Crossing scenario for a nonlinear non-Hermitian two-level system

The diabolic crossing scenario of two-state quantum systems can be generalized to a non-Hermitian case as well as to a nonlinear one. In the non-Hermitian case two different crossing types appear, distinguished according to the crossing or anticrossing of real parts or imaginary parts of the eigenvalues. In the nonlinear case additional stationary states can emerge, leading to looped structures in the eigenvalues. Here we discuss the basic properties of the most general situation, the combined nonlinear and non-Hermitian system. It is shown that the eigenvalues and eigenstates can be achieved from the real roots of a quartic equation. The corresponding crossing scenario is quite intricate and can be understood as a hybrid of the ones for the nonlinear Hermitian and the linear non-Hermitian systems. In addition, the implications of combined nonlinearity and non-Hermiticity on the system dynamics is studied in terms of a generalized Landau—Zener probability.     

Suppression of an acoustic mode by an elastic mode of a liquid-filled spherical shell resonator

The purpose of this paper is to report on the suppression of an approximately radial (radially symmetric) acoustic mode by an elastic mode of a water-filled, spherical shell resonator. The resonator, which has a 1-in. wall thickness and a 9.5-in. outer diameter, was externally driven by a small transducer bolted to the external wall. Experiments showed that for the range of drive frequencies (19.7-20.6 kHz) and sound speeds in water (1520-1570 m/s) considered in this paper, a nonradial (radially nonsymmetric) mode was also excited, in addition to the radial mode. Furthermore, as the sound speed in the liquid was changed, the resonance frequency of the nonradial mode crossed with that of the radial one and the amplitude of the latter was greatly reduced near the crossing point. The crossing of the eigenfrequency curves of these two modes was also predicted theoretically. Further calculations demonstrated that while the radial mode is an acoustic one associated with the interior fluid, the nonradial mode is an elastic one associated with the shell. Thus, the suppression of the radial acoustic mode is apparently caused by the overlapping with the nonradial elastic mode near the crossing point.     

An Interacting Two-Fluid Scenario for Quintom Dark Energy

The Quintom dark energy is a proposal that explains the recent observations that mildly favor the equation of state of dark energy ω crossing -1 near the past. The Quintom model is often constructed by two scalar fields, where one is the quintessence feld and another is the phantom field. The cosmological implication of the coupling of the two fields of the dark energy is out of question worth investigating. However, the consideration of the coupling in the field scenario is somewhat complex thus we propose an interacting two-fluid Quintom scenario for simplicity. The interaction between the two components is parametrized by a constant 71 in this scenario. The cosmological implications of this parametrization are investigated in detail in this paper. Also, a diagnostic for this model is performed by using the statefinder pairs {s, r} and {q, r}.     

基于HIAF SRing的并束实验设计及研究

超重核的真空衰变对于验证量子电动力学至关重要,由于过去的固定靶实验中,核外电子干扰正负电子对的测量,国际上尚未观测到该现象。提出基于HIAF SRing的并束实验方案,通过238U92+在自由空间碰撞,排除了核外电子的影响。根据亮度理论,结合对交叉角度、Laslett频移和束束相互作用的分析,优化得到1.9×1024 cm-2s-1的峰值亮度,基本满足了实验需求。Vacuum decay phenomenon of superheavy nucleus is a problem of fundamental interest to verify quantum electrodynamics. As the shell electrons interfere the detection of electron-positron pairs in the fixed target experiments in the past, it's still not corroborated. A new merging experiment scheme is proposed in this paper. The interference of shell electrons is eliminated by collisions of 238U92+ in free space. According to the luminosity theory and the analyses of crossing angle, Laslett tune shift and beam-beam interaction, an optimized peak luminosity of 1.9×1024 cm -2·s -1 is achieved. It meets the requirements of merging experiment essentially.     

