6+ ions on their environment and by the decrease of the number of oxygen vacancies in the structure. The dependence of the microhardness on the temperature is stepwise. The inhomogeneities observed are connected with different impurity phases. The microhardness is independent of the presence of tungsten above 375 °C, which indicates the absence of tungsten containing impurity phases at these temperatures.

Defect structure and physical properties of Y2O3

Abstract Undoped Y2O3 is, under given conditions (air, 460°C 700°C the ionic contribution of conductivity becomes significant. Grain boundaries cause the appearance of an additional relaxation process with substantionally higher activation energy, 1.25 eV, in comparison with the bulk, 0.9 eV. The decrease in conductivity of polycrystalline Y2O3 can be attributed to grain boundary effects. Significant softening of Y2O3 at temperatures T>700°C corresponds to increased participation of intersitial oxygen ions in the deformation process. Structural data, temperature dependence of electrical conductivity and microhardness, influence of partial oxygen pressure indicate the important role of oxygen intersititials in the defect structure of undoped Y2O3 at high temperatures and high oxygen pressure.

High orders of Weyl series for the heat content

This article concerns the Weyl series of spectral functions associated with the Dirichlet Laplacian in a d-dimensional domain with a smooth boundary. In the case of the heat kernel, Berry and Howls predicted the asymptotic form of the Weyl series characterized by a set of parameters. Here, we concentrate on another spectral function, the (normalized) heat content. We show on several exactly solvable examples that, for even d, the same asymptotic formula is valid with different values of the parameters. The considered domains are d-dimensional balls and two limiting cases of the elliptic domain with eccentricity ϵ: a slightly deformed disk (ϵ→0) and an extremely prolonged ellipse (ϵ→1). These cases include two-dimensional domains with circular symmetry and those with only one shortest periodic orbit for the classical billiard. We also analyse the heat content for the balls in odd dimensions d for which the asymptotic form of the Weyl series changes significantly.

Optimized t-expansion method for the Rabi Hamiltonian

Abstract A polemic arose recently about the applicability of the t -expansion method to the calculation of the ground state energy E 0 of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t -expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t -expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t -series, E 0 is assumed to be stationary with respect to the free parameters. A high accuracy of E 0 estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than 10 − 4 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E 1 , with the relative error smaller than 10 − 2 (1%).

Tricriticality for dimeric Coulomb molecular crystals in ground state

Abstract. We study the ground-state properties of a system of dimers. Each dimer consists in a pair of equivalent charges at a fixed distance, immersed in a neutralizing homogeneous background. All charges interact pairwisely by Coulomb potential. The dimer centers form a two-dimensional rectangular lattice with the aspect ratio α ∈ [0, 1] and each dimer is allowed to rotate around its center. The previous numerical simulations, made for the more general Yukawa interaction, indicate that only two basic dimer configurations can appear: either all dimers are parallel or they have two different angle orientations within alternating (checkerboard) sublattices. As the dimer size increases, two second-order phase transitions, related to two kinds of the symmetry breaking in dimer’s orientations, were reported. In this paper, we use a recent analytic method based on an expansion of the interaction energy in Misra functions which converges quickly and provides an analytic derivation of the critical behaviour. Our main result is that there exists a specific aspect ratio of the rectangular lattice α∗ = 0.71410684000071 . . . which divides the space of model’s phases onto two distinct regions. If the lattice aspect ratio α > α∗, we recover both types of the secondorder phase transitions and find that they are of mean-field type with the critical exponent β = 1/2. If α < α∗, the phase transition associated with the discontinuity of dimer’s angles on alternating sublattices becomes of first order. For α = α∗, the firstand second-order phase transitions meet at the tricritical point, characterized by the different critical index β = 1/4. Such phenomenon is known from literature about the Landau theory of one-component fields, but in our two-component version the scenario is more complicated: the component which is already in the symmetry-broken state at the tricritical point also interferes and exhibits unexpectedly the mean-field singular behaviour.

Separation of Wigner structures for two-dimensional equimolar binary mixtures of Coulomb particles

We study the lowest energy configurations of an equimolar binary mixture of classical pointlike particles with charges Q1 and Q2, such that q = Q2/Q1 ∈ [0, 1]. The particles interact pairwisely via 3D Coulomb potential and are confined to a 2D plane with a homogeneous neutralizing background charge density. In a recent paper by M. Antlanger and G. Kahl [Cond. Mat. Phys. 16, 43501 (2013)], using numerical computations based on evolutionary algorithm, six fully mixed structures were identified for 0 ≤ q . 0.59, while the separation of Q1 and Q2 pure hexagonal phases minimizes the energy for 0.59 . q < 1. Here, we introduce a novel structure which consists in the separation of two phases, the pure hexagonal one formed by a fraction of particles with the larger charge Q1 and the other mixed one containing different numbers of Q1 and Q2 charges. Using an analytic method based on an expansion of the interaction energy in Misra functions we show that this novel structure provides the lowest energy in two intervals of q values, 0 < q . 0.04707 and 0.58895 . q . 0.61367. This fact might inspire numerical methods, for both Coulomb and Yukawa interactions, to test more general separations which go beyond the separation of two pure phases.

Phase diagram and critical properties of Yukawa bilayers.

We study the ground-state Wigner bilayers of pointlike particles with Yukawa pairwise interactions, confined to the surface of two parallel hard walls at dimensionless distance η. The model involves as limiting cases the unscreened Coulomb potential and hard spheres. The phase diagram of Yukawa particles, studied numerically by Messina and Löwen [Phys. Rev. Lett. 91, 146101 (2003)], exhibits five different staggered phases as η varies from 0 to intermediate values. We present a lattice summation method using the generalized Misra functions which permits us to calculate the energy per particle of the phases with a precision much higher than usual in computer simulations. This allows us to address some tiny details of the phase diagram. Going from the hexagonal phase I to phase II is shown to occur at η=0. All second-order phase transitions are proved to be of mean-field type. We also derive the asymptotic shape of critical lines close to the Coulomb and hard-spheres limits. In and close to the hard-spheres limit, the dependence of the internal parameters of the present phases on η is determined exactly.

Simple phenomenological model of permeable electrode-solid electrolyte interface

Abstract The model is intended to find a way of separating bulk and interface components of ac conductivity. Dipole relaxation and diffusional potential of bulk, permeable electrode and one type of charge carriers are involved.