Single Bound State Research Articles

Scaling anomaly in string defect background

We show that the classical scale symmetry of a particle moving in string defect background is broken due to inequivalent quantization of the classical system, which leads to scaling anomaly. The consequence of this anomaly is the formation of single bound state in the coupling constant interval γ∈(-1,1). The inequivalent quantization is characterized by a 1-parameter family of self-adjoint extension parameter ω.It has been conjectured that the formation of loosely bound state in string defect background may lead to the so called anomalous scattering cross section for the particles, which has been experimentally observed in molecular physics. A plausible laboratory test for the anomalous scattering could be devised in condensed matter system.

Schrödinger equation with delta potential in superspace

A superspace version of the Schrödinger equation with a delta potential is studied using Fourier analysis. An explicit expression for the energy of the single bound state is found as a function of the super-dimension M in case M is smaller than or equal to 1. In the case when there is one commuting and 2 n anti-commuting variables also the wave function is given explicitly.

Spin effects in one-dimensional systems

We review the progress in the study of the 0.7 structure, a many-body spin effect observedin GaAs quantum wires. Electrical and thermal measurements show that the 0.7 structureis characterized by a spontaneous spin splitting which causes the spin-up subband to staynear the electrochemical potential as the channel is populated. The 0.7 structure is not anisolated phenomenon but is the first in a series of effects that occur whenever opposite spinsubbands are degenerate in energy. Bias spectroscopy shows how the levels move withincreasing source–drain bias as the 0.7 structure evolves into a structure near0.85(2e2/h). Our measurements do not support a Kondo effect from a single bound state in thechannel as a possible explanation of the 0.7 structure.

Inequivalent Quantization in the Field of a Ferromagnetic Wire

We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann’s method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ∈ℝ(mod2π). There exists a single bound state for the coupling constant η 2∈[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η 2<0, which supports bound state making the problem re-normalizable.

Fully Quantum Rovibrational Calculation of the He(H2) Bound and Resonance States

In a recent paper [J. Chem. Phys. 2005, 122, 124318], a full-dimensional quantum method, designed to efficiently compute the rovibrational states of triatomic systems with long-range interactions, was applied to the benchmark Li-(H2) ion-molecule system. The method incorporates several key features in order to accurately represent the rovibrational Hamiltonian using only modestly sized basis sets: (1) exact analytical treatment of Coriolis coupling; (2) a single bend-angle basis for all rotational states; (3) phase space optimization of the vibrational basis; (4) G(4) symmetry adaptation of the rovibrational basis. In this paper, the same methodology is applied for the first time to a van der Waals complex system, He(H2). As in the Li-(H2) study, all of the rovibrational bound states, and a number of resonance states, are computed to very high accuracy (1/10,000 of a wavenumber or better). Three different isotopologues are considered, all of which are found to have a single bound state with a very low binding energy. Several extremely long-lived Feshbach resonances are also reported.

4D gravity localized in non Bbb Z2-symmetric thick branes

We present a comparative analysis of localization of 4D gravity on a non Z_2-symmetric scalar thick brane in both a 5-dimensional Riemannian space time and a pure geometric Weyl integrable manifold. This work was mainly motivated by the hypothesis which claims that Weyl geometries mimic quantum behaviour classically. We start by obtaining a classical 4-dimensional Poincare invariant thick brane solution which does not respect Z_2-symmetry along the (non-)compact extra dimension. The scalar energy density of our field configuration represents several series of thick branes with positive and negative energy densities centered at y_0. The only qualitative difference we have encountered when comparing both frames is that the scalar curvature of the Riemannian manifold turns out to be singular for the found solution, whereas its Weylian counterpart presents a regular behaviour. By studying the transverse traceless modes of the fluctuations of the classical backgrounds, we recast their equations into a Schroedinger's equation form with a volcano potential of finite bottom (in both frames). By solving the Schroedinger equation for the massless zero mode m^2=0 we obtain a single bound state which represents a stable 4-dimensional graviton in both frames. We also get a continuum gapless spectrum of KK states with positive m^2>0 that are suppressed at y_0, turning into continuum plane wave modes as "y" approaches spatial infinity. We show that for the considered solution to our setup, the potential is always bounded and cannot adopt the form of a well with infinite walls; thus, we do not get a discrete spectrum of KK states, and we conclude that the claim that Weylian structures mimic, classically, quantum behaviour does not constitute a generic feature of these geometric manifolds.

