Transport theory of dissipative heavy-ion collisions

The non-perturbative quantum-statistical theory of dissipative heavy-ion collisions introduced earlier, is generalized by including explicitly the relative motion of the colliding nuclei. We start from the Liouville equation in the Wigner representation which allows for useful and illustrative interpretations of the resulting quantities and equations. Using the randomness of the coupling matrix elements and the semi-classical approximation for the relative motion we derive a general time-dependent transport equation for the macroscopic Wigner functions (phase-space distribution functions). The limits of weak and strong coupling are discussed.     

Microscopic irreversibility in the neutral kaon system and the thermodynamical arrow of time I. CPT symmetric case

The master equation for the reduced density matrix of the neutral kaon system interacting with a (low temperature) boson gas is derived. The equation is transformed under time reversal (assuming CPT conservation) and the equations of motion in the direct and inverted time schemes are compared. The equations of motion are solved, in a perturbation method, and the explicit approach to thermodynamical equilibrium is described. The entropy production function for the kaonic decaying system is defined and calculated. It is shown that although the equilibrium state and the total entropy change during the approach to it are the same in both time schemes, the details of the entropy time dependence of a coherent initial state are different, thus suggesting a relation between microscopic and macroscopic arrows of time.     

Computation of electric dipole matrix elements for hydrogen fluoride

The electric dipole matrix elements of hydrogen fluoride have been calculated by numerical integration for transitions involving large quantum numbers υ, J. Overtones have been included through Δυ = 5. Molecular wave functions obtained by numerical integration of the Schrödinger equation were used. The influence of the mechanical motion on the matrix elements has been determined for Morse and Rydberg-Klein-Rees (RKR) potential functions. The influence of the electric dipole-moment function approximations has been investigated by a comparison of matrix elements obtained with approximations having the form of a truncated polynomial and a wave-function expansion. The inaccuracies in the matrix elements caused by uncertainties in the dipole-moment coefficients have been investigated.     

Resonances in coupled channels in nuclear and particle physics

Starting from first principles this report gives account of the important latest developments on resonances in coupled channels in nuclear and hadronic physics. It also gives many new results which have remained hitherto unpublished. All types of poles of the S matrix are considered in coupled-channel problems, on all Riemann sheets. This review includes the classification of poles, their manifestation in the S matrix and cross sections, the dynamics of coupled channels, and the motion of poles when the channel coupling is changing. The case of channels with short-range plus long-range potentials is treated in detail. The special case of resonance plus particle channels is considered and exemplified by the A₁ and Q resonances. Many numerical examples and fits to experimental data are provided.     

Nonlinear Dynamics of Soft Boson Excitations in Hot QCD Plasma. I. Plasmon-Plasmon Scattering

On the basis of the pure gauge sector of the Blaizot-Iancu equation, we derive a kinetic equation of Boltzmann type, taking into account 2n+2-colorless plasmon decay processes, n=1, 2,…. Using the so-called Tsytovich correspondence principle, a direct connection between matrix elements of the plasmon decay processes and a certain effective current, generating these processes, is established. The procedure of calculating a matrix element for the simplest four-plasmon decay is considered comprehensively. The limiting value of the plasmon occupation number (∼1/g², where g is a strong coupling) wherein all plasmon decays with n≥1 contribute to the right-hand side of the Boltzmann equation, is defined. The iterative method of calculation of matrix elements for higher decay processes (n>1) is proposed, and a problem of their gauge-invariance is discussed. We proceed from the general reasons the problem of extending the suggested approach to the case of color plasmons is considered. The explicit form of a linearized Boltzmann equation for color plasmons is written out, and it is shown that this equation covariantly conserves the color current, resulting from color-plasmon number density.     

