Density field theory for a fluid interacting with the Yukawa potential. Role of the ideal entropy

We present a field theory to describe liquids where the field represents the density. In terms of this field, the Hamiltonian contains the ideal entropy and the interaction between the density fields. The approach is illustrated with the Yukawa interaction and presented in the grand canonical ensemble formalism. In this framework, first, we derive a relation specific to the field theory. This relation is equivalent to the ‘equation of motion’ in field theory for interacting quantum particles. Then, focusing on the effect of the fluctuations, we calculate thermodynamic quantities beyond the mean field. The pressure, the density and the compressibility at a given chemical potential in the quadratic approximation and beyond are given. The aim of this paper is to illustrate the importance and the role of the ideal entropy in this type of approach. The density and the compressibility at a given chemical potential are calculated perturbatively in various ways. Whether from their field theoretical definition, or deriving them from one another using the thermodynamical relations or also using the ‘equation of motion’, the results are in all ways of calculation consistent. However, the different calculations require different levels of expansion of the ideal entropy term involving in our case three and four body coupling constants. The consistency is then closely related to the form of the functional of the ideal entropy.     

类锂体系(Z=21—30)基态1s22s电离能和相对论项能的理论计算

使用全实加关联方法和里兹(Ritz)变分方法计算了类锂体系(Z=21—30)基态1s²2s的非相对论能量和波函数；包括动能修正、电子-电子接触项、轨道-轨道相互作用项以及Darwin项的相对论修正和质量极化项由全实加关联波函数的一阶微扰给出，量子电动力学修正QED(quantum electronic dynamic)由有效核电荷方法和类氢公式计算；给出了中等核电荷的高电离类锂体系基态的电离能、相对论效应的项能(term energy)，并将计算结果与实验数据进行了比较，表明FCPC 关键词： 类锂体系 全实加关联 电离能 项能     

类锂体系激发态1s2 nd(n=3,4,5)精细结构和项能的理论计算

使用全实加关联(fullcorepluscorrelation缩写为FCPC)和里兹(Ritz)变分方法计算了类锂体系(Z=11—20)激发态1s2nd(n=3,4,5)的非相对论能量和波函数;包括动能修正、电子电子接触项、轨道轨道相互作用项以及Darwin项的相对论修正和质量极化项由全实加关联波函数的一阶微扰给出,量子电动力学(quantumelectronicdynamics缩写为QED)修正由有效核电荷方法和类氢公式计算;给出了高电离类锂体系激发态的激发能、精细结构和项能(termenergy),并 关键词： 类锂体系 全实加关联 精细结构 激发能     

Nonmarkovian dynamics of stochastic differential equations with quadratic noise

We consider a stochastic differential equation with a quadratic nonlinearity in the noise. We derive equations for the steady state probability density and joint probability distribution valid beyond a markovian approximation. We do not assume that the strength of the random term is small. The equations are derived for the case of an Ornstein-Uhlenbeck noise and also for a dichotomic noise. A comparison is made. We discuss some examples for which correlation functions and the associated relaxation times are calculated.     

A Direct Calculation of First-Order Wave Function of Helium

We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one componentassociated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential.     

HL-2A 装置中利用可见光谱段轫致辐射测量有效离子电荷数

通过测量可见光谱段的轫致辐射(λ=535.1nm)强度,结合等离子体电子密度和电子温度,HL-2A     

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The multichannel bremsstrahlung measurement system on HL-2A tokamak has been using to observe the intensity of visible (535.1nm) bremsstrahlung radiation. Combined the intensity with plasma electron density and electron temperature, the effective ion charge measurements can be obtained on HL-2A tokamak. The 1×10¹⁹m⁻³ to4×10¹⁹m⁻³ experimental results show that when the plasma electron density increases from 1×10 m to 4×10 m , the effective ion charge number changes from 5 down to around 2. The bremsstrahlung radiation signal intensity is proportional to the quadratic plasma density. When the electron density is higher than 3×10¹⁹m⁻³, the multichannel bremsstrahlung measurement system can collect sufficient signal through the plasma, which enables the measurement of effective ion charge radial profile.     

The Wigner molecule in a 2D quantum dot

The charge density and pair correlation function of three interacting electrons confined within a two-dimensional disc-like hard-wall quantum dot are calculated by full numerical diagonalization of the Hamiltonian. The formation of a Wigner molecule in the form of equilateral triangular configuration for electrons is observed as the size of the dot is increased.     

