The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.     

Numerical simulation of the ionization dynamics of a two-electron quantum system in a femtosecond pulse

The ionization of a simple two-electron model system, viz., the one-dimensional negative hydrogen ion, is investigated using direct numerical integration of the time-dependent Schrödinger equation. The one-and two-electron ionization probabilities as functions of frequency and radiation intensity are obtained. It is shown that two-electron ionization is mediated by both direct and sequential mechanisms. The stabilization of the two-electron system against the ionization process is investigated. The data obtained are compared with calculations performed within the one-dimensional single-particle model of H^?. The photoelectron spectrum is analyzed in the region of parameters corresponding to the single-electron ionization regime.     

Current progress on heat conduction in one-dimensional gas channels

We give a brief review of the past development of model studies on one-dimensional heat conduction. Particularly, we describe recent achievements on the study of heat conduction in one-dimensional gas models including the hard-point gas model and billiard gas channel. For a one-dimensional gas of elastically colliding particles of unequal masses, heat conduction is anomalous due to momentum conservation, and the divergence exponent of heat conductivity is estimated as α≈0.33 in k ∼ L ^α . Moreover, in billiard gas models, it is found that exponent instability is not necessary for normal heat conduction. The connection between heat conductivity and diffusion is investigated. Some new progress is reported. A recently proposed model with a quantized degree of freedom to study the heat transport in quasi-one dimensional systems is illustrated in which three distinct temperature regimes of heat conductivity are manifested. The establishment of local thermal equilibrium (LTE) in homogeneous and heterogeneous systems is also discussed. Finally, we give a summary with an outlook for further study about the problem of heat conduction.     

Conditions for the formation of an H−/D− ion beam in a volume plasma source with a magnetic filter

A one-dimensional model for the transport of a plasma with two ion species across the magnetic field in a steady-state volume negative-ion source is proposed. The conditions in the magnetic filter adjacent to the plasma electrode optimum for the generation, formation, and extraction of an H⁻/D⁻ ion beam are found. The theoretical results are in good agreement with the experimental data.     

极板电压与间距对大气压射频氩等离子体放电参数的影响

 基于1维流体力学模型,对大气压射频裸露金属电极氩气放电过程进行了研究。模型中考虑了氩等离子体放电过程中主要发生的激发和电离等7个反应过程,对等离子体反应产生的主要粒子,包括电子、氩原子离子Ar⁺、氩分子离子Ar2⁺和氩激发态Ar^*等,建立连续性方程、动量方程和电流平衡方程。分析了极板电压、极板间距对上述粒子数密度分布的影响。给出了电子,Ar⁺,Ar^*和Ar₂⁺密度随极板电压及间距变化的时空演化过程。得出极板电压或极板间距的改变会使放电空间的电场发生改变,对应一定的极板间距,极板电压有一个最佳值,极板电压和间距的变化会使对应的极板间有一个最佳电场值,而对应最佳电场有一个等离子体气体间最佳反应系数,从而使放电空间粒子数密度发生改变。     

Prediction of melt depth in selected architectural materials during high-power diode laser treatment

The development of an accurate analysis procedure for many laser applications, including the surface treatment of architectural materials, is extremely complicated due to the multitude of process parameters and materials characteristics involved. A one-dimensional analytical model based on Fourier's law, with quasi-stationary situations in an isotropic and inhomogeneous workpiece with a parabolic meltpool geometry being assumed, was successfully developed. This model, with the inclusion of an empirically determined correction factor, predicted high-power diode laser-induced melt depths in clay quarry tiles, ceramic tiles and ordinary Portland cement that were in close agreement with those obtained experimentally. It was observed, however, that as the incident laser line energy increased (>15 W mm⁻¹ s^−1/2), the calculated and the experimental melt depths began to diverge at an increasing rate. It is believed that this observed increasing discrepancy can be attributed to the fact the model developed neglects sideways conduction which, although it can be reasonably neglected at low-energy densities, becomes significant at higher energy densities since one-dimensional heat transfer no longer holds true.     

