Nearest-neighbor Lattice Research Articles

Thermal rectification in mass-asymmetric one-dimensional anharmonic oscillator lattices with and without a ballistic spacer

In this work we perform a systematic analysis of various structural parameters that have influence on the thermal rectification effect, i.e. asymmetrical heat flow, and the negative differential thermal resistance —reduction of the heat flux as the applied thermal bias is increased— present in a one-dimensional, segmented mass-graded system consisting of a coupled nearest-neighbor harmonic oscillator lattice (ballistic spacer) and two diffusive leads (modeled by a substrate potential) attached to the lattice at both boundaries. At variance with previous works, we consider the size of the spacer as smaller than that of the leads. Also considered is the case where the leads are connected along the whole length of the oscillator lattice; that is, in the absence of the ballistic spacer. Upon variation of the system’s parameters it was determined that the performance of the device, as quantified by the spectral properties, is largely enhanced in the absence of the ballistic spacer for the small system-size limit herein considered.

Anomalous Behaviors of Quantum Emitters in Non-Hermitian Baths

Both non-Hermitian systems and the behavior of emitters coupled to structured baths have been studied intensely in recent years. Here, we study the interplay of these paradigmatic settings. In a series of examples, we show that a single quantum emitter coupled to a non-Hermitian bath displays a number of unconventional behaviors, many without Hermitian counterpart. We first consider a unidirectional hopping lattice whose complex dispersion forms a loop. We identify peculiar bound states inside the loop as a manifestation of the non-Hermitian skin effect. In the same setting, emitted photons may display spatial amplification markedly distinct from free propagation, which can be understood with the help of the generalized Brillouin zone. We then consider a nearest-neighbor lattice with alternating loss. We find that the long-time emitter decay always follows a power law, which is usually invisible for Hermitian baths. Our Letter points toward a rich landscape of anomalous quantum emitter dynamics induced by non-Hermitian baths.

Structural and vibrational behavior of 2H−NbSe2 at high pressures

The high-pressure structural and vibrational properties of a layered transition metal dichalcogenide $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$ were investigated using single-crystal x-ray diffraction and Raman spectroscopy, demonstrating its structural stability up to 35 GPa. The lattice compressibility changes character from being highly anisotropic at low pressures to largely isotropic at high pressures. Concomitantly, the interatomic bonds demonstrate highly anisotropic compression behavior with the Se-Se interlayer bonds compressing by >20%, while the intramolecular Se-Se distance shows a nonmonotonic pressure dependence with a maximum at \ensuremath{\sim}12 GPa. The nearest-neighbor central force lattice vibrational model yields pressure dependencies of the interatomic forces in qualitative agreement with bond length compression, providing insight into the vibrational properties of $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$ at high pressures.

NoBLE for Lattice Trees and Lattice Animals

We study lattice trees (LTs) and animals (LAs) on the nearest-neighbor lattice {mathbb {Z}}^d in high dimensions. We prove that LTs and LAs display mean-field behavior above dimension 16 and 17, respectively. Such results have previously been obtained by Hara and Slade in sufficiently high dimensions. The dimension above which their results apply was not yet specified. We rely on the non-backtracking lace expansion (NoBLE) method that we have recently developed. The NoBLE makes use of an alternative lace expansion for LAs and LTs that perturbs around non-backtracking random walk rather than around simple random walk, leading to smaller corrections. The NoBLE method then provides a careful computational analysis that improves the dimension above which the result applies. Universality arguments predict that the upper critical dimension, above which our results apply, is equal to d_c=8 for both models, as is known for sufficiently spread-out models by the results of Hara and Slade mentioned earlier. The main ingredients in this paper are (a) a derivation of a non-backtracking lace expansion for the LT and LA two-point functions; (b) bounds on the non-backtracking lace-expansion coefficients, thus showing that our general NoBLE methodology can be applied; and (c) sharp numerical bounds on the coefficients. Our proof is complemented by a computer-assisted numerical analysis that verifies that the necessary bounds used in the NoBLE are satisfied.