On the Hamiltonian formulation of incompressible ideal fluids and magnetohydrodynamics via Dirac?s theory of constraints

The Hamiltonian structures of the incompressible ideal fluid, including entropy advection, and magnetohydrodynamics are investigated by making use of Dirac?s theory of constrained Hamiltonian systems. A Dirac bracket for these systems is constructed by assuming a primary constraint of constant density. The resulting bracket is seen to naturally project onto solenoidal velocity fields.     

Stratified quantization approach to dissipative quantum systems: Derivation of the Hamiltonian and kinetic equations for reduced density matrices

A technique for describing dissipative quantum systems that utilizes a fundamental Hamiltonian, which is composed of intrinsic operators of the system, is presented. The specific system considered is a capacitor (or free particle) that is coupled to a resistor (or dissipative medium). The microscopic mechanisms that lead to dissipation are represented by the standard Hamiltonian. Now dissipation is really a collective phenomenon of entities that comprise a macroscopic or mesoscopic object. Hence operators that describe the collective features of the dissipative medium are utilized to construct the Hamiltonian that represents the coupled resistor and capacitor. Quantization of the spatial gauge function is introduced. The magnetic energy part of the coupled Hamiltonian is written in terms of that quantized gauge function and the current density of the dissipative medium. A detailed derivation of the kinetic equation that represents the capacitor or free particle is presented. The partial spectral densities and functions related to spectral densities, which enter the kinetic equations as coefficients of commutators, are evaluated. Explicit expressions for the nonMarkoffian contribution in terms of products of spectral densities and related functions are given. The influence of all two-time correlation functions are considered. Also stated is a remainder term that is a product of partial spectral densities and which is due to higher order terms in the correlation density matrix. The Markoffian part of the kinetic equation is compared with the Master equation that is obtained using the standard generator in the axiomatic approach. A detailed derivation of the Master equation that represents the dissipative medium is also presented. The dynamical equation for the resistor depends on the spatial wavevector, and the influence of the free particle on the diagonal elements (in wavevector space) is stated.     

Invariants and radiation of some nonstationary systems

In this paper formulas are obtained by means of the coherent-state method for calculating the radiation power of a nonstationary quantum system ofN charged particles whose Hamiltonian is a general quadratic form with respect to coordinates and momenta. The transitions between the coherent states and the Fock states of this system are discussed. The radiation is calculated both in the dipole approximation and strictly. As an example, the radiation of a charge in homogeneous varying electric and magnetic fields is found. The classical limit is considered.     

Tailoring steep density profile with unstable points

The mesoscopic properties of a plasma in a cylindrical magnetic field are investigated from the view point of test-particle dynamics. When the system has enough time and spatial symmetries, a Hamiltonian of a test particle is completely integrable and can be reduced to a single degree of freedom Hamiltonian for each initial state. The reduced Hamiltonian sometimes has unstable fixed points (saddle points) and associated separatrices. To choose among available dynamically compatible equilibrium states of the one particle density function of these systems we use a maximum entropy principle and discuss how the unstable fixed points affect the density profile or a local pressure gradient, and are able to create a steep profile that improves plasma confinement.     

金等离子体中7离子系统(Au47+～Au53+)的电荷态分布及其解析函数关系

根据扩展的相对论多组态Dirac-Fock理论计算得到的Au47 ~Au53 离子的平均离子寿命、能级能量和能级简并度,计算了各离子的电离速率常数、复合速率常数和配分函数,并由此得到了离子间的电离-复合平衡常数.基于这些数据,利用电离复合动力学方法研究了金等离子体内7离子系统在一定电子温度和电子密度下的电荷态分布和平均离化度.并给出了Au47 ~Au53 的离子丰度与电子温度和电子密度的函数关系.     

Nontrivial dynamics induced by a nonlinear Jaynes-Cummings Hamiltonian

The addition of a nonlinear term to the Jaynes-Cummings Hamiltonian induced a nontrivial discrete dynamics for the number of possible transitions of a given order, represented by a Fibonacci series. We describe the physics of the problem in terms of relevant operators which close a semi-Lie algebra under commutation with the Hamiltonian and therefore extending the generalized Bloch equations, already obtained for the linear case, to the nonlinear one. The initial conditions as well as a thermodynamical treatmetn of the problem is analyzed via the maximum entropy principle density operator. Finally, a generalized solution for the time-independent case is obtained and the solution for the field in a thermal state is recovered.     

Hyperfine field and isomer shift in ferromagnetic Fe−Cr alloys

The valence contact spin and charge densities at Fe sites in ferromagnetic Fe−Cr alloys are calculated using the discrete variational method. The hyperfine field at Fe nucleus is expressed as a linear sum of a core term, that is proportional to the local 3d moment, and a valence term, which is proportional to the valence spin density. The dependence of the hyperfine field, the contact charge density and the 4s magnetic moment on the number and orientation of chromium atoms in the first and second shells is studied. Comparison to experimental data is made.     

