Quasiclassical perturbation theory for quantum K-systems

A quantum-dynamical system satisfying the condition of stochastic instability in the classical limit is studied. Behavioural properties of perturbation-theory series in powers of ¢ for such systems are discussed. The quantum corrections in the expressions for physical averages over the density matrix are shown to increase exponentially at small times.     

Thermodynamic perturbation theory for simple polar fluids,I

The application of thermodynamic perturbation theory to the computation of the properties of simple polar fluids is considered. The Helmholtz free energy of a fluid of molecules interacting via a Stockmayer potential v ^S is computed through fourth order in μ, where μ is the dipole moment. Numerical results are obtained on the basis of both the ‘exact’ Monte-Carlo computations for a Lennard-Jones system and the Verlet-Weis perturbation-theoretic computations for that system. The results obtained on the latter basis are then compared with results for a fluid of molecules interacting via a central-force potential v ^ES that is conformal with the Lennard-Jones 6–12 potential and equivalent to the Stockmayer potential through order μ⁴. To facilitate the comparison the v ^ES results are computed according to the Verlet-Weis method. The v ^ES results and the fourth-order (in μ) v ^S results constitute two different approximations to the thermodynamics of the Stockmayer potential; the compressibility factors as well as the free energies of the two approximations are compared.

It is concluded that the thermodynamic contribution of the dipole term of v ^S is significant over the whole liquid region when μ²=εσ³, where ε and σ are the usual Lennard-Jones parameters. For this μ, the two approximations we consider give results in close agreement.     

Thermodynamic perturbation theory for simple polar fluids. II

The study of polar fluids begun in a previous paper is continued. Calculations for the Stockmayer potential are extended to include the term of order μ⁶, where μ is the dipole moment. The effects of higher-order terms are then approximated by means of a simple Padé extrapolation procedure, and the liquid-gas coexistence curve is located in this approximation. An orientation-independent but temperature-dependent potential that is thermodynamically equivalent to an arbitrary orientation-dependent potential is introduced and used to assess the lowest-order thermodynamic effects that result from the presence of quadrupole and octupole terms in the pair-potential. Several values of quadrupole and octupole moments representative of a dipolar molecule (HCl) as well as linear molecules (N₂, O₂ and CO₂, for which μ=0) are considered.     

Convergent perturbation expansions for Euclidean quantum field theory

Mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of Greens functions in Euclidean quantum field theory to arbitrary accuracy, including nonper-turbative contributions from large field fluctuations. Here we describe the expansions at the example of 3-dimensional ⁴-theory (in continuous space). They are not essentially more complicated than standard perturbation theory. Then ^th order term is expressed in terms ofO(n)-dimensional integrals, and is of order ^k if 4k–3n4k.Dedicated to the memory of Kurt Symanzik     

Optimized perturbation theory in quantum electrodynamics

The optimized perturbation expansions, Grunberg's fastest apparent convergence and Stevenson's principle of minimal sensitivity, are applied to some low-energy QED quantities. The optimization does not disturb the experimentally established values, and, at higher orders, its effects are in the direction of reducing small differences between theoretical and experimental values.     

A modified thermodynamic perturbation theory of Wertheim for heteronuclear molecules

The Wertheim thermodynamic perturbation theory (TPT1) is modified for fluids of heteronuclear molecules. The equation proposed by Mansoori–Carnahan–Starling and Leland has been applied for monomers instead of the Carnahan–Starling equation. The modified TPT is compared with simulation results and other theoretical results for heteronuclear dimer, trimer, and higher mers covering a wide range of size ratios. The modified TPT gives a useful method of extending the original TPT1 model to molecules of heteronuclear hard sphere cores without introducing any parameter such as shape factor α.     

Hopf algebra primitives in perturbation quantum field theory

The analysis of the combinatorics resulting from the perturbative expansion of the transition amplitude in quantum field theories, and the relation of this expansion to the Hausdorff series leads naturally to consider an infinite dimensional Lie subalgebra and the corresponding enveloping Hopf algebra, to which the elements of this series are associated. We show that in the context of these structures the power sum symmetric functionals of the perturbative expansion are Hopf primitives and that they are given by linear combinations of Hall polynomials, or diagrammatically by Hall trees. We show that each Hall tree corresponds to sums of Feynman diagrams each with the same number of vertices, external legs and loops. In addition, since the Lie subalgebra admits a derivation endomorphism, we also show that with respect to it these primitives are cyclic vectors generated by the free propagator, and thus provide a recursion relation by means of which the (n+1)-vertex connected Green functions can be derived systematically from the n-vertex ones.     

