Scaling Limits for the System of Semi-Relativistic Particles Coupled to a Scalar Bose Field

In this paper, the Hamiltonian for the system of semi-relativistic particles interacting with a scalar Bose field is investigated. A scaled total Hamiltonian of the system is defined and its scaling limit is considered. Then, a semi-relativistic Schrödinger operator with an effective potential is derived.     

Effective Mass of Radion via GW Mechanism with a Non-Minimally Coupled Bulk Scalar Field

In the Randall-Sundrum braneworld scenario via the Goldberger-Wise mechanism, the effective mass of 4D radion, where the bulk scalar field is coupled to 5D gravity, has been investigated in two different case of the self-coupling constants, infinite and finite cases. It is shown that in the finite case, the modulus parameter should be greater than the finite coupling constants.     

Cosmic Strings Coupled with a Massless Scalar Field

A scalar field generalization of Xanthopoulos's cylindrically symmetric solutions of the vacuum-Einstein equations is obtained. The obtained solution preserves the properties of the Xanthopoulos solution, which are regular on the axis, asymptotically flat, and free from the curvature singularities. The solution describes a stable, rotating cosmic string of infinite length interacting with gravitational and scalar waves.     

Ground State of a Quantum Particle Coupled to a Scalar Bose Field

We use methods from functional integration to prove the existence and uniqueness of the ground state of a confined quantum particle coupled to a scalar massless Bose field. For an external potential growing at infinity, the ground state exists under fairly general conditions while, for a decaying potential, an unphysical condition on the coupling strength is still needed.     

Constructing Phantom With a Nonminimally Coupled Complex Scalar Field

In view of the recent observation data indicating that the equation of state of the dark energy might be smaller than −1, this leads to introduction of phantom models featured by their negative kinetic energy to account for the regime of equation of state w < −1. In this paper, we discuss the possibility of using a nonminimally coupled complex scalar field as phantom to realize the equation-of-state parameter w < −1. The main equations which govern the evolution of the universe are obtained. The relations between the potential of the field and red-shift, namely, the reconstruction equations are derived. PACS 04.40.-b, 98.80.Cq, 98.80.Hw     

Exact Solutions for the Fluctuations in a Flat FRW Universe Coupled to a Scalar Field

Some exact solutions for the small-first-order perturbations of an FRW metric minimally coupled to a neutral massive scalar field are presented.     

Gravitational Frames and Scalar Field Dynamics

Scalar fields describe interesting phenomena such as Higgs bosons, dark matter and dark energy, and are found to be quite common in physical theories. These fields are susceptible to gravitational forces so that being massless is not enough to remain conformal invariant. They should also be connected directly to the scalar curvature. Because of this characteristics, we investigated the structure and interactions of scalar fields under the conformal transformations. We show how to reduce the quadratic quantum contributions in the single scalar field theory. In the multi-scalar field theories, we analyzed interactions in certain limits. We suggest a new method for stabilizing Higgs bosons.

     

Effective Field Theory for Few Particles in a Trap

In this contribution we show applications of effective field theory (EFT) to few-particle systems trapped in a harmonic oscillator potential. The principles of EFT allows to construct interactions among the particles in a systematic and improvable manner. We first consider systems of two-component fermions and show excellent agreements with the exact solution at unitarity (for the two- and three-body problem) and results obtained by other methods (in the four-body case). We then consider trapped systems of three nucleons and extract neutron–deuteron phase shifts, and show that the quartet scattering length is in good agreement with experimental data. We also show the collapse of the system in the J ^π  = 1/2⁺, T = 1/2 (triton) channel at Leading-Order when no three-nucleon force is included.     

Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field

We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantized electromagnetic field are described by minimal coupling, p→p−e A (x), where A(x) is the electromagnetic vector potential with an ultraviolet cutoff. If the interactions between the electrons and the quantized radiation field are turned off, the atom or molecule is assumed to have at least one bound state. We prove that, for sufficiently small values of the fine structure constant α, the interacting system has a ground state corresponding to the bottom of its energy spectrum. For an atom, we prove that its excited states above the ground state turn into metastable states whose life-times we estimate. Furthermore the energy spectrum is absolutely continuous, except, perhaps, in a small interval above the ground state energy and around the threshold energies of the atom or molecule. Received: 3 September 1998 / Accepted: 17 March 1999     

Dynamics of Solitons in Coupled System of Scalar Fields

The dynamics of interacting solitons of a system of two coupled nonlinear partial differential equations is studied numerically using a finite difference method in bi-dimensional spacetime. Stable, static topological solitons are obtained from an iterative-variational method, and used as initial solutions for the dynamical calculations. Some of the static solutions decay to stable solitons. Some subtle aspects of topological charges for the system under consideration are also discussed.     

The Causal Interpretation of Conformally Coupled Scalar Field Quantum Cosmology

We apply the causal interpretation of quantum mechanics to homogeneous and isotropic quantum cosmology, where the source of the gravitational field is a conformally coupled scalar field, and the maximally symmetric hypersurfaces have positive curvature. In order to simplify the system of coupled equations studied and study the quantum behavior near the singularity, we restricted ourselves to the cases where the scale factor is small. In this case, the general solution of the Wheeler–DeWitt equation is a discrete superposition of Hermitian polynomials multiplied by complex exponentials. Superpositions with up to two parcels are studied, and the phase diagrams of their corresponding Bohmian trajectories are analyzed in detail. Nonsingular periodic quantum solutions are found. We also find that singular quantum solutions present an inflationary era in the begining of the Universe. Numerical calculations indicates that these results remain valid for general superpositions.     

Radiative Energy Shifts of an Accelerated Multilevel Atom Coupled to the Derivative of a Scalar Field

We study the energy level shifts of an accelerated multilevel atom in dipole coupling to the derivative of a quantum massless scalar field and separately calculate the contributions of vacuum fluctuations and radiation reaction to the shifts. It is found that, in contrast to the case of a monopole-like interaction, both the vacuum fluctuations and radiation reaction contributions are changed by acceleration, and they all contain non-thermal correction terms. Our results suggest that the effect of acceleration on the energy shifts is dependent on the type of the interaction between the atom and the quantum field.     

Quasinormal Modes of a Coupled Scalar Field in the Acoustic Black Hole Spacetime

By using the third-order Wentzel-Kramers-Brillouin approximation and the monodromy methods, the quasnormal modes of a coupled scalar field in the canonical non-rotating acoustic black hole spacetime are investigated. It is shown that the coupling between the scalar field and background metric affects the quasinormal frequencies. At low overtones, both the real part and the magnitude of imaginary part increase with the couple factor ξ. For the larger ξ, both of them are almost linearly related to the couple factor. At high overtones, it is found that the frequency formula of the quasinormal modes is 2πω/κ = ln （ 1 ＋ 2 cos√9-24ξ/5 π） - i（2n ＋ 1）π, which means that 5 when ξ is larger, the real part is the linear function of ξ^1/2.     

Cosmological Dynamics of Scalar Field with Non-Minimal Kinetic Term

We investigate the dynamics of a scalar field in the framework of the scalar-tensor theory. A nontrivial behavior of the field in the vicinity of singular points of the kinetic term is observed. In particular, the singular points could serve as attractor for classical solutions.     

Saturated Multi-Photon-Absorption of a Nonmonochromatic Quantized Field

By extending a previously developed method [9] to the case of saturation, the interaction of a nonmonochromatic light beam with a saturable m-photon-absorber (m = 1, 2,…) is theoretically investigated for frequency widths of the incident light being small compared to the bandwidth of the absorber. It turns out that by averaging the exact Heisenberg equation of motion of the operator for the slowly varying field amplitude with respect to the atomic relaxation time and by taking the expectation value over the absorbing atomic system a reduced single-mode equation can be derived, which refers to a mode volume precisely defined in physical terms. The resulting reduced Heisenberg equation of motion for the radiation field is compared to the single-mode density matrix equation following from the method of SCULLY and LAMB . For ideal laser light and for chaotic light it is used to study the change of photon statistics in dependence on the degree of saturation and on the ratio of inhomogeneous and homogeneous linewidth.     

Exact Solutions of Dirac Equation on (1+1)-Dimensional Spacetime Coupled to a Static Scalar Field

We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.