Analytic theory of correlation energy and spin polarization in the 2D electron gas

We present an analytic theory of the pair distribution function and the ground-state energy in a two-dimensional (2D) electron gas with an arbitrary degree of spin polarization. Our approach involves the solution of a zero-energy scattering Schrödinger equation with an effective potential which includes a Fermi term from exchange and kinetic energy and a Bose-like term from Jastrow-Feenberg correlations. The form of the latter is assessed from an analysis of data on a 2D gas of charged bosons. We obtain excellent agreement with data from quantum Monte Carlo studies of the 2D electron gas. In particular, our results for the correlation energy show a quantum phase transition occurring at coupling strength r_s≈24 from the paramagnetic to the fully spin-polarized fluid.     

A new approach to electron-electron interactions in strongly correlated systems at arbitrary spin-polarization and temperature

The uniform electron fluid is the reference model for density functional calculations. Even for this system, many-body perturbation theory, and related methods become questionable when the density parameter r_s exceeds unity. Hence, quantum Monte Carlo (QMC) simulation has been almost the only applicable method. We review a new approach, which uses a mapping of the quantum fluid to a classical Coulomb fluid, based on density-functional concepts. It is applicable at finite temperatures and arbitrary spin polarizations as well, and correctly recovers even the logarithmic terms in the exchange and correlations energies close to T=0. We show by detailed comparison with available QMC data that the method yields accurate pair-distribution functions, spin-dependent energies, static local-field factors, Landau parameter-based quantities like m∗ and g∗, for strongly coupled electron fluids.     

Temperature dependences of the strengths of a carbon fiber and a three-dimensional reinforced carbon-carbon composite

At a fixed tension rate, the ultimate tensile strength of a carbon fiber decreases nonlinearly with increasing temperature T. This nonlinearity is caused by a change in the statistics of atomic vibrations from quantum (at T < 2250 K) to classical (at T > 2250 K) statistics. To take into account the quantum statistics, quantum function F _q is introduced into Zhurkov’s equation instead of temperature; the value of this function is calculated from the temperature dependence of the specific heat of carbon. This equation gives the values of the fracture activation energy (≈16 eV) and parameter γ (≈0.15 nm³). The strength of the three-dimensional reinforced carbon-carbon composite decreases up to ≈1800 K and increases as the temperature grows further. The decrease in the strength is explained by an increase in the rate of fiber and matrix fracture with increasing temperature, and the increase in the strength is explained by a decrease in the strength of the fiber-matrix adhesion bonds at high temperatures. As a result of this decrease, fibers begin to move with respect to each other under load, and the stresses applied to them level off. Although the fiber strength continues to decrease with increasing temperature, this effect increases the composite strength.     

Monte Carlo investigation of magnetic properties of a two-dimensional classical Heisenberg magnet

The equilibrium properties of a simple quadratic lattice of classical spins with nearest-neighbor Heisenberg interactions have been examined by a Monte Carlo Method. The susceptibility was found to have a singular temperature dependence χ ∝ exp (const/T²)/T above the Stanley-Kaplan transition temperature (T_SK). A plausible argument has been presented to explain peculiar properties of the 2?d Heisenberg magnet on the basis of the observed singular behavior of the susceptibility.     

Spin-polarized electron–electron quantum bilayers: Finite width effect

We study the effect of finite width on the ground-state of a spin-polarized electron–electron quantum bilayers (EEBL) system at temperature T=0. Correlations among carriers are treated beyond the static mean-field theories by using the quantum or dynamical version of Singwi, Tosi, Land and Sjölander (qSTLS) theory. Numerical results are presented for the pair-correlation function, the ground-state energy, the static density susceptibility, and the static local-field correction factor as a function of density parameter r_sl and interlayer spacing d. Interestingly, we find that the inclusion of finite width lowered the critical density, for the onset of Wigner crystal (WC) ground-state, as compared to the similar recent study of spin-polarized EEBL system without finite width effect. Further, spin-polarization effect is seen to introduce a marked change in the ground-state energy of the EEBL system as compared to the results of unpolarized EEBL system with finite width. Results of ground-state energies are also compared with the recent diffusion Monte Carlo (DMC) and variational Monte Carlo (VMC) simulation studies of spin-polarized EEBL system with zero width.     

Infrared behaviour of Yang-Mills theory at high temperatures

We employ Monte Carlo methods to probe the infrared structure of SU(2) Yang-Mills theory at high temperatures. In particular, we study the free energy of the gauge invariant non-abelian magnetic flux. The Monte Carlo support the conjecture that the magnetic flux is screened. The inverse magnetic screening length provides a non-perturbative infrared cut-off for the quantum statistics of the SU(2) gauge theory and is estimated to be about 0.24 g²T.     

