Ne-HCN体系v_3正则模下红外谱的理论研究

本文采用单双迭代耦合簇理论CCSD(T)方法,采用扩展的相关一致基组aug-cc-p VQZ以及中心键函数(3s3p2d2f1g),对Ne-HCN体系三维势能面和对应于HCN反对称伸缩振动(v_3正则模)下的红外谱进行了理论研究.在保持HCN分子质心不变的情况下,通过将对应不同正则坐标Q_3值的七个二维势能面进行六阶多项式插值可以得到Ne-HCN体系三维势能面.在振动绝热近似下,利用三维势V(Qi3,R,θ)计算得到体系基态v_3=0和第一激发态v_3=1两个振动平均势并用其计算了对应的振动能级.每个绝热势均有两个极小值分别对应于线性(全局极小)和近T型构型(局域极小).基态的全局极小值位于R=8.04 a0,阱深为-60.99 cm-1,第一激发态的全局极小值位于R=8.08 a0,阱深为-59.94 cm-1.在HCN分子v_3模式下,计算得到了104条红外谱线,并对该模式下的红外光谱常数进行预测.     

Exciton supersolidity in hybrid Bose-Fermi systems

We investigate the ground states of a Bose-Einstein condensate of indirect excitons coupled to an electron gas. We show that in a properly designed system the crossing of a roton minimum into the negative energy domain can result in the appearance of the supersolid phase, characterized by periodicity in both real and reciprocal space. Accounting for the spin-dependent exchange interaction of excitons we obtain ferromagnetic supersolid domains. The Fourier spectra of excitations of weakly perturbed supersolids show pronounced diffraction maxima which may be detected experimentally.     

C42+分子的T  e系统的Jahn-Teller效应与各向异性现象

依据Jahn-Teller效应理论与量子理论,利用群论和对称性分析的方法探讨了具有Td对称性构型的C42+分子的T  e 系统的Jahn-Teller效应与各向异性问题。构建了T  e系统的电声耦合哈密顿量,借助么正平移变换求出了系统的基态与激发态及其能量。结果发现,由于电声耦合作用的缘故,系统发生了Jahn-Teller畸变,畸变导致在系统的势能面上形成了3个具有D2d对称性的势阱。无论系统处在哪一个势阱中,系统原初三重简并的能级都将分裂为两条能级。畸变还导致C42+分子从Td对称性降低到D2d对称性,同时C42+分子的振动频率发生分解,而频率的分解致使C42+分子的各向同性遭到破坏而呈现出各向异性。     

C42+分子的T  e系统的Jahn-Teller效应与各向异性现象

依据Jahn-Teller效应理论与量子理论,利用群论和对称性分析的方法探讨了具有Td对称性构型的C42+分子的T  e 系统的Jahn-Teller效应与各向异性问题。构建了T  e系统的电声耦合哈密顿量,借助么正平移变换求出了系统的基态与激发态及其能量。结果发现,由于电声耦合作用的缘故,系统发生了Jahn-Teller畸变,畸变导致在系统的势能面上形成了3个具有D2d对称性的势阱。无论系统处在哪一个势阱中,系统原初三重简并的能级都将分裂为两条能级。畸变还导致C42+分子从Td对称性降低到D2d对称性,同时C42+分子的振动频率发生分解,而频率的分解致使C42+分子的各向同性遭到破坏而呈现出各向异性。     

Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states

A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the Miller-Robert-Sommeria (MRS) entropy under these sole constraints. We assume that these constraints are selected by properties of forcing and dissipation. We find that the vorticity fluctuations are Gaussian while the mean flow is characterized by a linear [`(w)]-y\overline{\omega}-\psi relationship. Furthermore, we prove that the maximization of entropy at fixed energy, circulation and microscopic enstrophy is equivalent to the minimization of macroscopic enstrophy at fixed energy and circulation. This provides a justification of the minimum enstrophy principle from statistical mechanics when only the microscopic enstrophy is conserved among the infinite class of Casimir constraints. Relaxation equations towards the statistical equilibrium state are derived. These equations can serve as numerical algorithms to determine maximum entropy or minimum enstrophy states. We use these relaxation equations to study geometry induced phase transitions in rectangular domains. In particular, we illustrate with the relaxation equations the transition between monopoles and dipoles predicted by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)]. We take into account stable as well as metastable states and show that metastable states are robust and have negative specific heats. This is the first evidence of negative specific heats in that context. We also argue that saddle points of entropy can be long-lived and play a role in the dynamics because the system may not spontaneously generate the perturbations that destabilize them.     

