A Confined Hydrogen Atom in Higher Space Dimensions

We compute ground state energies for the N-dimensional hydrogen atom confined in an impenetrable spherical cavity. The obtained results show their dependence on the size of the cavity and the space dimension N. We also examine the value of the critical radius of the cavity in different dimensions. Furthermore, the number of bound states was found for a given radius S, in different space dimensions. .     

Control of dissipation of energy via reservoirs of coherent states

Dynamic profiles of various chemical reactivity indices like chemical potential, chemical hardness, electrophilicity, susceptibility, etc., within a confined environment during the interaction of atoms with strong oscillating time dependent magnetic fields have been studied. In the present study hydrogen and helium atoms in ground state (n = 1), as well as in excited state (n = 20) are considered. Time-dependent Schrödinger equations are solved for the ground and excited states of hydrogen atom and the Rydberg state of the helium atom while a generalized nonlinear Schrödinger equation is solved for the ground state of the helium atom. Dirichlet type boundary condition has been used to implement confinement to the systems. With an increase in the degree of confinement the system gets harder and hence becomes more stable. Keeping the confinement radius fixed, systems get more stabilized in strong field compared to weak field.     

Relaxation in systems with hierarchical organization: Analytical derivation of the relaxation and dispersion functions

We report a successful attempt to derive a closed-form expression for the relaxation function of a complex system by solving a set of coupled kinetic equations connecting the excitation/de-excitation rates to the number of particles (such as electrical charges, dipoles, etc.) in excited states. Our approach, originating from developments in dielectric and mechanical relaxation studies, allows the use of a unified treatment for a wide array of natural processes which often pose challenges to theoretical modeling. We use the notions that (i) a dipole represents any pair formed by a particle in an excited state (such as an energy level in optically excited molecules, or an electrode in dielectric spectroscopy) and its image in the ground state (or reference electrode), that (ii) coupling between such dipoles may be described as particle transfer from one excited state to another with lower energy, and that (iii) the relaxation function for such a system of dipoles is mathematically equivalent to the cumulative distribution function of particles, i.e., the total number of particles that are still in an excited state at a time t following excitation. Taken together, these ideas naturally lead to the identification of two types of relaxation – parallel and serial relaxation – and allow one to tackle systems with either geometrical or physical self-similarity within a unified mathematical scheme.     

Dirac spinor solitons or bags

Explicit solutions of a non-linear Dirac equation in the four-dimensional Minkowski space have been found. They are continuous eigenfunctions of spin $\text{1}\text{2}$, energy and parity, and are confined to the interior of a sphere of definite radius a, with no tails outside the sphere. They are called solitons in the paper though the name of spinor droplets or bags may be more appropriate. Because of the Lorentz covariance of the Dirac equations, arbitrarily moving solitons can be obtained from the rest system solutions by applying proper Lorentz transformations.     

Coherent quasimodes and supermodes in a planar microcavity

A homogeneous microcavity is excited in two tightly focused spatially separated spots with a few μm distance. The radius of the generated cavity modes exceeds the excited regions such that the quasimodes of both spots overlap in space. Coherent coupling of the two spots via stimulated emission is observed, exhibiting a slightly lowered lasing threshold. Furthermore, the emission from both spots is phase locked with a phase difference of either 0 or π$\pi$, depending on their separation. Correspondingly, the distribution of the electromagnetic field is symmetric or anti-symmetric, and the emission occurs parallel to the cavity normal or symmetrically at non-zero angles, respectively. This behaviour is understood to be determined by the spatial distribution of gain and absorption across the active cavity medium, which we confirm by numerical calculations.     

Spontaneous emission of broadened molecules on the surface of a microdroplet

The spontaneous emission of a broadened molecule on the surface of a microsphere is studied. Through detailed analysis, we show that only weak coupling between a broadened atom (molecule) and the electromagnetic fields exists in a spherical dielectric cavity whether the sphere is small or large. From these results, we find an explicit expression for the spontaneous emission decay rate for a broadened surfactant molecule on the surface of a microdroplet with radius a, in which only 1/a and 1/a² components are exhibited. Then we apply this expression to a real experiment and obtain a consistent result with the experiment.     

Three-dimensional Wigner molecules formed from an assembly of confined but Coulombically repelling electrons

We first consider N Coulombically interacting electrons confined within a sphere of radius R by an infinite potential barrier. Scaling properties of the Hamiltonian are first discussed, followed by the virial theorem. In the limit of large R and N, it is shown that the problem can be reduced to the solution of N point charges −|e| constrained to move on the surface of a sphere of radius R_W here defined as Wigner radius. Finally, the results of the above model are compared with those of harmonically confined electrons.     