Dissipative tunneling at finite temperature

A simple theory is presented for the influence of a weakly coupled interaction system on the tunneling of a particle out of a metastable well. It is based on the standard model of momentum and energy transfer to an infinite set of oscillators and is applied to the case of phase tunneling in a Josephson contact. The distribution of the energy transfer and in particular the Debye-Waller factor for elastic processes is determined by the imaginary part of the dielectric function. For small damping γ the main influence of dissipation on the total tunneling probability is contained in a factor exp —AMγ(Δq)². The numerical coefficientA and the distance Δq under the barrier depend on the considered tunneling state andA(T) vanishes at a temperatureT ^* above which classical activation prevails. The tunneling probability of any level is therefore predicted to increase with temperature. In additional general expressions are derived for the correlation functions of a damped quantum oscillator in terms of the classical response of the interaction system.     

Saturation and condensate fraction reduction of cold alpha matter

The ground state energy of ideal α  -matter at T=0$T=0$ is analyzed within the framework of variational theory of Bose quantum liquids. Calculations are done for three local α–α potentials with positive volume integrals and two-body correlation functions obtained from the Pandharipande–Bethe equation. The energy per particle of α matter is evaluated in the cluster expansion formalism up to four-body diagrams, and using the HNC/0 and HNC/4 approximation for a Bose liquid. At low densities the two methods predict similar EOS whereas at higher densities they are sensitively different, the HNC approximation providing saturation at lower density, bellow the saturation value of nuclear matter. Inclusion of higher-order terms in the cluster expansion of the condensate fraction is leading to a stronger depletion of the alpha condensate with the density compared to the two-body approximation prediction.     

New exact approach to models of diffusion in one-dimensional random systems and optimal network kinetics in spin glass models

It is shown that in one-dimensional stochastic models with gaussian random energy levels along a quantum reaction coordinate the dominant, rate-determining time-scale does not follow the conventional Arrhenius law, but rather has a much stronger temperature dependence, of the form τ ～ exp[(B/k_BT)²], where B is proportional to the width of the energy distribution. The new activation law can be ascribed to the large number of energy barriers of varying heights which exist in the random structure, as distinct from the conventional case of a single barrier, leading to the Arrhenius form τ ～ T^p × exp(A/k_BT). In systems with random structure and configuration space which are not strictly one-dimensional it is discussed if the thermal energy bias of detailed balance may lead to a kinetics that is essentially restricted to an energetically optimal network at low temperatures, thus leading to an essentially one-dimensional diffusion. Several recent studies of spin glass models appear to support the relevance of this principle, and include the observation of the new activation law in Monte Carlo experiments.     

Simple classical mapping of the spin-polarized quantum electron gas: distribution functions and local-field corrections

We use the now well known spin unpolarized exchange-correlation energy E(xc) of the uniform electron gas as the basic "many-body" input to determine the temperature T(q) of a classical Coulomb fluid having the same correlation energy as the quantum system. It is shown that the spin-polarized pair distribution functions (SPDFs) of the classical fluid at T(q), obtained using the hypernetted chain equation, are in excellent agreement with those of the T = 0 quantum fluid obtained by quantum Monte Carlo (QMC) simulations. These methods are computationally simple and easily applied to problems which are currently beyond QMC simulations. Results are presented for the SPDFs and the local-field corrections to the response functions of the electron fluid at T = 0 and finite T.     

Instantons or monopoles: Dyons at finite temperature

This article in honor of Yurii Antonovich Simonov’s 70th birthday reviews some recent work related to the semiclassical approach to QCD at finite temperature based on classical solutions with nontrivial holonomy. By cooling Monte Carlo generated lattice SU(2) gauge fields, we investigate approximate solutions of the classical field equations as a possible starting point for rethinking the semiclassical approximation of the path integral. We show that old findings of cooling have to be reinterpreted in terms of Kraan-van Baal solutions with generically nontrivial holonomy instead of Harrington-Shepard caloron solutions with trivial holonomy. The latter represent only a subclass of possible topological configurations and for T < T _c seem to become suppressed due to quantum fluctuations.     

