Nonlinear soliton-like excitations in two-dimensional lattices and charge transport

We study soliton-like excitations and their time and space evolution in several two-dimensional anharmonic lattices with Morse interactions: square lattices including ones with externally fixed square lattice frame (cuprate model), and triangular lattices. We analyze the dispersion equations and lump solutions of the Kadomtsev-Petviashvili equation. Adding electrons to the lattice we find solectron bound states and offer computational evidence of how electrons can be controlled and transported by such acoustic waves and how electron-surfing occurs at the nanoscale. We also offer computational evidence of the possibility of long lasting, fast lattice soliton and corresponding supersonic, almost loss-free transfer or transport of electrons bound to such lattice solitons along crystallographic axes.     

Interactions between two-dimensional solitons in the diffractive-diffusive Ginzburg-Landau equation with the cubic-quintic nonlinearity

We report the results of systematic numerical analysis of collisions between two and three stable dissipative solitons in the two-dimensional (2D) complex Ginzburg-Landau equation (CGLE) with the cubic-quintic (CQ) combination of gain and loss terms. The equation may be realized as a model of a laser cavity which includes the spatial diffraction, together with the anomalous group-velocity dispersion (GVD) and spectral filtering acting in the temporal direction. Collisions between solitons are possible due to the Galilean invariance along the spatial axis. Outcomes of the collisions are identified by varying the GVD coefficient, β, and the collision “velocity” (actually, it is the spatial slope of the soliton’s trajectory). At small velocities, two or three in-phase solitons merge into a single standing one. At larger velocities, both in-phase soliton pairs and pairs of solitons with opposite signs suffer a transition into a delocalized chaotic state. At still larger velocities, all collisions become quasi-elastic. A new outcome is revealed by collisions between slow solitons with opposite signs: they self-trap into persistent wobbling dipoles, which are found in two modifications — horizontal at smaller β, and vertical if β is larger (the horizontal ones resemble “zigzag” bound states of two solitons known in the 1D CGL equation of the CQ type). Collisions between solitons with a finite mismatch between their trajectories are studied too.     

Effect of Fourier transform on the streaming in quantum lattice gas algorithms

All our previous quantum lattice gas algorithms for nonlinear physics have approximated the kinetic energy operator by streaming sequences to neighboring lattice sites. Here, the kinetic energy can be treated to all orders by Fourier transforming the kinetic energy operator with interlaced Dirac-based unitary collision operators. Benchmarking against exact solutions for the 1D nonlinear Schrodinger equation shows an extended range of parameters (soliton speeds and amplitudes) over the Dirac-based near-lattice-site streaming quantum algorithm.     

The lattice Boltzmann phononic lattice solid

I present a Boltzmann lattice gas-like approach for modeling compressional waves in an inhomogeneous medium as a first step toward developing a method to simulate seismic waves in complex solids. The method is based on modeling particles in a discrete lattice with wavelike characteristics of partial reflection and transmission when passing between links with different properties as well as phononlike interactions (i.e., collisions), with particle speed dependent on link properties. In the macroscopic limit, this approach theoretically yields compressional waves in an inhomogeneous acoustic medium. Numerical experiments verify the method and demonstrate its convergence properties. The lattice Boltzmann phononic lattice solid could be used to study how seismic wave anisotropy and attenuation are related to microfractures, the complex geometry of rock matrices, and their couplings to pore fluids. However, additional particles related to the two transverse phonons must be incorporated to correctly simulate wave phenomena in solids.     

Necklace solitons in Bessel photonic lattice: Stability and internal oscillation

Stability, internal modes and internal oscillation of 12-pearled necklace solitons in photorefractive crystal with imprinted Bessel photonic lattices are investigated. It is shown that the imaginary parts of internal modes are negligible comparing with real parts. The stable solitons perform long-distance and quasi-periodic oscillation of intensity and shape under the perturbation of internal modes.     

