Stability of Few-Body Systems and Quantum Monte-Carlo Methods

 Quantum Monte-Carlo methods are well suited to study the stability of few-body systems. Their capabilities are illustrated by studying the critical stability of the hydrogen molecular ion whose nuclei and electron interact through the Yukawa potential, and the stability of small helium clusters. Received September 21, 2001; accepted for publication November 8, 2001     

Scales and Universality in Few-Body Systems

The role of scales in the physics of large few-body systems is reviewed. They are evidenced by considering weakly-bound three and four particles, where point-like interactions are regularized and renormalized in a procedure characterized by the emergence of physical scales fixed by observables. The results obtained with renormalized zero-ranged two-body interactions are presented in the form of universal scaling plots, or correlations between observables, where we also consider results of several other model calculations, as well as experimental results obtained in nuclear physics and cold-atom laboratories. The universal correlations between few-body observables are useful to predict one in terms of another observable and we discuss applications in setting low energies properties of halo nuclei, molecular and cold atom systems.     

Representation Systems and Quantum Structures

Two important classes of quantum structures, namely orthomodular posets and orthomodular lattices, can be characterized in a classical context, using notions like partial information and points of view. Using the formalism of representation systems, we show that these quantum structures can be obtained by expressing conditions on the existence of particular points of view, of particular ways to observe a system. PACS: 02.70.Wz, 03.67.Lx.     

Relativistic Descriptions of Few-Body Systems

A brief review of relativistic effects in few-body systems, of theoretical approaches, recent developments and applications is given. Manifestations of relativistic effects in the binding energies, in the electromagnetic form factors and in three-body observables are demonstrated. The three-body forces of relativistic origin are also discussed.     

Hadronic Few-Body Systems in Chiral Dynamics

Hadronic composite states are introduced as few-body systems in hadron physics. The Λ(1405) resonance is a good example of the hadronic few-body systems. It has turned out that Λ(1405) can be described by hadronic dynamics in a modern technology, which incorporates coupled channel unitarity framework and chiral dynamics. The idea of the hadronic ${\bar KN}$ composite state of Λ(1405) is extended to kaonic few-body states. It is concluded that, due to the fact that K and N have similar interaction nature in s-wave ${\bar K}$ couplings, there are few-body quasibound states with kaons systematically just below the break-up thresholds, like ${\bar KNN, \,\bar KKN}$ and ${\bar KKK}$ , as well as Λ(1405) as a ${\bar KN}$ quasibound state and f ₀(980) and a ₀(980) as ${\bar KK}$ .     

Few-Body Systems Composed of Heavy Quarks

Within the past 10 years many new hadrons states were observed experimentally, some of which do not fit into the conventional quark model. This work is about the few-body systems composed of heavy quarks, including the charmonium-like states and some loosely bound states.     

Features in Distribution of Wavefunctions of Few-Body Systems

The bbody, 4-body and 5-body quantum mechanical systems with pairwise interactions having repulsive core and attractive tail and with completely symmetric permutation symmetry in the spatial wavefunctions are studied. The spatial distribution of the wavefunctions of the low-lying O⁺ states is investigated in detail. The features of the geometric structures and of the internal motions of each of these states are revealed. Certain modes of the internal motions are discovered.     

Quantum Discord in Nuclear Magnetic Resonance Systems at Room Temperature

We review the theoretical and the experimental researches aimed at quantifying or identifying quantum correlations in liquid-state nuclear magnetic resonance (NMR) systems at room temperature. We first overview, at the formal level, a method to determine the quantum discord and its classical counterpart in systems described by a deviation matrix. Next, we describe an experimental implementation of that method. Previous theoretical analysis of quantum discord decoherence had predicted the time dependence of the discord to change suddenly under the influence of phase noise. The experiment attests to the robustness of the effect, sufficient to confirm the theoretical prediction even under the additional influence of a thermal environment. Finally, we discuss an observable witness for the quantumness of correlations in two-qubit systems and its first NMR implementation. Should the nature, not the amount, of the correlation be under scrutiny, the witness offers the most attractive alternative.     

Universal Prohibited Zones in the Coordinate Space of Few-Body Systems

In some special zones of the high-dimensional coordinate space of few-body systems with identical particles, the operation of an element (or a product of elements) of the symmetry groups of the Hamiltonian on a quantum state might be equivalent to the operation of another element. Making use of the matrix representations of the groups, the equivalence of a pair of operations leads to a set of homogeneous linear equations imposed on the wave functions. When the matrix of these equations is non-degenerate, the wave functions will appear as nodal surfaces in these zones. In this case, these zones are prohibited. In this paper, tightly bound 4-boson systems with three types of interaction have been studied analytically and numerically. The existence of the universal prohibited zones has been revealed, and their decisive effect on the structures of the eigenstates is demonstrated.     

