一维互作用扭折-声子气体的统计理论

本文系统地研究并改进了位移型相变中一维互作用扭折-声子气体模型的统计理论。通过对扭折和声子的配分函数各自采用适当的路径积分表式并改进声子路径积分的计算方法,得到一个较合理且较普遍的巨配分函数表达式。在基态近似下,它可简化为一个与文献[6]相似的结果;在经典近似下,由它计算出的平均扭折密度与计算机模拟实验结果比文献上的符合得要好。     

非平衡统计场论与临界动力学(Ⅱ)——拉氏场论表述

本文从闭路格林函数生成泛函的连续积分表示出发,对傅氏变换取单圈近似,求得序参量的有效作用量。在闭路连续积分中取涨落二级近似,得到临界动力学的拉氏场论表述。文中指出改进现有理论的可能途径。 关键词：     

On the evaluation of the quantum corrections to periodic TDHF orbits

The evaluation of the leading order quantum correction to periodic mean-fields within the path integral approach is reinvestigated. The corresponding gaussian functional integral is well defined only after restoring the time-translation invariance broken by the time-dependent meanfield approximation. The particular structure of the action function permits one to restore the invariance in two different ways, that seem to exhibit an ambiguity in the evaluation of the leading order quantum correction. We prove, however, that both ways of restoring the time-translation invariance yield the same result, showing that the leading order quantum correction is uniquely defined within the path integral approach.     

Quantum adiabatic approximation to interacting boson-fermion systems

We present an adiabatic approximation method for the path integral of the Fermi field in the presence of a Bose field. The adiabatic phenomenon recently found by Berry and Simon is used for evaluating the Grassman path integral. Then we obtain the path integral of the effective action analogous to a magnetic field, and the quantization rule is derived by applying the semiclassical quantization method.     

Theoretical examination of electron–phonon interaction and superconductivity in the hexagonal pnictide SrPtAs

We have calculated the structural and electronic properties of SrPtAs in a hexagonal KZnAs-type of crystal structure using a generalized gradient approximation of the density functional theory and the ab initio planewave pseudopotential method. These results are used to further calculate the phonon dispersions curves and the phonon density of states using a linear response approach based on the density functional theory. Using the electronic and phonon results, the electron–phonon coupling is computed to be of the intermediate strength of 0.78. In large part, this is contributed by the phonon modes dominated by the vibrations of Pt and As atoms. The superconducting critical temperature is estimated to be 1.9 K, in good accord with its experimental value of 2.4 K.     

Non-equilibrium approach to transport phenomena in quantum crystals

A pure dielectric quantum crystal subjected to an external mechanical force is described by non-equilibrium Green’s functions. In equilibrium the leading approximation leads to the definition of elementary excitations, the phonons in the renormalized harmonic approximation. Their temperature dependent energies are to be determined as solutions of an integral equation. For hydrodynamic disturbances a generalized transport equation for a phonon number density is derived. A similar approximation for the spectral function yields an integral equation for space and time dependent quasiparticle energies which are expressed as functionals of the displacement field and the phonon distribution. The Boltzmann equation for the latter includes the quasi-particle interaction.     

Zeta function regularization of path integrals in curved spacetime

This paper describes a technique for regularizing quadratic path integrals on a curved background spacetime. One forms a generalized zeta function from the eigenvalues of the differential operator that appears in the action integral. The zeta function is a meromorphic function and its gradient at the origin is defined to be the determinant of the operator. This technique agrees with dimensional regularization where one generalises ton dimensions by adding extra flat dimensions. The generalized zeta function can be expressed as a Mellin transform of the kernel of the heat equation which describes diffusion over the four dimensional spacetime manifold in a fith dimension of parameter time. Using the asymptotic expansion for the heat kernel, one can deduce the behaviour of the path integral under scale transformations of the background metric. This suggests that there may be a natural cut off in the integral over all black hole background metrics. By functionally differentiating the path integral one obtains an energy momentum tensor which is finite even on the horizon of a black hole. This energy momentum tensor has an anomalous trace.     

