Note on Invariance of One-Dimensional Lattice-Boltzmann Equation

Invariance of the one-dimensional lattice Boltzmann model is proposed together with its rigorous theoretical background. It is demonstrated that the symmetry inherent in Navier-Stokes equations is not really recovered in the one-dimensional lattice Boltzmann equation （LBE）, especially for shock calculation. Symmetry breaking may be the inherent cause for the non-physical oscillations in the vicinity of the shock for LBE calculation.     

Polaron formation and hopping conductivity in the Holstein-Hubbard model

On the basis of the Holstein-Hubbard model the formation of polarons at finite densities is investigated by means of a variational approach appropriate for describing squeezing and correlation effects. An effective Hubbard model for the polarons is derived, where the correlations are treated within the slave-boson saddlepoint approximation. For low enough phonon frequencies, with increasing coupling an abrupt self-trapping transition from light to heavy polarons is found. With increasing density the squeezing effect increases, and the transition is shifted to higher couplings. In the case of an effective Coulomb repulsion, the self-trapping transition is shifted to lower couplings with increasing Hubbard interaction, and the effective polaron mass below the transition is enhanced. In the heavy polaron regime, the frequency-dependent polaron hopping conductivity is calculated. There occur qualitative finite-density and correlation effects on the zero-temperature absorption spectrum which are discussed with respect to their possible relevance to the midinfrared absorption in high-T _c superconductors.     

Distribution of Overlap Profiles in the One-Dimensional Kac--Hopfield Model

We study a one-dimensional version of the Hopfield model with long, but finite range interactions below the critical temperature. In the thermodynamic limit we obtain large deviation estimates for the distribution of the “local” overlaps, the range of the interaction, , being the large parameter. We show in particular that the local overlaps in a typical Gibbs configuration are constant and equal to one of the mean-field equilibrium values on a scale . We also give estimates on the size of typical “jumps”, i.e. the regions where transitions from one equilibrium value to another take place. Contrary to the situation in the ferromagnetic Kac-model, the structure of the profiles is found to be governed by the quenched disorder rather than by entropy. Received: 14 February 1996 / Accepted: 30 September 1996     

Fluctuations of the One-Dimensional Polynuclear Growth Model in Half-Space

We consider the multi-point equal time height fluctuations of the one-dimensional polynuclear growth model in half-space. For special values of the nucleation rate at the origin, the multi-layer version of the model is reduced to a process with a determinantal weight, for which the asymptotics can be analyzed. In the scaling limit, the fluctuations near the origin are shown to be equivalent to those of the largest eigenvalue of the orthogonal/symplectic to unitary transition ensemble at soft edge in random matrix theory.     

Minority Population in the One-Dimensional Schelling Model of Segregation

Schelling models of segregation attempt to explain how a population of agents or particles of two types may organise itself into large homogeneous clusters. They can be seen as variants of the Ising model. While such models have been extensively studied, unperturbed (or noiseless) versions have largely resisted rigorous analysis, with most results in the literature pertaining models in which noise is introduced, so as to make them amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory. We rigorously analyse the one-dimensional version of the model in which one of the two types is in the minority, and establish various forms of threshold behaviour. Our results are in sharp contrast with the case when the distribution of the two types is uniform (i.e. each agent has equal chance of being of each type in the initial configuration), which was studied in Brandt et al. (in: STOC ’12: proceedings of the 44th symposium on theory of computing, pp. 789–804, 2012) and Barmpalias et al. (in: 55th Annual IEEE symposium on foundations of computer science, Oct 18–21, Philadelphia, FOCS’14, 2014).

     

A One-Dimensional Model of Hydrogen Molecular Ion

We present a study on a one-dimensional hydrogen molecular ion under the Born-Oppenheimer approximation. A canonical transformation produces the classical system directlyto be a pendulum. The quantum Schrodinger equation is solved analytically and theelectronic energy curves show that the bound states of this 1D model differ from the 2D and 3DH₂⁺. The vibration spectroscopy is also obtained by employing the Morse's eigen wavefunctionsas basis vectors to diagonalize the Hamiltonian for R. The semiclassical quantization yieldselectronic energies in agreement with the quantum ones reasonably.     

Charge Gap in One-Dimensional Extended Hubbard Model

By using the bosonization and renormalization group methods, we have studied the low energy physical properties in one-dimensional extended Hubbard model. The formation of charge and spin gaps is investigated at the half-filled electron band. An analytical expression for the charge gap in terms of the Coulomb repulsive interaction strength U and the nearest-neighbour interaction parameter V is obtained.     

Phase Diagram of One-Dimensional Fermi Gas Model

The phase diagrams of one-dimensional g-ology model are studied. The known results of the XXZ spin 1/2 chain model are applied to extending the solutions to the massless range where the method of Gaussian wave functional is insufficient. The response functions of CDW, SDW, SS and TS are computed as temperature T→0.     

