Tensorial Relativistic Quantum Mechanics in (1+1) Dimensions and Boundary Conditions

The tensorial relativistic quantum mechanics in (1+1) dimensions is considered. Its kinematical and dynamical features are reviewed as well as the problem of finding the Dirac spinor for given finite multivectors. For stationary states, the dynamical tensorial equations, equivalent to the Dirac equation, are solved for a free particle, for a particle inside a box, and for a particle in a step potential.     

核的巨单极激发的求和规则和核物质的不可压缩性系数

采用近来在研究核基态中极为成功的相对论模型研究有限核的同位旋巨单极共振 ,从而给出核物质的不可压缩性系数 .讨论了建立在相对论平均场基态上的相对论无规位相近似的自洽处理 .自洽要求基态和巨共振激发态的研究从同一个有效拉氏量出发 .与相对论平均场的无海近似自洽 ,相对论无规位相近似不仅要包含正能态的粒子 -空穴激发 ,还必须考虑 Fermi海核子态和 Dirac海核子态激发的贡献 .用约束的相对论平均场方法得到核的巨单极共振的能量逆权重的求和规则 ,验证 Dirac海核子态的贡献 .比较理论计算和实验测量的巨单极共振的能量得到核物质的不可压缩性系数为 2 5 0 - 2 70 MeV. The isoscalar giant monopole resonance for finite nuclei and the nuclear matter incompressibility are studied in a consistent relativistic approach, which achieves a great success in describing the properties of nuclear ground states. The consistency in the relativistic random phase approximation (RRPA) built on the relativistic mean field (RMF) ground states are investigated. The RMF wave function of nucleus and the particle-hole residual interactions in RRPA are calculated from...     

相对论核多体理论中的自洽问题和求和规则

着重讨论了建立在相对论平均场基态上的相对论无规位相近似的自洽处理 .自洽处理要求基态和巨共振激发态的研究从同一个拉氏量出发,采用同一种建立在相对论下的完备基上的近似 .同时也讨论了自洽条件下Dirac海核子态的作用 ,指出 Dirac海核子态的贡献不能忽略 ,特别是在核的巨单极共振的情况.用约束的相对论平均场方法得到核的巨单极共振的能量逆权重的求和规则 ,从数值上验证了 Dirac海核子态的贡献. A consistent treatment is extremely important in relativistic approaches. We emphasized the consistent approach in relativistic random phase approximation built on relativistic mean filed ground states. The consistent treatment requires that the studies of the ground state and excited states of giant resonances are based on same effective Lagrangian, and on a same complete set of basis. It was found that the effect of the Dirac states could not be neglected, especially in the case of giant...     

随机边界对相对论气体玻色-爱因斯坦凝聚临界温度的影响

研究了随机边界对立方箱中相对论气体玻色-爱因斯坦凝聚临界温度的影响.在均匀分布、双模分布和高斯分布情况下,分别计算了临界温度与固定箱中的气体临界温度的比值,发现随机边界降低了系统的临界温度.相对于极端相对论情况,非相对论极限下的临界温度更低.     

Hilbert Expansion from the Boltzmann Equation to Relativistic Fluids

We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellians. The Maxwellians are constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum fluid states. In particular, for small Knudsen number, these solutions to the relativistic Boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic Euler equations.     

自旋粒子的相对论波函数

从相对论波动方程和Lorentz变换理论出发，讨论了自旋粒子的相对论波函数，并给出了求相对论粒子高自旋态的方法。     

Giant monopole and quadrupole states in the relativistic σ-ω model

Giant monopole and quadrupole states in the relativistic σ-ω model are studied with use of a local Lorentz boost and scaling method. In assuming nuclear matter, those excitation energies are expressed in a simple way in terms of the relativistic Landau parameters, and the expressions are formally very similar to nonrelativistic ones. In the σ-ω model, however, the values of the Landau parameters themselves are dominated by relativistic effects. Unlike the restoring forces depending on the Landau parameters, the mass parameters of these states are little affected by relativity.     

Stability of the Relativistic Maxwellian in a Collisional Plasma

The relativistic Landau-Maxwell system is the most fundamental and complete model for describing the dynamics of a dilute collisional plasma in which particles interact through Coulombic collisions and through their self-consistent electromagnetic field. We construct the first global in time classical solutions. Our solutions are constructed in a periodic box and near the relativistic Maxwellian, the Jüttner solution.Acknowledgements The research is supported in part by NSF grants.     

Relativistic theory of surface states

A Green's function method is used to investigate the role of relativistic effects in determining the electronic states in a semi-infinite Kronig-Penney model. Various boundary conditions are considered and it is found that relativistic effects do not introduce new surface states.     

Covariant Hamiltonian dynamics with negative-energy states

A relativistic quantum mechanics is studied for bound hadronic systems in the framework of the point form relativistic Hamiltonian dynamics. Negative-energy states are introduced taking into account the restrictions imposed by a correct definition of the Poincaré group generators. We obtain nonpathological, manifestly covariant wave equations that dynamically contain the contributions of the negative-energy states. Auxiliary negative-energy states are also introduced, specially for studying the interactions of the hadronic systems with external probes.     