Towards a nonperturbative path integral in gauge theories

We propose a modification of the Faddeev–Popov procedure to construct a path integral representation for the transition amplitude and the partition function for gauge theories whose orbit space has a non-Euclidean geometry. Our approach is based on the Kato–Trotter product formula modified appropriately to incorporate the gauge invariance condition, and thereby equivalence to the Dirac operator formalism is guaranteed by construction. The modified path integral provides a solution to the Gribov obstruction as well as to the operator ordering problem when the orbit space has curvature. A few explicit examples are given to illustrate new features of the formalism developed. The method is applied to the Kogut–Susskind lattice gauge theory to develop a nonperturbative functional integral for a quantum Yang–Mills theory. Feynman's conjecture about a relation between the mass gap and the orbit space geometry in gluodynamics is discussed in the framework of the modified path integral.     

Theoretical investigations on the structural, lattice dynamical and thermodynamic properties of XC (X=Si, Ge, Sn)

First-principles calculations, which is based on the plane-wave pseudopotential approach to the density functional perturbation theory within the local density approximation, have been performed to investigate the structural, lattice dynamical, and thermodynamic properties of SiC, GeC, and SnC. The results of ground state parameters, phase transition pressure and phonon dispersion are compared and agree well with the experimental and theoretical data in the previous literature. The obtained phonon frequencies at the zone-center are analyzed. We also used the phonon density of states and quasiharmonic approximation to calculate and predict some thermodynamic properties such as entropy, heat capacity, internal energy, and phonon free energy of SiC, GeC, and SnC in B3 phase.     

A first-principles study on the structural, lattice dynamical and thermodynamic properties of beryllium chalcogenides

First-principles calculations, which are based on the plane-wave pseudopotential approach to the density functional theory and the density functional perturbation theory within the local density approximation, have been performed to investigate the structural, lattice dynamical and thermodynamic properties of zinc blende (B3) structure beryllium chalcogenides: BeS, BeSe and BeTe. The results of ground-state parameters and phonon dispersion are compared and contrasted with the experimental and theoretical data of previous literature. The phonon frequencies at the zone-center are analyzed. We also used the phonon density of states and quasiharmonic approximation to calculate and predict some thermodynamic properties such as entropy, heat capacity, internal energy and free energy of the B3 phase beryllium chalcogenides.     

First principles lattice dynamical calculation of semiboride Be2B and its ternary alloys XBeB (X=Na, Mg, Al)

We present results of first principles total energy calculations of the structure, electronic and lattice dynamics for beryllium semiboride and its three ternary alloys using generalized gradient and local density approximations under the framework of density functional theory. The generalized gradient approximation is used for all compounds except MgBeB using the Perdew-Burke-Ernzehorf exchange correlation functional while local density approximations use the Perdew-Zunger ultrasoft exchange correlation functional. The calculated ground state structural parameters are in good agreement with those of experimental and previous theoretical studies. The electronic band structure calculations show that Be₂B may transform to a semiconductor after Al substitution. A linear response approach to density functional theory is used to calculate phonon dispersion curves and vibrational density of states. The phonon dispersion curves of Be₂B and AlBeB are positive indicating a dynamical stablility of the structure for these compounds. The phonon dispersion curves of NaBeB and MgBeB show the imaginary phonons throughout the Brillouin zone, which confirms dynamical instability as indicated in band structures for these alloys. We also present the partial phonon density of states for different species of Be₂B and AlBeB to bring out the details of the participation of different atoms in the total phonon density of state, particularly the role played by Al atom. The first time calculated phonon properties are clearly able to bring out the significant effect of isoelectronic substitution in Be₂B.     

Quantum tunneling of light particles in metals

The motion of a particle in a metallic crystal is studied for low temperatures where transitions between adjacent interstitial sites are caused by quantum tunneling. The influence of electrons and phonons on the hopping rate is taken into account by means of a functional integral method. The electronic influence may effectively be described by Ohmic damping which dominates the low temperature behavior of the defect motion. When subsequent tunneling transitions are statistically independent, the diffusion constant is found to obey a power law, D∼T^2K−1, where K depends on the defect-electron interaction. This power law is limited at low temperatures by the effects of phonon excitations. Near the transition between electron and phonon dominated behavior the diffusion constant has a minimum where the precise temperature dependence of the rate depends not only on phonon spectra but also on the processes limiting phonon lifetimes.     

