Double-well Model Research Articles

Analytical calculation of the Peierls–Nabarro pinning barrier for one-dimensional parametric double-well models

Lattice effects on the kink families of two models for one-dimensional nonlinear Klein–Gordon systems with double-well on-site potentials are considered. An analytical expression of the generalized Peierls–Nabarro pinning potential, valid for all double-well potential models of the same kind (including the double-Morse and sine hyperbolic Gordon potentials), is obtained and confronted with numerical simulations.

Quantum tunneling versus zero-point energy in double-well potential model for ferrroelectric phase transitions

Abstract The Ising model in a transverse field, which involves quantum tunneling in double potential wells, has been used for many years to describe ferroelectric phase transitions. An alternative model previously published takes into account the effect of a non-negligible zero-point energy in the double potential wells at the phase transition. A comparison of the respective Curie temperatures, spontaneous polarizations and susceptibilities shows that both models are nearly equivalent. Quantitative differences of the two methods are apparent at low temperature where the saturation polarization value with non-negligible zero-point energy is higher than the same quantity with the Ising model in a transverse field.

Effect of Local Relaxation on Complex Permittivity in a Double-Well Potential Model

Effect of Local Relaxation on Complex Permittivity in a Double-Well Potential Model

Microscopic mechanism of stability in yttria-doped zirconia

The relaxed configurations of yttria-stabilised zirconia (YSZ) between 3 and 10 mol % of Y2O3 were modeled using the pseudopotential technique. In the displacive limit of a double-well potential model, the vibrational mode corresponding to the soft phonon in pure c-ZrO2 was calculated for each Y2O3 composition. These anharmonic vibrations, associated with the stabilization of YSZ, were investigated within the self-consistent phonon approximation making obtainable the fine structure in spectral density. In studying the phonon dynamics, we use the displacement probability density, which can quantify very accurately the transition temperature necessary for stabilizing the YSZ cubic phase.

Mean Square Fluctuations of Hydrogen Atoms and Water-Biopolymer Interactions in Hydrated Saccharides

We have used the elastic neutron scattering technique to investigate the dynamics of the two main saccharidic components of starch: amylose and amylopectin. The measurements were carried out in the temperature range of 20 to 320 K and at different hydration levels from the dry state up to 0.47 g saccharide/g D 2O. In the dry samples, the atomic dynamics is harmonic up to approximately 300 K. In the hydrated samples a “glass-like” transition leading to an anharmonic dynamics is observed. The onset of the anharmonicity occurs at temperatures that increase from ∼180 K to 260 K upon decreasing hydration from 0.5 to 0.1 g saccharide/g D 2O. This behavior is qualitatively similar to that observed in hydrated globular proteins, but quantitative differences are present. Assuming a simple asymmetric double-well potential model, the temperature and hydration dependence of the transition have been described in terms of few physical parameters.

Statistical mechanics of nonlinear Klein–Gordon chains: the φ8-chain and the Gaussian double-well model

We study the statistical mechanics of two models of nonlinear Klein–Gordon chain: the ‘ φ 8-chain’ with the single-site potential v( y)= a( y 2−1) 4, and the Gaussian double-well model with v(y)= 1 2 ky 2+b exp(− 1 2 cy 2) where a, b, c and k are positive constants. The thermodynamics of the classical chains is investigated by the transfer-integral equation technique and the pseudo-Schrödinger equation approximation. The results for the heat capacity, the displacement correlation function, and the wave-vector-dependent susceptibility are compared with those of the familiar φ 4-chain. The partition functions of the quantum chains are calculated by the low-coupling effective potential method. The effects of quantum fluctuations on the low-temperature heat capacity are examined.

One approach to the control of intramolecular hydrogen transfer

One approach using the counterintuitive pulse sequence (CPS) is presented to control the intramolecular hydrogen transfer. We have applied the asymmetric double-well model to the substituted malonaldehyde and have shown the complete population transfer from one local minimum state to another one through the barrier using CPS. We also have found in our simulation that the high product yield is robust with respect to the changes of the laser parameters. The mechanism of the population transfer is elucidated with our approach with the Hückel theory in a systematic and pictorial way.

Mechanism of the Curie-Weiss Law in Ferroelectrics

A simple double-well potential model is established. It shows that the nature of the low-frequency dielectric constant in ferroelectrics is the additional hopping of the off-center ions in multi-site potential. The co-operative effect causes the fact that the Curie-Weiss law is obeyed. The mechanism of the molecular field is clarified.

A relation between long-range correlation and dielectric anomaly

A double-well potential model is established to explain the dielectric anomaly of ferroelectrics. The dielectric constant consists of two parts. One part is independent of the long-range correlation, following 1/T law. The other part originates from the long-range correlation, and can be described by the correlation length well. The deviation from Curie-Weiss law in a small size sample originates from the decrease of the long-range correlation.

