The relativistic interquark potential

A method for the calculation of interaction potentials in a momentum space is proposed which is based on exact calculations of the Lorentz structures of the corresponding interaction amplitudes. With this method the kernel of the QCD-motivated potential of a quark-antiquark relativistic system is obtained for different masses and an arbitrary angular momentum J. The calculation is performed taking into account the anomalous chromodynamic moments of the quarks. The case of the singlet state of a relativistic quark system is considered. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 87–94, November, 2006.     

Thermodynamics of relativistic quantum fields confined in cavities

We investigate the quantum thermodynamical properties of localised relativistic quantum fields, and how they can be used as quantum thermal machines. We study the efficiency and power of energy transfer between the classical gravitational degrees of freedom, such as the energy input due to the motion of boundaries or an impinging gravitational wave, and the excitations of a confined quantum field. We find that the efficiency of energy transfer depends dramatically on the input initial state of the system. Furthermore, we investigate the ability of the system to extract energy from a gravitational wave and store it in a battery. This process is inefficient in optical cavities but is significantly enhanced when employing trapped Bose Einstein condensates. We also employ standard fluctuation results to obtain the work probability distribution, which allows us to understand how the efficiency is related to the dissipation of work. Finally, we apply our techniques to a setup where an impinging gravitational wave excites the phononic modes of a Bose Einstein condensate. We find that, in this case, the percentage of energy transferred to the phonons approaches unity after a suitable amount of time. These results give a quantitative insight into the thermodynamic behaviour of relativistic quantum fields confined in cavities.     

Spacelike and timelike response of confined relativistic particles

Basic theoretical issues relating to the response of confined relativistic particles are considered including the scaling of the response in spacelike and timelike regions of momentum transfer and the role of final-state interactions. A simple single-particle potential model incorporating relativity and linear confinement is solved exactly and its response is calculated. The response is studied in common approximation schemes and it is found that final-state interactions effects persist in the limit that the three-momentum transferred to the target is large. The fact that the particles are bound leads to a nonzero response in the timelike region of four-momentum transfer equal to about 10% of the total strength. The strength in the timelike region must be taken into account to fulfill the particle number sum rule.Received: 1 November 2002, Published online: 15 July 2003PACS: 13.60.Hb Total and inclusive cross-sections (including deep-inelastic processes) - 12.39.Ki Relativistic quark model - 12.39.Pn Potential models     

A relativistic potential model

Using parity violating nucleon wave function effects we make predictions for spin asymmetries inpp and \(\bar p\) p scattering at moderate and high energies     

Single-lens equivalent systems for Grin lenses

In this paper, one simple single-lens optical systems equivalent to Grin lens of various lengths, which are immersed in either homogeneous or inhomogeneous medium, are proposed. Basing on this equivalent system, the imaging properties of Grin lens rod in paraxial approximation have been thoroughly studied. The proposed plain optical system will lead to a straightforward optical analysis of complex optoelectronics systems employing Grin lens rod.     

The relativistic bound states of a non-central potential

We investigate the relativistic effects of a moving particle in the field of a pseudoharmonic oscillatory ring-shaped potential under the spin and pseudospin symmetric Dirac wave equation. We obtain the bound-state energy eigenvalue equation and the corresponding two-components spinor wave functions by using the formalism of supersymmetric quantum mechanics (SUSYQM). Furthermore, the non-relativistic limits are obtained by simply making a proper replacement of parameters. The thermodynamic properties are also studied. Our numerical results for the energy eigenvalues are also presented.     

A relativistic Hartree-Fock model for quark systems

The “relativistic H—F” scheme is applied to baryons and finite multiquark sustems. A two-body confinement potential (r, r² or r³) and the one-gluon-exchange interaction are incorporated. The electric OGE term is treated consistently in all considered systems. With the electric OGE term included, the solutions indicate the little bag. (Os)-closed multiquark states, strange or non-strange, cannot be lower in energy than an aggregate of Δ or Λ.     

Polaritons in confined systems

Polaritons in confined systems are introduced and their dispersion is calculated. The amount of squeezing of confined excitons-polaritons in GaAs quantum wells is evaluated.     

The equivalent potential of water molecules for electronic structure of lysine

In order to get more reliable electronic structures of proteins in aqueous solution, it is necessary to construct a potential of water molecules for protein’s electronic structure calculation. The lysine is a hydrophilic amino acid. It is positively charged (Lys+) in neutral water solution. The first-principles, all-electron, ab initio calcula-tions, based on the density functional theory, have been performed to construct such an equivalent potential of water molecules for lysine (Lys+). The process consists of three parts. First, the electronic structure of the cluster containing Lys+ and water molecules is calculated. By adjusting the positions of water molecules, the geometric structure of the cluster having minimum total energy is determined. Then, based on the structure, the electronic structure of Lys+ with the potential of water molecules is calculated using the self-consistent cluster-embedding (SCCE) method. Finally, the electronic structure of Lys+ with the potential of dipoles is calculated. The dipoles are adjusted so that the electronic structure of Lys+ with the potential of dipoles is close to that of water molecules. Thus the equivalent potential of water molecules for the electronic structure of lysine is obtained. The major effect of water molecules on lysine’s electronic structure is raising the occupied eigenvalues about 0.5032 eV, and broadening energy gap 89%. The effect of water molecules on the electronic structure of lysine can be simulated by dipoles potential.     