Bipolarons and polarons in the Holstein-Hubbard model: analogies and differences

We consider a simple model of spring-mass block placed over a constant velocity v rolling plate. The map of the dynamic is presented in the (v,r) space where r accounts for the possible variation of the periodic shape profile of the rolling carpet. In order to characterize each type of motion, we found that evaluating the area of the phase space trajectories is more relevant than attempting on one hand, to solve analytically the asymptotic behavior, or on the other hand, to obtain an equivalent of the entropy and the free energy. First-order transition reveals to be the characteristic route from one type of motion to another. Later, we investigate the influence of the classical TMD¹ and TLCD² on the dynamic of this mass. Moreover, we numerically study the effects of a modified TMD. Reduced order parameter provides a quick overview of the whole system than phase space representations and bifurcation diagrams. Comparison of performances in the (v,r) space is made. It reveals the efficiency of the modified TMD. It comes out that the new TMD we designed stabilizes the system better than the two above control systems.     

Self-trapping phase diagram for the strongly correlated extended Holstein-Hubbard model in two-dimensions

The two-dimensional extended Holstein-Hubbard model is investigated in the strong correlation regime to study the nature of self-trapping transition and the polaron phase diagram in the absence of superconductivity. Using a series of canonical transformations followed by zero-phonon averaging the extended Holstein-Hubbard model is converted into an effective extended Hubbard model which is subsequently transformed into an effective t-J model in the strong correlation limit. This effective t-J model is finally solved using the mean-field Hartree-Fock approximation to show that the self-trapping transition is continuous in the anti-adiabatic limit while it is discontinuous in the adiabatic limit. The phase diagrams for the localization-delocalization transition, namely the phase line and the phase surface separating the small polaron and large polaron states are also shown.     

Markovian and Non-Markovian Dynamics in the One-Dimensional Transverse-Field XY Model

Journal of Statistical Physics - We consider an anisotropic spin-1/2 XY Heisenberg chain in the presence of a transverse magnetic field. Selecting the nearest neighbor pair spins as an open quantum...     

One-Dimensional Traffic Model to Consider Priority of the Stochastic Deceleration

A one-dimensional cellular automaton model of traffic flow is proposed to introduce the different delay probabilities in the steps of rules and the stochastic deceleration prior to the deterministic one when the anticipation velocity of vehicle is larger than the headway. The fundamental diagram shows the capacity of road more approaches to the observed data compared with that by the NaSch model. Moreover, the model is able to reproduce the complicated behavior of the real traffic, such as the metastability state, the separation of different phases and the effect of hysteresis. It is concluded that the order arrangement of the stochastic deceleration and deterministic acceleration has indeed remarkable effect on traffic flow and the modification presented in this paper is reasonable and realistic.     

Effects of Bond Alternation on the Ground-State Phase Diagram of One-Dimensional XXZ Model

The ground-state properties and quantum phase transitions (QPTs) of the one-dimensional bond-alternative XXZ model are investigated by the infinite time-evolving block decimation (iTEBD) method.The bond-alternative effects on its ground-state phase diagram are discussed in detail.Once the bond alternation is taken into account,the antiferromagnetic phase (Δ 1) will be destroyed at a given critical point and change into a disordered phase without nonlocal string order.The QPT is shown to be second-order,and the whole phase diagram is provided.For the ferromagnetic phase region (Δ-1),the critical point r c always equals 1 (independent of Δ),and the QPT for this case is shown to be first-order.The dimerized Heisenberg model is also discussed,and two disordered phases can be distinguished by with or without nonlocal string orders.Both the bipartite entanglement and the fidelity per site,as two kinds of model-independent measures,are capable of describing all the QPTs in such a quantum model.     

Effects of Bond Alternation on the Ground-State Phase Diagram of One-Dimensional XXZ Model

The ground-state properties and quantum phase transitions (QPTs) of the one-dimensional bond-alternative XXZ model are investigated by the infinite time-evolving block decimation (iTEBD) method. The bond-alternative effects on its ground-state phase diagram are discussed in detail. Once the bond alternation is taken into account, the antiferromagnetic phase (Δ > 1) will be destroyed at a given critical point and change into a disordered phase without nonlocal string order. The QPT is shown to be second-order, and the whole phase diagram is provided. For the ferromagnetic phase region (Δ < -1), the critical point r^c always equals 1 (independent of Δ), and the QPT for this case is shown to be first-order. The dimerized Heisenberg model is also discussed, and two disordered phases can be distinguished by with or without nonlocal string orders. Both the bipartite entanglement and the fidelity per site, as two kinds of model-independent measures, are capable of describing all the QPTs in such a quantum model.     

Pseudospin Wave State in One-Dimensional Half-Filled Hubbard Model

All the eigenfunctione with spin S = (M - 1)/2 of one-dimeneional half-filled Hubbard model are obtained by ueing a eimple method (M is the number of the sites). These eigenfunctions depend on U, t, and the momentum k. It ie shown that the eigenetates we obtained can describe varioue kinde of pseudospin waves with wave vector k and these pseudoepin wave etates are accompanied with a charge transferring. This is in agreement with the exact diagonalisation results for emall eitee ring.