Field theory reformulated without self-energy parts. Kinetic extension for the Lee model

An alternative formulation of field theory is possible such that self-energy contributions do no longer appear as dynamical processes. The dynamics is now described by kinetic-like equations of motion, involving more degrees of freedom than in the original formulation, plus a constraint propagating in time. Considering situations outside the equivalence conditions provides a natural irreversible extension of quantum field. The relevance of such extension relies on the positivity and normalization of the extension. The feasibility is examplified here on the Lee model without focusing on a particular sector. The tool used is the single subdynamics approach [Trends Stat. Phys. 3 (2000) 115]. A partial treatment of the Lee model along those lines have been considered for a particular sector [Prog. Theor. Phys. 109 (2003) 881]. We intend to consider here a set of sectors using a reduction formalism [Physica A 171 (1991) 159] which provides directly the required properties. Outside the equivalence conditions, our approach couples sectors and the resulting statistical mixture changes its composition with time.     

Hydrodynamics from kinetic models of conservative economies

In this paper, we introduce and discuss the passage to hydrodynamic equations for kinetic models of conservative economies, in which the density of wealth depends on additional parameters, like the propensity to invest. As in kinetic theory of rarefied gases, the closure depends on the knowledge of the homogeneous steady wealth distribution (the Maxwellian) of the underlying kinetic model. The collision operator used here is the Fokker-Planck operator introduced by J.P. Bouchaud and M. Mezard [Wealth condensation in a simple model of economy, Physica A 282 (2000) 536-545], which has been recently obtained in a suitable asymptotic of a Boltzmann-like model involving both exchanges between agents and speculative trading by S. Cordier, L. Pareschi and one of the authors [S. Cordier, L. Pareschi, G. Toscani, On a kinetic model for a simple market economy, J. Stat. Phys. 120 (2005) 253-277]. Numerical simulations on the fluid equations are then proposed and analyzed for various laws of variation of the propensity.     

Optical Operator Method in Two-Mode Case and Entangled Fresnel Operator＇s Decomposition

Based on the entangled Fresnel operator （EFO） proposed in [Commun. Theor. Phys. 46 （2006） 559], the optical operator method studied by the IWOP technique （Ma et al., Commun. Theor. Phys. 49 （2008） 1295） is extended to the two-mode case, which gives the decomposition of the entangled Fresnel operator, corresponding to the decomposition of ray transfer matrix [A, B, C, D]. The EFO can unify those optical operators in two-mode case. Various decompositions of EFO into the exponential canonical operators are obtained. The entangled state representation is useful in the research.     

Theoretical ROVibrational Energies (TROVE): A robust numerical approach to the calculation of rovibrational energies for polyatomic molecules

We present a new computational method with associated computer program TROVE (Theoretical ROVibrational Energies) to perform variational calculations of rovibrational energies for general polyatomic molecules of arbitrary structure in isolated electronic states. The (approximate) nuclear kinetic energy operator is represented as an expansion in terms of internal coordinates. The main feature of the computational scheme is a numerical construction of the kinetic energy operator, which is an integral part of the computation process. Thus the scheme is self-contained, i.e., it requires no analytical pre-derivation of the kinetic energy operator. It is also general, since it can be used in connection with any internal coordinates. The method represents an extension of our model for pyramidal XY₃ molecules reported previously [S.N. Yurchenko, M. Carvajal, P. Jensen, H. Lin, J.J. Zheng, W. Thiel, Mol. Phys. 103 (2005) 359]. Non-rigid molecules are treated in the Hougen-Bunker-Johns approach [J.T. Hougen, P.R. Bunker, J.W.C. Johns, J. Mol. Spectrosc. 34 (1970) 136]. In this case, the variational calculations employ a numerical finite basis representation for the large-amplitude motion using basis functions that are generated by Numerov-Cooley integration of the appropriate one-dimensional Schrödinger equation.     

Photon statistics in the stochastic limit of QED without dipole approximation

In this paper we investigate the distribution of the Heisenberg evolution of the number operator in the stochastic limit of the quantum electromagnetic field without dipole approximation. We prove that in this case the usual Poisson statistics of the free fields has to be replaced by a hypergeometric series whose coefficients we compute explicitly. The physical effects of the new statistics should manifest themselves in situation which are not yet in the relativistic regime, but in which the dipole approximation is no longer valid. The text was submitted by the authors in English.     

