A quantum dissipative system in an anisotropic non-linear absorbing environment

A canonical quantization scheme is represented for a quantum system interacting with a non-linear absorbing environment. The environment is taken anisotropic and the main system is coupled to its environment through some coupling tensors of various ranks. The non-linear response equation of the environment against the motion of the main system is obtained. The non-linear Langevin-Schrödinger equation is concluded as the macroscopic equation of motion of the dissipative system. The effect of non-linearity of the environment is investigated on the spontaneous emission of an initially excited two-level atom imbedded in such an environment.     

Hopf-algebraic renormalization of QED in the linear covariant gauge

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.     

Analytical expressions for partial wave two-body Coulomb transition matrices at ground-state energy

Leaning upon the Fock method of the stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere the possibility of the analytical solving of the Lippmann–Schwinger integral equation for the partial wave two-body Coulomb transition matrix at the ground bound state energy has been studied. In this case new expressions for the partial p$p$-, d$d$- and f$f$-wave two-body Coulomb transition matrices have been obtained in the simple analytical form. The developed approach can also be extended to determine analytically the partial wave Coulomb transition matrices at the energies of excited bound states.     

Recent Results on Recurrent Solutions and Limit Distributions of SDEs

The limit distribution for homogeneous Markov processes is studied extensively and well understood, but it is not the case for inhomogeneous Markov processes. In this paper, we review some recent results on inhomogeneous Markov processes generated by non-autonomous stochastic (partial) differential equations (SDE in short). Under some suitable conditions, we show that the distribution of recurrent solutions of SDEs constitutes the limit distribution of the corresponding inhomogeneous Markov processes.     

Closed-form solutions of general second order linear recurrences and applications

Two closed-form solutions of a general second order linear recurrence with variable coefficients are established. The first form is combinatorial in nature and is derived through the use of a set which counts the number of elements which are two units apart. The second form is closely related to continued fractions and is derived through the use of continued fraction-like relation. Several applications including a number of verifications of conjectures produced from the Ramanujan Machine are worked out, which illustrate its versatility in this respect.     

线性互补问题基于模同步块多重分裂方法的收敛性

通过利用不动点迭代来研究线性互补问题,根据基模同步多重分裂迭代方法将其线性互补问题的系数矩阵是点的形式推广到块H+的形式,并且分析了当系数矩阵是块矩阵时线性互补问题解的收敛情况。     

Stripe Order and Spin Dynamics in Nickelates

We report zero field μSR experiments on the lanthanum nickelate La_2−x Sr _x NiO_4+δ system with strontium doping level x between 0 and 0.6. In a single crystal with x=0.33 the internal field distribution shows two separated signals reflecting the antiferromagnetic domains and the non magnetic antiphase domain walls in the spin and charge ordered state below 190 K. Below 70 K a broadening of the low field line is observed. A similar behavior is observed in polycrystalline samples with 0.2≤x≤0.5. This revised version was published online in September 2006 with corrections to the Cover Date.     

Global existence inL 1 for the modified nonlinear Enskog equation in ℝ3

A global existence theorem with large initial data inL ¹ is given for the modified Enskog equation in ³. The method, which is based on the existence of a Liapunov functional (analog of theH-Boltzmann theorem), utilizes a weak compactness argument inL ¹ in a similar way to the DiPerna-Lions proof for the Boltzmann equation. The existence theorem is obtained under certain condition on the behavior of the geometric factorY. The condition onY amounts to the fact that theL ¹ norm of the collision term grows linearly when the local density tends to infinity.     

Phase space density representations in fluid dynamics

Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable.     

S-wave baryons in an equally mixed scalar-vector square root potential model of independent quarks

A relativistic model of independent quarks based on Dirac equation with an equally mixed scalar-vector square root confining potential is used to compute the quark core contributions to the static properties like magnetic moments, charge radii and axial vector coupling constant ratios of the baryon octet. The results obtained with appropriate corrections due to centre-of-mass motion agree fairly well with experimental values. The model is also extended to the study of magnetic moments of the quark core of baryons in the charmed andb-flavoured sectors and the overall predictions so obtained compare well with other model predictions.