From quantum cellular automata to quantum lattice gases

A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial, exactly unitary, partitioning cellular automata. We find a one-parameter family of evolution rules which are best interpreted as those for a one-particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second, of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.     

格子气的声振荡衰减

采用格子气数值方法模拟了共振腔中气体声振荡衰减过程．计算结果表明：格子气中声振荡衰减的规律和经典理论结果一致；衰减系数随频率增加而减小，并且随密度增加而减小．该结果可以用来说明一些大学统计物理教科书中的一个经典例子存在不完善之处．本中采用了一种新的扭转9-bit格子气模型和并行计算方法，这些结果对今后研究格子气中的热声问题有参考价值．     

Phase transition in a lattice gas of hard spheres with second-neighbor exclusions on the simple cubic lattice

Using reflection positivity and the Peierls argument, we prove the existence of an ordered phase at sufficiently high activity for a lattice gas of hard spheres on the simple cubic lattice with first- and second-neighbor exclusions.     

Linear response and relaxation in quantum lattice systems

For spin-lattice systems, the Kubo formula, expressing the relaxation function in terms of the linear response function, is found to be exact in the thermodynamic limit. In addition, analyticity properties are obtained.     

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 exact energy conservation property of the quantum lattice Boltzmann algorithm

The quantum lattice Boltzmann algorithm offers a unitary and readily parallelisable discretisation of the Dirac equation that is free of the fermion-doubling problem. The expectation of the discrete time-advance operator is an exact invariant of the algorithm. Its imaginary part determines the expectation of the Hamiltonian operator, the energy of the solution, with an accuracy that is consistent with the overall accuracy of the algorithm. In the one-dimensional case, this accuracy may be increased from first to second order using a variable transformation. The three-dimensional quantum lattice Boltzmann algorithm uses operator splitting to approximate evolution under the three-dimensional Dirac equation by a sequence of solutions of one-dimensional Dirac equations. The three-dimensional algorithm thus inherits the energy conservation property of the one-dimensional algorithm, although the implementation shown remains only first-order accurate due to the splitting error.     

The computational complexity of the Lorentz lattice gas

The Lorentz lattice gas is studied from the perspective of computational complexity theory. It is shown that using massive parallelism, particle trajectories can be simulated in a time that scales logarithmically in the length of the trajectory. This result characterizes the logical depth of the Lorentz lattice gas and allows us to compare it to other models in statistical physics.     

Damage spreading in a driven lattice gas model

We studied damage spreading in a Driven Lattice Gas (DLG) model as a function of the temperature T$T$, the magnitude of the external driving field E$E$, and the lattice size. The DLG model undergoes an order–disorder second-order phase transition at the critical temperature _Tc(E)$T_c\left(E\right)$, such that the ordered phase is characterized by high-density strips running along the direction of the applied field; while in the disordered phase one has a lattice-gas-like behavior. It is found that the damage always spreads for all the investigated temperatures and reaches a saturation value _Dsat$D_{sat}$ that depends only on T$T$. _Dsat$D_{sat}$ increases for T<_Tc(E=∞)$T<T_c(E=\infty )$, decreases for T>_Tc(E=∞)$T>T_c(E=\infty )$ and is free of finite-size effects. This behavior can be explained as due to the existence of interfaces between the high-density strips and the lattice-gas-like phase whose roughness depends on T$T$. Also, we investigated damage spreading for a range of finite fields as a function of T$T$, finding a behavior similar to that of the case with E=∞$E=\infty$.     

Properties of nano-scale soliton-like excitations in two-dimensional lattice layers

Nano-scale soliton-like supersonic, intrinsic localized excitations in two-dimensional atomic anharmonic lattice layers are here considered. We study the propagation, the velocity and other soliton-like features at head-on collisions of such lattice excitations created by using suitable initial mechanical and thermal conditions. Noteworthy is that narrow, highly-energetic solitons moving along one lattice row are very robust, accompanied by weak anti-phase oscillations in the lateral direction.     

Implementation of the quantum Fourier transform

A quantum Fourier transform (QFT) has been implemented on a three qubit nuclear magnetic resonance (NMR) quantum computer to extract the periodicity of an input state. Implementation of a QFT provides a first step towards the realization of Shor's factoring and other quantum algorithms. The experimental implementation of the QFT on a periodic state is presented along with a quantitative measure of its efficiency measured through state tomography. Experimentally realizing the QFT is a clear demonstration of the ability of NMR to control quantum systems.     