Alternative analysis to perturbation theory in quantum mechanics

We develop an alternative approach to the time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function; additionally we can analyze the time evolution of the system for any initial condition, which may be bothersome in the standard method. To verify our results, we apply our method to the harmonic oscillator perturbed by a quadratic potential. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained.     

Feynman integral and perturbation theory in quantum tomography

We present a definition for tomographic Feynman path integral as representation for quantum tomograms via Feynman path integral in the phase space. The proposed representation is the potential basis for investigation of Path Integral Monte Carlo numerical methods with quantum tomograms. Tomographic Feynman path integral is a representation of solution of initial problem for evolution equation for tomograms. The perturbation theory for quantum tomograms is constructed.     

On the stationary perturbation theory in quantum mechanics

A simple method is proposed for solving the Shcrödinger equation in the presence of a perturbation. Formally exact expressions are obtained in the form of infinite series for the energies and wave functions without assuming that the perturbation is small. Under the additional assumption that it is small (in accordance with a well-defined criterion of smallness) the obtained results yield directly the results of Schrödinger's perturbation theory. The developed approach contains in compact form various formulations of perturbation theory. The calculations use neither the complex technique of projection operators nor the complicated formalism of Green's functions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 33–36, November, 1980.     

Thermodynamic perturbation theory for the (12-6-n) fluids

A perturbation method in which attractive forces are taken as perturbation of the repulsive (reference) forces is applied to calculate the thermodynamic properties of (12-6-n) fluids in terms of the properties of hard-sphere fluid. The numerical values of the thermodynamic properties (free energy per particle, compressibility and excess internal energy) for a range of temperature and density are given for (12-6-8) fluids. Further, two perturbation schemes are adopted to evaluate the total radial distribution function using the EXP version of the optimized cluster theory (OCT). The numerical results are reliable as reported at two states (T* = 1·036,ρ* = 0·65 andT* = 0·719ρ* = 0·85) for the (12-6-8) fluid and the Lennard-Jones (12-6) fluid as well.     

Generalized perturbation theory of classical fluids in the critical region

Perturbation theories of classical fluids are extended in the critical region by decomposition of the attractive part of the pair interaction. The generalized theory is in agreement with scaling, has the correct dependence on dimensionality and on the range of the forces and offers a method to compute critical indices.     

Two-flavor quark matter in the perturbation theory with full thermodynamic consistency

Direct extrapolation of the strong interaction between quarks in pure perturbative calculation has a problem of thermodynamic inconsistency.A new term determined by thermodynamic consistency requirement could resolve it.This new term plays an important role at lower density in describing the equation of state of quark matter,while it is negligible at high density.Accordingly,the density behavior of the sound velocity becomes more reasonable,and the maximum mass of quark stars can be as large as two times the solar mass.     

The dielectric constant of polarizable fluids from the renormalized perturbation theory

A perturbation theoretical equation for the dielectric constant of polarizable dipolar fluids is proposed. For the fluctuation of the dipole moment, namely for the Kirkwood g-factor, a formula is given on the basis of Wertheim's renormalized perturbation theory. Using this formula, a series expansion for ?(p) is suggested on the basis of the Kirkwood equation, which gives an implicit function for ? as a function of ¶. The same series expansion can be derived from the Clausius-Mosotti equation—thus it proves to be independent of the boundary conditions. The resulting equation gives excellent results for the dielectric constant of the polarizable Stockmayer fluid producing good agreement with computer simulation data. The series expansion gives better results than the Kirkwood equation itself.     

On perturbation expansions for associated fluids

A feasibility study of applicability of a perturbation expansion for evaluating properties of highly associated fluids is undertaken. It is shown that the long-range electrostatic forces can be considered as a mild perturbation only, provided that the reference potential includes the hydrogen bonding interaction. Perturbed Monte Carlo simulations on two different shortrange reference systems defined for the realistic ST2 water potential show that the structures of the ST2 water and appropriately chosen reference fluids are practically identical and that the expansion of the Helmholtz free energy converges.