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.     

Plasma Crystal in (3 + 1) Dimensions

JETP Letters - A quasi-two-dimensional plasma crystal in (3 + 1) dimensions has been experimentally observed for the first time; i.e., three spatial coordinates of each microparticles of the...     

Singularity Free Stars in (2+1) Dimensions

We present some new types of non-singular model for anisotropic stars with constant Λ and variable Λ based on the Krori and Barua (KB) metric in (2+1) dimensions. The solutions obtained here satisfy all the regularity conditions and its simple analytical form helps us to study the various physical properties of the configuration.     

General relativity in a (2 + 1)-dimensional space-time

General relativity is formulated for a (2+1)-dimensional space-time. Solutions to the vacuum field equations are locally flat. There are no gravitational waves and no Newtonian attraction between masses. The geometry around a point mass is a cone (locally flat) where the angle deficit at the apex is proportional to the mass. A uniform density planet has a spherical cap interior and a conical exterior solution. A convex polyhedron represents a closed universe with point masses at its vertices and approximates a static spherical universe of uniform density dust.     

Thermodynamics of a Charged Hairy Black Holein (2+1) Dimensions

In this paper we study thermodynamics, statistics and spectroscopic aspects of a charged black hole with a scalar hair coupled to the gravity in (2+1) dimensions. We obtained effects of the black hole charge and scalar field on the thermodynamical and statistical quantities. We find that scalar charge may increase entropy, temperature and probability, while may decrease black hole mass, free and internal energy. Also electric charge increases probability and decreases temperature and internal energy. Also we investigate stability of the system and find that the thermodynamical stability exists.     

Stability of Charged Thin-Shell Wormholes in (2+1) Dimensions

In this paper we construct charged thin-shell wormholes in (2+1)-dimensions applying the cut-and-paste technique implemented by Visser, from a BTZ black hole which was discovered by Bañados, Teitelboim and Zanelli (Phys. Rev. Lett. 69:1849, 1992), and the surface stress are determined using the Darmois-Israel formalism at the wormhole throat. We analyzed the stability of the shell considering phantom-energy or generalised Chaplygin gas equation of state for the exotic matter at the throat. We also discussed the linearized stability of charged thin-shell wormholes around the static solution.     

Folded Solitary Waves and Foldons in(2+1) Dimensions

A general type of localized excitations, folded solitary waves and foldons, is defined and studied bothanalytically and graphically. The folded solitary waves and foldons may be “folded“ in quite complicated ways andpossess quite rich structures and abundant interaction properties. The folded phenomenon is quite universal in the realnatural world. The folded solitary waves and foldons are obtained from a quite universal formula and the universalformula is valid for some quite universal (2 1)-dimensional physical models. The “universal“ formula is also extendedto a more general form with many more independent arbitrary functions.     

Novel Rotating Hairy Black Hole in （2 ＋ 1） Dimensions

We present some novel rotating hairy black hole metric in （2 ＋ 1） dimensions, which is an exact solution to the field equations of the Einstein-scalar-AdS theory with a non-minimal coupling. The scalar potential is determined by the metric ansatz and consistency of the field equations and cannot be prescribed arbitrarily. In the simplified, critical ease, the scalar potential contains two independent constant parameters, which are respectively related to the mass and angular momentum of the black hole in a particular way. As long as the angular momentum does not vanish, the metric can have zero, one or two horizons. The case with no horizon is physically uninteresting because of the curvature singularity lying at the origin. We identify the necessary conditions for at least one horizon to be present in the solution, which imposes some bound on the mass-angular momentum ratio. For some particular choice of pararneters our solution degenerates into some previously known black hole solutions.     

Zero Tension Kardar-Parisi-Zhang Equation in (d + 1)–Dimensions

The joint probability distribution function (PDF) of the height and its gradients is derived for a zero tension d + 1-dimensional Kardar-Parisi-Zhang (KPZ) equation. It is proved that the height's PDF of zero tension KPZ equation shows lack of positivity after a finite time t _c . The properties of zero tension KPZ equation and its differences with the case that it possess an infinitesimal surface tension is discussed. Also potential relation between the time scale t _c and the singularity time scale t _c.v→0 of the KPZ equation with an infinitesimal surface tension is investigated.     

Folded Solitary Waves and Foldons in （2＋1） Dimensions

A general type of local/zed excitations, folded solitary waves and foldons, is defined and studied both analytically and graphically. The folded solitary waves and foldons may be “folded“ in quite complicated ways and possess qnite rich structures and abundant interaction properties. The folded phenomenon is quite universal in the real natural world. The folded solitary waves and foldons are obtained from a quite universal formula and the universal formul is valid for some quite universal (2 1)-dimensional physical mode/s. The “universal“ formula is also extended to a more general form with many more independent arbitrary functions.     