Irreversibility and entropy production in transport phenomena,III—Principle of minimum integrated entropy production including nonlinear responses

A new variational principle of steady states is found by introducing an integrated type of energy dissipation (or entropy production) instead of instantaneous energy dissipation. This new principle is valid both in linear and nonlinear transport phenomena. Prigogine’s dream has now been realized by this new general principle of minimum “integrated” entropy production (or energy dissipation). This new principle does not contradict with the Onsager–Prigogine principle of minimum instantaneous entropy production in the linear regime, but it is conceptually different from the latter which does not hold in the nonlinear regime. Applications of this theory to electric conduction, heat conduction, particle diffusion and chemical reactions are presented.     

Entanglement and factorized ground states in two-dimensional quantum antiferromagnets

Making use of exact results and quantum Monte Carlo data for the entanglement of formation, we show that the ground state of anisotropic two-dimensional S=1/2 antiferromagnets in a uniform field takes the classical-like form of a product state for a particular value and orientation of the field, at which the purely quantum correlations due to entanglement disappear. Analytical expressions for the energy and the form of such states are given, and a novel type of exactly solvable two-dimensional quantum models is therefore singled out. Moreover, we show that the field-induced quantum phase transition present in the models is unambiguously characterized by a cusp minimum in the pairwise-to-global entanglement ratio R, marking the quantum-critical enhancement of multipartite entanglement.     

The surface of liquid4He at nonzero temperatures

We outline a general approach to microscopic evaluation of the properties of strongly interacting, spatially inhomogeneous Bose systems at finite temperatures. A minimum principle for the Helmholtz free energy is used together with an appropriate trial density matrix to generalize the correlated variational wave function theory that has proven so successful in the treatment of the ground states and elementary excitations of quantum fluids at zero temperature. Euler-Lagrange equations are obtained that determine the optimal structure through the one-and two-body densities and the optimal density fluctuation operators and energies characterizing the elementary excitations. Some results of an application of this correlated density matrix theory to the⁴He liquid-vapor interface are presented, with particular focus on the characterization of resonant vapor modes.     

Quantum phase transitions in matrix product systems

We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties. While some of the characteristics of these transitions are familiar, like the appearance of singularities in the thermodynamic limit, diverging correlation length, and vanishing energy gap, others differ from the standard paradigm: In particular, the ground state energy remains analytic, and the entanglement entropy of a half-chain stays finite. Examples demonstrate that these kinds of transitions can occur at the triple point of "conventional" QPTs.     

Quantum entanglement in a soluble two-electron model atom

We investigate the entanglement properties of bound states in an exactly soluble two-electron model, the Moshinsky atom. We present exact entanglement calculations for the ground, first and second excited states of the system. We find that these states become more entangled when the relative inter-particle interaction becomes stronger. As a general trend, we also observe that the entanglement of the eigenstates tends to increase with the states’ energy. There are, however, “entanglement level-crossings” where the entanglement of a state becomes larger than the entanglement of other states with higher energy. In the limit of weak interaction, we also compute (exactly) the entanglement of higher excited states. Excited states with anti-parallel spins are found to involve a considerable amount of entanglement even for an arbitrarily weak (but non zero) interaction. This minimum amount of entanglement increases monotonically with the state’s energy. Finally, the connection between entanglement and the Hartree-Fock approximation in the Moshinsky model is addressed. The quality of the ground-state Hartree-Fock approximation is shown to deteriorate, and the corresponding correlation energy to grow, as the entanglement of the (exact) ground state increases. The present work goes beyond previous related studies because we fully take into account the identical character of the two constituting particles in the entanglement calculations, and provide analytical, exact results both for the ground and the first few excited states.     