Internal friction and relaxation mechanism of F-doped SiO 2 glasses

The internal friction and the Young's moduli of pure SiO 2, SiO 2 –4 mol% F and –8 mol% F glasses were measured in the temperature range of 1.6–250 K. The temperature dependencies of the internal friction were not different except for their peak values, which showed differences of a few percent at 35 K. In contrast, the Young's moduli of F-doped SiO 2 glasses were 7.5% (–4 mol% F) and 15% (–8 mol% F) less than that of pure SiO 2 glass, respectively. Both temperature dependencies were analyzed on the basis of Debye relaxation by the distributed double-well potential model.

From kinks to compactonlike kinks

We show that, in the continuum limit, the generalized \ensuremath{\Phi}-four or double-well model with nonlinear coupling can exhibit compactonlike kink solutions for some specific velocity regimes and when the nonlinear coupling between pendulums is dominant. Our numerical simulations point out that the static compacton is stable and the dynamic compacton is unstable. Our study is extended to other topological systems where compacton solutions can also be found. A nice feature is that a mechanical analog of the double-well system can be constructed in the form of an experimental lattice of coupled pendulums, which, in the strong coupling limit, allows the observation of these entities.

Localization effects in a double-well model

Eigenfunctions of a generic double-well potential are calculated and found to be of two distinct kinds. The transition from delocalized to localized form, driven by time- independent and time-dependent perturbations, is examined in detail. It is shown that a polar diagram provides a useful description of the localization effects. PACS Nos. 3100, 3110, and 3115 R´ esum´ e : Nous calculons les fonctions propres d'un potentiel generique a deux minima et trouvons qu'elles sont de deux types distincts. Nous examinons en detail la transition entre solutions delocalisee et localisee et qui est generee par des perturbations independantes et dependantes du temps. Nous montrons qu'un diagramme polaire donne une description utile des effets de localisation. (Traduit par la r ´

Dichotomous collective proton dynamics in ice

The collective proton dynamics in ice is studied on the basis of the two-dimensional (2D) nonlinear lattice model which takes the dichotomous branching of proton transfers in hydrogen-bonded networks into account. The essential point of this model is that the network topology of the square proton lattice satisfies the Bernal-Fowler ice rules of the 3D ice crystal structure. The model is considered as a straightforward extension of the standard 1D coupled double-well oscillator model described by the discrete nonlinear Klein-Gordon equation to two dimensions while imposing the ice rules. This generalization under the ice constraints has been shown to be unique. A relation between the boundary conditions and topological charge (like Gauss' law) is established. For any domain of the square ice lattice with nonzero topological charge and an ideal ice configuration chosen randomly on its boundary, the extended positive $({\mathrm{H}}_{3}{\mathrm{O}}^{+})$ and negative $({\mathrm{OH}}^{\mathrm{\ensuremath{-}}})$ ionic defects are described in terms of 2D vector topological solitons. The definition of the 2D kinks and antikinks is given by using Gauss' law. An anisotropic generalization of the 2D ice model and an appropriate numerical scheme allows us to study the dynamical properties of the 2D solitons in comparison with the corresponding 1D solutions. Particularly, contrary to the 1D case, the existence of a nonzero Peierls-Nabarro relief has been proved to exist in all cases, even if intersite proton-proton interactions are infinitely strong, so that the free 2D soliton dynamics is impossible in the ice crystal. On the other hand, our studies of the thermalization of the 2D ice lattice clearly demonstrate the crucial role of the cooperativity of hydrogen bonding in the nucleation and dynamics of the defect pairs ${\mathrm{H}}_{3}{\mathrm{O}}^{+}$ and ${\mathrm{OH}}^{\mathrm{\ensuremath{-}}},$ explaining their very low density known from experimental data in ice physics.

Renormalization group approach to multiple-arc random matrix models

We study critical and universal behaviors of unitary invariant non-gaussian random matrix ensembles within the framework of the large- N renormalization group. For a simple double-well model we find an unstable fixed point and a stable inverse-gaussian fixed point. The former is identified as the critical point of single/double-arc phase transition with a discontinuity of the third derivative of the free energy. The latter signifies a novel universality of large- N correlators other than the usual single arc type. This phase structure is consistent with the universality classification of two-level correlators for multiple-arc models by Ambjørn and Akemann. We also establish the stability of the gaussian fixed point in the multi-coupling model.

Semiquantum chaos in the double well.

The phenomenon of semiquantum chaos is analyzed in a classically regular double-well oscillator model. Here it arises from a doubling of the number of effectively classical degrees of freedom, which are nonlinearly coupled in a Gaussian variational approximation (TDHF) to full quantum mechanics. The resulting first-order nondissipative autonomous flow system shows energy dependent transitions between regular behavior and semiquantum chaos, which we monitor by Poincar\'e sections and a suitable frequency correlation function related to the density matrix. We discuss the general importance of this form of deterministic chaos and point out the necessity to study open (dissipative) quantum systems, in order to observe it experimentally. \textcopyright{} 1996 The American Physical Society.

