Thermodynamic Properties of Non-equilibrium States in Quantum Field Theory

Within the framework of relativistic quantum field theory, a novel method is established which allows for distinguishing non-equilibrium states admitting locally a thermodynamic interpretation. The basic idea is to compare these states with global equilibrium states (KMS states) by means of local thermal observables. With the help of such observables, the states can be ordered into classes of increasing local thermal stability. Moreover, it is possible to identify states exhibiting certain specific thermal properties of interest, such as a definite local temperature or entropy density. The method is illustrated in a simple model describing the spatio-temporal evolution of a “big heat bang.”     

Nonequilibrium Gas and Generalized Billiards

Generalized billiards describe nonequilibrium gas, consisting of finitely many particles, that move in a container, whose walls heat up or cool down. Generalized billiards can be considered both in the framework of the Newtonian mechanics and of the relativity theory. In the Newtonian case, a generalized billiard may possess an invariant measure; the Gibbs entropy with respect to this measure is constant. On the contrary, generalized relativistic billiards are always dissipative,and the Gibbs entropy with respect to the same measure grows under some natural conditions. In this article, we find the necessary and sufficient conditions for a generalized Newtonian billiard to possess a smooth invariant measure, which is independent of the boundary action: the corresponding classical billiard should have an additional first integral of special type. In particular,the generalized Sinai billiards do not possess a smooth invariant measure. We then consider generalized billiards inside a ball, which is one of the main examples of the Newtonian generalized billiards which does have an invariant measure. We construct explicitly the invariant measure, and find the conditions for the Gibbs entropy growth for the corresponding relativistic billiard both formonotone and periodic action of the boundary.     

Quantum mechanics of relativistic spinless particles

A relativistic one-particle, quantum theory for spin-zero particles is constructed uponL ²(x, ct), resulting in a positive definite spacetime probability density. A generalized Schrödinger equation having a Hermitian HamiltonianH onL ²(x, ct) for an arbitrary four-vector potential is derived. In this formalism the rest mass is an observable and a scalar particle is described by a wave packet that is a superposition of mass states. The requirements of macroscopic causality are shown to be satisfied by the most probable trajectory of a free tardyon and a nontrivial framework for charged and neutral particles is provided. The Klein paradox is resolved and a link to the free particle field operators of quantum field theory is established. A charged particle interacting with a static magnetic field is discussed as an example of the formalism.     

Representations of relativistic causality structure by an operator density current

We consider a causality structure for localization of relativistic systems (elementary as well as composed ones). It may be called also relativistic causality logic. We propose to construct representations of such causality structure in terms of an operator-valued probability density current satisfying several postulates.     

Density functional. Theory and application to atoms and molecules

The density functional theory is one of the most efficient and promising methods of quantum physics and chemistry. It is a theory of electronic structure formulated in terms of the electron density as the basic unknown function instead of the electron wave function. According to the fundamental theorems of Hohenberg and Kohn, the electron density carries all the information one might need to determine any property of the electron system. However, the way of obtaining it, is not at all trivial. In this report, the recent advances are summarized. After a review of the Hohenberg–Kohn theorems, the method of constrained search and the Kohn–Sham scheme, exact theorems, relations and inequalities are discussed. There are several important concepts of chemistry (e.g. electronegativity, hardness, softness) that have recently obtained a firm foundation in the density functional theory. The optimized potential method and the methods that generate the potential from the electron density are reviewed. The local and nonlocal approximate functionals are compared. Extensions of the ground-state density functional theory (excited states, time-dependent, relativistic and finite temperature) are summarized. A review of the applications to atoms and molecules is presented.     

