PT-Symmetric Quantum Field Theories and the Langevin Equation

Many non-Hermitian but PT-symmetric theories are known to have a real, positive spectrum, and for quantum-mechanical versions of these theories, there exists a consistent probabilistic interpretation. Since the action is complex for these theories, Monte Carlo methods do not apply. In this paper a field-theoretic method for numerical simulations of PT-symmetric Hamiltonians is presented. The method is the complex Langevin equation, which has been used previously to study complex Hamiltonians in statistical physics and in Minkowski space. We compute the equal-time one-point and two-point Green's functions in zero and one dimension, where comparisons to known results can be made. The method should also be applicable in four-dimensional space-time. This approach may grant insight into the formulation of a probabilistic interpretation for path integrals in PT-symmetric quantum field theories.     

Nonperturbative Operator Quantization of Strongly Nonlinear Fields

At present an algebra of strongly interacting fields is unknown. In this paper it is assumed that the operators of a strongly nonlinear field can form a non-associative algebra. It is shown that such an algebra can be described as an algebra of some pairs. The comparison of presented techniques with the Green's functions method in superconductivity theory is made. A possible application to the QCD and High-T _c superconductivity theory is discussed.     

Some non-perturbative semi-classical methods in quantum field theory (a pedagogical review)

A pedagogical introduction is given to non-perturbative semi-classical methods for finding solutions to quantum field theories. Both the weak coupling method based on a time-independent classical solution, and the WKB method based on all periodic orbits are developed in detail, proceeding ffrom elementary quantum mechanics to field theory in stages. Both methods are then illustrated in model field theories. The [λø⁴]₂ theory to which the weak coupling method is applied yields a new family of “kink” states whose properties are discussed.The WKB method is illustrated by quantizing “soliton” and “doublet” solutions of the two-dimensional sine-Gordon theory. The results are compared to consequences of Coleman's equivalence proof relating this system to the massive Thirring model. The speculation that solitons may be fermions is discussed, along with indications that the WKB method may ne yielding exact mass ratios for this theory.A final section is devoted to solutions of more realistic four-dimensional models containing fermions, internal symmetry etc. Some quark-confinement models and vortex type solutions come under this category. General remarks are made on this family of solutions, and illustrated using 't Hooft's monopole solution.     

Quantum group symmetries and non-local currents in 2D QFT

We construct and study the implications of some new non-local conserved currents that exist is a wide variety of massive integrable quantum field theories in 2 dimensions, including the sine-Gordon theory and its generalization to affine Toda theory. These non-local currents provide a non-perturbative formulation of the theories. The symmetry algebras correspond to the quantum affine Kac-Moody algebras. TheS-matrices are completely characterized by these symmetries. FormalS-matrices for the imaginary-coupling affine Toda theories are thereby derived. The application of theseS-matrices to perturbed coset conformal field theory is studied. Non-local charges generating the finite dimensional Quantum Group in the Liouville theory are briefly presented. The formalism based on non-local charges we describe provides an algernative to the quantum inverse scattering method for solving integrable quantum field theories in 2d.     

回旋速调管注波互作用瞬态非线性理论与模型研究

本文利用自洽非线性理论对回旋速调管放大器中的电子注-波互作用进行了时域瞬态分析,建立了多腔回旋速调管非线性理论,给出了相应的电子运动方程和复数形式的互作用瞬态场方程.探讨了调制腔、中间腔、和输出腔中注-波互作用的模型和研究方法,考虑了电子速度零散对注-波互作用的影响.最后利用FORTRAN语言给出并分析了一支Kα波段四腔回旋速调管注-波互作用的数值计算结果,经与实验值和PIC模拟结果相比较,三者较为符合. 关键词： 回旋速调管 电子注-波互作用 瞬态非线性理论     

等离子体-腔混合模耦合腔行波管非线性注-波互作用分析

 用模式展开的方法分析了等离子体-腔混合模耦合腔行波管的非线性注-波互作用过程，导出了其考虑相对论效应的非线性注-波互作用自洽工作方程组。用格林函数法求解各向异性背景等离子体（介电常数张量）下的空间电荷场。编写了计算机模拟软件，用来分析等离子体-腔混合模耦合腔行波管的增益、效率、输出功率、瞬时带宽等重要的非线性特性，计算结果表明：工作在等离子体-腔混合模式下的耦合腔行波管，瞬时带宽达到20%~30%，效率达到50%以上。     