Late-time acceleration and phantom divide line crossing with?non-minimal coupling and Lorentz-invariance violation

We consider two alternative dark-energy models: a Lorentz-invariance preserving model with a non-minimally coupled scalar field and a Lorentz-invariance violating model with a minimally coupled scalar field. We study accelerated expansion and the dynamics of the equation of state parameter in these scenarios. While a minimally coupled scalar field does not have the capability to be a successful dark-energy candidate with line crossing of the cosmological constant, a non-minimally coupled scalar field in the presence of Lorentz invariance or a minimally coupled scalar field with Lorentz-invariance violation have this capability. In the latter case, accelerated expansion and phantom divide line crossing are the results of the interactive nature of this Lorentz-violating scenario.     

Band crossing in the particle-rotor model

The sharpness of the backbending associated with a two-band crossing is shown to be an oscillating function of the degree of shell filling in a particle-rotor model that includes an exact treatment of the two-body recoil term. Both the even-and the odd-nucleon cases are considered. A detailed comparison is made with the cranking model, and also the physical implications of the results are discussed.     

Modified Holographic Dark Energy and Phantom Behaviour of Randall-Sundrum Brane

In this work, we discuss the evolution of modified Holographic Dark Energy (HDE) derived from the UV/IR cutoff in the Randall-Sundrum II (RS-II) braneworld scenario. Choosing future event horizon as the IR cutoff, it is seen that the equation of state parameter for the modified HDE can cross the phantom crossing line ω=−1.     

Effect of Induced Transition on the Quantum Entanglement and Coherence in Two-Coupled Double Quantum Dot System

Studying quantum properties in solid-state systems is a significant avenue for research. In this scenario, double quantum dots appear as a versatile platform for technological breakthroughs in quantum computation and nanotechnology. This work inspects the thermal entanglement and quantum coherence in two-coupled DODs, where the system is exposed to an external stimulus that induces an electronic transition within each subsystem. The results show that the introduction of external stimulus induces a quantum level crossing that relies upon the Coulomb potential changing the degree of quantum entanglement and coherence of the system. Thus, the quantum properties of the system can be tuned by changing the transition frequency, leading to the enhancement of its quantum properties.     

Sharp Lower Bounds for the Dimension of the Global Attractor of the Sabra Shell Model of Turbulence

In this work we derive lower bounds for the Hausdorff and fractal dimensions of the global attractor of the Sabra shell model of turbulence in different regimes of parameters. We show that for a particular choice of the forcing term and for sufficiently small viscosity term ν, the Sabra shell model has a global attractor of large Hausdorff and fractal dimensions proportional to log  ν ⁻¹ for all values of the governing parameter ε, except for ε =1. The obtained lower bounds are sharp, matching the upper bounds for the dimension of the global attractor obtained in our previous work. Moreover, the complexity of the dynamics of the shell model increases as the viscosity ν tends to zero, and we describe a precise scenario of successive bifurcations for different parameters regimes. In the “three-dimensional” regime of parameters this scenario changes when the parameter ε becomes sufficiently close to 0 or to 1. We also show that in the “two-dimensional” regime of parameters, for a certain non-zero forcing term, the long-term dynamics of the model becomes trivial for every value of the viscosity. AMS Subject Classifications: 76F20, 76D05, 35Q30     

Quintom cosmology: Theoretical implications and observations

We review the paradigm of quintom cosmology. This scenario is motivated by the observational indications that the equation-of-state of dark energy across the cosmological constant boundary is mildly favored, although the data are still far from being conclusive. As a theoretical setup we introduce a no-go theorem existing in quintom cosmology, and based on it we discuss the conditions for the equation-of-state of dark energy realizing the quintom scenario. The simplest quintom model can be achieved by introducing two scalar fields with one being quintessence and the other phantom. Based on the double-field quintom model we perform a detailed analysis of dark energy perturbations and we discuss their effects on current observations. This type of scenario usually suffers from a manifest problem due to the existence of a ghost degree-of-freedom, and thus we review various alternative realizations of the quintom paradigm. The developments in particle physics and string theory provide potential clues indicating that a quintom scenario may be obtained from scalar systems with higher derivative terms, as well as from non-scalar systems. Additionally, we construct a quintom realization in the framework of braneworld cosmology, where the cosmic acceleration and the phantom divide crossing result from the combined effects of the field evolution on the brane and the competition between four- and five-dimensional gravity. Finally, we study the outsets and fates of a universe in quintom cosmology. In a scenario with null energy condition violation one may obtain a bouncing solution at early times and therefore avoid the Big Bang singularity. Furthermore, if this occurs periodically, we obtain a realization of an oscillating universe. Lastly, we comment on several open issues in quintom cosmology and their connection to future investigations.     