Fast polariton relaxation in strongly coupled organic microcavities

We consider the regime of strong light-matter coupling in an organic microcavity, where large Rabi splitting can be achieved. As has been shown, the excitation spectrum of such a structure, besides coherent polaritonic states, contains a number of strongly spatially localized incoherent excited states. These states form the majority of the excited states of the microcavity and are supposed to play the decisive role in the relaxation dynamics of the excitations in the microcavity. We consider the non-radiative transition from an incoherent excited state into one of the coherent states of the lower polaritonic branch accompanied by emission of a high-energy intramolecular phonon. It is shown that this process may determine the lifetime of incoherent excited states in the microcavity. This observation may be important in the discussion of pump–probe experiments with short pulses. This process may also play an important role for the population of the lowest energy states in organic microcavities, and hence in the problem of condensation of cavity polaritons.     

Born-Oppenheimer breakdown effects and hyperfine structure in the rotational spectra of SbF and SbCl

Pure rotational spectra have been measured for the ground electronic states of SbF and SbCl. The molecules were prepared by laser ablation of Sb metal in the presence of SF₆ or Cl₂, respectively. Their spectra were measured with a cavity pulsed jet Fourier transform microwave spectrometer. Although both molecules have two unpaired electrons, they are subject to Hund’s coupling case (c), and have X₁0⁺ ground states. The spectra have been interpreted with the formalism of ¹Σ⁺ molecules. For both molecules spectra of several isotopomers have been measured in the ground and first excited vibrational states. Large hyperfine splittings attributable to both nuclear quadrupole coupling and nuclear spin-rotation coupling have been observed. A Dunham-type analysis has produced unusually large Born-Oppenheimer breakdown parameters, which are interpreted in terms of the electronic structures of the molecules.     

Properties of the absorption spectrum due to the Gamma;1+ → Γ4− transition

We present results for the absorption spectrum due to a localized Γ₁⁺ → Γ₄^? transition that take into account the properties of the linear electron- phonon (e-p) interactions transforming as Γ₁⁺, Γ₃⁺ and Γ₅⁺ in the excited electronic state, in the cases of strong and weak e-p interaction coupling. We show that in the strong e-p interaction coupling limit the asymmetric shape of the structured band is due to the commutation relations of the e-p interaction matrices. Moreover, in the weak coupling limit we present an expression for the spectrum line shape obtained by taking into account the time ordering of the e-p interaction matrices and the phonon propagators at all times. It is shown in the latter case that the densities of phonon states corresponding to the electronic excited state are different from those corresponding to the ground state, and the e-p coupling constants are redefined due to the Jahn-Teller interactions.     

Electron state density and electron diffusion coefficient in energy space in nonideal nonequilibrium plasmas

We suggest a model for a hydrogenic low-temperature nonequilibrium nonideal plasma that allows the kinetic parameters of the plasma to be calculated by the method of molecular dynamics by taking into account the interparticle interaction. The charges interact according to Coulomb’s law; for unlike charges, the interaction is assumed to be equal to a constant at a distance smaller than several Bohr radii. For a system of particles, we solve the classical equations of motion under periodic boundary conditions. The initial conditions are specified in such a way that the electrons have a positive total energy. We consider the temperatures 1-50 K and densities n = 10⁹?10¹⁰ cm^?3 produced in an experiment through laser cooling and resonant excitation. We calculate the electron state density as a function of the plasma coupling parameter and the electron diffusion coefficient in energy space for highly excited (Rydberg) electron states close to the boundary of the discrete and continuum spectra.     

Brunnian and Efimov N-Body States

The Efimov effect was originally formulated for three particles. The underlying principle of model independence is extended in this article in several directions. We present our definitions of the concepts of universality and scale independence. In this context we review briefly the scaling relations established for two- and three-body structures of nuclear halos. We emphasize the difference between the two extremes of weak binding named Efimov and Brunnian states. They arise respectively for two-body interactions at threshold of binding either two or N particles. We restrict the Hilbert space to include no more than two-body correlations, and discuss the derived excited N-body Efimov states both for zero- and finite-range two-body interactions. Then we investigate the relation between radius and binding energy extremely close to threshold of binding the Brunnian N-body system. Radii of both ground and first excited states for N?=?4, 5, 6 remain finite as the binding energy vanishes, and the distances between pairs of particles are substantially larger than the range of the two-body potential. The radii decrease with N and increase with excitation energy. The computed radii are larger for the complete than for the restricted Hilbert space. Model independence at the Brunnian threshold is strongly indicated.     

Spherically compressed helium atom described by perturbative and variational methods

We analyze the energy spectrum of the three lowest-lying S symmetry states for the spherically confined helium atom as a function of the box radius by using an approach based on a time independent perturbation theory and two variational methods. The first treatment depends on exact solutions for confined one-electron atoms, whereas in the latter two methods exponents and linear coefficients are variationally optimized via {s,t,u}-Hylleraas functions and Generalized {r₁,r₂,r₁₂}-Hylleraas basis sets that fulfill appropriate boundary conditions. Although it is found that throughout most of the box radii here analyzed the variational energies for the three states lie below those perturbatively obtained, an opposite trend occurs toward the weak and strong confinement regions for the singlet excited and triplet states, respectively.     

