Master Equation for Quantum Brownian Motion Derived by Stochastic Methods

The master equation for a linear open quantum system in a general environment is derived using a stochastic approach. This is an alternative derivation to that of Hu, Paz, and Zhang, which was based on the direct computation of path integrals, or to that of Halliwell and Yu, based on the evolution of the Wigner function for a linear closed quantum system. We first show by using the influence functional formalism that the reduced Wigner function for the open system coincides with a distribution function resulting from averaging both over the initial conditions and the stochastic source of a formal Langevin equation. The master equation for the reduced Wigner function can then be deduced as a Fokker-Planck equation obtained from the formal Langevin equation.     

LHC能区的部分子分布函数

大型强子对撞机(LHC)能探测到核子中很小x的动力学区域.在此动力学区域部分子的密度很大,根据高扭度修正过的AP演化方程(MDAP方程),分析了此区域的部分子饱和问题.发现在LHC能区不会出现饱和现象,但部分子分布会由于高扭度效应而明显被抑制,出现部分饱和现象.根据MDAP演化方程,还对LHC能区的部分子分布进行了预言     

The mellin transform technique for the extraction of the gluon density

A new method is presented to determine the gluon density in the proton from jet production in deeply inelastic scattering. By using the technique of Mellin transforms not only for the solution of the scale evolution equation of the parton densities but also for the evaluation of scattering cross sections, the gluon density can be extracted in next-to-leading order QCD. The method described in this paper is, however, more general, and can be used in situations where a repeated fast numerical evaluation of scattering cross sections for varying parton distribution functions is required.     

Jet calculus beyond leading logarithms

It is shown that the evolution of hadronic jets produced in hard processes can be studied in terms of a simple parton branching picture, beyond the leading log approximation of QCD. The jet calculus is generalized to any given order of logs (but always to all orders of α_s. We discuss the general structure of the formalism. Universality of jet evolution is discussed. We consider also jet calorimetry measure and the multiplicity distribution of final states in a form which allows a systematic improvement of approximation. To the next-to-leading order, we prove the finiteness and elucidate the scheme dependence of parton subprocess probabilities. The physical inclusive cross section is shown to be scheme independent: next-to-leading results for e⁺e^? → q (non-singlet) + X agree with those of Curci and others.     

One-loop factorization for inclusive hadron production in p-A collisions in the saturation formalism

We demonstrate the QCD factorization for inclusive hadron production in p-A collisions in the saturation formalism at one-loop order, with explicit calculation of both real and virtual gluon radiation diagrams. In particular, we find that the cross section can be written into a factorization form in the coordinate space at the next-to-leading order, while the naive form of the convolution in the transverse momentum space does not hold. The collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final-state hadron, as well as the rapidity divergence with small-x dipole gluon distribution of the nucleus are factorized into the splittings of the associated parton distribution and fragmentation functions and the energy evolution of the dipole gluon distribution function. The hard coefficient function is evaluated at one-loop order, and contains no divergence.     

The evolution of parton distributions at small x

We investigate parton distributions at small x using moments of the Gribov-Lipatov-Altarelli-Parisi (GLAP) evolution equation with respect to x. In this representation the kernel of the GLAP equation contains singularities in the moment variable ω at ω = 0. We show that the importance of these singularities at small x depends on the form of the starting distributions. We examine the range of x in which the GLAP equation is valid. The restrictions on the range of x depend on the form of the starting distributions. We investigate whether the GLAP equation can be used to interpolate data in the HERA region. Results are given for the structure function F₂ at small x. A possible method of determining the gluon distribution from F₂ is discussed.     

Microscopic theory of dispersive transport in disordered semiconductors

A theory of dispersive transport based on the microscopic master equation is presented. The theory agrees with previous approaches and unifies them but is much more general. By means of the two-site effective medium approximation of Movaghar et al. we derive a generalised master equation for the averaged propagator of the carriers the kernel of which can be calculated directly from the microscopic transfer rates and distribution functions. We give analytic expressions for the transient current i(t) including the conditions for the transition from dispersive to Gaussian transport for three relevant hopping models. The influence of multiple trapping is treated by means of the coherent potential approximation. We find the same results for trapping with an exponentiak trap depth distribution and fixed-range hopping over energy barriers with an exponential barrier height distribution.     

Unintegrated parton distributions and prompt photon hadroproduction

We introduce a general expression which enables the parton distribution, unintegrated over the parton transverse momentum, to be obtained from the conventional parton densities. We use the formalism to study the effects of the transverse momentum of the incoming partonic system on the calculation of the transverse momentum spectra of prompt photons produced in high energy pp and collisions. For the purposes of illustration, we use the double logarithm approximation. For large we calculate the effect directly from the perturbative formalism, whereas for small we bound the effect using two extreme hypotheses. In both domains we find that the shapes of the prompt photon spectra are not significantly modified, although the cross sections are enhanced. Received: 18 November 1999 / Published online: 27 January 2000     

First passage time problems for a class of master equations with separable kernels

We discuss first passage time problems for a class of one-dimensional master equations with separable kernels. For this class of master equations the integral equation for first passage time moments can be transformed exactly into ordinary differential equations. When the separable kernel has only a single term the equation for the mean first passage time obtained is exactly that for simple diffusion. The boundary conditions, however, differ from those appropriate to simple diffusion. The equations for higher moments differ slightly from those for simple diffusion. Analysis is presented, of a generalization of a model of a random walk with long-range jumps first investigated by Lindenberg and Shuler. Since the equations can be solved exactly one can study the behavior of boundary conditions in the continuum limit. The generalization to a larger number of terms in the separable kernel leads to higher order equations for the first passage time moments. In each case, boundary conditions can be found directly from the original master equation.     