Statistics of the number of records for random walks and Lévy flights on a 1D lattice

We study the statistics of the number of records Rn for a symmetric, n-step, discrete jump process on a 1D lattice. At a given step, the walker can jump by arbitrary lattice units drawn from a given symmetric probability distribution. This process includes, as a special case, the standard nearest neighbor lattice random walk. We derive explicitly the generating function of the distribution P(Rn) of the number of records, valid for arbitrary discrete jump distributions. As a byproduct, we provide a relatively simple proof of the generalized Sparre Andersen theorem for the survival probability of a random walk on a line, with discrete or continuous jump distributions. For the discrete jump process, we then derive the asymptotic large n behavior of P(Rn) as well as of the average number of records E(Rn). We show that unlike the case of random walks with symmetric and continuous jump distributions where the record statistics is strongly universal (i.e. independent of the jump distribution for all n), the record statistics for lattice walks depends on the jump distribution for any fixed n. However, in the large n limit, we show that the distribution of the scaled record number Rn/E(Rn) approaches a universal, half-Gaussian form for any discrete jump process. The dependence on the jump distribution enters only through the scale factor E(Rn), which we also compute in the large n limit for arbitrary jump distributions. We present explicit results for a few examples and provide numerical checks of our analytical predictions.

A pressure-based regularized lattice-Boltzmann method for the simulation of compressible flows

A new pressure-based lattice-Boltzmann method (HRR-p) is proposed for the simulation of flows for Mach numbers ranging from 0 to 1.5. Compatible with nearest-neighbor lattices (e.g., D3Q19), the model consists of a predictor step comparable to classical athermal lattice-Boltzmann methods, appended with a fully local and explicit correction step for the pressure. Energy conservation—for which the Hermitian quadrature is not accurate enough on such a lattice—is solved via a classical finite volume MUSCL-Hancock scheme based on the entropy equation. The Euler part of the model is then validated for the transport of three canonical modes (vortex, entropy, and acoustic propagation), while its diffusive/viscous properties are assessed via thermal Couette flow simulations. All results match the analytical solutions with very limited dissipation. Last, the robustness of the method is tested in a one-dimensional shock tube and a two-dimensional shock–vortex interaction.

Jammed systems of oriented dimers always percolate on hypercubic lattices

Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Here we consider jammed states of the RSA process of nonoverlapping dimers(objects occupying two nearest-neighbor lattice sites) in a hypercubic lattice of arbitrary space dimension D ⩾ 2. We show that each dimer in such a state belongs to a percolating cluster.

The controllability Gramian of lattice graphs

The control of networked dynamical systems continues to receive much attention across the engineering and scientific research fields. Here, we investigate the control of lattice systems which provides analytical insight into the relationship between network structure and controllability. First we derive the exact expression for the individual elements of the controllability Gramian of infinite lattice systems. Second, we focus on nearest neighbor lattices for which the distance between nodes appears in the expression for the controllability Gramian. We show that common control energy metrics scale exponentially with respect to the maximum of all the distances between driver nodes and target nodes.

Monte Carlo modeling of ferromagnetism of nano-graphene monolayer within Ising model

Abstract Ferromagnetism of nano-graphene layer within Ising model was studied. All results were obtained by using Monte Carlo simulation based on Metropolis algorithm. By applying external magnetic field at room temperature, a gradual transition between ferromagnetic and paramagnetic phases was obtained. This indicates to a potentiality of such a monolayer to be used as a magnetic field sensor. The existence of hysteresis, was established, which strongly depends on the type and magnitude of the interaction strength between the nearest neighbor lattice nodes (spins). Gradual two-step transition between ferromagnetic and paramagnetic phases near absolute zero temperature, was obtained. The results of numerical simulations are in agreement with the available experimental works of other authors.

