Collective dynamics of multicellular systems

We have studied the collective behaviour of a one-dimensional ring of cells for conditions when the individual uncoupled cells show stable, bistable and oscillatory dynamics. We show that the global dynamics of this model multicellular system depends on the system size, coupling strength and the intrinsic dynamics of the cells. The intrinsic variability in dynamics of the constituent cells are suppressed to stable dynamics, or modified to intermittency under different conditions. This simple model study reveals that cell–cell communication, system size and intrinsic cellular dynamics can lead to evolution of collective dynamics in structured multicellular biological systems that is significantly different from its constituent single-cell behaviour.     

Modeling of intercellular synchronization in the Drosophila circadian clock

In circadian rhythm generation,intercellular signaling factors are shown to play a crucial role in both sustaining intrinsic cellular rhythmicity and acquiring collective behaviours across a population of circadian neurons.However,the physical mechanism behind their role remains to be fully understood.In this paper,we propose an indirectly coupled multicellular model for the synchronization of Drosophila circadian oscillators combining both intracellular and intercellular dynamics.By simulating different experimental conditions,we find that such an indirect coupling way can synchronize both heterogeneous self-sustained circadian neurons and heterogeneous mutational damped circadian neurons.Moreover,they can also be entrained to ambient light-dark(LD) cycles depending on intercellular signaling.     

4f-electron-phonon interaction and collective 4f-excitations in PrF3

The results of Ramanspectroscopic and Fourier transform FIR spectroscopic investigations of PrF₃ are presented. Some doubly degenerate optical phonons show magnetic-field dependent splitting and anomalous temperature dependent energy renormalisation. The excitations of the 4f-system can not be treated in the single-ion approximation because Davydow splittings and collective magnetic moments are observed. It is proved that all these effects result from a simple Jahn-Teller type coupling of the 4f- and the phonon system. The excitation energies of the coupled system are determined by a Greensfunction treatment of the problem.This work was supported by the Deutsche Forschungsgemeinschaft     

Quantum leakage of collective excitations of atomic ensemble induced by spatial motion

We generalize the conception of quantum leakage for the atomic collective excitation states. By making use of the atomic coherence state approach, we study the influence of the atomic spatial motion on the symmetric collective states of 2-level atomic ensemble due to inhomogeneous coupling. In the macroscopic limit, we analyze the quantum decoherence of the collective atomic state by calculating the quantum leakage for a very large ensemble at a finite temperature. Our investigations show that the fidelity of the atomic system will not be good in the case of atom numberN→∞. Therefore, quantum leakage is an inevitable problem in using the atomic ensemble as a quantum information memory. The detailed calculations shed theoretical light on quantum processing using atomic ensemble collective qubit.     

Synchronization in multicell systems exhibiting dynamic plasticity

Collective behaviour in multicell systems arises from exchange of chemicals/ signals between cells and may be different from their intrinsic behaviour. These chemicals are products of regulated networks of biochemical pathways that underlie cellular functions, and can exhibit a variety of dynamics arising from the non-linearity of the reaction processes. We have addressed the emergent synchronization properties of a ring of cells, diffusively coupled by the end product of an intracellular model biochemical pathway exhibiting non-robust birhythmic behaviour. The aim is to examine the role of intercellular interaction in stabilizing the non-robust dynamics in the emergent collective behaviour in the ring of cells. We show that, irrespective of the inherent frequencies of individual cells, depending on the coupling strength, the collective behaviour does synchronize to only one type of oscillations above a threshold number of cells. Using two perturbation analyses, we also show that this emergent synchronized dynamical state is fairly robust under external perturbations. Thus, the inherent plasticity in the oscillatory phenotypes in these model cells may get suppressed to exhibit collective dynamics of a single type in a multicell system, but environmental influences can sometimes expose this underlying plasticity in its collective dynamics.      

