The classical limit of temperature Green's function expansions

Rules are obtained for calculating the classical limit of Green's function diagrammatic expansions. The classical cluster expansion is derived by calculating the classical limit of the exact Green's function. Other operators of interest in linear response theory may be calculated in the classical limit. The retarded real-time spin density correlation function, proportional to the magnetic susceptibility, is shown to be exactly proportional to the density in this limit. The relation of this work to other approaches is discussed.     

On the infrared singularities of Green's functions in quantum electrodynamics

We present a formal calculation of the infrared singularity structure of the fermion propagator in QED based on the Faddeev-Kulish asymptotic solution. The Renormalization program is reviewed in the context of the BPHZ subtraction scheme and a refinement of the Renormalization group methods is employed to study the infrared singularities in perturbation theory.     

Localization and averaged Green's functions

We present a counterexample to the idea that localization in a random material can be determined from the ensemble averaged Green's function.     

Stabilizer formalism for operator quantum error correction

Operator quantum error correction is a recently developed theory that provides a generalized and unified framework for active error correction and passive error avoiding schemes. In this Letter, we describe these codes using the stabilizer formalism. This is achieved by adding a gauge group to stabilizer codes that defines an equivalence class between encoded states. Gauge transformations leave the encoded information unchanged; their effect is absorbed by virtual gauge qubits that do not carry useful information. We illustrate the construction by identifying a gauge symmetry in Shor's 9-qubit code that allows us to remove 3 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties. This opens the path to possible improvements of the error threshold of fault-tolerant quantum computing.     

Induced moment antiferromagnet in an external magnetic field—II: Green's function theory

A two level two sublattice antiferromagnetic induced moment system is examined in the Green's function theory in the random phase approximation. Attentions are drawn to the effects of an externally applied magnetic field. It is shown that a “soft mode” behavior occurs at the transition field similar to that observed at the transition temperature in the absence of a field. The transition becomes first order in the RPA. The sublattice magnetizations and the transition field are significantly lowered compared to the molecular field theory results.     

Green's function equations of motion for a many-fermion system: II. Inhomogeneous system at finite temperature

The equations of motion for many-time causal Green's functions are extended to an inhomogeneous many-fermion system at finite temperature. The boundary condition that the perturbation vanishes in the remote past and distant future (adiabatic hypothesis) is used to determine the unperturbed propagator. The temperature enters the theory only as a parameter. Thus there is no need for analytic continuations in the complex temperature-time plane. The theory is used to derive thermal Hartree-Fock theory and Wick's theorem at finite temperature. A linked cluster perturbation expansion at finite temperature is obtained by iterating the equations of motion, without unlinked disconnected diagrams even appearing. After integration over frequency, the present theory gives the perturbation theory rules in terms of global propagators that Baym and Sessler obtained from the imaginary-time theory.     

Binding energy of positively charged acceptors in germanium - a Green's function Monte Carlo calculation

Recent spectroscopic measurements in Ge reveal positively charged acceptors consisting of an extra hole bound to a double or triple acceptor. Using the effective-mass approximation and a pseudo-atom model which permits up to four holes in the 1s ground state, we calculate the binding energies of these positively charged acceptors by the Green's function Monte Carlo method. For double acceptors the results of the pseudo-atom model compare favorably with experiments, whereas for triple acceptors the differences are significant.     

Green's function analysis of the optically allowed vibrations of crystals: Application to diboron tetrafluoride

The Green's function method developed for the study of the molecular vibrations has been extended to the optically allowed vibrations of crystals taking B₂F₄ as an example. Isotopic rules for the i.r. active fundamentals have been derived. The force constants and the frequencies of ¹⁰B₂F₄ have also been estimated.     

String correction for baryon orbital excitations

The correction to the string junction three-quark potential in a baryon due to the proper moment of inertia of the QCD string is calculated. The magnitudes of the string corrections in P wave heavy baryons are estimated.     

On Milne's quantum number function

The quantum number function N(E) introduced by Milne is studied in detail. It is shown that N(E) is not uniquely defined for energies different from the bound state values. The density of states $\text{d}\text{N}\text{d}\text{E}$ is nowhere unique and not necessarily positive.     

Generating functional approach to the Green's functions diagrammatic technique for spin and pseudospin lattice systems: I. General theory

The theory of the irreducible many-point Green's functions, describing spin and pseudospin lattice systems, is formulated with the help of the generating functional approach. The diagrammatic technique for the generating functional is also developed. Special attention is paid to the construction and summation of the diagrammatic series for the one- and two-point Green's functions. Closed formulae for the one-point Green's function and the generalized Vaks-Larkin- Pikin equation are obtained. The $\text{1}\text{z}$ expansion scheme near the critical temperature of the order-disorder phase transition, is discussed, where z denotes the effective number of nearest- neighbours for a given site in a crystal lattice.     