Theory of Ferroelectric ZrO2 Monolayers on Si

We use density functional theory and Monte Carlo lattice simulations to investigate the structure of ZrO$_{2}$ monolayers on Si(001). Recently, we have reported on the experimental growth of amorphous ZrO$_{2}$ monolayers on silicon and their ferroelectric properties, marking the achievement of the thinnest possible ferroelectric oxide [M. Dogan et al. Nano Lett., 18 (1) (2018)]. Here, we first describe the rich landscape of atomic configurations of monocrystalline ZrO$_{2}$ monolayers on Si and determine the local energy minima. Because of the multitude of low-energy configurations we find, we consider the coexistence of finite-sized regions of different configurations. We create a simple nearest-neighbor lattice model with parameters extracted from DFT calculations, and solve it numerically using a cluster Monte Carlo algorithm. Our results suggest that up to room temperature, the ZrO$_{2}$ monolayer consists of small domains of two low-energy configurations with opposite ferroelectric polarization. This explains the observed ferroelectric behavior in the experimental films as a collection of crystalline regions, which are a few nanometers in size, being switched with the application of an external electric field.

Anisotropic-Exchange Magnets on a Triangular Lattice: Spin Waves, Accidental Degeneracies, and Dual Spin Liquids

We present an extensive overview of the phase diagram, spin-wave excitations, and finite-temperature transitions of the anisotropic-exchange magnets on an ideal nearest-neighbor triangular lattice. We investigate transitions between five principal classical phases of the corresponding model: ferromagnetic, N\'{e}el, its dual, and the two stripe phases. Transitions are identified by the spin-wave instabilities and by the Luttinger-Tisza approach. Some of the transitions are direct and others occur via intermediate phases with more complicated forms of ordering. In a portion of the N\'{e}el phase, we find spin-wave instabilities to a long-range spiral-like state. In the stripe phases, quantum fluctuations are mostly negligible, leaving the ordered moment nearly saturated even for the $S=1/2$ case. However, for a two-dimensional surface of the full 3D parameter space, the spin-wave spectrum in one of the stripe phases exhibits an enigmatic accidental degeneracy manifested by pseudo-Goldstone modes. As a result, despite the nearly classical ground state, the ordering transition temperature in a wide region of the phase diagram is significantly suppressed from the mean-field expectation. We identify this accidental degeneracy as due to an exact correspondence to an extended Kitaev-Heisenberg model with emergent symmetries that naturally lead to the pseudo-Goldstone modes. There are previously studied dualities within the Kitaev-Heisenberg model on the triangular lattice that are exposed here in a wider parameter space. One important implication of this correspondence for the $S=1/2$ case is the existence of a region of the spin-liquid phase that is dual to the spin-liquid phase discovered recently by us. We complement our studies by the density-matrix renormalization group of the $S=1/2$ model to confirm some of the duality relations and to verify the existence of the dual spin-liquid phase.

A novel quantum image encryption algorithm based on crossover operation and mutation operation

In this paper, a new algorithm of image encryption based on random selection of crossover operation and mutation operation is proposed. Crossover operation and mutation operation come from genetic algorithm that gets high-quality solutions to optimization. First, quantum chaos sequence and two-dimensional logistic sequence are XORed with plain-image. And then, adjacent pixels of the image are carried out bit-level crossover operation and crossover bits rely heavily on chaotic maps for chaotic property. Finally, two different bits of each pixel are employed to perform mutation for high randomness. In order to obtain the high complexity and unpredictability further, quantum chaotic map is coupled with nearest-neighboring coupled-map lattices (NCML). Computer simulations and statistical analyses show that the proposed algorithm has more than 1045 bits key space, low correlation closed to 0, ideal information entropy closed to 8, acceptable speed performance 4.7081Mbt/s and resistance to various attacks.

Topography of Spin Liquids on a Triangular Lattice.