On the structure of the supplementary series of unitary, irreducible representations of the proper, orthochronous Lorentz group

Representations from the supplementary series of unitary, irreducible representations of the proper, orthochronous Lorentz group are classified according to the parameter z, 0&amp;lt;z&amp;lt;1. The representations with 0&amp;lt;z&amp;lt;1∕2 are qualitatively different from those with 1∕2&amp;lt;z&amp;lt;1. This is shown in the form of the following theorem: the Casimir operator of the little group of a spacelike vector has for 0&amp;lt;z&amp;lt;1∕2 a single bound state, i.e., a single normalizable eigenstate which disappears for 1∕2&amp;lt;z&amp;lt;1. To this end the scalar product for the supplementary series is explicitly calculated in both regions, 0&amp;lt;z&amp;lt;1∕2 and 1∕2&amp;lt;z&amp;lt;1 in a coordinate system provided by common eigenfunctions of the Casimir operator of the little group of a spacelike vector and the commuting generator of a parabolic rotation. The choice of this coordinate system allows to use the well established properties of the Kontorovich-Lebedev pair of integral transforms.

Distinctive features of the biological catch bond in the jump-ramp force regime predicted by the two-pathway model

The receptor-ligand unbinding in the biological catch bond is analyzed within a simple model that comprises a single bound state and two unbinding pathways. This model is investigated in detail for the jump-ramp force regime, where the pulling force quickly jumps to a finite value and then is ramped linearly with time. Two qualitative criteria are identified that distinguish the catch bond from the slip bond. First, the rupture force probability density of the catch-bond exhibits a maximum-minimum pair, which develops at finite forces. In contrast, the slip bond produces a maximum that first appears at zero force. Second, the catch bond can be identified over a wide range of ramp rates by high rupture probabilities at low forces relative to the probability at the maximum, in contrast to the slip bond, where the probability at the maximum always corresponds to the most likely rupture force. Both distinctive features of the catch bond are masked by large jump forces, indicating that the catch bond is best identified in experiments with moderate loading rates and small jump forces. The catch-bond lifetime in the constant force regime is related to the probability density in the jump-ramp regime, allowing one to determine the bond lifetime for a constant force by measuring the initial probability density in the jump-ramp experiments with different jump forces and a fixed ramp rate. The key analytic results are illustrated with the P -selectin/P-selectin glucoprotein ligand-1 bond.

Three-body problem for ultracold atoms in quasi-one-dimensional traps

We study the three-body problem for both fermionic and bosonic cold atom gases in a parabolic transverse trap of lengthscale $a_\perp$. For this quasi-one-dimensional (1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length $a$, and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths, $a_{ad}$ and $b_{ad}$. In the tightly bound `dimer limit', $a_\perp/a\to\infty$, we find $b_{ad}=0$, and $a_{ad}$ is linked to the 3D atom-dimer scattering length. In the weakly bound `BCS limit', $a_\perp/a\to-\infty$, a connection to the Bethe Ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is non-universal: $a_{ad}$ and $b_{ad}$ depend both on $a_\perp/a$ and on a parameter $R^*$ related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.