Nonlinear dynamics of a two-dimensional lattice

The dynamics of the nonlinear excitations in a two-dimensional (2D) φ⁴-diatomic lattice, with nonlinear on-site electron-phonon coupling at the polarizable ion site has been presented, without considering the self consistent phonon approximation. One of the major results obtained from our calculations is in the understanding of continuous structural phase transition, where we have obtained the minimum in soft mode frequency at a soft mode temperatureT _s (>T _c), not at critical temperatureT _c. This occurs due to the anisotropy of such 2D systems.     

Resistivity exponent of two-dimensional lattice animals

We calculate the average resistanceR(L) of lattice animals spanningL×L cells on the square lattice using exact and Monte Carlo methods. The dynamical resistivity exponent, defined asR(L) L , is found to be =1.36±0.07. This contradicts the Alexander-Orbach conjecture, which predicts 0.8. Our value for differs from earlier measurements of this quantity by other methods yielding =1.17±0.05 and 1.22±0.08 by Havlin et al.On leave from the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.     

Computer simulation study of a two-dimensional dipolar lattice

Summary The present work reports Monte Carlo calculations on a classical square lattice, consisting of purely dipolar plane rotators with identical dipole moments. Dipolar interactions are known not be essential for nematic ordering, but they can play a significant role in some specific cases; along the lines of the lattice model approximation already used in simulation work on liquid crystals, our system can be considered as an extreme case of nematogenic potential model. The system possesses an antiferroelectric ground state and, at higher temperature, it undergoes a transition to an orientationally disordered phase; comparison with the mean-field treatment of the transition is also reported. The structural properties were investigated by calculating orientational correlation functions, and found to exhibit some qualitative differences with respect to other potential models previously investigated for nematics. Simulation results indicate a close qualitative similarity with a three-dimensional analogue investigated in our previous work.

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Riassunto Il presente lavoro riporta calcoli Monte Carlo per un reticolo classico quadrato, costituito da rotatori piani puramente dipolari, con identici momenti. è noto che le interazioni dipolari non sono essenziali per l'ordinamento nematico, ma esse possono avere un ruolo significativo in alcuni casi specifici; lungo le linee dell'approssimazione a modello reticolare già applicata in lavori di simulazione per cristalli liquidi, il nostro sistema può pertanto venire considerato come un caso estremo di modello di potenziale nematogenico. Il sistema possiede stato fondamentale antiferroelettrico ed, a temperatura piú elevata, transisce ad una fase orientazionalmente disordinata; si riportano per confronto i risultati della trattazione a campo medio per tale transizione. Le proprietà strutturali furono investigate calcolando funzioni di correlazione orientazionale, e si è trovato che esse mostrano qualche differenza qualitativa rispetto ad altri modelli di potenziale previamente studiati per nematici. I risultati di simulazione indicano una stretta somiglianza qualitativa con un analogo tridimensionale investigato in nostri precedenti lavori.

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Резюме В этой работе предлагаются вычисления по методу Монте-Карло для классической квадратичной решетки, состоящей нз чнсто дипольных плоских ротаторов с тождественными дипольными моментами. Известно, что дипольные взаимодействия не являются существенными для нематического упорядочения, но они могут играть существенную роль в некоторых специфических случаях: в частности, в приближении модельной решетки, уже использованном при моделировании на жидких кристаллах, наша система может рассматриваться как предельный случай модели немтическочо потенциала. Рассмотренная система обладает антиферромагнитным основным состоянием и при высоких температурах она претерпевает переход в ориентационно разупорядоченную фазу; также проводится сравнение с рассмотрением этого перехода с помощью среднего поля. Исследуются структурные свойства, вычисляя ориентационные корреляционные функции. Обнаружено существование некоторых качественных различий по сравнению с моделями потенциалов, ранее использованных для нематиков. Результаты моделирования обнаруживают качественное подобие с трехмерным аналогом, исследованным в нашей предыдущей работе.

