Double-quadratic Potential Research Articles

Observational constraints on two-field warm inflation

We study the two-field warm inflation models with a double quadratic potential and a linear temperature dependent dissipative coefficient. We derived the evolution equation of all kinds of perturbations without assuming slow-roll approximation, and obtained the curvature power spectrum at the end of inflation with a fully numerical method. Then we compute the scalar spectral index $n_s$, tensor-to-scalar ratio $r$ for several representative potentials, and compare our results with observational data. At last, we use Planck data to constrain the parameters in our models. This work is a natural extension of single-field warm inflation, and the aim of this work is to present some features of multi-field warm inflation using a simple two-field model.

Size effects on a two-dimensional hexagonal lattice with application to lithium iodate.

We consider a two-dimensional hexagonal nonlinear lattice with two sites per unit cell and an on-site double quadratic potential, which can describe some phase transitions in lithium iodate. We investigate the strip version of this model. The phonon stability and phase diagram of this strip-lattice model are determined and compared to those of the infinite model to derive size effects on the static structure of the lattice. Furthermore, our phase diagram provides theoretical support for the hypothesis of the existence of an intermediate modification of ${\mathrm{LiIO}}_{3}$ during the transition from \ensuremath{\alpha}-${\mathrm{LiIO}}_{3}$ to \ensuremath{\gamma}-${\mathrm{LiIO}}_{3}$.

Domain-wall interactions and ground states for a classical one-dimensional lattice

Abstract We study a one-dimensional lattice model with an on-site double-quadratic potential, where first- and second-neighbour interactions are taken into account. We investigate commensurate states of the model and we study in detail the interactions between domain walls as a function of the spatial distribution of those walls within two and four-wall structures. We then find the spatial distribution of the walls which corresponds to the lowest energy of the structure and identify the unit cells associated with the ground states. We then suggest a method incorporating domain-wall interactions to build up the phase diagram of the model using a two-step process: first, we determine by the above process the ground states of the model in the parameter space that is considered. Second, we determine classically the parameter regions corresponding to each ground state.

Periodic structures and interfacial energies in a two-dimensional nonlinear lattice, with application to lithium iodate

A two-dimensional hexagonal nonlinear lattice with two sites per unit cell and an on-site double-quadratic potential is investigated. The phonon stability and phase diagram of this model, which can represent several phases of lithium iodate, are determined. A method to calculate the structure and energy of an interface between two phases is presented and applied to the interface between the two enantiomorphic forms of alpha -LiIO3.

Domain walls in a linear chain of atoms lying in double quadratic potential and interacting with second nearest neighbors

Abstract Some crystals with the incommensurate phase can be modeled by a chain of atoms lying in the double quadratic potential and interacting with up to the second nearest neighbors. Domain wall problems in the commensurate phase of such crystals were studied. The structure, the formation energy and the activation energy were obtained and discussed.

Statistical mechanics of supercoiling-induced B-to-Z transitions in a closed circular DNA: One-dimensional model system with a double quadratic displacement potential and long range interactions

A configurational partition function for transitions between the right-handed B helix and the left-handed Z helix in a closed circular double stranded DNA is formulated in an idealized model. The twisting potential of base pairs is assumed to be a double quadratic potential with two minima at the B and Z forms and nearest neighbor coupling between base pair twists to be harmonic. In addition, long range interactions attributable to the conservation of linking number between two closed DNA strands are approximated by a harmonic potential of the writhing number that is equal to the linking number minus the total twist. Interactions between phonons and B-Z junctions are neglected as well as interactions between junctions. The configuration partition function is formulated for two cases, one that all base pairs can take the Z form as well as the B form, and another that only part of DNA can take the Z form. Then it is applied to analyzing B-to-Z transitions induced by changing the linking number of a closed circular DNA. The characteristics of B-to-Z transitions are examined in detail as well as experimental data analyses.

Periodic structures in a two-dimensional lattice

A two-dimensional lattice with harmonic interactions to nearest and next-nearest neighbours is studied in detail. The local anharmonic ion-electron interaction is described by a double-quadratic potential. The ground state is a periodic structure with different periods for variable parameters. In a simple mean-field approximation, it is found that with changing temperature, transitions between different periodic structures are possible.