Slater sum for the one-dimensional sech2 potential in relation to the kinetic energy density

In earlier work on the one-dimensional sech2 potential energy [I. A. Howard and N.H. March, Int. J. Quantum Chem. 91, 119 (2003)] it has been shown that both electron density ρ(x) and kinetic energy t(x) are low-order polynomials in the potential V(x), for a small number of bound states. Here all attention is focused on the continuum states for the sech2 potential with a single bound state. The tool employed is the Slater sum, which satisfies a partial differential equation. This is first solved explicitly for the bound state, and then the solution is generalized to apply to the continuum. Again, considerable simplification is exhibited for this specific choice of potential. A brief discussion is included of a central sech2(r) potential.

Metastable States in Parametrically Excited Multimode Hamiltonian Systems

Consider a linear autonomous Hamiltonian system with m time periodic bound state solutions. In this paper we study their dynamics under time almost periodic perturbations which are small, localized and Hamiltonian. The analysis proceeds through a reduction of the original infinite dimensional dynamical system to the dynamics of two coupled subsystems: a dominant m-dimensional system of ordinary differential equations (normal form), governing the projections onto the bound states and an infinite dimensional dispersive wave equation. The present work generalizes previous work of the authors, where the case of a single bound state is considered. Here, the interaction picture is considerably more complicated and requires deeper analysis, due to a multiplicity of bound states and the very general nature of the perturbation's time dependence. Parametric forcing induces coupling of bound states to continuum radiation modes, of bound states directly to bound states, as well as coupling among bound states, which is mediated by continuum modes. Our analysis elucidates these interactions and we prove the metastability (long life time) and eventual decay of bound states for a large class of systems. The key hypotheses for the analysis are: appropriate local energy decay estimates for the unperturbed evolution operator, restricted to the continuous spectral part of the Hamiltonian, and a matrix Fermi Golden rule condition, which ensures coupling of bound states to continuum modes. Problems of the type considered arise in many areas of application including ionization physics, quantum molecular theory and the propagation of light in optical fibers in the presence of defects.

Formation of atomic tritium clusters and bose-einstein condensates.

We present an extensive study of the static and dynamic properties of systems of spin-polarized tritium atoms. In particular, we calculate the two-body |F,m(F)>=|0,0> s-wave scattering length and show that it can be manipulated via a Feshbach resonance at a field strength of about 870 G. Such a resonance might be exploited to make and control a Bose-Einstein condensate of tritium in the |0,0> state. It is further shown that the quartet tritium trimer is the only bound hydrogen isotope and that its single vibrational bound state is a Borromean state. The ground state properties of larger spin-polarized tritium clusters are also presented and compared with those of helium clusters.

Cold collisions between argon atoms and hydrogen molecules

by considering a complex square-well potential. We demonstrate that many of the important features of a numerically exact coupled-channel calculation may be qualitatively understood in terms of this simple model. W ith the aid of the complex scattering length, a kinetic model may be constructed for describing the relaxation of vibrationally or rotationally excited trapped molecules 2 . The relaxation may be due to direct collisional quenching or to the formation and decay of van der Waals complexes. When the end-over-end angular momentum of the complex is zero and the vibrational stretching quantum number is the lar gest possible integer that allows the complex to be bound, it is possible to use effective range theory to compute the lifetimes for predissociation 2,21 . The numerical tests that confirmed the reliability of the effective range theory were performed on He H 2 that supported only a single bound state. In the present work, we perform similar tests for Ar H 2 where several bound states exist. It was previously demonstrated 21 that predissociation of the most weakly bound state of a van der Waals complex is influenced by the same quasiresonant vibration-rotation energy transfer that is found in atom-diatom collisions 22 . It was also shown that the proximity of closed quasiresonant channel thresholds provides a strong influence on the lifetimes 21 . In the present work, we study the analytic structure of the threshold behavior obtained using both parametrizations of the Ar-H2 potential-ener gy surface and investigate whether quasiresonant dynamics has any influence on the more deeply bound states of the complex. The paper is organized as follows: in Sec. II, we describe a few qualitative features of the potential-energy surface that are important for our investigations. Section III provides a review of the standard close-coupling formalism that we used to obtain an extensive database of rovibrational rate coefficients and predissociation lifetimes for both of the parametrized surfaces. In Sec. IV, we demonstrate how a complex square-well potential may be used to provide a qualitative description of several of the key results that are found from the numerically exact coupled-channel calculations. These results are presented in Sec. V. Conclusions to our investigation are given in Sec. VI.