Renormalization of the Regularized Relativistic Electron-Positron Field

We consider the relativistic electron-positron field interacting with itself via the Coulomb potential defined with the physically motivated, positive, density-density quartic interaction. The more usual normal-ordered Hamiltonian differs from the bare Hamiltonian by a quadratic term and, by choosing the normal ordering in a suitable, self-consistent manner, the quadratic term can be seen to be equivalent to a renormalization of the Dirac operator. Formally, this amounts to a Bogolubov-Valatin transformation, but in reality it is non-perturbative, for it leads to an inequivalent, fine-structure dependent representation of the canonical anticommutation relations. This non-perturbative redefinition of the electron/positron states can be interpreted as a mass, wave-function and charge renormalization, among other possibilities, but the main point is that a non-perturbative definition of normal ordering might be a useful starting point for developing a consistent quantum electrodynamics. Received: 8 March 2000 / Accepted: 7 July 2000     

The Effect of Quark Mass and α-α Term on qq Condensation in QCD Vacuum

Beginning with the QCD Lagrangian in the global color symmetry model, we have derived a Hamiltonian including the lowest order current-current coupling. Taking instantaneous quadratic interaction kernel and using the Bogoliubov-Valatin transformation, we have got an effective Hamiltonian for computation. This Hamiltonian is similar to that introduced by Le Yaouanc et al., except that the α-α term has been considered here. We calculated the qq condensation in the BCS type of vacuum with quark mass and α-α term included. Our calculation shows that the value of qq condensation has increased by at least 10% with the α-α term included.     

Entropy balance,time reversibility,and mass transport in dynamical systems

We review recent results concerning entropy balance in low-dimensional dynamical systems modeling mass (or charge) transport. The key ingredient for understanding entropy balance is the coarse graining of the local phase-space density. It mimics the fact that ever refining phase-space structures caused by chaotic dynamics can only be detected up to a finite resolution. In addition, we derive a new relation for the rate of irreversible entropy production in steady states of dynamical systems: It is proportional to the average growth rate of the local phase-space density. Previous results for the entropy production in steady states of thermostated systems without density gradients and of Hamiltonian systems with density gradients are recovered. As an extension we derive the entropy balance of dissipative systems with density gradients valid at any instant of time, not only in stationary states. We also find a condition for consistency with thermodynamics. A generalized multi-Baker map is used as an illustrative example. (c) 1998 American Institute of Physics.     

Autocorrelation functions of the blackbody radiation in cavities with walls of finite conductivity

Electromagnetic equilibrium fluctuations in cavities with non ideal metallic walls are considered. On the boundary the electric and magnetic fields are connected by Leontovich's boundary condition. With the aid of Maxwell's equations and Leontovich's relation the response of the EM-field to a polarization field is calculated. The correlation functions of the EM-field are then given by the fluctuation dissipation theorem. For cube shaped cavities explicit considerations are made. Expressing the surface impedance by a frequency independent conductivity the volume averaged autocorrelation functions of the EM-field and the total energy density are calculated. Besides the contributions due to the normal modes an additional term is found which characterizes the contributions due to the evanescent waves existing near the internal surface of the cavity. As a consequence of the frequency dependence of the impedance this term shows aT ^7/2 dependence.     

Wave packet molecular dynamics–density functional theory method for non‐ideal plasma and warm dense matter simulations

A new wave packet molecular dynamics–density functional theory (WPMD‐DFT) method is proposed for atomistic simulations of non‐ideal plasma and warm dense matter. The method is based on the WPMD approach, where the electronic exchange and correlation effects are treated using an additional energy term taken from DFT. This term is calculated by integration over the mesh values of the wave packet density. The local density approximation is implemented so far. WPMD‐DFT is meant as a replacement for the anti‐symmetrized WPMD (AWPMD) method which is more time consuming and lacks electron correlation. In this paper, we compare the results obtained by WPMD‐DFT, WPMD, AWPMD, classical molecular dynamics, and path integral Monte Carlo methods for the internal energy of the hydrogen plasma in the temperature range 10–50 kK and electron number density from 10²⁰ to 10²⁴ cm^?3. We also demonstrate the ability to handle the simultaneous dynamics of electrons and ions by calculating the electron–ion temperature relaxation. The scalability of the WPMD‐DFT method with the number of electrons is shown for implementations in central processing unit and graphical processing unit.