Quantum Monte Carlo Investigation of the magnetic properties of weakly interacting antiferromagnetic chains with an alternating exchange interaction with spin S = 1/2

An approximation dependence of the spontaneous magnetic moment at a site, σ/σ(0) ? 1 = and the antiferromagnet-singlet state phase boundary, J ₂/J ₁ = 0.52(3)δ, are determined by the quantum Monte Carlo method in the self-consistent sublattice molecular field approximation for weakly inter-acting (J ₂) antiferromagnetic chains with spin S = 1/2 and alternating exchange interaction (J ₁ ± δ). The Néél temperature and a number of critical temperatures which could be related with the filling energy of two singlets (ΔS ^z = 0) and one triplet (ΔS ^z = 1) spin bands, each of which is split by the sublattice field (h ^{x, y} ≠ h ^z into two subbands, are determined on the basis of the computed correlation radii of the two-and four-spin correlation function, the squared total spin 〈 (S ^z)²〉 with respect to the longitudinal components, the dimerization parameter, and the correlation functions between the nearest neighbors with respect to longitudinal and transverse spin components. On the basis of the Monte Carlo calculations, the critical temperatures and possible energy gaps at the band center are determined for the antiferromagnets CuWO₄ and Bi₂CuO₄ and for the singlet compounds (VO)₂P₂O₇ and CuGeO₃, agreeing satisfactorily with existing results, and new effects are also predicted.     

Scattering times in AlGaN/GaN two-dimensional electron gas from magnetotransport measurements

The various scattering times of two-dimensional electron gas were investigated in modulation-doped Al_0.22Ga_0.78N/GaN quantum wells by means of magnetotransport measurements. The ratio of transport and quantum scattering times, τ_t/τ_q∼1, shows that the dominant mobility-limiting mechanisms are short-range scattering potentials. The low-field magnetoresistance shows the weak antilocalization and localization phenomenon from which the spin-orbit scattering and inelastic scattering times are obtained. The inelastic scattering time is found to follow the T⁻¹ law, indicating that electron-electron scattering with small energy transfer is the dominant inelastic process.     

H_2+He流体混合物在部分离解区的物态方程

H2+He流体混合物在高温高压下由于氢的离解化学反应形成由H2,H,He三种粒子构成的混合体系,此时粒子间的相互作用较为复杂,离解能也会由于粒子间的这种复杂相互作用而降低.本文利用自洽流体变分理论来研究部分离解区H2+He流体混合物的高温高压物态方程,模型考虑了各种粒子间的相互作用及由温致和压致效应引起的离解能降低的自洽变分修正,并通过自洽流体变分过程对非理想的离解平衡方程求解得到粒子数密度分布,进而对自由能求导获得体系的热力学状态参量.计算结果与已有的冲击波实验数据、蒙特卡罗模拟及其他理论计算进行了比较.     

Interfacial Adsorption in Two-Dimensional Potts Models

The interfacial adsorption W at the first-order transition in two-dimensional q-state Potts models is studied. In particular, findings of Monte Carlo simulations and of density-matrix renormalization group calculations at q=16 are consistent with the analytic result, obtained in the Hamiltonian limit at large values of q, that Wt ^–1/3 on approach to the bulk critical temperature T _c, t=|T _c–T|/T _c. In addition, the numerical findings allow to estimate corrections to scaling. Our study supports and quantifies a previous conclusion by Bricmont and Lebowitz based on low temperature expansions.     

Gauge field thermodynamics for the SU(2) Yang-Mills system

After reviewing the euclidean formulation of the thermodynamics for quantum spin systems, we develop the corresponding formalism for SU(N) gauge fields on the lattice. The results are then evaluated for the SU(2) system, using Monte Carlo simulation on lattices of (space × temperature) size 10³ × 2,3,4,5. At high temperature, the system exhibits Stefan-Boltzmann behaviour, with three gluonic colour degrees of freedom. At T_c ≈ 43Λ_L (215 MeV), the transition to “hadronic” behaviour occurs, signalled by a sharp peak in the specific heat. From the behaviour below the deconfinement transition (T<T_c), we obtain m_G ≈ 200Λ_L (1000 MeV) for the mass of the lowest gluonium state (glueball).     

Compressibility of a two-dimensional electron gas in a parallel magnetic field

The thermodynamic compressibility of a two-dimensional electron system in the presence of an in-plane magnetic field is calculated. We use accurate correlation energy results from quantum Monte Carlo simulations to construct the ground state energy and obtain the critical magnetic field B_c required to fully spin polarize the system. Inverse compressibility as a function of density shows a kink-like behavior in the presence of an applied magnetic field, which can be identified as B_c. Our calculations suggest an alternative approach to transport measurements of determining full spin polarization.     

Exchange-correlation and layer-thickness effects in quasi-two dimensional electron liquids

We demonstrate a replacement of the non-uniform sub-band density of quasi-2D electron layers by an effective uniform-slab density. Exchange, correlation and Fermi-liquid properties are determined via a mapping of the electron liquid to a classical fluid, using the hyper-netted-chain equation inclusive of bridge corrections, (i.e. the CHNC), as a function of the density, spin-polarization, layer width and the temperature. Our parameters-free theory is in good accord with quantum simulations, with effective-mass and spin-susceptibility results for 2D layers found in GaAs/AlGaAs structures.