Self-consistent Green’s function formalism for acoustic and light scattering. Part 3: Unitarity and symmetry

This paper completes two previous papers in which we have developed the self-consistent Green’s function formalism for acoustic and light scattering. It is concerned with the unitarity and symmetry properties of the interaction and far field scattering operator of this formalism. We will show that these are primarily mathematical properties, and that the principles of energy conservation and reciprocity, which express our physical experience, can be modeled by these mathematical properties. For this we have to distinguish two experimental configurations, and only one of these configurations will allow us to relate energy conservation to unitarity. Closely related to this are questions concerning the definition and measurability of the scattering quantities and the importance of the optical and generalized optical theorem. These questions will be also discussed from the point of view of the self-consistent Green’s function formalism.     

The interaction between matter and a field’s single-mode as a quantum game

We introduce a game admitting both classical and quantal players. Strategies are determined by the initial conditions of the associated dynamical system, whose time evolution is characterized by the existence of attractors that represent the possible results of the game. The physics associated to the interaction between matter and a single-mode of an electromagnetic field within a cavity is cast in these game theory terms.     

Finite temperature formalism for composite quantum particles

This Letter provides the missing part of the newly constructed many-body formalism for composite quantum particles: the introduction of a finite temperature. The finite T formalism we propose deeply relies on the existence of a compact closure relation for the (overcomplete) set of N-composite-particle states. As a first application, we here calculate the energy mean value of the exciton gas outside the condensation regime. We show that carrier exchanges increase its temperature dependence compared to elementary bosons, a signature of the degree-of-freedom increase resulting from the particle composite nature.     

A mathematical interpretation of Dirac's formalism part a: Dirac bases in trajectory spaces

In this paper the notion of Dirac basis will be introduced. It is the continuous pendant of the discrete basis for Hilbert spaces. The introduction of this new notion is closely related to the theory of generalized functions. Here De Graaf's theory will be employed. It is based on the triplet $\text{S}{}_{\mathrm{<mtext>X,</mtext><mtext>A</mtext>}}\text{?X?}\text{T}{}_{\mathrm{<mtext>X,</mtext><mtext>A</mtext>}}$ where X is a Hilbert space. In a well specified way any member of $\text{T}{}_{\mathrm{<mtext>X,</mtext><mtext>A</mtext>}}$ can be expanded with respect to a Dirac basis. Both the introduction of Dirac bases and a new interpretation of Dirac's bracket notion will lead to a mathematical rigorization of various aspects of Dirac's formalism for quantum mechanics. This rigorization goes much beyond earlier proposals.     

A mathematical interpretation of Dirac's formalism part b: generalized eigenfunctions in trajectory spaces

Starting with a Hilbert space $\text{L}{}_2\text{(}\text{R}\text{,μ)}$ we introduce the dense subspace $\text{R}\text{(}\text{L}{}_2\text{(}\text{R}\text{,μ))}$ where $\text{R}$ is a positive self-adjoint Hilbert–Schmidt operator on $\text{L}$₂(R,μ). For the space $\text{R}\text{(}\text{L}{}_2\text{(}\text{R}\text{,μ))}$ a measure-theoretical Sobolev lemma is proved. The results for the spaces of type $\text{R}\text{(}\text{L}{}_2\text{(}\text{R}\text{,μ))}$ are applied to nuclear analyticity spaces $\text{S}{}_{\mathrm{<mtext>X,</mtext><mtext>A</mtext>}}\text{=}\text{?}\text{t>0}\text{e}{}^{\mathrm{<mtext>-t</mtext><mtext>A</mtext>}}\text{(X)}$, where e^?t$\text{A}$ is a Hilbert–Schmidt operator on the Hilbert space X for each t>0. We solve the so-called generalized eigenvalue problem for a general self-adjoint operator $\text{P}$ in X.     

Poisson's ratio for polycrystals

Accepted views concerning Poisson's ratio for central-force polycrystals are amended. For pulycrystals the ratio can vary from 1/4, which is actually a lower limit. An upper limit of Poisson's ratio exists also. Both limits can be calculated from single-crystal elastic data. The limits correspond to Voigt's and Reuss's states of uniform local strain and of uniform local stress, respectively.