     

Dipole solitons in an optical lattice with longitudinal modulation

In this paper, we numerically demonstrate the (1+1)-dimensional dipole solitons can exist in a new Kerr-type optical lattice with longitudinal modulation that fades away and boosts up alternately. The solitons whose two dipoles simultaneously located at one lattice site and at two adjacent lattice sites are investigated, respectively. The results show that, in the two cases, the dipole solitons can be stably trapped in this kind of lattice by properly adjusting lattice parameters and soliton parameters when the repulsive force of dipoles balances the centripetal force resulting from the lattice potential effect on dipole solitons. In addition, the trapping of dipole solitons with an incident angle or the initial center position is discussed.     

Phase transitions in lattice gases of hard-core molecules having two orientations

A number of hard-core lattice gases in which a lattice site can be occupied by a molecule in either of two possible orientations are proved to undergo order-disorder phase transitions. Examples include lattice gases of trigonal planar molecules on a triangular lattice, tetrahedral molecules on a bodycentered cubic lattice, and linear molecules on a square lattice.This research was supported by The Robert A. Welch Foundation Grant P-446 and by the TCU Research Foundation.     

Boundary conditions for lattice Boltzmann simulations

A heuristic interpretation of no-slip boundary conditions for lattice Boltzmann and lattice gas simulations is developed. An improvement is suggested which consists of including the wall nodes in the collision operation.     

Stability of soliton lattice phase in the bilayer quantum Hall state under tilted magnetic fields

The bilayer quantum Hall (QH) state at the filling factor ν=1 shows various fascinating quantum phenomena due to the layer degree of freedom called ‘pseudospin’. We report an experimental evidence of the soliton lattice (SL) phase, which is a domain structure of pseudospin, by the appearance of a local maximum of magnetoresistance near the ν=1 QH state. We investigate the stability of the SL phase by changing B and the total electron density n_T. Detailed magnetotransport measurements under tilted magnetic fields were carried out to obtain a B–n_T plane phase diagram containing the C, IC and SL phases. We found the SL phase is only stable at low n_T region. Namely, the C–SL–IC phase transition occurs only at low n_T region as B increases. On the contrary, the C–IC phase transition directly occurs without passing through the SL phase at high n_T region.     

An improvement of the lattice theory of dislocation for a two-dimensional triangular crystal

The structure of dislocation in a two-dimensional triangular crystal has been studied theoretically on the basis of atomic interaction and lattice statics. The theory presented in this paper is an improvement to that published previously.Within a reasonable interaction approximation, a new dislocation equation is obtained, which remedies a fault existing in the lattice theory of dislocation. A better simplification of non-diagonal terms of the kernel is given. The solution of the new dislocation equation asymptotically becomes the same as that obtained in the elastic theory, and agrees with experimental data. It is found that the solution is formally identical with that proposed phenomenologically by Foreman et al, where the parameter can be chosen freely, but cannot uniquely determined from theory. Indeed, if the parameter in the expression of the solution is selected suitably, the expression can be well applied to describe the fine structure of the dislocation.     

Optical Abelian lattice gauge theories

We discuss a general framework for the realization of a family of Abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models that make them suitable for quantum simulations. Within this class, we study in detail the phases of a U(1)$U\left(1\right)$-invariant lattice gauge theory in 2+1$2+1$ dimensions, originally proposed by P. Orland. By using exact diagonalization, we extract the low-energy states for small lattices, up to 4×4$4\times 4$. We confirm that the model has two phases, with the confined entangled one characterized by strings wrapping around the whole lattice. We explain how to study larger lattices by using either tensor network techniques or digital quantum simulations with Rydberg atoms loaded in optical lattices, where we discuss in detail a protocol for the preparation of the ground-state. We propose two key experimental tests that can be used as smoking gun of the proper implementation of a gauge theory in optical lattices. These tests consist in verifying the absence of spontaneous (gauge) symmetry breaking of the ground-state and the presence of charge confinement. We also comment on the relation between standard compact U(1)$U\left(1\right)$ lattice gauge theory and the model considered in this paper.     