Quantum measurement of coherent tunneling between quantum dots

We describe the conditional and unconditional dynamics of two coupled quantum dots when one dot is subjected to a measurement of its occupation number by coupling it to a third readout dot via the Coulomb interaction. The readout dot is coupled to source and drain leads under weak bias, and a tunnel current flows through a single bound state when energetically allowed. The occupation of the quantum dot near the readout dot shifts the bound state of the readout dot from a low conducting state to a high conducting state. The measurement is made by continuously monitoring the tunnel current through the readout dot. We show that there is a difference between the time scale for the measurement-induced decoherence between the localized states of the dots, and the time scale on which the system becomes localized due to the measurement.

Mathematical analysis of the photoelectric effect

We study the photoelectric effect on the example of a simplifi ed model of an atom with a single bound state, coupled to the quantized electromagnetic field. For this model, we show that Einstein’s prediction for the ph otoelectric effect is qualitatively and quantitatively correct to leading order in the coupling parameter. More specifically, considering the ionization of the atom by an in cident photon cloud consisting of N photons, we prove that the total ionized charge is additive i n the N involved photons. Furthermore, if the photon cloud is approaching the atom from a large distance, the kinetic energy of the ejected electron is shown to be given by the difference of the photon energy of each single photon in the photon cloud and the ionization energy.

Renormalization of the inverse square potential

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element.

Laser-induced resonance states as dynamic suppressors of ionization in high-frequency short pulses

An adiabatic-Floquet formalism is used to study the suppression of ionization in short laser pulses. In the high-frequency limit the adiabatic equations involve only the pulse envelope where transitions are purely ramp effects. For a short-ranged potential having a single-bound state we show that ionization suppression is caused by the appearance of a laser-induced resonance state, which is coupled by the pulse ramp to the ground state and acts to trap ionizing flux.

Ionization and scattering for short-lived potentials

We consider perturbations of a model quantum system consisting of a single bound state and continuum radiation modes. In many problems involving the interaction of matter and radiation, one is interested in the effect of time-dependent perturbations. A time-dependent perturbation will couple the bound and continuum modes causing ‘radiative transitions’. Using techniques of time-dependent resonance theory, developed in earlier work on resonances in linear and nonlinear Hamiltonian dispersive systems, we develop the scattering theory of short-lived (\( (\mathcal{O}(t^{ - 1 - {\varepsilon }} ))\)(t−1−ε)) spatially localized perturbations. For weak pertubations, we compute (to second order) the ionization probability, the probability of transition from the bound state to the continuum states. These results can also be interpreted as a calculation, in the paraxial approximation, of the energy loss resulting from wave propagation in a waveguide in the presence of a localized defect.

Investigation of the binding of a positron to magnesium and zinc atoms

We present the results of an analysis of the scattering phase shifts for positrons scattered from magnesium and zinc atoms which indicate that both atoms can form a single bound state with a positron. An estimate of the binding energy is given in each case.

Photoionization by pulses with a modulated frequency

The dynamics of the bound-state populations and the photoelectron spectra are calculated for model atomic systems irradiated by a pulse with a harmonically modulated frequency. For a system including a single bound state a model is adopted, which takes into account the threshold behavior typical of negative ions and admits continuum-continuum transitions. For a model one-dimensional atom the results are obtained through a numerical integration of the Schr\odinger equation. The case of a resonant ionization is also considered. The modulation of the frequency results in changing the instantaneous rate of decay of the initial state, in inducing additional population oscillations for multilevel systems, and in additional peaks in the photoelectron spectra.