Statistical theory of nuclear cross section fluctuations

We present formulas for the auto- and cross-correlation functions of various observables, taking into account the influence of direct reactions. These formulas are valid in the limit of strong absorption, and are deduced from the statistics of the nuclear matrix elements. We thereby put fluctuation theory on a new basis, and extend its domain of validity by including direct reactions. We obtain an explicit expression for the correlation length. Numerical calculations show that our formulas apply only in the strong-absorption limit, and that significant deviations occur for medium or weak absorption. We apply our results to the calculation of the cross-correlation function for the cross sections for elastic and inelastic proton scattering on⁸⁸Sr through the 3/2⁺ isobaric analogue resonance.     

Level density fluctuations and random matrix theory

The main purpose of this work is to elucidate whether there are significant differences in the local fluctuation properties between two-body (TBRE) and orthogonal (OE) ensembles of random matrices. Emphasis is put on the validity of ergodic properties, and results obtained by numerical means are discussed from that point of view. Spectral and ensemble averaging procedures are compared. All the local properties studied show compatibility between TBRE and OE results, and no significant evidence of inconsistency of theoretical predictions and experimental data is found.     

Regge theory for multiparticle amplitudes

The asymptotic behavior of multiparticle scattering amplitudes is discussed and reviewed with an emphasis on the analytic structure of the amplitudes as a function of the channel invariants. Single and multiple asymptotic limits of the Regge and helicity type are defined and a recipe is given for obtaining the asymptotic behavior of amplitudes in these limits controlled by exchanges of factorizable Regge poles and constrained by analyticity requirements. Applications to inclusive cross sections and the decoupling theorems for a pomeron Regge pole are reviewed as illustrative consequences of unitarity for multi-Regge theory. The present understanding of the relationship of cuts in angular momentum to unitarity is also described and suggestions given for further research. An effort has been made to keep the discussion pedagogical, while at the same time providing an entree to the literature.     

The Bohm-Vigier subquantum fluctuations and nonlinear field theory

Utilising as starting point the double solution theory of Louis de Broglie and the Bohm-Vigier hypothesis of subquantum fluctuations, an attempt is made to give an example of the nonlinear field theory in which the guidance theorem of de Broglie can be realised. The simplest scalar model is considered.     

Some connections between the classical theory of fluctuations and quantum field theory

A number of authors have noticed that the ground state of the harmonic oscillator can be represented as the motion of a classical charged particle under the influence of a fluctuating electromagnetic field, provided the effect of radiative reaction is taken into account. Their work is reviewed and some new results are obtained which extend the treatment to excited states.     

Statistical mechanism of multiparticle production in hadron-nuclei collisions

On the basis of simple statistical arguments applied to the parton model, some important peculiarities of the hadron- nuclei high-energy interaction are interpreted. In particular, the weak dependence of secondaries on the mass number and KNO-scaling are explained.     

Current density and field fluctuations in a conducting medium

We study thermal fluctuations in a conducting medium which may be spatially non-uniform and anisotropic. The fluctuation spectra for charge and current density, and for the electromagnetic fields, are expressed in terms of the basic propagators of the macroscopic equations. The theory is based on an application of the generalized Nyquist theorem.     

Statistical interpretation of the p-adic quantum field theory

A p-adic generalization of the frequency theory of probability is developed. Within the framework of this theory frequency meaning is imparted to probabilities belonging to the field of p-adic numbers. The Bargmann-Fock representation is constructed for the p-adic field theory. A frequency interpretation of quantum states in the Bargmann-Fock representation is proposed. The p-adic generalization is essentially an introduction of new quantum states which are meaningless from the point of view of the standard theory of probability based on Kolmogorov's axiomatics.Moscow Institute of Electronic Engineering. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 51–55, November, 1992.     

