Fast impurity solver for dynamical mean field theory based on second order perturbation around the atomic limit

This paper proposes an impurity solver for the dynamical mean field theory (DMFT) study of the Mott insulators, which is based on the second order perturbation of the hybridization function. After careful benchmarking with quantum Monte Carlo results on the anti-ferromagnetic phase of the Hubbard model, it concludes that this impurity solver can capture the main physical features in the strong coupling regime and can be a very useful tool for the LDA (local density approximation) +,DMFT studies of the Mott insulators with long range order.     

Modified Perturbation Theory of an Anharmonic Oscillator

A modification of the perturbation theory of a symmetrical anharmonic oscillator is suggested. A more complex zero-order approximation of perturbation theory that considers to a certain degree anharmonicities is chosen rather than a harmonic oscillator model. This approximation is an analog of the self-consistent field model well known in the theory of many-particle systems. A comparison of modified and conventional perturbation theories demonstrates that the modified perturbation theory has much wider applicability range. It can be used for larger values of the parameters at which the conventional perturbation theory becomes inapplicable, namely, for strong anharmonicity and upper energy levels.     

An Orbital‐Free Quantum Hypernetted Chain Model Based Perturbation Theory for Equation of State of Hydrogen and Helium in Warm Dense Regime

We present in this work, a thermodynamic perturbation theory for equation of state of hydrogen and helium in the warm dense regime. The system is modeled as a mixture of classical point ions and quantum electrons. A perturbation series for Helmholtz free energy and correlation functions of the ions and electrons as a function of density and temperature is proposed. Combining the classical thermodynamic perturbation theory and the orbitial‐free quantum hyper‐netted chain theory, a systematic procedure to obtain the terms of the perturbation series is developed. The ion‐ion correlations are treated within the hyper‐netted chain approximation and the ion‐electron correlations are treated within the Thomas‐Fermi‐Dirac‐Weizsäcker approximation. The method has been applied to obtain isotherms of hydrogen and helium in the warm dense regime. The isotherms are compared with available ab‐initio data and the results are analyzed. A good agreement with ab‐initio data has been observed for pressures greater than one Mbar. Advantages and limitations of the present method are discussed along with possible future improvements. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adsorption isotherm of a Lennard-Jones nitrogen in a carbon slitlike pore

A density functional perturbation approximation based both on second-order perturbation theory and on the pore average density has been proposed to study the adsorption hysteresis of nitrogen in a carbon slit pore. The main advantage of the present approximation is that it is computationally much simpler than the original density functional approximation based on the second-order perturbation theory of liquids, and can be applied to several model fluids confined in a strong external field in order to study their structural and thermodynamic properties. The calculated adsorption hysteresis for the confined Lennard-Jones nitrogen is in very good agreement with computer simulation, even if its accuracy slightly deteriorates for the desorption branch. The calculated equilibrium particle density distributions also compare well with computer simulations, and are better than those of a density functional theory based on the so-called mean-field approximation.     

Theoretical study of the helio hydrogen cyanide dication HeCNH2+

The structure and stability of the helio hydrogen cyanide molecular ion, HeCNH²⁺, is investigated by standard quantum chemical methods. Single reference calculations are carried out using second-order perturbation theory (MP2), the coupled cluster expansion in the CCSD approximation, and the hybrid approach using a perturbative estimate of the triple excitation energy component designated CCSD(T). Multireference calculations using a complete active space (CASSCF) and a second-order perturbation theory estimate of correlation effects (CASPT2) are reported.     

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonic model of a two-dimensional oscillator having Kratzer potential energy functionis used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interactionbetween the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a real polyatomic molecular species.     

Observers and Locality in Everett Quantum Field Theory

A model for measurement in collapse-free nonrelativistic fermionic quantum field theory is presented. In addition to local propagation and effectively-local interactions, the model incorporates explicit representations of localized observers, thus extending an earlier model of entanglement generation in Everett quantum field theory (Rubin in Found. Phys. 32:1495–1523, 2002). Transformations of the field operators from the Heisenberg picture to the Deutsch-Hayden picture, involving fictitious auxiliary fields, establish the locality of the model. The model is applied to manifestly-local calculations of the results of measurements, using a type of sudden approximation and in the limit of massive systems in narrow-wavepacket states. Detection of the presence of a spin-1/2 system in a given spin state by a freely-moving two-state observer illustrates the features of the model and the nonperturbative computational methodology. With the help of perturbation theory the model is applied to a calculation of the quintessential “nonlocal” quantum phenomenon, spin correlations in the Einstein-Podolsky-Rosen-Bohm experiment.     

量子干涉效应中干涉角和散射角的研究

利用波恩近似理论对双原子激发态转动传能进行了剖析,更深入的研究了原子分子碰撞过程中量子干涉效应相关信息．利用各项异性相互作用势和直线轨迹近似建立了新的量子干涉模型,讨论了原子与分子碰撞时散射角和微分干涉角的关系,得到了干涉角和各向异性参数及转动量子数的关系．     

THE EMC EFFECT AND THE LIGHT-CONE QUANTUM FIELD THEORY

We indicate that final state interactions can be neglected if one calculate deep inelastic lepton nucleus scattering in the time-ordered perturbation theory in the infinite momentum frame,or its equivalent,the light-cone perturbation theory in an ordinary frame.We thus extend the light-cone quantum field theory to baryon-meson field to establish a relativistic composite model of nuclei,and then apply the impulse approximation to deep inelastic lepton nucleus scattering in this model.     