Distribution of double-well potentials in SiO 2 and SiO 2: Ge glasses

The temperature dependence of the internal friction and the elastic modulus of pure SiO 2 and SiO 2: Ge glasses measured by 50 kHz composite oscillator method have been analyzed on the basis of the double-well potential model. The density of relaxation strength and the distribution of the asymmetry parameter have been determined uniquely for pure SiO 2, SiO 2 5% GeO 2, and SiO 2 10%GeO 2 specimens by fitting the asymmetry potential model to the internal friction and elastic modulus data. The asymmetry parameter is found to increase with the doping of Ge atoms.

A diffuse phase transition in superconducting YBa 2(Cu 1 − xMn x) 3O 7 − δ (MZn, Ni, Cr) compounds

Dielectric and magnetic behaviour of the YBa 2(Cu 1 − x M x ) 3O 7 − δ (MZn, Ni, Cr and x ⩽ 0.10) system was investigated. The results suggest a diffuse phase transition to a relaxor-type ferroelectric state. Taking into account the double-well model of high-temperature superconductivity and using double-well parameters from the Abrahams-Kurtz-Jamieson (AKJ) relation for ferroelectric phase transition in oxide perovskite, the unrenormalizable barrier heights are calculated. The values could be related to an excitonic mechanism of superconductivity. Small anomalies observed in the static dielectric constants coincide with the Néel points of the corresponding nonsuperconductive phases in YBa 2(Cu 1 − x M x ) 3O 7 − δ compounds.

Nonlinearity of the Enthalpic Response Function to a Temperature Jump and Its Interpretation Based on Fragility in Liquid Glasses

Abstract Irreversible enthalpy-relaxation processes were tracked under a constant temperature condition by the temperature jump method for liquid 1,3-diphenyl-1,1,3,3-tetramethyldisiloxane with an adiabatic calorimeter, and simulated based on a double-well potential model with a computer. The processes were observed to show remarkable nonexponentialities and were characterized in terms of a stretched exponential function. The nonexponentiality parameter (β) depended strongly on the magnitude of the temperature jump, indicating the nonlinearity of the relaxation processes. The results of the nonlinearity parameter (δ) combined with those of 1,2-propanediol and glycerol indicated that the nonlinearity originated primarily due to the fragility of the liquid, namely the non-Arrhenius property of the relaxation times. The degree of the nonlinearity was smaller in the endothermic processes than in the exothermic ones. The difference is discussed based on the results of a computer simulation.

Small polarons and the electronic properties of Mo2S3.

We investigate the small-polaron mechanism as a possible explanation of electrical-conduction and electrical-noise properties of the linear chain material ${\mathrm{Mo}}_{2}$${\mathrm{S}}_{3}$. Experimental conductivity and noise data obtained in earlier papers [Phys. Rev. B 38, 3973 (1988); Phys. Rev. B 39, 5139 (1989)] are analyzed in terms of a small-polaron mechanism and a double-well potential model. We interpret the observed electronic properties in terms of kinetic equations describing the interaction of free carriers with fluctuations of density of the lattice. Appropriate kinetics equations to describe this interaction, which leads to small-polaron formation, are derived. These equations are found to explain quantitatively both the nonequilibrium electronic properties and electrical noise in ${\mathrm{Mo}}_{2}$${\mathrm{S}}_{3}$.

Small-bipolaron hopping conductivity in chalcogenide glasses.

We applied a simplified microscopic two-site double-well model of small bipolarons (SB's) executing thermally enhanced adiabatic tunneling to calculate the complex dynamic conductivity of chalcogenide glasses in good quantitative agreement with the experimental data for ${\mathrm{As}}_{2}$${\mathrm{Se}}_{3}$. It was found that in these materials (i) the primary mechanism for the ac conductivity is SB hopping, which at low temperatures involves adiabatic tunneling in the atomic subsystem; (ii) the intersite distance (not the energy disparity) is the principal source of the relaxation time dispersion; (iii) the stretched bonds of the size of 4.0\ifmmode\pm\else\textpm\fi{}0.6 \AA{} with the concentration of the order of ${10}^{21}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ are responsible for observed dielectric losses in a wide range of temperatures (0--600 K) and frequencies (${10}^{2}$--${10}^{8}$ Hz); (iv) the spatial distribution of the SB sites as well as of their occupation numbers are strongly affected by the pair Coulombic correlations. Both the temperature and the frequency dependencies of the real part of the ac conductivity as well as of the dielectric losses' tangent have been discussed.