Connected kernel methods in nuclear reactions: (III). Effective interactions

The recently derived connected kernel equation (CKE) for N-body scattering operators is applied to direct nuclear reactions. A spectral representation is derived for the kernel of the CKE in order to obtain manageable approximations. This allows the kernel to be split into orders corresponding to the propagation of different numbers of bound clusters. By formally solving one part of the kernel at a time, the CKE is written as a hierarchy of nested equations in increasingly many variables. The first equation of this hierarchy is a set of coupled channel Lippmann-Schwinger equations coupling together all two-cluster channels. These equations reduce to the usual coupled channel equations for inelastic scattering and to the coupled channel Born approximation for rearrangement reactions when weak coupling assumptions are made. The second equation of the hierarchy is a two-variable integral equation for the effective interactions appearing in the coupled channel equations. The driving terms and kernel of this integral equation are obtained from the third equation of the hierarchy which is a three-variable integral equation and so forth. The use of the spectral expansion results in a renormalized theory in the sense that the bound state and reaction problems are separated. This permits the inclusion of nuclear models in the theory in a straightforward manner. The hierarchy is applied to a particular example, that of nucleon-nucleus scattering. For this case the hierarchy is truncated at the level allowing no more than three clusters in the continuum. By suppressing exchange and keeping only one-particle transfer and single-nucléon knockout channels, a set of equations for the optical potentials and transfer operators is obtained. These equations provide a three-body treatment of the single scattering approximation to the optical potential. Iteration of the equations yields the usual single scattering approximation in first order including three-body off-shell effects. After suppression of Fermi motion and off-shell effects, the standard impulse approximation is recovered. Modifications of the method for other cases are discussed and other possible applications suggested.     

Quasi-relativistic treatment of the low-lying KCs states

The potential energy curves, permanent and transition dipole moments as well as spin-orbit and angular coupling matrix elements between the KCs electronic states converging to the lowest three dissociation limits were evaluated in the basis of the spin-averaged wavefunctions corresponding to pure Hund’s coupling case (a). The quasi-relativistic matrix elements have been obtained for a wide range of internuclear distance by using of small (9-electrons) effective core pseudopotentials of both atoms. The core-valence correlation has been accounted for a large scale multi-reference configuration interaction method combined with semi-empirical core polarization potentials. The static dipole polarizabilities of the ground X¹Σ⁺ and a³Σ⁺ states were extracted from the closed-shell coupled-cluster energies by the finite-field method. Among the singlet and triplet Σ⁺ states manifold the pronounced avoided crossing effect between repulsive walls of the (2,3)³Σ⁺ states has been discovered and analyzed by finite-difference calculation of radial coupling matrix elements. The resulting transition dipole moments and potentials were used to predict radiative lifetimes and emission branching ratios of excited vibronic states while the calculated angular coupling matrix elements were transformed to Λ-doubling constants of the (1,2)¹Π states and magnetic g-factor of the ground state. The accuracies of the present results are discussed by comparing with experimental data and preceding calculations.     

Atoms near magnetodielectric bodies: van der Waals energy and the Casimir-Polder force

Based on macroscopic QED in linear, causal media, a consistent theory for the Casimir-Polder force acting on an atom positioned near dispersing and absorbing magnetodielectric bodies is presented. The perturbative result for the van der Waals energy is shown to exhibit interesting new features in the presence of magnetodielectric bodies. To go beyond perturbation theory, we start with the center-of-mass equation of motion and derive a dynamical expression for the Casimir-Polder force acting on an atom prepared in an arbitrary electronic state. For a nondriven atom in the weak coupling regime, the force as a function of time is shown to be a superposition of force components that are related to the electronic density matrix elements at a chosen time. These force components depend on the position-dependent polarizability of the atom, which correctly accounts for the body-induced level shifts and broadenings.     

Analysis of decay of πN resonances into Nππ channels

Couplings of πN resonances with masses between 1.65 and 1.97 GeV/c² to Δπ and ?N channels are determined using the scattering matrix elements resulting from inelastic partial-wave analyses of πN → Nππ. The inelastic amplitudes were derived using an isobar model with a π-exchange based high partial-wave input. These couplings are compared to those derived from an analysis of πN → Nππ without a high partial-wave input. Some (weak) evidence for coupling of the ?N channel to the P31(1910) resonance seen in elastic phase-shift analyses is found.     

Effect of the concentration-dependent spin-charge correlations on the evolution of the energy structure of the 2D Emery model

It is shown using the 2D Emery model that the strong coupling between the spin subsystem of copper ions in the singlet state and the subsystem of oxygen holes considerably reduces the spectral intensity of the correlation function for holes on the Fermi contour. Spin-charge correlations are manifested in the existence of two channels. The first channel is due to the p-d exchange coupling of spins of the oxygen and copper holes. The second channel appears as a result of spin-correlated hoppings, when the motion of holes over oxygen ions is accompanied by spin-flip processes (i.e., simultaneous changes in the spin projections of an oxygen hole and a copper ion). It is established as a result of self-consistent calculations that the allowance for the concentration dependence of spin correlators and multicenter spin-charge correlators appearing in the dispersion equation ensures a decrease in the energy of the system and considerably affects the evolution of the Fermi surface under hole doping.     