Global Existence Proof for Relativistic Boltzmann Equation with Hard Interactions

By combining the DiPerna and Lions techniques for the nonrelativistic Boltzmann equation and the Dudyński and Ekiel-Jeżewska device of the causality of the relativistic Boltzmann equation, it is shown that there exists a global mild solution to the Cauchy problem for the relativistic Boltzmann equation with the assumptions of the relativistic scattering cross section including some relativistic hard interactions and the initial data satisfying finite mass, energy and entropy. This is in fact an extension of the result of Dudyński and Ekiel-Jeżewska to the case of the relativistic Boltzmann equation with hard interactions. This work was supported by NSFC 10271121 and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, the Ministry of Education of China, and sponsored by joint grants of NSFC 10511120278/10611120371 and RFBR 04-02-39026.     

Electronic and optical properties under pressure effect of alkali metal oxides

We report results of first-principles calculations for the electronic and optical properties under pressure effect of Li₂O, Na₂O, Ki₂O and Rb₂O compounds in the cubic antifluorite structure, using a full relativistic version of the full-potential augmented plane-wave plus local orbitals (FP-APW+lo) method based on density functional theory, within the local density approximation (LDA) and the generalized gradient approximation (GGA). Moreover, the alternative form of GGA proposed by Engel and Vosko (GGA-EV) is also used for band structure calculations. The calculated equilibrium lattices and bulk moduli are in good agreement with the available data. Band structure, density of states, and pressure coefficients of the fundamental energy gap are given. The critical point structure of the frequency dependent complex dielectric function is also calculated and analyzed to identify the optical transitions. The pressure dependence of the static optical dielectric constant is also investigated.     

Thermodynamic Bethe ansatz for generalized extensive statistics

We investigate properties of the entropy density related to a generalized extensive statistics and derive the thermodynamic Bethe ansatz equation for a system of relativistic particles obeying such a statistics. We investigate the conformal limit of such a system. We also derive a generalized Y-system. The Gentile intermediate statistics and the statistics of γ-ons are considered in detail. In particular, we observe that certain thermodynamic quantities for the Gentile statistics majorize those for the Haldane–Wu statistics. Specifically, for the effective central charges related to affine Toda models we obtain nontrivial inequalities in terms of dilogarithms.     

An Entropy Functional for Riemann-Cartan Space-Times

By viewing space-time as a continuum elastic medium and introducing an entropy functional for its elastic deformations, T. Padmanabhan has shown that general relativity emerges from varying the functional and that the latter suggests holography for gravity and yields the Bekenstein-Hawking entropy formula. In this paper we extend this idea to Riemann-Cartan space-times by constructing an entropy functional for the elastic deformations of space-times with torsion. We show that varying this generalized entropy functional permits to recover the full set of field equations of the Cartan-Sciama-Kibble theory. Our generalized functional shows that the contributions to the on-shell entropy of a bulk region in Riemann-Cartan space-times come from the boundary as well as the bulk and hence does not suggest that holography would also apply for gravity with spin in space-times with torsion. It is nevertheless shown that for the specific cases of Dirac fields and spin fluids the system does become holographic. The entropy of a black hole with spin is evaluated and found to be in agreement with Bekenstein-Hawking formula.     

热动平衡态下热等离子体内的离子丰度研究

用相对论哈特里-福克-斯莱特自洽场方法计算热等离子体内的原子结构和平均离化度，应用玻耳兹曼关系和熵涨落理论，对一定温度、物质密度下的热等离子体内的离子丰度作了细致的研究，给出了一种快速求解离子丰度的物理方法，研究了离子离化度、丰度的变化规律. 关键词：     

金属钒弹性波速与热力学函数的理论计算

在全电子水平上,基于广义梯度近似(GGA)的密度泛函理论和全势能线性缀加平面波方法(FLAPW)计算了钒的晶格参数,弹性波速和格临爱森参数.在德拜模型的基础上,利用弹性波速方法和原子位移方法分别计算了钒的德拜频率,以及在标准条件下(298.15 K,1atm)的热容,熵等热力学函数,并与实验值进行了比较.     