Velocity autocorrelation function in lattice gases from the ring kinetic theory. Comparison with numerical simulations

We obtain the complete time dependence of the velocity autocorrelation function (VACF) for lattice gas cellular automata, usingring kinetic theory. This theory accounts for the simplest correlated collisions that improve on the molecular chaos approach, and yields a closed equation for the VACF that we evaluate for both infinite and finite systems. We compare our analytical results with numerical simulations at all times, as well as with long-time results of the mode coupling theories, finding a very good agreement for all times at all densities.     

Localized self-trapping in two-dimensional molecular lattice with interaction between Wannier-Mott excitons and phonon lattice

We investigate the interactions of lattice phonons with Wannier-Mott exciton, the exciton that has a large radius in two-dimensional molecular lattice, by the method of continuum limit approximation, and obtain that the self-trapping can also appear in two-dimensional molecular lattice with a harmonic and nonlinear potential. The exciton effect on molecular lattice does not distort the molecular lattice but only makes it localized and the localization can also react, again through phonon coupling, to trap the energy and prevents its dispersion.     

Perturbed soliton-like molecular excitations in a deformed DNA chain

We study the nonlinear dynamics of a deformed Deoxyribonucleic acid (DNA) molecular chain which is governed by a perturbed sine-Gordon equation coupled with a linear wave equation representing the lattice deformation. The DNA chain considered here is assumed to be deformed periodically which is the energetically favourable configuration, and the periodic deformation is due to the repulsive force between base pairs, stress in the helical backbones and due to the elastic strain force in both the strands. A multiple scale soliton perturbation analysis is carried out to solve the perturbed sine-Gordon equation and the resultant perturbed kink and antikink solitons represent open state configuration with small fluctuation. The perturbation due to periodic deformation of the lattice changes the velocity of the soliton. However, the width of the soliton remains unchanged.     

Dynamics of surface dipole and tripole solitons in nonlocal nonlinear media with optical lattice field

We find the existence conditions for stationary dipole and tripole surface solitons formed at the interface of a nonlocal nonlinear medium and a lattice with linearly modulated frequency. We investigate how the degree of nonlocality, the depth, and the modulation frequency of the optical lattice field affect on the existence of the surface solitons and their dynamics. The relationship between the power and the model parameters is identified. The stability of the surface dipole and tripole solitons is numerically investigated.     

On some variational approximations in two-dimensional classical lattice systems

A new derivation is presented of some variational approximations for classical lattice systems that belong to the class of cluster-variation methods, among them the well-known Bethe-Peierls and Kramers-Wannier approximations. The limiting behavior of a hierarchical sequence of cluster-variation approximations, the so-calledC hierarchy, is discussed. It is shown that this hierarchy provides a monotonically decreasing sequence of upper boundsf _n on the free energy per lattice sitef and thatf _n f asn . Our results are based on extension theorems for states given on subsets of the lattice, which might be of some independent interest, and on an application of transfer matrix concepts to the variational characterization of translation-invariant equilibrium states.     

Turing instability for a two-dimensional Logistic coupled map lattice

In this Letter, stability analysis is applied to a two-dimensional Logistic coupled map lattice with the periodic boundary conditions. The conditions of Turing instability are obtained, and various patterns can be exhibited by numerical simulations in the Turing instability region. For example, space-time periodic structures, periodic or quasiperiodic traveling wave solutions, stationary wave solutions, spiral waves, and spatiotemporal chaos, etc. have been observed. In particular, the different pattern structures have also been observed for same parameters and different initial values. That is, pattern structures also depend on the initial values. The similar patterns have also been seen in relevant references. However, the present Letter owes to pattern formation via diffusion-driven instabilities because the system is stable in the absence of diffusion.