The Kondo effect in periodic narrow-band systems

The Kondo divergences owing to interaction of current carriers with local moments in highly correlated electron systems are considered within the Hubbard and s-d exchange models with infinitely strong on-site interaction, the many-electron Hubbard representation being used. The picture of density of states containing a peak at the Fermi level is obtained. Various forms of the self-consistent approximation are used. The problem of the violation of analytical properties of the Green's function is discussed. Smearing of the “Kondo” peak owing to spin dynamics and finite temperatures is investigated. Received 25 November 1999 and Received in final form 31 January 2000     

非相干非线性光学理论方法及其进展

文章主要综述了非相干非线性光学的几种理论方法,包括互相干函数法、相干密度法、自洽模理论、Wigner转换法、近似射线光学法和热动力学法等.其中,着重阐述了近期发展起来的理论方法——热动力学法,并对其原理进行了概括.对这几种理论方法的理解和探讨对非相干非线性光学效应的研究具有很重要的指导意义,有利于非相干非线性光学理论的进一步发展和完善.     

Mean fields and self consistent normal ordering of lattice spin and gauge field theories

Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived.     

Gravity on Finite Groups

Gravity theories are constructed on finite groups G. A self-consistent review of the differential calculi on finite G is given, with some new developments. The example of a bicovariant differential calculus on the nonabelian finite group S ₃ is treated in detail, and used to build a gravity-like field theory on S ₃. Received: 11 November 1999 / Accepted: 11 December 2000     

On self-consistent approximations for random anharmonic systems

A model with random 1-, 2-, and 3-point potentials is used to study the elementary excitations in substitutionally disordered crystals. The equations of motion for the 1- and 2-point Green's functionsG(1),G(12) are derived and averaged over the ensemble of random configurations. An extension of the coherent potential method is proposed, which leads to a self-consistent set of equations for the averaged 1- and 2-point Green's functions, including corresponding conditional averages. The theory takes into account that randomness effects the anharmonic interactions both via the explicit configuration dependence of the cubic vertices and via the implicit dependence through the Green's functions. The final equations take a similar form as in the usual CPA if the harmonic potential of the pure system and the harmonic single-site impurity potential are replaced by corresponding functionals of averaged and conditionally averaged 1- and 2-point functions, and the definition of the single-site mass-operator is appropriately generalized.Work supported by the Deutsche ForschungsgemeinschaftExtract from thesis, D 26     

On some aspects of the definition of scattering states in quantum field theory

The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering states. As the strong limit is not suitable for the definition of scattering states in quantum field theory, some other limiting procedure is needed. Two possibilities are considered, the abelian limit and adiabatic switching. Formulas for the scattering states based on both methods are discussed, and it is found that generally there are significant differences between the two approaches. As an illustration of the applications and the features of these formulas, S-matrix elements and energy corrections in two quantum field theoretical models are calculated using (generalized) old-fashioned perturbation theory. The two methods are found to give equivalent results.     

Short-range correlations in nuclear matter using Green's functions within a discrete pole approximation

We treat short-range correlations in nuclear matter, induced by the repulsive core of the nucleon–nucleon potential, within the framework of self-consistent Green's function theory. The effective in-medium interaction sums the ladder diagrams of both the particle–particle and hole–hole type. The demand of self-consistency results in a set of nonlinear equations which must be solved by iteration. We explore the possibility of approximating the single-particle Green's function by a limited number of poles and residues.     

The Vilkovisky-DeWitt effective action for quantum gravity

The Vilkovisky-DeWitt effective action for gauge theories is reviewed and then discussed in the context of N-dimensional quantum gravity and quantum Kaluza-Klein theory. The formalism gives an effective action which is gauge-independent and gauge and field-parametrization invariant. These features are illustrated for the vacuum energy of N-dimensional gravity. The Bunch-Parker local momentum space approach is used to calculate also the induced Ricci scalar term in the expansion of the effective action in powers of the curvature. The effective field equations are applied to the self-consistent dimensional reduction of five-dimensional Kaluza-Klein theory. A solution exists, but is found to be physically unacceptable.     

Two-Dimensional Field Theories

Quantum field theories in space with the dimensionality 1 + 1 are considered. Quantum electrodynamics, quantum chromodynamics, sufficiently nonlinear models (with soliton solutions) and gravitational theory are discussed from the common viewpoint. The possible correspondence of two-dimensional field models to physical reality is analyzed.     