On the definition and evolution of states in relativistic classical and quantum mechanics

Some of the problems associated with the construction of a manifestly covariant relativistic quantum theory are discussed. A resolution of this problem is given in terms of the off mass shell classical and quantum mechanics of Stueckelberg, Horwitz and Piron. This theory contains many questions of interpretation, reaching deeply into the notions of time, localizability and causality. A proper generalization of the Maxwell theory of electromagnetic interaction, required for the well-posed formulation of dynamical problems of systems with electromagnetic interaction is discussed, and some of the significance of recently found (classical) relativistic chaotic behavior is pointed out. Many results of a technical nature have been achieved in this framework; in this paper, some of these are reviewed, but I shall concentrate on a discussion of the basic ideas and foundations of the theory.On sabbatical leave from School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel.     

Relativistic density functional calculations for Pt2

First full-relativistic density functional calculations with the extension of the spin-polarization functional for the relativistic density functional theory in their collinear and noncollinear form are presented here for the molecular system Pt2. The agreement with experiment is very good.     

石墨弹性波速与热力学函数的理论计算

在全电子水平上,基于广义梯度近似(GGA)的密度泛函理论和全势能线性缀加平面波方法(FLAPW)计算了石墨的晶体参数和弹性波速;在德拜模型的基础上,利用弹性波速方法和原子位移方法分别计算了石墨的德拜频率;采用统计物理方法计算了石墨在标准条件下(298.5 k,1 atm)的热容,熵,升华焓等热力学函数,并与实验值进行了比较.     

Lattice vibrational properties of Al2X (X = Sc,Y) from density functional theory calculations

The phonon dispersion curves of the C15-type of Al₂Sc and Al₂Y compounds are investigated, using density functional theory within the generalized gradient approximation (GGA), based on the “direct method”. The obtained results show that both compounds are dynamically stable. The temperature dependence of the various thermodynamical quantities such as internal energy, free energy, entropy, and heat capacity are also predicted under the harmonic approximation, and the observed trends are discussed in detail.     

The problem of causality in an indeterministic science

A differentiation between the principles of causality and strict determinism is suggested, the principle of strict determinism being considered to be incompatible with current scientific theory, while the principle of causality is supported by all contemporary scientific knowledge. In this paper the importance of the principle of causality in indeterministic causal theories is discussed, non-relativistic quantum mechanics being considered in detail. Indeterministic causality and its relation to relativistic quantum theory is also discussed.     

Crystal growth and dislocations

The article attempts to review the present stage of the density functional theory for noncollinear magnetic states and its application to particular physical problems. The discussion starts with basic theorems of the theory and derivation of the Kohn-Sham equation for a noncollinear magnet. Special features of solving this equation are illustrated using the augmented-spherical-wave method generalized to the noncollinear magnetic structures as an example. Particular attention is devoted to the symmetry of the problem. It is shown that a traditional approach of the space group theory fails in the case of a noncollinear magnetic state. A generalized approach based on the notion of the spin space groups is presented which allows a consequent treatment of the symmetry properties of both nonrelativistic and relativistic problems. This approach allows the development of an exact procedure for a first-principles calculation of an incommensurate spiral structure and gives a sound basis for the calculation and physical interpretation of the noncollinear magnetic structures caused by the effects of relativity. Application of the theory to the first-principles determination of the complex noncollinear magnetic structures of various systems are discussed. Applications include the spiral structure of fcc Fe, the uncompensated magnetic structure in U3X4 and compensated magnetic structure in U2P2Sn, and two different types of weak ferromagnetism in Fe2O3 and Mn3Sn. It is shown how the calculation technique can be applied to studies of unenhanced and enhanced non-uniform magnetic susceptibilities as well as susceptibilities in fields noncollinear to the atomic moments. Illustrating results of the calculation of the susceptibility of various systems are presented. The last part of the review is devoted to applications of the theory of noncollinear magnetism to studies of temperature effects in the electronic properties of itinerant magnets.