Electronic structure and optical properties of gold nanoparticles

Based on nonempirical calculations of the Au₃₂ cluster, it is found that excited states from which only the quadrupole transition to the ground state is possible arise upon excitation of gold nanoparticles by photons with energies exceeding the minimum energy gap between occupied and vacant states. The possible role of such transitions in lasing of the nanoscale laser called the spaser is discussed.     

Metastable states in homogeneous Ising models

Metastable states of homogeneous 2D and 3D Ising models are studied under free boundary conditions. The states are defined in terms of weak and strict local minima of the total interaction energy. The morphology of these minima is characterized locally and globally on square and cubic grids. Furthermore, in the 2D case, transition from any spin configuration that is not a strict minimum to a strict minimum is possible via non-energy-increasing single flips.     

Energy dissipation and stability of propagating surfaces

Thermodynamic equilibrium states are given by the minimum of a convex free energy function with suitable boundary conditions. Nonconvexity may lead to the coexistence of several phases and the classical Gibbs phase rule allows constructing their equilibrium properties (e.g., density or pressure). Within the framework of nonequilibrium thermodynamics, the maximization of energy dissipation (under suitable boundary conditions) can be used as an extremal principle to find stationary states. We show that stationary states generally exist for convex energy dissipation functions and that nonconvexity leads to metastable and unstable states. A geometric argument, similar in spirit to Gibbs' double-tangent construction, yields the stability limits of stationary states. This argument is applied to study a classical problem of materials science, namely the motion of a grain boundary under the influence of solute drag.     

氩原子基态波函数和能量的解析计算

以第一性原理和变分原理为基础,给出了氩原子基态波函数的一种解析表达式,计算了基态氩原子(含类氩离子)的能量,导出了所涉及的所有积分的解析表达式.对氩原子,所得到的能量理论值与实验值的相对误差为0.22%.     

Anomalous Optical and Electronic Properties of CaTiO3 Perovskites

With the help of the first-prlnciples full potential linearized augmented plane wave method, absorption coefficients, reflect/vity, dielectric behavior and electronic properties, including electronic energy bands, density of states and charge density distributions, are studied for the tetragonal and cubic CaTiO3. By considering the thermal expansion effects, an approximate method is proposed for the study of the stability of ground state and a tendency of phase transition, based on the minimum free energy principle. Subsequently, numerical calculations are carried out by using the first-principles perturbation method. We demonstrate that the high-temperature phase is cubic. It is shown that optical spectra in tetragonal phase exhibit single-peak feature and differ from multi-peak character in cubic. We find that strong orbital hybridization results in the co-valent bonds between Ti 3d and O 2p electrons and forms two-type dipoles （Ti-Ol and Ti-02） in tetragonal, while the Ti-O dipoles are identical in cubic. It is argued that crystal structure determines the dipole distributions and leads to some electron states among which the dipole-dipole transit/on forbidden is a key, causing such anomalous optical phenomena with the insulator characteristics. The predicted charge density distribution and the tendency of phase transition from tetragonal to cubic are in good agreement with experimental observations.     

Bound states of the Josephson degrees of freedom and trap oscillations

It is shown that the interaction of the Josephson degrees of freedom with states of condensate motion can produce their equilibrium bound states. As a result of the appearance of these states, first, the tunneling splitting is significantly increased in double-well trapped condensates. Second, the bound states can realize an absolute minimum of the thermodynamic energy for a sufficiently strong interaction. Transition to the new ground state is a second-order phase transition. The existence of the bound state leads to an equilibrium distortion of the condensate shape. This implies that the Josephson states can be detected by observing the change in the condensate shape.     

Monte Carlo simulation of a random-field Ising antiferromagnet

Phase transitions in the three-dimensional diluted Ising antiferromagnet in an applied magnetic field are analyzed numerically. It is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second-order phase transition to first-order transition to a new phase characterized by a spin-glass ground state and metastable energy states at finite temperatures.     

Boundary Hamiltonian Theory for Gapped Topological Orders

We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces,with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by(bi-) modules over Frobenius algebras.