Newton-Leibniz integration for ket-bra operators in quantum mechanics (V)—Deriving normally ordered bivariate-normal-distribution form of density operators and developing their phase space formalism

We show that Newton-Leibniz integration over Dirac’s ket-bra projection operators with continuum variables, which can be performed by the technique of integration within ordered product (IWOP) of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480], can directly recast density operators and generalized Wigner operators into normally ordered bivariate-normal-distribution form, which has resemblance in statistics. In this way the phase space formalism of quantum mechanics can be developed. The Husimi operator, entangled Husimi operator and entangled Wigner operator for entangled particles with different masses are naturally introduced by virtue of the IWOP technique, and their physical meanings are explained.     

Dynamic fluctuations in optical bistability

We present results on the time correlation function of a system undergoing absorptive optical bistability. We first use the Zwanzig-Mori formalism to calculate time correlation functions both near marginal stability points and in the coexistence region. Near marginal stability the theory predicts large deviations from a single exponential form of the correlation function. The truncated continued fraction expansion is shown to become inapplicable close to the coexistence point. The difficulties are due to the presence of long time scales, viz. the very large mean first passage times between the two metastable steady states. When these scales are important we show that the memory kernel relaxation is no longer faster than that of a field fluctuation. An increase in the size of the system increases the disparity of the time scales and thus exacerbates the problems of the projection operator formalism as used here following reference [14].We next present an ansatz for the correlation function incorporating the four major time scales important near coexistence, the two single branch relaxation times and the two mean first passage times for transitions between the stable states. This form of the correlation function avoids the difficulties cited in connection with the use of the projection operator method.     

Neutrino dispersion properties in an external magnetic field

The neutrino self-energy operator Σ(p) in a magnetic field is calculated for the case of high-energy neutrinos, this corresponding to the crossed field approximation. The probability of the neutrino decay ν → e ^? W ⁺ is found by using the imaginary part of the operator Σ(p). A simple analytic result is obtained in the parameter region that is the most interesting from the physical point of view and which was not considered earlier. The contribution of an external magnetic field to the neutrino magnetic moment is calculated. The result obtained here for this contribution corrects formulas available previously.     

Spectrum of the fokker-planck operator representing diffusion in a random velocity field

We study spectral properties of the Fokker-Planck operator that represents particles moving via a combination of diffusion and advection in a time-independent random velocity field, presenting in detail work outlined elsewhere [J. T. Chalker and Z. J. Wang, Phys. Rev. Lett. 79, 1797 (1997)]. We calculate analytically the ensemble-averaged one-particle Green function and the eigenvalue density for this Fokker-Planck operator, using a diagrammatic expansion developed for resolvents of non-Hermitian random operators, together with a mean-field approximation (the self-consistent Born approximation) which is well controlled in the weak-disorder regime for dimension d>2. The eigenvalue density in the complex plane is nonzero within a wedge that encloses the negative real axis. Particle motion is diffusive at long times, but for short times we find a novel time dependence of the mean-square displacement, approximately t(2/d) in dimension d>2, associated with the imaginary parts of eigenvalues.     

An Operator Method of the Theory of Optical Coherence and Radiometry

This paper presents a quantum mechanical formalism of the classical coherence theory, within which the generalized radiance function defined in the time domain is regarded as a phase space representative of a time-dependent correlation operator of a polychromatic field. The theory deals with both stationary and nonstationary fields and, for a stationary field, provides a new operator formalism of the usual theory of optical coherence developed in the space-frequency domain. New results include an operator representation of the mutual coherence function, an operator version of the Wiener-Khintchine theorem, and an operator theorem that projects the correlation operator of a polychromatic field onto a particular spectral component. As illustrative examples, the previous formulas regarding the relationship between temporal coherence and spatial coherence, and the relationship between spectral properties and coherence properties are derived from the new operator formulas. The correspondence of the present formalism to the usual formalism using Dirac notation to describe the propagation of a stationary, partially coherent, quasi-monochromatic field is also considered.