激光驱动飞片过程中激光烧蚀深度的计算

利用激光体烧蚀模型,数值模拟了激光驱动飞片的加速过程,包括激光的吸收和飞片的速度历史等。在光强为GW/cm2量级的激光作用下,激光烧蚀产生的等离子体的流体力学运动可用改编的1维La-grange流体力学计算程序SSS来描述。通过计算得到不同激光能量下的飞片密度剖面,由此给出金属薄膜的烧蚀深度与实验测量值进行比对,二者符合得较好。     

Modulated photoreflectance characterization of ion-implanted semiconductor wafers

Modulated PhotoReflectance (MPR) measurements on semiconductor wafers implanted with boron or silicon ions in the dose range 5×10¹⁰–5×10¹⁵ ions/cm² are presented. Correspondingly, a one-dimensional theoretical multilayer model is established. In the theory, as the implant dose is lower than a critical value, the variation of the MPR signal is contributed mainly by the implanted defects and damages. However, when the dose is above the critical dose, the change of the MPR signal is chiefly due to the formation and growth of an amorphous layer. The theoretical results are in good agreement with those of experiments.     

A comparative study of Hartree-Fock iteration techniques

We present and discuss various Hartree-Fock iteration techniques which are all derived from the simple gradient iteration step where one proceeds along the slope of steepest descent of the energy functional. Particular attention is paid to modern numerical applications where the single-particle wave functions are represented in a coordinate or momentum space grid. A quantitative, comparison is given using a one-dimensional model space. As an example the optimum method thus found is applied in a realistic three-dimensional calculation of ¹⁶O.     

The thermodynamic parameters of phonon-soliton equilibrium in one-dimensional Frenkel-Kontorova systems

The temperature dependences of the internal energy of a canonical ensemble of Frenkel-Kontorova systems, which are one-dimensional chains of material points linked by elastic bonds in a periodic potential, were studied by the Monte Carlo method with importance sampling. Such a model is an example of a system in which local contraction-extension states that can move as sole waves, solitons, are possible. The calculation results are analyzed on the basis of the model of an equilibrium reaction between a chain phonon and soliton that occurs at the given temperature. The model was used to estimate the thermodynamic parameters of phonon-soliton equilibrium and obtain the dependences of the enthalpy of equilibrium “reaction” on the incommensurability parameter of the chain γ. The enthalpy of this process was found to be described by a linear dependence on γ^−1/2 with a high correlation degree (r ² = 0.994).     

1D-3D crossover in hopping conduction of carbynes

D.C. and A.C. conductivities of carbyne samples were studied over the temperature range 1.8–300 K at frequencies 10 MHz–1 GHz. It was established that a variation in the fraction of sp ² bonds in carbynes induces transition from one-to two-and then to three-dimensional conduction. In the one-dimensional hopping conduction regime, the resistivity of carbynes depends on temperature as ρ=ρ₀exp[(T ₀/T)^1/2], whereas Coulomb correlations are insignificant. The Hunt model of one-dimensional A.C. conductivity is experimentally confirmed.     

Exceptional points in multichannel resonance quantization

We derive from the quantization condition of a multichannel resonance problem the behaviour of resonance energies close to an exceptional point (EP) where two resonance energies coalesce. The formalism is applied to a one-dimensional model of the molecular ion H₂ ⁺. Although the approach does not use a matrix diagonalization procedure, all known results about exceptional points are present, including the transfer from one resonance to another when following a loop encircling the EP. We study how the resonance wave functions behave along loops around the EP, as well as the associated geometric phases.     

Absence of Charge-Resonance-Enhanced Ionization in Attosecond Pulse Photoionization： Numerical Result on One-Dimensional H2^＋

We present a numerical result of photoionization rate for the one-dimensional molecular hydrogen ion model exposed to intense light of 1 × 10^16-2×10^16 W/cm^2, 55-as pulse duration, and 800nm wavelength. In contrast to the previous calculation result of charge-resonance-enhanced ionization for lower intensity and much longer pulse, our result exhibits an ionization saturation. The numerical results are interpreted in the field-dressed potential picture as over-the-barrier liberation of electrons. This extremely short pulsewidth and relatively high field phenomenon requests experimental demonstration.     

