Spherical model of the Stark effect in external scalar and vector fields

The Bohr-Sommerfeld quantization rule and the Gamow formula for the width of quasistationary level are generalized by taking into account the relativistic effects, spin and Lorentz structure of interaction potentials. The relativistic quasi-classical theory of ionization of the Coulomb system (V_{Coul}=-\xi/r) by radial-constant long-range scalar (S_{l.r.}=(1-\lambda)(\sigma r+V_0)) and vector (V_{l.r.}=\lambda(\sigma r+V_0)) fields is constructed. In the limiting cases the approximated analytical expressions for the position E_r and width \Gamma of below-barrier resonances are obtained. The strong dependence of the width \Gamma of below-barrier resonances on both the bound level energy and the mixing constant \lambda is detected. The simple analytical formulae for asymptotic coefficients of the Dirac radial wave functions at zero and infinity are also obtained.Comment: 25 pages, 4 figures. Submitted to Int. J. Mod. Phys.

The quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the theory of heavy-light mesons

We construct a relativistic potential quark model of $D$, $D_s$, $B$, and $B_s$ mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy quark is considered a local source of the gluon field. The effective interquark interaction is described by a combination of the perturbative one-gluon exchange potential $V_{\mathrm{Coul}}(r)=-\xi/r$ and the long-range Lorentz-scalar and Lorentz-vector linear potentials $S_{\mathrm{l.r.}}(r)=(1-\lambda)(\sigma r+V_0)$ and $V_{\mathrm{l.r.}}(r)=\lambda(\sigma r+V_0)$, where $0\leqslant\lambda<1/2$. Within the quasiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of $D$, $D_s$, $B$, and $B_s$ mesons, which ensure a high accuracy of calculations even for states with the radial quantum number $n_r\sim 1$. We show that the fine structure of P-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters: the strong-coupling constant $\alpha_s$ and the coefficient $\lambda$ of mixing of the long-range scalar and vector potentials $S_{\mathrm{l.r.}}(r)$ and $V_{\mathrm{l.r.}}(r)$. The quasiclassical formulas for asymptotic coefficients of wave function at zero and infinity are obtained.Comment: 22 pages, 6 figure

Quasiclassical Approximation in the Non-Relativistic and Relativistic Problems of Tunneling Ionization of a Hydrogen-Like Atom in a Uniform Electric Field

A recurrent scheme for finding the quasiclassical solution of the onedimensional equation obtained after the separation of variables in the Schrödinger equation in parabolic coordinates is derived. The method of quasiclassical localized states is developed for the Dirac equation with an arbitrary axially symmetric potential of barrier type which does not allow complete separation of the variables. By means of the proposed quasiclassical methods the non-relativistic and relativistic wavefunctions for hydrogenlike (H-like) atoms in an external uniform electrostatic field of intensity F are constructed in the classically forbidden and allowed regions. The general analytical expressions of the leading term of the asymptotic behaviour (at small F) of the ionization rate of an H-like atom in the uniform electrostatic field are obtained for the non-relativistic and relativistic cases

Quasiclassical Approximation in the Non-Relativistic and Relativistic Problems of Tunneling Ionization of a Hydrogen-Like Atom in a Uniform Electric Field

A recurrent scheme for finding the quasiclassical solution of the onedimensional equation obtained after the separation of variables in the Schrödinger equation in parabolic coordinates is derived. The method of quasiclassical localized states is developed for the Dirac equation with an arbitrary axially symmetric potential of barrier type which does not allow complete separation of the variables. By means of the proposed quasiclassical methods the non-relativistic and relativistic wavefunctions for hydrogenlike (H-like) atoms in an external uniform electrostatic field of intensity F are constructed in the classically forbidden and allowed regions. The general analytical expressions of the leading term of the asymptotic behaviour (at small F) of the ionization rate of an H-like atom in the uniform electrostatic field are obtained for the non-relativistic and relativistic cases

Матричні елементи диполь-дипольної взаємодії між двома дворівневими атомами, розташованими на довільній відстані один від одного

Purpose. As a standard model for describing the processes of a resonant transmission of quantum information on arbitrary distances is the system of two identical two-level atoms, one of which is under radiation of the field of real photons. Such a system can serve as a basis for the construction of an element basis of quantum computers. The purpose of this paper is to study the different modes of dynamics of a system of two identical two-level atoms when they interacts with the field of real photons.Methods. In this paper, we propose a general approach to the description of the processes for the transfer of quantum information from one atom-qubit to another on the arbitrary interatomic distances, which includes two types of new physical effects: the attenuation of quantum states and the retardation of the dipole-dipole interaction.Results. The optical properties of a system of two identical two-level atoms in collective (symmetric Ψs and antisymmetric Ψa) Bell states at arbitrary interatomic distances are investigated. The closed analytical expressions for the shifts and widths of the considered collective states are considered, taking into account the retarded dipole-dipole interaction of atoms. In calculation of the radial matrix elements of the dipole-dipole interaction, the wave functions of the model Fues potential are used.Conclusions. A detailed study of the mechanisms of resonant transmission of the excitation energy at arbitrary distances between the two-element atoms has an important practical significance for the physical realization of the logical operator CNOT.Исследовано оптические свойства системы из двух одинаковых двухуровневых атомов в коллективных (симметричном Ψs и антисимметричного Ψa) белловских состояниях при произвольных межатомных расстояниях. Получены замкнутые аналитические выражения для сдвигов и ширин рассматриваемых коллективных состояний с учетом запизнюючеи диполь-дипольного взаимодействия атомов. При исчислении радиальных матричный элементов диполь-дипольного взаимодействия использованы волновые функции модельного потенциала Фьюса.Досліджено оптичні властивості системи з двох однакових дворівневих атомів у колективних (симетричному Ψs і антисиметричному Ψa) беллівських станах при довільних міжатомних відстанях. Отримано замкнуті аналітичні вирази для зсувів і ширин розглядуваних колективних станів з урахуванням запізнюючої диполь-дипольної взаємодії атомів. При обчисленні радіальних матричний елементів диполь-дипольної взаємодії використано хвильові функції модельного потенціалу Фьюса

Emergent quantum criticality, Fermi surfaces, and AdS2

Gravity solutions dual to d-dimensional field theories at finite charge density have a near-horizon region, which is AdS2×Rd-1. The scale invariance of the AdS2 region implies that at low energies the dual field theory exhibits emergent quantum critical behavior controlled by a (0+1)-dimensional conformal field theories (CFT). This interpretation sheds light on recently-discovered holographic descriptions of Fermi surfaces, allowing an analytic understanding of their low-energy excitations. For example, the scaling behavior near the Fermi surfaces is determined by conformal dimensions in the emergent IR CFT. In particular, when the operator is marginal in the IR CFT, the corresponding spectral function is precisely of the “marginal Fermi liquid” form, postulated to describe the optimally doped cuprates.National Science Foundation (U.S.) (Grant No. NSF PHY05-51164)United States. Dept. of Energy (cooperative research agreement DE-FG0205ER41360)United States. Dept. of Energy (Outstanding Junior Investigator Program in High Energy Physics