Application of Permanent Magnets for Particle Extraction from Cyclic Accelerators with Constant Orbit Radius

Closed orbits with almost constant radius in an induction synchrotron with a permanent magnetic field are formed using the method of particle reflection by fields of permanent magnets. In this study we consider the application of such permanent magnets for automatic particle extraction from cyclic accelerators with R = const, B = var. The problem of formation of orbits with almost constant radius in a cyclic accelerator with a permanent leading magnetic field was considered in [1]. In this study we consider the application of such permanent magnets for automatic particle extraction from cyclic accelerators with R = const, B = var.     

On a possible unification of gravitational and weak interactions

Within the framework of Cartan's generalization of Einstein's theory of gravitation one can achieve a unification of gravitational and weak interactions by appropriate choice of the parameter that couples spin and torsion. The proposed spin-torsion coupling has negligible cosmic effects except at stages of evolution when 10⁸¹ nucleons are confined to a sphere with a radius of about one astronomical unit. For a single nuclear particle the gravitational effects of mass and spin balance at a radius of about 1% of its Compton wavelength, thus stabilizing it against gravitational collapse.This essay received the fourth award from the Gravity Research Foundation for 1975 (Editor).     

A numerical comparison of three different approaches to the weak or intermediate coupling model for 2 particle — 1 hole states

The secular equation of the usual shell-model approach to 2 particle (p) — 1 hole (h) states is transcribed in such a way that it can be viewed as the simultaneous coupling of a hole to a (pp) vibrationand a particle to a particle-hole vibration. The resulting diagonalisation problem is built up by the subsolutions of the (ph) and (pp) TDA, i.e. no matrix elements of the bare two-body interaction enter the equations. We discuss the mathematical properties of the new equations and compare them to the usually applied formulation of the weak or intermediate coupling model. Finally we give a numerical study for the low-lying states of negative parity of O¹⁷.     

Beyond mean field approach to the beta decay of medium mass nuclei relevant for nuclear astrophysics

The Gamow-Teller strength distributions for the β decay of the ground state as well as the lowest excited states of the rp-process waiting point nuclei ⁶⁸Se and ⁷²Kr are obtained within the complex Excited Vampir variational approach using realistic effective interactions and a rather large model space. The shape mixing is consistently described for both the states in the even-even parent and the states in the odd-odd daugther nucleus. The influence of the shape mixing accounted by the different effective interactions used and comparison with the available data are presented. The possible influence of the decay of the lowest excited states of the parent nuclei in the astrophysical environment of X-ray bursts is discussed.Gamow-Teller strength distributions, β-decay half-lives, and β-delayed neutron emission probabilities for neutron-rich Zr nuclei are investigated for the first time within the complex Excited Vampir approach using a large model space. Comparison with available data and predictions relevant for the astrophysical r process are presented.     

Conformal symmetry of relativistic and nonrelativistic systems and AdS/CFT correspondence

The nonlinear realization of conformal so(2,d) symmetry for relativistic systems and the dynamical conformal so(2,1) symmetry of nonrelativistic systems are investigated in the context of AdS/CFT correspondence. We show that the massless particle in d-dimensional Minkowski space can be treated as the system confined to the border of the AdS_d+1 of infinite radius, while various nonrelativistic systems may be canonically related to a relativistic (massless, massive, or tachyon) particle on the AdS₂ × S^d−1. The list of nonrelativistic systems “unified” by such a correspondence comprises the conformal mechanics model, the planar charge-vortex and three-dimensional charge-monopole systems, the particle in a planar gravitational field of a point massive source, and the conformal model associated with the charged particle propagating near the horizon of the extreme Reissner-Nordström black hole.     

Spontaneous emission from cylindrical atomic cloud: Collective eigenstates and non-local effects

We consider collective emission of a single photon stored in a cloud of N two-level atoms (with energy ?ω) confined inside an infinite cylinder and discuss eigenstates of this system, their decay rates and collective frequency shifts. We found that states with wave number k_z ≥ ω/c do not decay and analogous to guiding modes in dielectric waveguides. Evolution of such states is qualitatively different in local (Markovian) and non-local regimes. We found that in the Markovian regime there is no photon emission. In contrast, non-local (memory) effects result in emission and reabsorption of the photon so that probability to find atoms excited oscillates with a collective Rabi frequency. Cross-over between local and non-local behavior can be observed by increasing radius of the cylinder or wave number k_z of the excited atomic state. Similar behavior can also be observed in slab geometry and tested in synchrotron experiments on collective excitation of solid-state samples by increasing thickness of the nuclear layer.     

Scalars coupled to fermions in 1+1 dimensions

Using a method introduced in an earlier paper, we study a Bose field coupled to a Fermi field in 1+1 space-time dimensions. We employ the standard Hamiltonian formalism in which one computes the eigenvalues and eigenvectors of the Hamiltonian matrix. The matrix elements are computed using states defined on a lattice in momentum space. The results are compared with known strong and weak coupling limits. Bound states and renormalization effects are studied. We find that the choice of bare masses which give specified physical masses can be non-unique once a critical couplingλ _μ has been exceeded.