Quantitative analysis of photoacoustic IR spectra

Photoacoustic spectroscopy is a method for directly measuring the absorption properties of gases and condensed matter. We have developed a photoacoustic gas cell for a rapid-scan Fourier spectrometer. With this cell we can extend the spectral range down to 180 cm^–1; more than one octave lower than previously reported useful broadband measurements. The photoacoustic spectrum of a microscope cover glass was measured from 180 ... 200 cm^–1 and normalized with respect to the spectrum of carbon black as a reference material. Starting from the one-dimensional equation of heat conduction we derived an expression for the surface temperature of single and double-layer samples. We calculated the surface temperature of the glass lamella and divided it by the corresponding values for carbon black using the thermal conductivity of carbon black as a fitting parameter. We show that the one-dimensional model calculation reproduces the experimental spectrum over the whole spectral range.     

Empirical and theoretical fusion barriers for1H and4He: Connections to evaporation from hot nuclei

Fusion excitation functions for¹H and⁴He have been compared to a one-dimensional, barrier-penetration model. In contrast to fusion for heavier nuclei this simple model is completely adequate, except for the statically deformed targed²³³U. Empirical barrier heights are obtained and compared to those from two theoretical nuclear potentials. These empirical barriers (from cold reactants) are used as input for calculating evaporation spectra that arise from hot nuclear emitters. The excess of observed low-energy¹H and⁴He emission signals information content concerning distortions of the hot nuclei.     

A comment on the common one-dimensional derivation of the van der Waals forces

In many physical text-books a simple one-dimensional model is used to derive the characteristic 1/R ⁷-dependence of the attractive van der Waals forces. We show that this calculation is wrong. The long range forces in this simple model are not attractive but repulsive proportional to 1/R ⁶. Only a three-dimensional calculation yields the correct behavior.     

A dynamic scattering approach for a gated interacting wire

A scattering approach for correlated one-dimensional systems is developed. The perfect contact to charge reservoirs is encoded in time-dependent boundary conditions. The conductance matrix for an arbitrary gated wire, respecting charge conservation, is expressed through a dynamic scattering matrix. Two applications are developed. First, it is shown that the dc conductance is equal to e ²/h for any model with conserved total left- and right-moving charges. Second, the ac conductance matrix is explicitly computated for the Tomonaga-Luttinger model (TLL). Received 31 August 1998     

Electroproduction and annihilation scaling laws in a dual model

Scaling laws for large virtual photon mass (q²) in electroproduction and annihilation are studied in the framework of a simple planar dual model. We find, as has recently been conjectured, that the scaling behaviour depends on the number of space-time dimensions spanned by large momenta. In particular, for a certain range of parameters in the model, we find that the annihilation cross section is dominated by the one-dimensional configuration and increases with q² relative to its canonical behaviour while the electroproduction total cross section is dominated by the two-dimensional configuration and has the canonical Bjorken scaling behavior. In general the scaling laws and therefore the structure of events in the model are distinctively different from the conventional parton model. The problem of consistency of planar dual tree diagrams with unitarity sum rules is discussed.     

Quantum corrections to ϕ 4 model solutions and applications to Heisenberg chain dynamics

The Heisenberg spin chain is considered in ? ⁴ model approximation. Quantum corrections to classical solutions of the one-dimensional ? ⁴ model within the correspondent physics are evaluated with account of rest d-1 dimensions of a d-dimensional theory. A quantization of the model is considered in terms of spacetime functional integral. The generalized zeta-function formalism is used to renormalize and evaluate the functional integral and quantum corrections to energy in a quasiclassical approximation. The results are applied to appropriate conditions of the spin chain model and its dynamics, for which elementary solutions, energy and the quantum corrections are calculated.     

Density of states for the lowest landau level of a three-dimensional disordered system

A Quantum Monte Carlo investigation of a one-dimensional two band model with strong correlations in one band is presented. This two band model can be considered as a one-dimensional realization of the highT _c cuprates. In particular, the densities in the two bands, the formation of magnetic moments and the spin-spin correlations are studied as a function of particle number. The Quantum Monte Carlo results are compared with a simple mean field theory describing antiferromagnetic correlations, a variational Gutzwiller type calculation and a mapping to an effective one band model.