Quantum Entanglement in Relativistic Three-Particle Systems

The relativistic three-particle systems are studied within the framework of Relativistic Schrödinger Theory (RST), with emphasis on the determination of the energy functional for the stationary bound states. The phenomenon of entanglement shows up here in form of the exchange energy which is a significant part of the relativistic field energy. The electromagnetic interactions become unified with the exchange interactions into a relativistic U(N) gauge theory, which has the Hartree–Fock equations as its non-relativistic limit. This yields a general framework for treating entangled states of relativistic many-particle systems, e.g., the N-electron atoms.     

Contrasting Classical and Quantum Vacuum States in Non-inertial Frames

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In particular, there is a distinction between the “Minkowski vacuum” for a box at rest in an inertial frame and a “Rindler vacuum” for an accelerating box which has fixed spatial coordinates in an (accelerating) Rindler frame. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. The behavior of classical zero-point radiation in a noninertial frame is found by tensor transformations and still depends only upon the geodesic separations, now expressed in the non-inertial coordinates. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. The classical analysis gives no grounds for the “heating effects of acceleration through the vacuum” which appear in the literature of quantum field theory. Thus this distinction provides (in principle) an experimental test to distinguish the two theories.     

Ab initio calculation of the spectroscopic properties of TlF<Superscript>−</Superscript>

The potential curves of the ground states of the TlF molecule and TlF^? anion are ab initio calculated by the relativistic coupled clusters method using a generalized relativistic pseudopotential. The corresponding spectroscopic parameters are calculated and it is shown that TlF^? is stable in the lowest vibrational states. The information obtained is necessary for preparing a new series of experiments aimed at searching for CP-noninvariant effects in nucleon-nucleon interactions on the basis of the TlF molecule.     

Tetraquarks Production in Quark-Gluon Plasma with Diquarks

We present a way to calculate tetraquarks ratios for quark gluon plasma with diquarks, The ratios of tetraquarks over baryons produced from quark matter are high than hadronic gas model limits. It is a better way to search for four-quark states in relativistic heavy ion collisions. It may become a criterion to judge whether quark-gluon plasma has formed to search for four-quark states in relativistic heavy ion collisions.     

Relativistic studies of the decay constants of S wave and P wave mesons

Relativistic corrections are important in hadronic physics since even for the heavy hadrons there are sizable relativistic corrections. Therefore one should use a relativistic model to describe the higher excited states. This note summarizes our predictions for the decay constants of the S wave and P wave heavy mesons by means of the instantaneous relativistic Bethe Salpeter equation (Salpeter equation).     

Relativistic studies of the decay constants of S wave and P wave mesons

Relativistic corrections are important in hadronic physics since even for the heavy hadrons there are sizable relativistic corrections. Therefore one should use a relativistic model to describe the higher excited states. This note summarizes our predictions for the decay constants of the S wave and P wave heavy mesons by means of the instantaneous relativistic Bethe Salpeter equation （Salpeter equation）.     

Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Photonic analogues of the relativistic Kronig-Penney model and of relativistic surface Tamm states are proposed for light propagation in fibre Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in the FBG realizes the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral response of the FBG. For the semi-infinite FBG Tamm surface states can appear and can be visualized as narrow resonance peaks in the transmission spectrum of the grating.     

Relativistic inverse scattering problem for a superposition of a nonlocal separable and a local quasipotential

Within the relativistic quasipotential approach to quantum field theory, the relativistic inverse scattering problem is solved for the case where the total quasipotential describing the interaction of two relativistic spinless particles having different masses is a superposition of a nonlocal separable and a local quasipotential. It is assumed that the local component of the total quasipotential is known and that there exist bound states in this local component. It is shown that the nonlocal separable component of the total interaction can be reconstructed provided that the local component, an increment of the phase shift, and the energies of bound states are known.     

Exploration of Pseudospin Symmetry in the Resonant States

Taking ^120Sn as an example, we discuss the pseudospin symmetry in the single proton resonant states by examining the energies, widths and the wavefunctions. The information of the single proton resonant states in spherical nuclei are extracted from an analytic continuation in the coupling constant method within the framework of the self-consistent relativistic mean field theory under the relativistic boundary condition. We find small energy splitting in a pair of pseudospin partners in the resonant states. The lower components of the Dirac wavefunctions of a pseudospin doublet agree well in the region where nuclear potential dominates. It is concluded that the pseudospin symmetry is also well conserved for the resonant states in realistic nuclei.     

New relativistic effects in the dynamics of nonlinear hydrodynamical waves

In Newtonian and relativistic hydrodynamics the Riemann problem determines the evolution of a fluid which is initially characterized by two states having different rest-mass density, pressure, and velocity. When the fluid is allowed to relax, one of three possible wave patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a relativistic Riemann problem when velocities tangential to the initial discontinuity are present. A smooth transition from one wave pattern to another can be produced by varying the initial tangential velocities while maintaining the initial states unmodified. These special relativistic effects are produced by the Lorentz factors and do not have a Newtonian counterpart.