On the general structure of nonlinear equations integrable by the general linear spectral problem

Two beams of indistinguishable fermions from independent sources cannot produce an interference pattern that changes when the wavefunction of each single-fermion state for one beam is multiplied by — 1; they cannot produce interference the way photons from independent sources can. This means the changes in neutron interference caused by a magnetic field applied to one of the beams cannot be interpreted as equivalent to changes that could be made by rotating the source of one beam by 2π radians. If it is assumed that rotation by 2π radians cannot be observed, the argument made here becomes a simple proof that particles with half-integral spin cannot be bosons.     

On axially symmetric soliton solutions of the coupled scalar-vector-tensor equations in general relativity

The inverse scattering theory used by Belinsky and Zakharov to obtain soliton solutions of the of the Einstein equations is here applied to the case of a five-dimensional space and interpreted in the framework of the Jordan-Kaluza-Klein theory. For two solitons exact, stationary, axially symmetric and asymptotically flat solutions are obtained.     

Relativistic coupled cluster method

Relativistic coupled cluster method (CCM) is applied to compute the low lying excited and ion states of strontium and ytterbium atom. The resulting excitation and ionization energies are in excellent agreement with experimental data and with other correlated calculations. The nuclear magnetic dipole hyperfine constants (A) and electric quadrupole hyperfine constants (B) of excited states are also evaluated and are in accord with experiment. We further address the basis set dependency of the computed properties.     

Stochastic coupled cluster theory

We describe a stochastic coupled cluster theory which represents excitation amplitudes as discrete excitors in the space of excitation amplitudes. Reexpressing the coupled cluster (CC) equations as the dynamics of excitors in this space, we show that a simple set of rules suffices to evolve a distribution of excitors to sample the CC solution and correctly evaluate the CC energy. These rules are not truncation specific and this method can calculate CC solutions to an arbitrary level of truncation. We present results of calculation on the neon atom, and nitrogen and water molecules showing the ability to recover both truncated and full CC results.     

Quantum computing for the Lipkin model with unitary coupled cluster and structure learning ansatz

We report a benchmark calculation for the Lipkin model in nuclear physics with a variational quantum eigensolver in quantum computing. Special attention is paid to the unitary coupled cluster (UCC) ansatz and structure learning (SL) ansatz for the trial wave function. Calculations with both the UCC and SL ansatz can reproduce the ground-state energy well; however, it is found that the calculation with the SL ansatz performs better than that with the UCC ansatz, and the SL ansatz has even fewer quantum gates than the UCC ansatz.     

光-力耦合受激布里渊散射方程组

 采用位移形式表征各向同性介质的运动，从而对传统的SBS耦合波方程组进行改造，使之适用于多维的情况并体现光学理论和力学理论的耦合。采用有限差分方法数值求解了光学-力学耦合型后向SBS方程组，得到了瞬态的位移场、速度场和应力场。计算结果表明，当泵浦光光强为2.0×10 ¹⁵W/m ²时，SBS可激发厚度为1cm的K9玻璃样品的表面产生出0.1nm量级的位移和10m/s量级的速度，对应的应力幅度达到10MPa量级。     

Solution of the quantum coupled mode equations

From our quantum theory of multiwave mixing, we obtain coupled mode equations that treat the sideband fields quantum mechanically. This allows the inclusion of the effects of quantum noise on the sideband fields. We solve the quantum coupled mode equations for arbitrary atomic and pump/probe detunings, and illustrate our results for the generation of squeezed states of light using four-wave mixing.     

On the general structure of nonlinear evolution equations integrable by the two-dimensional matrix spectral problem

A generalization of the AKNS-technique to the two-dimensional arbitrary order matrix spectral problem is given. The general form of the integrable equations and their Bäcklund transformations in 1+2 dimensions are found. The reduction problem is discussed.     

Integrability of coupled KdV equations

The integrability of coupled KdV equations is examined. The simplified form of Hirota’s bilinear method is used to achieve this goal. Multiple-soliton solutions and multiple singular soliton solutions are formally derived for each coupled KdV equation. The resonance phenomenon of each model will be examined.     

Solutions of coupled KdV-type equations

We consider a family of coupled (Ito type) KdV equations in 1+1 dimensions and use Hlavatý's technique to obtain a class of explicit wave-type solutions.     