Field-induced percolation in a polarized lattice gas

We introduce a lattice gas model with particles carrying a charge either +1 or –1 and drifting in opposite directions due to the presence of an external field. Our numerical simulations show the formation of polarized clusters elongated along the direction of the field. At low enough temperatures the clusters percolate through the system in a similar way as in the strip phase of the driven lattice gas model. A possible application of the model can be found in microemulsions.     

基于傅里叶变换光谱技术的Zoom-FFT算法研究

在分析经典的Zoom-FFT算法基础上,提出一种基于傅里叶变换光谱技术的Zoom-FFT算法,用matlab仿真常规FFT算法和Zoom-FFT算法,对不同采样步长的干涉条纹进行数据处理,通过反演出的光谱曲线图和原始光谱曲线图可以看出:采样步长小于20 m时,FFT和Zoom-FFT算法都可以反演出光谱;而当采样步长大于20 m且小于33.3 m时,FFT算法未能反演出光谱,而Zoom-FFT算法仍然可以反演出光谱。     

一维光晶格中玻色凝聚气体的干涉

对捕限在三维轴对称谐振势阱叠加一维光晶格的组合势中的玻色凝聚气体，文章基于平均场G-P方程并运用传播子方法，求解玻色凝聚气体基态波函数及其随时间的演化，给出了物质波干涉图样的空间分布与光晶格势周期结构之间的关系.研究表明，运用这一方法得到的光晶格势中物质波干涉条纹与光学中的多光束干涉相类似，并且与Andrews 和Peil等人的实验结果一致.物质波干涉图样随时间的演化也与Sadhan K. Adhikari通过直接数值求解G-P方程所得结果基本相同. 关键词： 玻色凝聚气体 子凝聚原子云 光晶格势 干涉     

Phase transitions in lattice gas models for water

Water-like lattice gases on the triangular and body-centered cubic lattices are investigated. Molecules may reside on the lattice sites in either of two possible orientations, a hydrogen bond being formed between molecules on neighboring sites if they have the proper orientation with respect to one another. For a range of chemical potential at sufficiently low temperatures, the models are shown to have an ordered phase consisting of an open, hydrogen-bonded, icelike structure. The models are shown to be transitionfree at sufficiently high temperature, indicating the existence of a critical point.Research supported in part by the U.S. National Science Foundation, Grant CHE-7726177, and by The Robert A. Welch Foundation, Grant P-446.     

Diffusion in zeolites as flow of lattice gas

The diffusivityD of pure substances in idealized zeolite crystals is analyzed on the basis of the hopping model and its various extensions. Forces between neigboring molecules are taken into account as well as multiple adsorption in cages and the possibility of extended jumps. Finally, the case of correlated jumps is considered. For each model,D is approximated for small concentrations and in the saturation limit. Only the model with cages permitting at least three molecules is capable of reproducing the prevalent observed behavior.     

Thermodynamic properties of electron gas in complex-shaped quantum well

Thermodynamic properties of degenerate two-dimensional electron gas in complex-shaped quantum well are studied. We determine the equation of state, chemical potential, entropy and heat capacity of the electron gas. An influence of profile and parameters of the quantum well on thermodynamic characteristics are investigated.     

Influence of a uniform driving force on tracer diffusion in a one-dimensional hard-core lattice gas

The influence of a uniform driving force on tracer diffusion is investigated for a one-dimensional lattice gas where particles jump stochastically to unoccupied neighboring sites. A new, simple calculation is presented for the diffusion coefficient of a tracer particle with respect to its average drift, obtained recently by rigorous methods by De Masi and Ferrari. A theoretical expression describing the tracer particle mean square displacement approximately for all times is derived and found to be in excellent agreement with the results of Monte Carlo simulations.     

Staggered diffusivities in lattice gas cellular automata

The majority of LGCAs has spurious conservation laws, the so-called staggered invariants, first discovered by Kadanoff, McNamara, and Zanetti. Consequently there are additional hydrodynamic modes of diffusive type, which modify mode coupling theories and the nonlinear fluid dynamic equations. The diffusivities of these staggered modes are evaluated in the mean field approximation for LGCAs on triangular lattices, starting from the Green-Kubo formulas for the staggered diffusivities.     

Recurrence properties of Lorentz lattice gas cellular automata

Recurrence properties of a point particle moving on a regular lattice randomly occupied with scatterers are studied for strictly deterministic, nondeterministic, and purely random scattering rules.On leave from Institute of Oceanology, USSR Academy of Sciences, 117218 Moscow, USSR