The Master Equation for Two-Level Accelerated Systems at Finite Temperature

In this work, we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which perform the role of a reservoir in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism by suitably redefining the vacuum of the macroscopic system. As applications, we initially investigate the behaviour of a Fermi oscillator in the presence of a heat bath consisting of a set of Fermi oscillators and that of an atomic two-level system interacting with a scalar radiation field, considered as a reservoir, by constructing the corresponding master equation which governs the time evolution of both sub-systems at finite temperature. Finally, we calculate the energy variation rates for the atom and the field, as well as the atomic population levels, both in the inertial case and at constant proper acceleration, considering the two-level system as a prototype of an Unruh detector, for admissible couplings of the radiation field.     

Reconstruction of non-forward evolution kernels

We develop a framework for the reconstruction of the non-forward kernels which govern the evolution of twist-two distribution amplitudes and off-forward parton distributions beyond leading order. It is based on the knowledge of the special conformal symmetry breaking part induced by the one-loop anomaly and conformal terms generated by forward next-to-leading order splitting functions, and thus avoids an explicit two-loop calculation. We demonstrate the formalism by applying it to the chiral odd and flavour singlet parity odd sectors.     

改进的部分子演化模型及其对EMC效应和核Drell－Yan过程的解释

用解析方法证明了部分子演化模型可为双重Ｘ重新标度模型提供物理基础，进而利用修正的Ａｌｔｅｒａｌｌｉ－Ｐａｒｉｓｉ方程描述小ｘ区域的核遮蔽和反遮蔽效应，以改进部分子演化模型，使我们不必引入核遮蔽因子便可统一地描述ＥＭＣ效应、核遮蔽和反遮蔽效应．最后，利用改进的部分子演化模型相当好地解释了核Ｄｒｅｌｌ－Ｙａｎ过程的实验数据．     

Engineering Classical Capacity of Generalized Pauli Channels with Admissible Memory Kernels

In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian evolution. We provide instructive examples for qubit and qutrit evolution. Interestingly, similar behavior is not observed when analyzing time-local master equations.     

Partonic Structure of the Pomeron in the Modified GLR Equation

The gluon recombination effect in the pomeron is studied by using the modified Gribov-Levin-Ryskin evolution equation. We find that the measured parton distributions in the pomeron can be generated dynamically from a purely gluonic input on assuming a small size for the pomeron.     

Charmed-particle production by neutrinos with the Weinberg SU(4) currents

Charmed-particle production by neutrinos is investigated with the quark parton model formalism. Emphasis is placed on the largest effects which can be tolerated by the present experimental data as well as those suggested by more conventional parton models.     

QED corrections to the evolution of parton distributions

We study the systematic inclusion of QED corrections in the evolution of parton distributions. corrections modify the evolution equation for parton distributions. They introduce additional parton distributions, like the photon distribution in the nucleon, and lead to additional mixing effects. We discuss the modifications for a realistic model of N_f,up up-type flavours and N_f,down down-type flavours. We have implemented these corrections into a numerical program and we quantify the size of these effects in a toy model. The corrections reach the order of 1%.     

How can we properly define the Q2 dependent parton distribution function in QCD?

We discuss how we can properly define the Q² dependent parton distribution functions in quantum chromodynamics within the framework of the operator product expansion and renormalization group techniques. It is proposed that the moments of the parton distribution functions at Q² should be defined as the hadronic expectation values of the twist-2 operators renormalized at Q². The integro-differential equations for the parton densities obtained by Altarelli and Parisi are reproduced in the leading logarithmic approximation. An application of our present formalism will be given in the case of a longitudinal structure function.     

微扰QCD演化过程中存在遮蔽效应的一个证据

核子的纵向结构函数F_L以及虚光子吸收的纵向和横向散射截面的比值R_L在小X区域主要取决于胶子的分布函数.而胶子的初始分布函数的形式决定了在演化过程中是否要考虑遮蔽效应.利用新的动力学演化方程分析了F_L和R_L,发现在部分子演化过程中存在遮蔽现象.     

On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model

We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori–Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.     

Spinor fields in the theory of relativity and a generalization of Heisenberg's nonlinear spinor equation

Some years ago it was shown that the nonlinear term of Heisenberg's spinor equation can be derived by torsion of the Minkowski space (Cartan space). This result is applied in the investigations of this paper. As the Heisenberg equation does not show any connection with recent phenomenological theories in high energy physics, like the parton or quark model, the problems of the metric of space-time are discussed from the aspect of fundamental axioms of topology (Hausdorff space). It will be shown that Feynman's relativistic parton theory can be derived by means of a quantised de Sitter space, where the constant curvature can assume only discrete values. It is also possible to derive the Dirac equation from the same mathematical considerations. A nonlinear spinor equation will be formulated which contains the parton theory and the nonlinear term of the Heisenberg equation as different approaches in the theory of elementary particles.