Localized fields on scalar global defects

We investigate the localization of modes on the worldvolume of a p  -brane embedded in (p+d+1$p+d+1$)-dimensional spacetime. The p  -brane here is such that its profile is regarded as a scalar global defect and the localized modes are scalar modes that come from the fluctuations around such defect. The effective action on the brane is computed and the induced potentials are typically ?⁴${?}^4$-type potentials that are flatter for lower d-dimensions. We also make a connection of such scalar global defects with black p-branes in certain limits.     

D维Q变形谐振子模型

利用玻色产生、湮没算符建立了Ｄ维ｑ变形各向同性谐振子模型，ｑ变形各向同性谐振子的维数Ｄ是任意的，并且还得出了它的能谱公式。     

Quasinormal modes of D-dimensional de Sitter spacetime

We calculate the exact values of the quasinormal frequencies for an electromagnetic field and a gravitational perturbation moving in D-dimensional de Sitter spacetime (D ≥ 4). We also study the quasinormal modes of a real massive scalar field and compare our results with those of other references.     

Electromagnetic quasinormal modes of D-dimensional black holes II

By using the sixth order WKB approximation we calculate for an electromagnetic field propagating in D-dimensional Schwarzschild and Schwarzschild de Sitter (SdS) black holes its quasinormal (QN) frequencies for the fundamental mode and first overtones. We study the dependence of these QN frequencies on the value of the cosmological constant and the spacetime dimension. We also compare with the results for the gravitational perturbations propagating in the same background. Moreover we compute exactly the QN frequencies of the electromagnetic field propagating in D-dimensional massless topological black hole and for the charged D-dimensional Nariai spacetime we calculate exactly the QN frequencies of the coupled electromagnetic and gravitational perturbations.     

D-dimensional Smorodinsky-Winternitz potential: Coherent state approach

In this study, we construct the coherent states for a particle in the D-dimensional maximally superintegrable Smorodinsky-Winternitz potential. We, first, map the system into 2D harmonic oscillators, second, construct the coherent states of them by evaluating the transition amplitudes. Third, in the Cartesian and the hyperspherical coordinates, we find the coherent states and the stationary states of the original sytem by reduction.     

Electromagnetic quasinormal modes of D-dimensional black holes

Using the monodromy method we calculate the asymptotic quasinormal frequencies of an electromagnetic field moving in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes (D ≥ 4). For the D-dimensional Schwarzschild anti-de Sitter black hole we also compute these frequencies with a similar method. Moreover, we calculate the electromagnetic normal modes of the D-dimensional anti-de Sitter spacetime.     

D-dimensional massless particle with extended gauge invariance

We propose the model ofD-dimensional massless particle whose Lagrangian is given by theN-th extrinsic curvature of world-line. The system hasN+1 gauge degrees of freedom constitutingW-like algebra; the classical trajectories of the model are space-like curves which obey the conditionsk _N+a=k_N−a, k_2N =0,a=1, ...,N−1,N≤[(D−2)/2], while the firstN curvaturesk _i remain arbitrary. We show that the model admits consistent formulation on the anti-DeSitter space. The solutions of the system are the massless irreducible representations of Poincaré group withN nonzero helicities, which are equal to each other. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Entropy spectrum of the D-dimensional massless topological black hole

There are exact solutions to Einstein’s equations with negative cosmological constant that represent black holes whose event horizons are manifolds of negative curvature, the so-called topological black holes. Among these solutions there is one, the massless topological black hole, whose mass is equal to zero. Hod proposes that in the semiclassical limit the asymptotic quasinormal frequencies determine the entropy spectrum of the black holes. Taking into account this proposal, we calculate the entropy spectrum of the massless topological black hole and we compare with the results on the entropy spectra of other topological black holes.     