Statistical model of current-coupled ion channels in nerve membranes

A statistical model of a driven system is developed. Its microscopic elements are the ion channels through a nerve membrane. Their conductances are stochastically switching under the competing influences of thermal noise and local membrane voltage. A current flow through the membrane induces a coupling between the channels via the electrolytes surrounding the membrane. The long range of the coupling permits a generalized mean field theory for the stationary membrane current as a function of the applied electrode voltage. We derive analytically the macroscopic conductance-voltage-temperature relation for the spatially uniform current state. It shows analogues of first and second order phase transitions. The critical temperature diverges at a finite coupling strength. The theory fits sodium conductance characteristics measured on nerve axon membranes from various species by a variation of only the coupling strength. This supports the hypothesis that this simplest possible model for sodium channels is universal for all species.The work of this author was partially supported by the Deutsche Forschungsgemeinschaft     

Introduction to the theory of electronic non-adiabatic coupling terms in molecular systems

The Born–Oppenheimer treatment leads to the adiabatic framework where the non-adiabatic terms are the physical entities responsible for the coupling between adiabatic states. The main disadvantage of this treatment is in the fact that these coupling terms frequently become singular thus causing difficulties in solving the relevant Schroedinger equation for the motion of the nuclei that make up the molecular systems. In this review, we present the line integral approach which enables the formation of the adiabatic-to-diabatic transformation matrix that yields the friendlier diabatic framework. The review concentrates on the mathematical conditions that allow the rigorous derivation of the adiabatic-to-diabatic transformation matrix and its interesting physical properties. One of the findings of this study is that the non-adiabatic coupling terms have to be quantized in a certain manner in order to yield single-valued diabatic potentials. Another important feature revealed is the existence of the topological matrix, which contains all the topological features of a given molecular system related to a closed contour in configuration space. Finally, we present an approximation that results from the Born–Oppenheimer treatment which, in contrast to the original Born–Oppenheimer approximation, contains the effect of the non-adiabatic coupling terms. The various derivations are accompanied by examples which in many cases are interesting by themselves.     

二维多流体域耦合声场的光滑有限元解法

针对声学有限元分析中四节点等参单元计算精度低,对网格质量敏感的问题,将光滑有限元法引入到多流体域耦合声场的数值分析中,提出了二维多流体域耦合声场的光滑有限元解法。该方法在Helmholtz控制方程与多流体域耦合界面的声压/质点法向速度连续条件的基础上,得到二维多流体耦合声场的离散控制方程,并采用光滑有限元的分区光滑技术将声学梯度矩阵形函数导数的域内积分转换形函数的域边界积分,避免了雅克比矩阵的计算。以管道二维多流体域耦合内声场为数值分析算例,研究结果表明,与标准有限元相比,对单元尺寸较大或扭曲严重的四边形网格模型,光滑有限元的计算精度更高。因此光滑有限元能很好地应用于大尺寸单元或扭曲严重的网格模型下二维多流体域耦合声场的预测,具有良好的工程应用前景。      

A study of self-organizing processes of nonlinear stochastic variables

A general theory is given for the time evolution of nonlinear stochastic variables a(t) = {a_i(t)} whose statistical distribution is changing due to the self-organization of “macroscopic” order. The dynamics of a(t) is conveniently expressed by self-consistent equations for the ensemble average x(t) = 〈a(t)〉, the supersystem, and for the deviations ξ(t) = a(t)?x(t), the subsystem; the systems are connected to each other by feedback loops in their dynamics. The time dependence of the variance and the correlation function ofξ(t) are studied in terms of relaxation toward local equilibrium underx(t) and dynamical coupling withx(t). A special example shows that the stochastic motions of subsystems are pulled together by the motion of the supersystem through feedback loops, and that this pull-together phenomenon occurs when symmetry-breaking instability exists in nonlinear systems.     

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.