Single-Particle Momentum Distributions for Bosonic Trimer States in Two and Three Dimensions

For a system formed by three bosons interacting by a pairwise zero-range potential we show how the functional form of the asymptotic momentum distribution changes drastically when passing from bi (2D) to tridimensional (3D) regime, mainly affected by the absence/presence of the Efimov effect in 2D/3D. The spectator functions and the momentum distribution are calculated analytically for both regimes.     

String Non(anti)commutativity for Neveu-Schwarz Boundary Conditions

The appearance of non(anti)commutativity in superstring theory, satisfying the Neveu-Schwarz boundary conditions is discussed in this paper. Both an open free superstring and also one moving in a background antisymmetric tensor field are analyzed to illustrate the point that string non(anti)commutativity is a consequence of the nontrivial boundary conditions. The method used here is quite different from several other approaches where boundary conditions were treated as constraints. An interesting observation of this study is that, one requires that the bosonic sector satisfies Dirichlet boundary conditions at one end and Neumann at the other in the case of the bosonic variables X ^μ being antiperiodic. The non(anti)commutative structures derived in this paper also leads to the closure of the super constraint algebra which is essential for the internal consistency of our analysis.     

Two-Body Scattering in(1+1) Dimensions by a Semi-relativistic Formalism and a Hulthén Interaction Potential

Scattering solutions of two-body Spinless Salpeter Equation(SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulth′en potential in one spatial dimension. Transmission and reflection coefficients are calculated and discussed.     

Evolutional Properties of Localized Excitations for Generalized Broer-Kaup System in （2＋1） Dimensions

Using a special Painleve-Baecklund transformation as well as the extended mapping approach and the linear superposition theorem, we obtain new families of variable separation solutions to the （2＋1）-dimensional generalized Broer-Kaup （GBK） system. Based on the derived exact solution, we reveal some novel evolutional behaviors of localized excitations, i.e. fission and fusion phenomena in the （2＋1）-dimensional GBK system.     

Form-preserving Transformations for the Time-dependent Schrödinger Equation in (n + 1) Dimensions

We define a form-preserving transformation (also called point canonical transformation) for the time-dependent Schrödinger equation (TDSE) in (n+1) dimensions. The form-preserving transformation is shown to be invertible and to preserve L ²-normalizability. We give a class of time-dependent TDSEs that can be mapped onto stationary Schrödinger equations by our form-preserving transformation. As an example, we generate a solvable, time-dependent potential of Coulombic ring-shaped type together with the corresponding exact solution of the TDSE in (3+1) dimensions. We further consider TDSEs with position-dependent (effective) masses and show that there is no form-preserving transformation between them and the conventional TDSEs, if the spatial dimension of the system is higher than one.     

Effects of Boundary Conditions and Relative Dimensions of a Solution System on Scaling Laws

A two-dimensional hydrodynamic model is employed to analyze the characteristics of crystal growth from solution with only the variation of the solution density caused by the temperature change taken into account. In that case all the characteristics of the solution system only depend on three numbers: the Rayleigh number Ra, the Prandtl number Pr and the Schemidt number Sc. In certain regions of the parameter (Ra, Pr and Sc) spaces, some scaling laws are generated: the scales of the temperature distribution index S_θ, the concentration distribution index S_ø (see text), the fluid velocity and the growth rate of crystal are given by power functions of Ra, Pr and Sc. The effects of the geometrical shape and the boundary condition of the solution system on the scaling laws are studied. When the ratio X of the height to the length of the solution system changes, the scaling laws are still valid and only the coefficients of power functions are changed, which are also power functions of A. The scaling laws are valid both under the isothermal temperature boundary condition and the adiabatic boundary condition at the surfaces of the top and the bottom sides of the solution system. The only difference is that the ratio of S_θ to Ra is greater for the latter than for the former. In certain ranges of Ra, there are no differences between the other power functions for the two cases.     

Modified Kadomtsev-Petviashvili Equation in (3+1) Dimensions:Multiple Front-Wave Solutions

A modified Kadomtsev-Petviashvili(mKP) equation in(3+1) dimensions is presented.We reveal multiple front-waves solutions for this higher-dimensional developed equation,and multiple singular front-wave solutions as well.The constraints on the coefficients of the spatial variables,that assure the existence of these multiple front-wave solutions are investigated.We also show that this equation fails the Pamlevi test,and we conclude that it is not integrable in the sense of possessing the Pain/eve property,although it gives multiple front-wave solutions.