The equivalent potential of water molecules for electronic structure of alanine

Using ab initio calculations based on density functional theory, an equivalent potential of water molecules for the electronic structure of Ala in solution has been obtained. The calculation process consists of three steps: first, the geometric structure of Ala + nH₂O system is determined by searching for the lowest energy of the system using free cluster calculation method. Second, based on the geometric structure obtained, the electronic structure of Ala with the potential of water molecules is calculated using a self-consistent cluster-embedding method. Finally, after replacing water molecules with dipoles, the electronic structure of Ala with the potential of dipoles is calculated. The dipoles are adjusted so the electronic structure of Ala with the potential of dipoles is close to that of water molecules. The calculated results show that the main effect of water molecules is to raise the state for methyl CH₃ by about 0.14 Ry, raising all other eigenvalues by about 0.059 Ry, and widening the energy gap by about 25%. In contrast, the replacement of water molecules by dipoles is comparatively efficient, showing that the effect of water molecules on the electronic structure of Ala can be simulated by a dipole potential, which would be a shortcut calculation.     

The equivalent potential of water molecules for electronic structure of cysteine

In order to get more reliable electronic structure of protein in aqueous solution, it is necessary to construct a simple, easy-use equivalent potential of water molecules for protein's electronic structure calculation. The first-principles, all-electron, ab initio calculations have been performed to construct the equivalent potential of water molecules for the electronic structure of Cys. The process consists of three steps. First, the electronic structure of the cluster containing Cys and water molecules is calculated. Then, based on the structure, the electronic structure of Cys with the potential of water molecules is calculated using the self-consistent cluster-embedding method. Finally, the electronic structure of Cys with the potential of dipoles is calculated. The dipoles are adjusted so the electronic structure of Cys with the potential of dipoles is close to that of water molecules. The calculations show that the major effect of water molecules on Cys' electronic structure is lowering the occupied electronic states by about 0.032 Ry, and broadening energy gap by 16%. The effect of water molecules on the electronic structure of Cys can be simulated by dipoles potential.     

The Lax representation for an integrable class of relativistic dynamical systems

We exhibit the Lax pair for the class of relativistic dynamical systems recently introduced by Ruijsenaars and Schneider, whose equations of motion read, whereB is an arbitrary constant and the Weierstrass elliptic function.For the 3 academic years 1983–1986     

The Hamiltonian in relativistic systems of interacting particles

The dynamics of a system of relativistically interacting particles is determined by a set of constraints, some combination of which has been frequently identified with the Hamiltonian. These constraints differ from the generators of the Poincaré transformations, among whichp ₀ generates translations along the time axis and hence is to be considered as the energy of the system. There are thus grounds for consideringP ₀ as the appropriate Hamiltonian. In this paper we establish a close relationship between transformations generated by the constraints and those generated by the Poincaré generators. In particular we find that the true Hamiltonian is a rather complicated but well-defined function ofp ₀ and all the constraints. We show that the generators of the entire algebra of the Poincaré group can be realized in such a fashion that the Hamiltonian is correctly included among them, and such that particle world lines in Minkowski space-time generated by this Hamiltonian transform correctly under the Poincaré group.This work was partially supported by the National Science Foundation Grant No. PHY 79-0887 to Syracuse University and by Grant No. PHY 79-09405 to Yeshiva University.     

库仑势加新环形势的相对论束缚态

在标量势等于矢量势的条件下，获得了库仑势加新环形势的Klein-Gordon方程和Dirac方程的束缚态的精确解. 对于Klein-Gordon方程，获得了精确的能谱方程和归一化的波函数. 对于Dirac方程，给出了精确的能谱方程和归一化的旋量波函数. 关键词： 库仑势加新环形势 束缚态 精确解     

Stable first-order particle-frame relativistic hydrodynamics for dissipative systems

We propose a stable first-order relativistic dissipative hydrodynamic equation in the particle frame (Eckart frame) for the first time. The equation to be proposed was in fact previously derived by the authors and a collaborator from the relativistic Boltzmann equation. We demonstrate that the equilibrium state is stable with respect to the time evolution described by our hydrodynamic equation in the particle frame. Our equation may be a proper starting point for constructing second-order causal relativistic hydrodynamics, to replace Eckart's particle-flow theory.     

The equivalent dipole potential of water for the electronic structure of threonine

The equivalent potential of water for the electronic structure of threonine (Thr) in solution is constructed by the first-principles, all-electrons, ab initio calculations. The main process of calculation consists of three steps. First, the geometric structure of the cluster containing Thr and water molecules is calculated by the free cluster calculation. Then, based on the obtained geometric structure, the electronic structure of Thr with the potential of water molecules is calculated using the self-consistent cluster-embedding method. Finally, the electronic structure of Thr with the potential of dipoles is calculated. The results show that the major effect of water on the electronic structure of Thr is to raise the occupied molecular orbitals near the Fermi level by about 0.01 Ry on average, and its energy gap is almost not changed. The effect of water on the electronic structure of Thr can be simulated by dipoles potential.     

Incommensurate diffusion in confined systems

Molecular simulations corroborate the existence of the disputed window effect, i.e., an increase in diffusion rate by orders of magnitude when the alkane chain length increases so that the shape of the alkane is no longer commensurate with that of a zeolite cage. This window effect is shown to be characteristic for molecular sieves with pore openings that approach the diameter of the adsorbate. Furthermore, the physical compatibility between the adsorbate and the adsorbent has a direct effect on the heat of adsorption, the Henry coefficients, the activation energy, and the frequency factors.