Complexity of D-dimensional hydrogenic systems in position and momentum spaces

The internal disorder of a D-dimensional hydrogenic system, which is strongly associated to the non-uniformity of the quantum-mechanical density of its physical states, is investigated by means of the shape complexity in the two reciprocal spaces. This quantity, which is the product of the disequilibrium or averaging density and the Shannon entropic power, is mathematically expressed for both ground and excited stationary states in terms of certain entropic functionals of Laguerre and Gegenbauer (or ultraspherical) polynomials. We emphasize the ground and circular states, where the complexity is explicitly calculated and discussed by means of the quantum numbers and dimensionality. Finally, the position and momentum shape complexities are numerically discussed for various physical states and dimensionalities, and the dimensional and Rydberg energy limits as well as their associated uncertainty products are explicitly given. As a byproduct, it is shown that the shape complexity of the system in a stationary state does not depend on the strength of the Coulomb potential involved.     

Stam's principle D-dimensional uncertainty-like relationships and some atomic properties

Several D-dimensional uncertainty-like relationships for N-body systems are obtained by means of the Fisher's information entropies in position and momentum spaces and the Stam's uncertainty principle. In addition, these relationships, the Fisher's entropies and the Stam's inequality are analysed numerically for all ground state neutral atoms from hydrogen (Z = 1) to lawrencium (Z = 103) using highly accurate Roothaan-Hartree-Fock wavefunctions.     

Fingerprints of quantal Wigner solid-like correlations in D-dimensional assemblies

After a brief summary of the mechanism of quantal Wigner electron crystallization, we emphasize experimental situations in three, two, and one dimensions in which fingerprints of Wigner solid-like correlations are in evidence. Special stress is placed on the way applied magnetic fields can aid Wigner localization, as first pointed out in relation to n-type InSb by Durkan et al. (1968). Semiconductor heterojunctions with a two-dimensional electron fluid in the presence of a transverse magnetic field are given some prominence in relation to melting of the Wigner solid and its connection with magnetic properties. It is also proposed that a Wigner “hole” solid may be induced by a magnetic field of 60 T in a specific high $T_{\mathrm{c}}$ cuprate and that the fulleride phase diagram may also contain Wigner solids.     

Dispersionless envelope lattice solitons on a D-dimensional nonlinear lattice

We show by using the real exponential approach that the d-dimensional discrete nonlinear Schrödinger equation has more general dispersionless envelope lattice soliton solutions than the known bright soliton and kink solutions. Depending on the values of the parameters, the new solutions can describe both bright and dark lattice solitons. Especially, we find novel “W”-like envelope lattice solitons.     

Exactly solvable models of conformal-invariant quantum field theory in D-dimensional space

The method for exact solution of a certain class of models of conformal quantum field theory in D-dimensional Euclidean space is proposed. The method allows one to derive closed differential equations for all the Green functions and also algebraic equations to scale dimensions of all field. A scalar field P of a scale dimension d_p = D − 2 is needed for nontrivial solutions to exist. At D ≠ 2 this field is converted to a constant that coincides with the central charge of two-dimensional theories. A new class of D = 2 models has been obtained, where the infinite-parametric symmetry is not manifest. The two-dimensional Wess-Zumino model is used to illustrate the method of solution.     

Existence conditions and spreading properties of extreme entropy D-dimensional distributions

The extremization of the information-theoretic measures (Fisher information, Shannon entropy, Tsallis entropy), which complementary describe the spreading of the physical states of natural systems, gives rise to fundamental equations of motion and/or conservation laws. At times, the associated extreme entropy distributions are known for some given constraints, usually moments or radial expectation values. In this work, first we give the existence conditions of the maxent probability distributions in a D-dimensional scenario where two moments (not necessarily of consecutive order) are known. Then we find general relations which involve four elements (the extremized entropy, the other two information-theoretic measures and the variance of the extremum density) in scenarios with different dimensionalities and moment constraints.     

Self consistent theory of fluctuations near D-dimensional superconducting phase transitions

Nonlinear fluctuation contributions in the vicinity of the transition temperature for D-dimensional superconductors (D = 0…3) are treated in self-consistent Hartree approximation to the Ginzburg-Landau free energy. The results concern specific heat, correlation length, and the effect of a magnetic field on the specific heat (for D = 2).