Deformed quantum harmonic oscillator with diffusion and dissipation

A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master equation and of equations of motion for observables depend on the deformation function. The steady-state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation.     

Reconciling phase diffusion and Hartree–Fock approximation in condensate systems

Despite the weakly interacting regime, the physics of Bose–Einstein condensates is widely affected by particle–particle interactions. They determine quantum phase diffusion, which is known to be the main cause of loss of coherence. Studying a simple model of two interacting Bose systems, we show how to predict the appearance of phase diffusion beyond the Bogoliubov approximation, providing a self-consistent treatment in the framework of a generalized Hartree–Fock–Bogoliubov perturbation theory.     

转动传能中的量子干涉--干涉角和转动量子数的关系

沙国河等人在CO(A1∏(v=0)~e3∑-(v=1))体系与He,Ne和Ar碰撞诱导转动传能中首次观测到了量子干涉效应,并测量了干涉度。从理论上进一步研究原子-双原子分子体系碰撞诱导转动传能中量子干涉效应与转动量子数以及能量间隔的关系是十分必要的。我们考虑长程相互作用势,应用一级玻恩近似和直线轨迹近似,分别计算了CO(A1∏(v=0)~e3∑-(v=1))体系和He,Ne,Ar碰撞诱导转动传能中不同转动量子数以及不同能量间隔下的干涉角,得到了干涉角随转动量子数和能量间隔的变化趋势。这些结果对设计、分析这种类型的实验有一定的指导意义。     

Perturbation theory for double-time temperature-dependent Green functions

A perturbation theory is developed for normal many-particle systems by expanding the inverse of the advanced and retarded Green functions. Both systems with direct interactions and systems with interactions through a quantum field are considered. For the former, the infinite set of coupled equations is written down and the various methods of decoupling discussed. Systems with weak, hard sphere type, or coulomb interactions are considered and the connections with other methods discussed. For systems with quantum field interactions, the chain of equations involves both fermion and boson Green functions and the first approximation can be much better than in earlier cases. This latter approach seems to be more convenient when collective oscillations are important.     

Nonnegative entropy production in the hydrodynamics of a multiparticle quantum system

Compatibility is examined for the second law of thermodynamics and the author’s procedure for converting from quantum statistical mechanics to nonlocal hydrodynamics. The procedure involves the transition from statistics to hydrodynamics in a reversible fashion. It is shown that in this class of external forces, the law of nondecreasing entropy applies at least in the nonlinear perturbation theory approximation. This approach has advantages by comparison with other schemes for passing to the hydrodynamic limit. Earth Physics Institute, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 60–66, May, 1998.     

Post-Hartree-Fock methods and dynamic correlation in atoms and molecules

The methods of calculation of the matrix of the exchange-correlation interaction are considered within the framework of one post-Hartree-Fock one-electron method of investigation of the properties of many-electron systems. Such post-Hartree-Fock methods are based on two-step variational self-consistent calculations of the spin orbitals and superposition coefficients of configurations in the multiconfiguration approximation. The post-Hartree-Fock method used involves an approach related to the extended Koopmans’ theorem, which, in turn, proves to be a high-energy approximation for quantum Green’s functions. Obvious application areas of the calculations of the exchange-correlation interaction within the framework of the method proposed are the multiparticle perturbation theory, the parameterization of the energy representation as a functional of the single-particle density matrix, and the theory of Green’s functions in the multiconfiguration approximation. A relativistic generalization of the method with the aim of calculating the radiative corrections for many-electron atoms and for problems of interaction with an external field in the nonstationary Floquet theory is possible.     

Quantenfeldtheorie wechselwirkender Vielteilchensysteme zur semiklassischen Beschreibung von kollektiver Bewegung mit großen Amplituden

By using path integral methods a collective quantum field theory of interacting many-body systems is developed, the classical limit of which is given by the time-dependent mean-field approximation. In this way the mean-field approximation is embedded into the full quantum mechanics and the quantum corrections to the “classical” mean-field approximation can be systematically evaluated. By including the dominant quantum corrections to the mean-field approximation a semiclassical theory of large amplitude collective motions in many-body-systems, which show a highly nonlinear dynamic and are not accessible to perturbation theoretical methods, is derived. The semiclassical theory is developed explicitly for bound states and decay processes like nuclear fission. In the case of bound states this leads to the quantization of the time-dependent Hartree-Fock-Theory, which is demonstrated for a uniform nuclear rotation.     

含时的线性驱动简并参量放大系统的量子起伏

导出在P表象中含时的线性驱动简并参量放大Fokker-Planck方程，并求其解.在阈值以下或阈值附近，含时驱动Fokker-Planck方程的解与线性理论或阈值附近的微扰理论预言的基本相符.在阈值以上，含时驱动Fokker-Planck方程解的短期行为也与线性近似解相近，但当τ增大后的长期行为完全区别于线性理论的结果. 关键词： 含时的线性驱动简并参量放大 Fokker-Planck方程 量子起伏