Relativistic Covariance of Light-Front Few-Body Systems in Hadron Physics

We study the light-front covariance of a vector-meson decay constant using a manifestly covariant fermion field theory model in (3 + 1) dimensions. The light-front zero-mode issues are analyzed in terms of polarization vectors and method of identifying the zero-mode operator and of obtaining the light-front covariant decay constant is discussed.     

Quantum Spinor Structures for Quantum Spaces

A general theory of quantum spinor structures on quantum spaces is presented within the formalism of quantum principal bundles. Quantum analogs of basic objects of the classical theory are constructed: Laplace and Dirac operators, quantum versions of Clifford and spinor bundles, a Hodge *-operator, integration operators. Quantum phenomena are discussed, including an example of the Dirac operator associated to a quantum Hopf fibration.     

Highlights and Prospects of Hyperspherical Approach in Few-Body Quantum-Mechanical Systems

The binding energy of excitonium negative ion for ground ¹S-state in bulk conductors: Ge, Si, CdSe and for green and yellow lines of Cu₂O in hyperspherical coordinate method are found. Angular and radial correlations between electrons are taken into account by the channel functions, which are the eigen-functions of operator on the surface of sphere in six-dimensional sphere. The calculation of energies have been done using the adiabatic and Born-Oppenheimer approximations. In Born-Oppenheimer approximation is enough to give a binding energy with only 1.2% error, in adiabatic approximation this error drops to 0.7 %.     

用光学-光学双共振光谱技术研究Cs蒸气中的共振交换碰撞

利用窄带半导体激光器泵浦所有具有相同z分量速度的基态Cs原子至激发态,研究了Cs(6P_3/2, v) +Cs(6S_1/2, v′)→Cs(6S_1/2, v) +Cs(6P_3/2, v′)的共振交换碰撞过程。与泵浦光反向平行的另一单模激光器激发6P_3/2至8S_1/2态,以检测6P_3/2态原子的速度分布,确定激发态原子的热能化效应。通过测量8S_1/2→6P_1/2荧光的尖峰强度与相应的多普勒背景的强度比,得到共振交换碰撞速率系数为k=9.62×10-7 cm3·s-1。证明了在纯碱金属蒸气中,由共振交换机制产生的热能化效应的大小比由速度改变碰撞引起的大3个数量级。     

Geometrical Tools for Quantum Euclidean Spaces

We apply one of the formalisms of noncommutative geometry to ℝ ^N _q , the quantum space covariant under the quantum group SO _q (N). Over ℝ ^N _q there are two SO _q (N)-covariant differential calculi. For each we find a frame, a metric and two torsion-free covariant derivatives which are metric compatible up to a conformal factor and which have a vanishing linear curvature. This generalizes results found in a previous article for the case of ℝ³ _q . As in the case N=3, one has to slightly enlarge the algebra ℝ ^N _q ; for N odd one needs only one new generator whereas for N even one needs two. As in the particular case N=3 there is a conformal ambiguity in the natural metrics on the differential calculi over ℝ ^N _q . While in our previous article the frame was found “by hand”, here we disclose the crucial role of the quantum group covariance and exploit it in the construction. As an intermediate step, we find a homomorphism from the cross product of ℝ ^N _q with U _q so(N) into ℝ ^N _q , an interesting result in itself. Received: 4 March 2000 / Accepted: 11 October 2000     

Form Factors of Few-Body Systems: Point Form Versus Front Form

We present a relativistic point-form approach for the calculation of electroweak form factors of few-body bound states that leads to results which resemble those obtained within the covariant light-front formalism of Carbonell et al. (Phys. Rep. 300:215–347, 1998). Our starting points are the physical processes in which such form factors are measured, i.e. electron scattering off the bound state, or the semileptonic weak decay of the bound state. These processes are treated by means of a coupled-channel framework for a Bakamjian–Thomas type mass operator. A current with the correct covariance properties is then derived from the pertinent leading-order electroweak scattering or decay amplitude. As it turns out, the electromagnetic current is affected by unphysical contributions which can be traced back to wrong cluster properties inherent in the Bakamjian–Thomas construction. These spurious contributions, however, can be separated uniquely, as in the covariant light-front approach. In this way we end up with form factors which agree with those obtained from the covariant light-front approach. As an example we will present results for electroweak form factors of heavy–light systems and discuss the heavy-quark limit which leads to the famous Isgur–Wise function.