Statistical scattering theory, the supersymmetry method and universal conductance fluctuations

This paper describes a novel analytical approach to the problem of conductance fluctuations in mesoscopic systems which, in particular, gives account of the influence of the coupling to external leads. We consider the case of a linear disordered sample in the metallic regime, which is coupled to two ideally conducting external leads. Using the many-channel approximation to Landauer's formula, we relate the conductance to the total transmission probability through the sample. The microscopic Hamiltonian of the quasi-one-dimensional disordered sample is formulated in terms of a random matrix, and the elements of the associated scattering matrix which determine the transmission are constructed from statistical scattering theory. We show that in addition to the Thouless energy, E_c, and the mean level spacing, d, there exists in the theory, a third energy scale, Γ, determined by the number of channels in the leads and the strength of the coupling between disordered sample and leads. Related to Γ, is a new length scale, L₀. We find that for sample lengths L >L₀, the properties of the conductance depend only weakly on the coupling to the external leads and, for very large L, become identical with those of quasi-one-dimensional conductors in the weak localization limit. On the other hand, for L < L₀, the coupling to the leads strongly affects the behaviour of both the average and the variance of the conductance. The magnitude of L₀ is typically several magnitudes of ten times the elastic mean free path and thus comparable to the sizes of experimental devices. A further novel aspect of our work is the demonstration that the assumption of GOE statistics for the Hamiltonian is sufficient to yield universal conductance fluctuations.     

Statistical mechanics and stability of random lattice field theory

The averaging procedure in the random lattice field theory is studied by viewing it as a statistical mechanics of a system of classical particles. The corresponding thermodynamic phase is shown to determine the random lattice configuration which contributes dominantly to the generating function. The non-abelian gauge theory in four (space plus time) dimensions in the annealed and quenched averaging versions is shown to exist as an ideal classical gas, implying that macroscopically homogeneous configurations dominate the configurational averaging. For the free massless scalar field theory with O(n) global symmetry, in the annealed average, the pressure becomes negative for dimensions greater than two when n exceeds a critical number. This implies that macroscopically inhomogeneous collapsed configurations contribute dominantly. In the quenched averaging, the collapse of the massless scalar field theory is prevented and the system becomes an ideal gas which is at infinite temperature. Our results are obtained using exact scaling analysis. We also show approximately that SU(N) gauge theory collapses for dimensions greater than four in the annealed average. Within the same approximation, the collapse is prevented in the quenched average. We also obtain exact scaling differential equations satisfied by the generating function and physical quantities.     

Statistical field theory for simple fluids: mean field and Gaussian approximations

We present an exact field theoretical representation of the statistical mechanics of simple classical liquids with short-range pairwise additive interactions. The action of the field theory is obtained by performing a Hubbard-Stratonovich transformation of the configurational Boltzmann factor. The mean field and Gaussian approximations of the theory are derived and applications to the liquid-vapour transition considered.     

A field theory approach to cosmological density perturbations

Adiabatic perturbations propagate in the expanding universe like scalar massless fields in some effective Robertson–Walker space–time.     

Statistical mechanics of structural fluctuations

The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture by constructing a renormalized Hamiltonian. The relative volumes occupied by each of the coexisting structures define the corresponding geometric probabilities. In the case of a frozen heterophase system these probabilities should be given a priori. And in the case of a thermal heterophase mixture the structural probabilities are to be defined self-consistently by minimizing a thermodynamical potential. This permits to find the temperature behavior of the probabilities which is especially important near the points of structural phase transitions. The presence of these structural fluctuations yields a softening of a crystal and a decrease of the effective Debye temperature. These effects can be directly seen by nuclear gamma resonance since the occurrence of structural fluctuations is accompanied by a noticeable sagging of the Mössbauer factor at the point of structural phase transition. The structural fluctuations also lead to the attenuation of sound and increase of isothermic compressibility.     

Asymptotic completeness and multiparticle structure in field theories

The ideas developed in Part I (ref. [1]) are applied to the recently constructed massive Gross-Neveu model. We define in this case an irreducible kernel satisfying a regularized Bethe-Salpeter equation which is convenient to derive asymptotic completeness in the 2-particle region. As in Part I, the method allows direct graphical definition of general irreducible kernels and is well suited to the analysis of asymptotic completeness and related results in more general energy regions.A large part of the paper is devoted to a new self-contained construction (via phase space expansion) of the Gross-Neveu model. The presentation is somewhat simpler than previous ones, is more complete on some points and is best suited to our purposes.