Spin systems with frustrated anisotropic interactions are of significant interest due to possible exotic ground states. We have explored their phase diagram on a nearest-neighbor triangular lattice using the density-matrix renormalization group and mapped out the topography of the region that can harbor a spin liquid. We find that this spin-liquid phase is continuously connected to a previously discovered spin-liquid phase of the isotropic J_{1}-J_{2} model. The two limits show nearly identical spin correlations, making the case that their respective spin liquids are isomorphic to each other.

A Lattice Model of Charge-Pattern-Dependent Polyampholyte Phase Separation.

In view of recent intense experimental and theoretical interests in the biophysics of liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs), heteropolymer models with chain molecules configured as self-avoiding walks on the simple cubic lattice are constructed to study how phase behaviors depend on the sequence of monomers along the chains. To address pertinent general principles, we focus primarily on two fully charged 50-monomer sequences with significantly different charge patterns. Each monomer in our models occupies a single lattice site, and all monomers interact via a screened pairwise Coulomb potential. Phase diagrams are obtained by extensive Monte Carlo sampling performed at multiple temperatures on ensembles of 300 chains in boxes of sizes ranging from 52 × 52 × 52 to 246 × 246 × 246 to simulate a large number of different systems with the overall polymer volume fraction ϕ in each system varying from 0.001 to 0.1. Phase separation in the model systems is characterized by the emergence of a large cluster connected by intermonomer nearest-neighbor lattice contacts and by large fluctuations in local polymer density. The simulated critical temperatures, Tcr, of phase separation for the two sequences differ significantly, whereby the sequence with a more "blocky" charge pattern exhibits a substantially higher propensity to phase separate. The trend is consistent with our sequence-specific random-phase-approximation (RPA) polymer theory, but the variation of the simulated Tcr with a previously proposed "sequence charge decoration" pattern parameter is milder than that predicted by RPA. Ramifications of our findings for the development of analytical theory and simulation protocols of IDP LLPS are discussed.

Critical Point Confluence Phenomenon.

Experimental observation of coexisting isotropic chiral liquids for a single molecular substance has motivated creation of a simple lattice model to investigate phase transitions in such systems. Specifically, this model permits the simultaneous existence of two distinct types of critical points, the familiar liquid-vapor case, and a case involving spontaneous chiral symmetry breaking within the fluid system. The molecular interactions involved may extend beyond nearest neighbor lattice cells. The mean field approximation has been invoked to attain explicit results, which include a description of the singular situation for which the two critical points undergo confluence in the temperature-density plane. In particular, this confluence enhances the chiral symmetry breaking phenomenon, leading to a modified critical exponent.

A Novel Color Image Encryption Algorithm Based on Quantum Chaos Sequence

In this paper, a novel algorithm of image encryption based on quantum chaotic is proposed. The keystreams are generated by the two-dimensional logistic map as initial conditions and parameters. And then general Arnold scrambling algorithm with keys is exploited to permute the pixels of color components. In diffusion process, a novel encryption algorithm, folding algorithm, is proposed to modify the value of diffused pixels. In order to get the high randomness and complexity, the two-dimensional logistic map and quantum chaotic map are coupled with nearest-neighboring coupled-map lattices. Theoretical analyses and computer simulations confirm that the proposed algorithm has high level of security.

Spatial competition of the ground states in 1111 iron pnictides

Using nuclear quadrupole resonance, the phase diagram of 1111 $R$FeAsO$_{1-x}$F$_x$ ($R$$=$La, Ce, Sm) iron pnictides is constructed as a function of the local charge distribution in the paramagnetic state, which features low-doping-like (LD-like) and high-doping-like (HD-like) regions. Compounds based on magnetic rare earths (Ce, Sm) display a unified behavior, and comparison with La-based compounds reveals the detrimental role of static iron $3d$ magnetism on superconductivity, as well as a qualitatively different evolution of the latter at high doping. It is found that the LD-like regions fully account for the orthorhombicity of the system, and are thus the origin of any static iron magnetism. Orthorhombicity and static magnetism are not hindered by superconductivity but limited by dilution effects, in agreement with 2D (respectively 3D) nearest-neighbor square lattice site percolation when the rare earth is nonmagnetic (respectively magnetic). The LD-like regions are not intrinsically supportive of superconductivity, on the contrary of the HD-like regions, as evidenced by the well-defined Uemura relation between the superconducting transition temperature and the superfluid density when accounting for the proximity effect. This leads us to propose a complete description of the interplay of ground states in 1111 pnictides, where nanoscopic regions compete to establish the ground state through suppression of superconductivity by static magnetism, and extension of superconductivity by proximity effect.