The structure of the space of solutions of Einstein’s equations coupled with scalar fields

Following the work of Arms, Fischer, Marsden and Moncrief, it is proved that the space of solutions of Einstein’s equations coupled with self-gravitating mass-less scalar fields has conical singularities at each spacetime possessing a compact Cauchy surface of constant mean curvature and a nontrivial set of simultaneous Killing fields, either all spacelike or including one (independent) timelike.     

Global solutions for the coupled maxwell-dirac equations

This letter is a result announcement. The evolution group of coupled Maxwell-Dirac equations is intertwined with the evolution group of the free equations by a time-independent mapping on a domain which contains more than the free electromagnetic field. As a consequence, there exist global solutions with a nonzero electron field.     

Multi-symplectic method for the coupled Schrodinger-KdV equations

In this paper, we present a multi-symplectic Hamiltonian formulation of the coupled Schrtidinger-KdV equations （CS＇KE） with periodic boundary conditions. Then we develop a novel multi-symplectic Fourier pseudospectral （MSFP） scheme for the CSKE. In numerical experiments, we compare the MSFP method with the Crank-Nicholson （CN） method. Our results show high accuracy, effectiveness, and good ability of conserving the invariants of the MSFP method.     

Cosmological solutions for the coupled Einstein-Yang-Mills-Higgs equations

The coupled system of Einstein-Yang-Mills-Higgs equations is solved numerically for a Robertson-Walker symmetric universe. The open universe must be excluded because, for this situation, the coupled system is unable to produce energy-momentum densityT in agreement with the Robertson-Walker symmetry. For the closed universe, inflation solutions do occur if an early re-collapse is avoided by suitable choice of the initial conditions. The energy exchange between the minimally coupled Higgs and Yang-Mills subsystems is very small so that the inflating power of the Higgs field cannot be disturbed by the presence of the Yang-Mills field. After the inflation phase the influence of the Yang-Mills field is completely negligible (cosmic no-hair theorem).     

利用耦合的Riccati方程组构造微分-差分方程精确解

通过引入耦合的Riccati方程组得到一个构造非线性微分-差分方程精确解的代数方法.作为实例,将该方法应用到了一般格子方程,相对论的Toda格子方程和(2+1)维Toda格子方程.借助符号计算软件Mathematica,获得了这些方程的扭结型孤波解和复数解.该方法也适合求解其他非线性微分-差分方程的精确解. 关键词： 耦合Riccati方程组 格子方程 相对论的Toda格子方程 (2+1)维Toda格子方程     

光-力耦合受激布里渊散射方程组

采用位移形式表征各向同性介质的运动,从而对传统的SBS耦合波方程组进行改造,使之适用于多维的情况并体现光学理论和力学理论的耦合。采用有限差分方法数值求解了光学-力学耦合型后向SBS方程组,得到了瞬态的位移场、速度场和应力场。计算结果表明,当泵浦光光强为2.0×1015W/m2时,SBS可激发厚度为1cm的K9玻璃样品的表面产生出0.1nm量级的位移和10m/s量级的速度,对应的应力幅度达到10MPa量级。     

Master equations for coupled systems

A formalism to cope with the problem of dynamically coupled systems is developed. A time-dependent projection operator of the type given by Willis-Picard and Grabert-Weidlich is used to derive a time-convolutionless master equation from the Liouville equation for the total composite system. A systematic perturbational expansion formula with respect to the interaction between systems is also given. Finally, the comparison with the usual non-Markoffian master equation is discussed.     

Analysis of the percolation cluster structure

An implementation of algorithms for constructing and analyzing the cluster structure for a square quadruply connected lattice in the uncorrelated percolation problem is considered. Subsets of the complete superior hull and the skeleton of a percolation cluster are singled out using a modification of the Hoshen—Kopelman relabeling algorithm and the Bellman principle of optimality. The critical nature of the percolation process is demonstrated using the method for statistical tests, and the behavior of mass dimension is analyzed for various subsets of a percolation cluster.     

Synchronized cluster formation in coupled laser networks

We experimentally investigate the phase dynamics of laser networks with homogenous time-delayed mutual coupling and establish the fundamental rules that govern their state of synchronization. We identified a specific substructure that imposes its synchronization state on the entire network and show that for any coupling configuration the network forms at most two synchronized clusters. Our results indicate that the synchronization state of the network is a nonlocal phenomenon and cannot be deduced by decomposing the network into smaller substructures, each with its individual synchronization state.     

Orthogonality properties of the coupled equations for rearrangement collisions

The orthogonality properties required for a rigorous formulation of the coupled equations method for reactions involving particle exchanges and rearrangements are presented without the explicit use of multichannel projection operators.