Theoretical investigation of the antimagnetic rotation in ~(104)Pd

The particle-number-conserving method based on the cranked shell model is used to investigate the antimagnetic rotation band in ~(104) Pd. The experimental moments of inertia and reduced B(E2) transition probabilities are reproduced well. The J~((2))/B(E2) ratios are also discussed. The occupation probability of each orbital close to the Fermi surface and the contribution of each major shell to the total angular momentum alignment as function of rotational frequency are analyzed. The backbending mechanism of the ground state band in ~(104) Pd is understood clearly and the configuration of the antimagnetic rotation after backbending is clarified. In addition, the crossing of a four quasiparticle state with this antimagnetic rotation band is also predicted. By examining the closing of the angular momenta of four proton holes towards the neutron angular momentum, the "two-shears-like" mechanism for this antimagnetic rotation is investigated and two stages of antimagnetic rotation in ~(104) Pd are clearly seen.     

Electronic structure of three-dimensional quantum dots

We study the electronic structure of three-dimensional quantum dots using the Hartree-Fock approximation. The confining potential of the electrons in the quantum dot is assumed to be spatially isotropic and harmonic. For up to 40 interacting electrons the ground-state energies and ground-state wavefunctions are calculated at various interaction strengths. The quadrupole moments and electron densities in the quantum dot are computed. Hund's rule is confirmed and a shell structure is identified via the addition energies and the quadrupole moments. While most of the shell structure can be understood on the basis of the unperturbed non-interacting problem, the interplay of an avoided crossing and the Coulomb interaction results in an unexpected closed shell for 19 electrons. Received 5 November 2001 / Received in final form 12 November 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: vorrath@physnet.uni-hamburg.de     

Effect of one-dimensional diffusion on void nucleation

Nucleation of voids via the stochastic accumulation of vacancies is considered when one-dimensionally migrating self-interstitials are present. A system instability signaling a non-equilibrium phase transition is found to occur when the mean free path of the one-dimensionally moving self-interstitials becomes comparable with the average distance between the voids at a sufficiently high void-number density. At this point, due to the exponential dependence of void nucleation probability on the net vacancy flux, the nucleation of voids is much more favored at the void lattice positions. At the same time, voids initially nucleated at positions where neighboring voids are non-aligned will shrink away. The shrinkage of non-aligned voids is caused entirely by the stochastic fluctuations in point-defect fluxes received by the voids. These two processes leave the aligned voids to form a regular lattice. The formation of the void lattice in this way can be accomplished at a void swelling of below 1%, in agreement with experimental observation. PACS 61.80.Az; 61.72.Cc; 05.65.+b     

High-spin states in neutron-rich Dy isotopes populated in deep-inelastic reactions

High-spin states in neutron-rich Dy isotopes, populated in deep-inelastic processes produced by the interaction of 234 MeV ³⁷Cl ions with a ¹⁶⁰Gd target, have been studied using the highly sensitive EUROBALL IV gamma-ray detector array. The previously known level schemes for ^{159,160,161,162}Dy have been extended to significantly higher spin ( ? 30?) and the i _13/2 band crossing in ¹⁵⁹Dy has been observed for the first time. The experimental results are discussed within the framework of cranked shell model and projected shell model calculations with particular reference to the observed delayed band crossing in ¹⁶²Dy. Received: 20 October 2000 / Accepted: 16 January 2001     