SIMULATION ANALYSIS OF THE TOTALLY ASYMETRIC SIMPLE EXCLUSION PROCESS TO DETERMINE THE PROFIL OF THE ONE-BODY CORRELATION FUNCTION, TWO-BODY CORRELATION FUNCTION, AND THREE-BODY CORRELATION FUNCTION AROUND THE ENDS OF THE LATTICE WITH LATTICE NUMBER VARIATION

This study aimed to determine the behavior of one-body, two-body, and three-body correlation functions of the model dynamics TASEP with sequential updating rules and open boundary conditions on vehicular traffic around the end of the traffic light. The study began with the determination of algorithm to model the dynamics of TASEP and coding, with the variation of the input rate (α) , the output rate (β), and the number of lattice sites (N). Then the program run with specific time limit (t) and number of systems (M). The value of the one-body correlation function determines the average occupancy of particles in lattice site-i at time t. Two-body correlation function determines the average occupancy of particle at site-i when there is another particle occupying the nearest neighbor lattice, i+1, at time t. Three-body correlation function determines the average occupancy of particles to occupy lattice site-i when there are other particles occupying the nearest and next nearest neighbor lattice sites, i+1 and i+2, at time t. The value of the one-body correlation function turns out to be larger than the value of the two-body correlation function. The value of the two-body correlation function is larger than the value of the three-body correlation function for all phases. The correlation between a vehicle to another vehicle will be even greater. Keywords: TASEP, sequential updating, n-body correlation function

A new encryption algorithm for color images based on total chaotic shuffling scheme

This paper proposes a novel image encryption algorithm based on a quantum chaotic map, nearest-neighboring coupled-map lattices and permutation-diffusion architecture. First, a keystream generated by a quantum chaotic map is used to permute the pixels of the R, G and B components concurrently and make the three components affect one other. Next, the random circular shift operation was performed, resulting in permuted pixels to rearrange bits of each pixel. Finally, the new algorithm employs keystreams generated by the nearest-neighboring coupled-map lattices to diffuse the relationship between the cipher image and the plain image. To generate the initial conditions and parameters of the chaotic maps, a 128 bit long external secret key is used. The results of several experimental analyses on the randomness, sensitivity, and correlation of the cipher images show that the proposed algorithm has a high security level and high sensitivity and can be adopted for network security and secure communications.

Singlet-Triplet Excitations and Long-Range Entanglement in the Spin-Orbital Liquid Candidate FeSc2S4.

Theoretical models of the spin-orbital liquid (SOL) FeSc2S4 have predicted it to be in close proximity to a quantum critical point separating a spin-orbital liquid phase from a long-range ordered magnetic phase. Here, we examine the magnetic excitations of FeSc2S4 through time-domain terahertz spectroscopy under an applied magnetic field. At low temperatures an excitation emerges that we attribute to a singlet-triplet excitation from the SOL ground state. A threefold splitting of this excitation is observed as a function of applied magnetic field. As singlet-triplet excitations are typically not allowed in pure spin systems, our results demonstrate the entangled spin and orbital character of singlet ground and triplet excited states. Using experimentally obtained parameters we compare to existing theoretical models to determine FeSc2S4's proximity to the quantum critical point. In the context of these models, we estimate the characteristic length of the singlet correlations to be ξ/(a/2)≈8.2 (where a/2 is the nearest neighbor lattice constant), which establishes FeSc2S4 as a SOL with long-range entanglement.