Quantum thermal transport in nanostructures

In this colloquia review we discuss methods for thermal transport calculations for nanojunctions connected to two semi-infinite leads served as heat-baths. Our emphases are on fundamental quantum theory and atomistic models. We begin with an introduction of the Landauer formula for ballistic thermal transport and give its derivation from scattering wave point of view. Several methods (scattering boundary condition, mode-matching, Piccard and Caroli formulas) of calculating the phonon transmission coefficients are given. The nonequilibrium Green's function (NEGF) method is reviewed and the Caroli formula is derived. We also give iterative methods and an algorithm based on a generalized eigenvalue problem for the calculation of surface Green's functions, which are starting point for an NEGF calculation. A systematic exposition for the NEGF method is presented, starting from the fundamental definitions of the Green's functions, and ending with equations of motion for the contour ordered Green's functions and Feynman diagrammatic expansion. In the later part, we discuss the treatments of nonlinear effects in heat conduction, including a phenomenological expression for the transmission, NEGF for phonon-phonon interactions, molecular dynamics (generalized Langevin) with quantum heat-baths, and electron-phonon interactions. Some new results are also shown. We briefly review the experimental status of the thermal transport measurements in nanostructures.     

On the algebraic structure ofN=2 string theory

InN=2 string theory the chiral algebra expresses the generations and anti-generations of the theory and the Yukawa couplings among them and is thus crucial to the phenomenological properties of the theory. Also the connection with complex geometry is largely through the algebras. These algebras are systematically investigated in this paper. A solution for the algebras is found in the context of rational conformal field theory based on Lie algebras. A statistical mechanics interpretation for the chiral algebra is given for a large family of theories and is used to derive a rich structure of equivalences among the theories (dihedralities). The Poincaré polynomials are shown to obey a resolution series which cast these in a form which is a sum of complete intersection Poincaré polynomials. It is suggested that the resolution series is the proper tool for studying allN=2 string theories and, in particular, exposing their geometrical nature.     

Molecular g-tensors from analytical response theory and quasi-degenerate perturbation theory in the framework of complete active space self-consistent field method

The molecular g-tensor is an important spectroscopic parameter provided by electron para magnetic resonance (EPR) measurement and often needs to be interpreted using computational methods. Here, we present two new implementations based on the first-order and second-order perturbation theories to calculate the g-tensors within the complete-active space self-consistent field (CASSCF) wave function model. In the first-order method, the quasi-degenerate perturbation theory (QDPT) is employed for constructing relativistic CASSCF states perturbed with the spin–orbit coupling operator, which is described effectively in one-electron form with the flexible nuclear screening spin–orbit approximation introduced recently by us. The second-order method is a newly reported approach built upon the linear response theory which accounts for the perturbation with respect to external magnetic field. It is implemented with the coupled–perturbed CASSCF (CP-CASSCF) approach, which provides an equivalent of untruncated sum-over-states expansion. The comparison of the performances between the first-order and second-order methods is shown for various molecules containing light to heavy elements, highlighting their relative strength and weakness. The formulations of QDPT and CP-CASSCF approaches as well as the derivation of the second-order Douglas–Kroll–Hess picture change of Zeeman operators are given in detail.     

Methods of Quantum Field Theory with Rapidly Increasing Spectral Functions

A review of the methods of constructing the scattering amplitudes and Green functions in the non-renormalizable quantum field theories with rapidly increasing spectral functions is given. Such theories as the theories with the chiral Lagrangians, those which describe the interactions with gravitational fields and the theories of weak interactions can be taken as examples. Three big groups of these methods are presented here. In particular, these are as follows: construction of the scattering amplitude in x-space (the function F(x)), construction of the scattering amplitude in momentum space (the function F˜ (p)) and definition of the scattering amplitudes by solving the appropriate equations (in x- or p-Space). This works was reported at the Second International Symposium on Non-local Quantum Field Theory in 1970 at Azau, USSR.     

Molecular dynamics study of electron gas models for liquid water

The frozen density electron gas model proposed by Gordon and Kim for rare gas systems has been implemented in a molecular dynamics code. This code has been applied to investigate various options for extending this scheme to inter-molecular interactions in liquid water. We have compared a number of gradient corrections to the Thomas-Fermi kinetic energy. We also explored a more empirical approach based on adaptation of the frozen molecular electron density to the condensed phase environment. Consistent with experience from force field methods, enhancement of the molecular dipole moment proved to be necessary to reproduce the properties of the liquid. The best models we investigated are a gradient corrected expansion of the simple local density Hamiltonian applied in the original Gordon and Kim model. In addition, these models observed a modified molecular electron density carrying the same dipole moment of 2.95 D as has been observed by recent ab initio molecular dynamics studies based on fully self-consistent Kohn-Sham methods. Possible implications of this finding for force field models are discussed.