Exact solutions for shells collapsing towards a pre-existing black hole

The gravitational collapse of a star is an important issue both for general relativity and astrophysics, which is related to the well-known “frozen star” paradox. This paradox has been discussed intensively and seems to have been solved in the comoving-like coordinates. However, to a real astrophysical observer within a finite time, this problem should be discussed in the point of view of the distant rest-observer, which is the main purpose of this Letter. Following the seminal work of Oppenheimer and Snyder (1939), we present the exact solution for one or two dust shells collapsing towards a pre-existing black hole. We find that the metric of the inner region of the shell is time-dependent and the clock inside the shell becomes slower as the shell collapses towards the pre-existing black hole. This means the inner region of the shell is influenced by the property of the shell, which is contrary to the result in Newtonian theory. It does not contradict the Birkhoff's theorem, since in our case we cannot arbitrarily select the clock inside the shell in order to ensure the continuity of the metric. This result in principle may be tested experimentally if a beam of light travels across the shell, which will take a longer time than without the shell. It can be considered as the generalized Shapiro effect, because this effect is due to the mass outside, but not inside as the case of the standard Shapiro effect. We also found that in real astrophysical settings matter can indeed cross a black hole's horizon according to the clock of an external observer and will not accumulate around the event horizon of a black hole, i.e., no “frozen star” is formed for an external observer as matter falls towards a black hole. Therefore, we predict that only gravitational wave radiation can be produced in the final stage of the merging process of two coalescing black holes. Our results also indicate that for the clock of an external observer, matter, after crossing the event horizon, will never arrive at the “singularity” (i.e. the exact center of the black hole), i.e., for all black holes with finite lifetimes their masses are distributed within their event horizons, rather than concentrated at their centers. We also present a worked-out example of the Hawking's area theorem.     

“Teleparallel” dark energy

Using the “teleparallel” equivalent of General Relativity as the gravitational sector, which is based on torsion instead of curvature, we add a canonical scalar field, allowing for a nonminimal coupling with gravity. Although the minimal case is completely equivalent to standard quintessence, the nonminimal scenario has a richer structure, exhibiting quintessence-like or phantom-like behavior, or experiencing the phantom-divide crossing. The richer structure is manifested in the absence of a conformal transformation to an equivalent minimally-coupled model.     

Hf高自族态推转壳模型PNC方法研究

用推转壳模型ＰＮＣ方法研究了１６６Ｈｆ９４－１７０Ｈｆ９８核，计算了这三个核晕带和次晕带间的带交叉频率、带间互作用强度、顺排角动量和转动惯量等，并与实验值作了比较，结果表明在Ｎｉｌｓｓｏｎ势参数完全按照Ｌｕｎｄ系统学选取的情况下，理论计算值与实验值符合得较好．     

Merging of single-particle levels in finite Fermi systems

Properties of the distribution of single-particle levels adjacent to the Fermi surface in finite Fermi systems are studied, focusing on the case in which these levels are degenerate. The interaction of the quasiparticles occupying these levels lifts the degeneracy and affects the distance between the closest levels on opposite sides of the Fermi surface, as the number of particles in the system is varied. In addition to the familiar scenario of level crossing, a new phenomenon is uncovered, in which the merging of single-particle levels results in the disappearance of well-defined single-particle excitations. Implications of this finding are discussed for nuclear, solid-state, and atomic systems. The text was submitted by the authors in English.     

Novel defect structures in nematic liquid crystal shells

We use double-emulsion drops to experimentally investigate the defect structures of spherical shells of nematic liquid crystals. We uncover a rich scenario of coexisting defect structures dictated by the unavoidable finite thickness of even the thinnest shell and by the thickness variation around the sphere. These structures are characterized by a varying number of disclination lines and pairs of surface point defects on the inner and outer surfaces of the nematic shell. In the limit of very thick shells the defect structure ultimately merges with that of a bulk nematic liquid crystal drop.