New mean-field theories for the liquid–vapour transition of charged hard spheres

The phase behaviour of the primitive model of electrolytes is studied in the framework of the various mean-field approximations obtained recently by means of methods pertaining to statistical field theory (J.-M. Caillol, J. statist. Phys., 115, 1461 (2004); extended version: arXiv:cond-mat/0305465). The role of the regularization of the Coulomb potential at short distances is discussed in detail and the link to more traditional approximations of the theory of liquids is discussed. The values computed for the critical temperatures, chemical potentials, and densities are compared with available Monte Carlo data and other theoretical predictions.     

An “observer decomposition” for Everett's theory

Several authors have noted that Everett's theory needs a specification of a special decomposition in order to account for our perceived experience, including quantum measurement results. It is suggested here that a possible way to arrive at such a specification is to relate it to the internal structure of the observer himself.     

A “Master” perturbation series for the transition amplitude in a light field

We derive a “master” perturbation series for the quantum amplitude for a given transition process induced by laser-matter interaction. The result is derived using a complete set of basis functions depending on a real parameter λ. It provides a one-parameter (λ) family of infinitely many equivalent series representations of one and the same transition amplitude defined in the minimal coupling (MC) “velocity gauge”. As a first application of the master series we put λ = 0 and 1 in the formula and immediately obtain the two well-known perturbation series, traditionally derived in the “velocity” and “length” gauges. The master formula can be used to obtain any number of equivalent perturbation series by simply choosing a real number for λ; e.g., a “hybrid perturbation” series follows from putting λ = 1/2 in the formula.     

Green's function theory of the spin-Peierls transition in X−Y chains

Using a Green's function formalism, we derive from a new microscopic Hamiltonian, the transition temperature equation for the spin-Peierls transition in X−Y quasi-one-dimensional (1D) spin systems. The obtained equation has already been obtained by Beni and Pincus [1] in a different fashion.     

Analyticity of scattering for the ϕ4 theory

We consider scattering for the equation (+m ²)+³=0 on four-dimensional Minkowski space. Form>0, one-to-one and onto wave operatorsW _± :HH are known to exist for all 0, whereH denotes the Hilbert space of finite-energy Cauchy data. We prove that the maps (,u)W _± (u) and (,u)(W _± )^–1 (u) are continuous from [0, )×H toH, and extend to real-analytic functions from an open neighborhood of {0}×H×{0}×H to the Hilbert spaceH _–1 of Cauchy data with Poincaré-invariant norm. Form=0, wave operatorsW _± are known to exist as diffeomorphisms ofH for all 0, where hereH denotes the Hilbert space of finite Einstein energy Cauchy data. In this case we prove that the maps (,u)(W _± ) (u) and (,u)(W _± )^–1 (u) extend to real-analytic functions from a neighborhood of [0, )×H×H toH.     

Reply to the Comments of Sharipov on “Symmetry of the Linearized Boltzmann Equation”

This is a reply to the comments by Sharipov on the papers published in J. Stat. Phys. 136:751 (2009) and in J. Stat. Phys. 136:945 (2009). The present reply will show that the comments do not apply to the papers.     

Comment on “analytic scattering theory for many-body systems below the smallest three-body threshold”

The proof of [1, Lemmas 2.1–2.3] is completed, showing that the operators of multiplication byk ² inH ^t,, |t|1, =0, ±2, have spectrum ⁺ and generate the holomorphic semigroups , Re<0.It is pointed out, that [1, (5.54)] does not hold. Accordingly, a new version of [1, Theorem 5.15] is proved, saying that (5.44) defines an isomorphism of.     

Determination of nonlinear σ-ω-ρ model parameters in the relativistic mean-field theory by nuclear-matter properties

The parameters of the σ-ω-ρ model in the relativistic mean-field theory with nonlinear σ-meson self-interaction are determined by nuclear-matter properties, which are taken as those extracted by fits to data based on nonrelativistic nuclear models. The values of the relevant parameters are C _σ ²∼ 94, C _ω ²∼ 32, C _ρ ²∼ 26, b∼ - 0.09, c∼ 1, and the σ-meson mass m _σ∼ 370 MeV, while the value of the calculated nuclear- surface thickness is t∼ 1.4 fm. The field system is shown to be stable, since the σ-meson self-interaction energy is a lower bound in this whole parameter region with positive c. On the other hand, the effective nucleon mass M^* is larger than 0.73M, if the symmetry incompressibility K_s is assumed to be negative and the nuclear-matter incompressibility K₀ is kept less than 300 MeV. Received: 27 June 2001 / Accepted: 5 October 2001     

“Almost” mean-field ising model: An algebraic approach

We study the thermodynamic limit of the algebraic dynamics for an almost mean-field Ising model, which is a slight generalization of the Ising model in the mean-field approximation. We prove that there exists a family of relevant states on which the algebraic dynamics ^t can be defined. This ^t defines a group of automorphisms of the algebra obtained by completing the standard spin algebra with respect to the quasiuniform topology defined by our states.     

Spectral Properties of the Linearized Boltzmann Operator in L p for 1≤p≤∞

The spectrum of both classical and relativistic Boltzmann operator for hard interactions in a whole space is shown to be independent of p in L ^p for 1≤p<∞. It consists of a half-plane $\operatorname{Re} \lambda\leq -\nu_{0}$ and countably many branches in the strip $-\nu_{0}<\operatorname{Re} \lambda \leq0$ . Moreover the resolvent set is independent of p for all 1≤p≤∞ but in L ^∞ this operator possesses in addition to the continuous also an uncountable set of point spectrum.     

Complete Gauge theory for the whole Poincaré group

Gauge theories for nonsemisimple groups are examined. A theory for the Poincaré group with all the essential characteristics of a Yang-Mills theory necessarily possesses extra equations. Inonü-Wigner contractions of gauge theories are introduced which provide a Lagrangian formalism, equivalent to a Lagrangian de Sitter theory supplemented by weak constraints.Work supported by FINEP under Contract No. B/76/80/146/00/00.Fellow of the CNPq, Brasilia.     

Unconventional large-N limit of the Gaussian effective potential and the phase transition in λφ 4 theory

In the conventional large-N limit the coupling constant is required to scale as 1/N. While the Gaussian effective potential (GEP) is known to contain the exact result in this limit, it shows a phase transition only when 1/N (in units of the renormalized mass in the symmetric vacuum). Here we determine the asymptotic behaviour, asN, of and other quantities at the phase transition of the GEP. We find _crit to be finite in 0+1 dimensions; of order 1/lnN in 1+1 dimensions; 1/N ^1/3 in 2+1 dimensions; and in 3+1 dimensions. The GEP's first-order phase transition is shown to become asymptotically second-order in 1+1 dimensions and below. We also discuss non-integer dimensions and the approach to the non-trivial autonomous theory in 3+1 dimensions.