Thermodynamics of quantum dissipative many-body systems

We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permits us to get manageable PQSCHA expressions for quantum thermal averages with a classical Boltzmann factor involving an effective potential and an inner Gaussian average that describes the fluctuations originating from the interplay of quanticity and dissipation. The application of the PQSCHA to a quantum phi(4) chain with Drude-like dissipation shows nontrivial effects of dissipation, depending upon its strength and bandwidth.     

Bose-Einstein condensation in interacting gases

We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the one-particle density operator with more flexibility than in mean-field theories, since it does not necessarily coincide with that of an ideal gas with adjustable parameters (chemical potential, etc.). In a first step, a simple approximation is used (Ursell-Dyson approximation), which allow us to recover results which are similar to those of the usual mean-field theories. In a second step, a more precise treatment of the correlations and velocity dependence of the populations in the system is elaborated. This introduces new physical effects, such as a change of the velocity profile just above the transition: the proportion of atoms with low velocities is higher than in an ideal gas. A consequence of this distortion is an increase of the critical temperature (at constant density) of the Bose gas, in agreement with those of recent path integral Monte-Carlo calculations for hard spheres. Received 13 November 1998     

Multi-instantons and exact results IV: Path integral formalism

This is the fourth paper in a series devoted to the large-order properties of anharmonic oscillators. We attempt to draw a connection of anharmonic oscillators to field theory, by investigating the partition function in the path integral representation around both the Gaussian saddle point, which determines the perturbative expansion of the eigenvalues, as well as the nontrivial instanton saddle point. The value of the classical action at the saddle point is the instanton action which determines the large-order properties of perturbation theory by a dispersion relation. In order to treat the perturbations about the instanton, one has to take into account the continuous symmetries broken by the instanton solution because they lead to zero-modes of the fluctuation operator of the instanton configuration. The problem is solved by changing variables in the path integral, taking the instanton parameters as integration variables (collective coordinates). The functional determinant (Faddeev–Popov determinant) of the change of variables implies nontrivial modifications of the one-loop and higher-loop corrections about the instanton configuration. These are evaluated and compared to exact WKB calculations. A specific cancellation mechanism for the first perturbation about the instanton, which has been conjectured for the sextic oscillator based on a nonperturbative generalized Bohr–Sommerfeld quantization condition, is verified by an analytic Feynman diagram calculation.     

On the Bosonization of the Many Electron Problem

The Garbaczewski bosonization procedure is applied to the many-electron problem. It leads to a non-local c-number path integral representation for the trace of the evolution operator which also depends on a mapping of the lattice points in the natural numbers. This mapping is needed for the implementation of the bosonization. We argue that the non-local interactions and the dependence on the mapping can be disregarded in the limit of small electron c-number field. We can then discuss the physics of the saddle point contribution. In the discussion the effects of the Pauli exclusion principle are introduced phenomenologically.     

A study of two-dimensional models

We investigate the (1+1) dimensional Rothe Stamatescu (RS) and Thirring models. A functional integral method based on a chiral change of fermionic variables is used to obtain the general class of solutions in the RS model. The results are then reproduced in an operator formalism. Finally a connection of the solutions with perturbation theory is briefly discussed. The functional method is then applied to reproduce the familiar one parameter class of solutions existing in the Thirring model. An operator fit differing from the standard ones is proposed which is consistent with the solutions obtained by the path integral approach.     

Superconductivity in hydrogenated carbon nanostructures

We present an application of density functional theory for superconductors to superconductivity in hydrogenated carbon nanotubes and fullerane (hydrogenated fullerene). We show that these systems are chemically similar to graphane (hydrogenated graphene) and like graphane, upon hole doping, develop a strong electron phonon coupling. This could lead to superconducting states with critical temperatures approaching 100 K, however this possibility depends crucially on if and how metallization is achieved.