三体系统中的Efimov态(英文)

通过求解Faddeev方程, 研究了量子三体系统中的Efimov效应。 改进了变分方法对于求解激发态的不足。 在不同的两体作用下得到了三体系统中的Efimov态。 讨论了在不同质量比的三体系统中出现Efimov态的条件。 并由三体计算的结果分析了具有两个价中子的核系统在两体存在束缚态时可能存在的Efimov效应。We studied the Efimov effect in a three body system by solving the Faddeev equations. Different models and interactions were considered. The occurrence of Efimov states was discussed. The possible Efimov state was clearly presented and its properties were investigated.     

Universality of the three-body parameter for Efimov states in ultracold cesium

We report on the observation of triatomic Efimov resonances in an ultracold gas of cesium atoms. Exploiting the wide tunability of interactions resulting from three broad Feshbach resonances in the same spin channel, we measure magnetic-field dependent three-body recombination loss. The positions of the loss resonances yield corresponding values for the three-body parameter, which in universal few-body physics is required to describe three-body phenomena and, in particular, to fix the spectrum of Efimov states. Our observations show a robust universal behavior with a three-body parameter that stays essentially constant.     

Scales, Universality and Finite-Range Correction in Three-body Systems

The scale invariance manifested by the weakly-bound Efimov states implies that all the Efimov spectrum can be merged in a single scaling function. By considering this scaling function, the ratio between two consecutive energy levels, ${E_3^{\rm (N+1)}}$ and ${E_3^{\rm (N)}}$ , can be obtained from a two-body low-energy observable (usually the scattering length a), given in units of the three-body energy level N. The zero-ranged scaling function is improved by incorporating finite range corrections in first order of r ₀/a (r ₀ is the potential effective range). The critical condition for three-identical bosons in s-wave, when the excited ${E_3^{\rm (N+1)}}$ state disappears in the 2 + 1 threshold, is given by ${\sqrt{E_2/E_3^{\rm (N)}} \approx 0.38+0.12 ({r_0}/{a})}$ .     

The Efimov effect in a four-body system

It is shown, using a Born-Oppenheimer model, that the four-body Efimov effect may occur in a system consisting of three identical heavy particles and one light particle, if the light-heavy interaction leads to a zeroenergy two-heavy-one-light bound state.     

The Efimov effect. Discrete spectrum asymptotics

We study a three-particle Schrödinger operatorH for which none of the two-particle subsystems has negative bound states and at least two of them have zero energy resonances. We prove that under this condition the numberN(z) of bound states ofH belowz<0 has the asymptotics asz-0, where the coefficient depends only on the ratio of masses of the particles.     

Many-body systems and the Efimov effect

We employ a Birman-Schwinger type analysis to derive estimates on the number of bound-states of certainN-body systems with threshold-energy =inf _ess(H) supposed to be zero. For many-body systems without any substructure we show that eigenvalues of the Schrödinger operatorH absorbed at =0 are in the point-spectrum ofH. Furthermore we characterize a multiparticle equivalent of the Efimov effect.     

The 4He Trimer as an Efimov System

We review the results obtained in the last four decades which demonstrate the Efimov nature of the ⁴He three-atomic system.     

Nonadiabatic corrections to the adiabatic Efimov potential

Abstact: The composition of forward-going projectile spectator matter in fixed-target Pb+Pb collisions at 158 A · GeV at the CERN SPS has been studied as a function of centrality. The data were measured with the NA49 veto calorimeter. We observe that forward-going spectator matter in central collisions consists of 9 neutrons, 7 protons, and half a deuteron on average. At large impact parameters most spectator nucleons are bound in fragments. The relative resolution of the average impact parameter derived from the measurement of spectator neutrons is roughly 19% in the range from zero to half maximum impact parameters. Received: 16 February 1998 / Revised version: 30 March 1998     

利用光子回声技术产生光的三体纠缠态的研究

量子纠缠是实现量子通信和量子计算的重要资源,其中多体纠缠更是构建量子网络实现全局量子计算的基础。本文主要研究如何利用经典的光子回声技术实现光量子态的三体纠缠。在自由空间中向掺杂稀土离子的固态离子系综中射入经典光场,当离子体系达到相位重构条件时即可获得三束存在纠缠的量子光场。基于本方案纠缠产生的技术特点,发现其在提高量子中继器的工作效率上有着潜在的应用价值。     

Efimov Trimers Near the Zero-crossing of a Feshbach Resonance

Near a Feshbach resonance, the two-body scattering length can assume any value. When it approaches zero, the next-order term given by the effective range is known to diverge. We consider the question of whether this divergence (and the vanishing of the scattering length) is accompanied by an anomalous solution of the three-boson Schrödinger equation similar to the one found at infinite scattering length by Efimov. Within a simple zero-range model, we find no such solutions, and conclude that higher-order terms do not support Efimov physics.     

Log-Periodic Oscillations in the Photo Response of Efimov Trimers

The photoassociation of Efimov trimer, composed of three identical bosons, is studied using the long wavelength approximation. It is shown that for identical particles the leading contribution comes from the r ² s-mode operator and from the quadrupole d-mode operator. Log-periodic oscillations are found in the photoassociation response function, both near the energy threshold for the leading s-wave reaction, and in the high frequency tail for all partial waves.     

The Universality Classes in the Parabolic Anderson Model

We discuss the long time behaviour of the parabolic Anderson model, the Cauchy problem for the heat equation with random potential on $\mathbb{Z}^{d}We discuss the long time behaviour of the parabolic Anderson model, the Cauchy problem for the heat equation with random potential on. We consider general i.i.d. potentials and show that exactly four qualitatively different types of intermittent behaviour can occur. These four universality classes depend on the upper tail of the potential distribution: (1) tails at ∞ that are thicker than the double-exponential tails, (2) double-exponential tails at ∞ studied by G?rtner and Molchanov, (3) a new class called almost bounded potentials, and (4) potentials bounded from above studied by Biskup and K?nig. The new class (3), which contains both unbounded and bounded potentials, is studied in both the annealed and the quenched setting. We show that intermittency occurs on unboundedly increasing islands whose diameter is slowly varying in time. The characteristic variational formulas describing the optimal profiles of the potential and of the solution are solved explicitly by parabolas, respectively, Gaussian densities. Our analysis of class (3) relies on two large deviation results for the local times of continuous-time simple random walk. One of these results is proved by Brydges and the first two authors in [BHK04], and is also used here to correct a proof in [BK01].     

Universality of the basic interactions

We propose the unification of weak, electromagnetic and strong interactions within a gauge theory based on the chiral group of elementary fermions (quarks and leptons). Several consequences, in particular one with respect to neutral currents in the weak interactions, are discussed.     

Correlated trapped bosons and the many-body Efimov effect

We study two-body correlations in systems of identical bosons. We use a Faddeev type of decomposition of the wave function where all pairs of particles are treated equally. At large scattering length appears a series of Efimov-like states, i.e., spatially extended, model-independent many-body bound states inside the trap. They may play a role in the decay of Bose-Einstein condensates.