梯度耦合下神经元网络中靶波和螺旋波的诱发研究

神经系统内数量众多的神经元电活动的群体行为呈现一定的节律性和自组织性. 当网络局部区域存在异质性或者受到持续周期性刺激, 则在网络内诱发靶波, 且这些靶波如'节拍器'可调制介质中行波的诱发和传播. 基于Hindmarsh-Rose 神经元模型构造了最近邻连接下的二维神经元网络, 研究在非均匀耦合下神经元网络内有序波的诱发问题. 在研究中, 选定网络中心区域的耦合强度最大, 从中心向边界的神经元之间的耦合强度则按照阶梯式下降. 研究结果表明, 在恰当的耦合梯度下, 神经元网络内诱发的靶波或螺旋波可以占据整个网络, 并有效调制神经元网络的群体电活动, 使得整个网络呈现有序性. 特别地, 当初始值为随机值时, 梯度耦合也可以诱发稳定的有序态. 这种梯度耦合对网络群体行为调制的研究结果有助于理解神经元网络的自组织行为.     

Stability of incoherence in a population of coupled oscillators

We analyze a mean-field model of coupled oscillators with randomly distributed frequencies. This system is known to exhibit a transition to collective oscillations: for small coupling, the system is incoherent, with all the oscillators running at their natural frequencies, but when the coupling exceeds a certain threshold, the system spontaneously synchronizes. We obtain the first rigorous stability results for this model by linearizing the Fokker-Planck equation about the incoherent state. An unexpected result is that the system has pathological stability properties: the incoherent state is unstable above threshold, butneutrally stable below threshold. We also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise.     

Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case

We theoretically investigate the collective phase synchronization between interacting groups of globally coupled noisy identical phase oscillators exhibiting macroscopic rhythms. Using the phase reduction method, we derive coupled collective phase equations describing the macroscopic rhythms of the groups from microscopic Langevin phase equations of the individual oscillators via nonlinear Fokker-Planck equations. For sinusoidal microscopic coupling, we determine the type of the collective phase coupling function, i.e., whether the groups exhibit in-phase or antiphase synchronization. We show that the macroscopic rhythms can exhibit effective antiphase synchronization even if the microscopic phase coupling between the groups is in-phase, and vice versa. Moreover, near the onset of collective oscillations, we analytically obtain the collective phase coupling function using center-manifold and phase reductions of the nonlinear Fokker-Planck equations.     

Random global coupling induces synchronization and nontrivial collective behavior in networks of chaotic maps

The phenomena of synchronization and nontrivial collective behavior are studied in a model of coupled chaotic maps with random global coupling. The mean field of the system is coupled to a fraction of elements randomly chosen at any given time. It is shown that the reinjection of the mean field to a fraction of randomly selected elements can induce synchronization and nontrivial collective behavior in the system. The regions where these collective states emerge on the space of parameters of the system are calculated.     

一个全局耦合不连续映像格子中的冻结化随机图案模式

本文研究了一类既不连续又不可逆分段线性映像构成的全局耦合映像格子系统中的一类典型集体动力学行为, 即冻结化随机图案模式. 计算了平均同步序参量和最大李雅普诺夫指数随耦合强度的变化. 结果显示, 当耦合强度超过某个阈值后, 在给定动力学变量的初始下, 系统几乎都能达到完全或部分同步状态, 出现冻结化随机图案. 这些现象表明, 耦合映像格子系统中存在着多个共存的吸引子. 因此, 其冻结化图案的结构和分布敏感地依赖于格点动力学变量初始值的选取. 感兴趣地是, 即使当单映像处于混沌状态时, 格点间的耦合仍能将系统调制到规则的运动状态, 这种特征对于混沌控制具有重要的利用价值. 上述丰富动力学行为的出现是由于单映像中不连续性和不可逆性相互作用的结果.     

Odd-odd nuclei as the core-particle-hole systems and chirality

Odd-odd nuclei treated as core-particle-hole systems with various collective cores and various particle-hole configurations are investigated within the Core-Particle-Hole Coupling (CPHC) model. A new symmetry, called the S-symmetry, is identified as a combination of the α-parity of the collective core and the proton-neutron symmetry of the valence proton and neutron in particle-hole configurations involving single-particle states with the same quantum numbers. It is found that the S-symmetric odd-odd nuclei show signatures which are usually considered as fingerprints of nuclear chirality, namely doublet band structure with a particular pattern of electromagnetic transitions. Reported results imply that the rigid rotor with a symmetric valence proton-neutron configuration is only a special case of the system with the novel S-symmetry. Therefore, it is an open question whether the chiral fingerprints discussed so far identify uniquely the orthogonal coupling of angular momentum in the intrinsic system.     

Dislocation Coupling-Induced Transition of Synchronization in Two-Layer Neuronal Networks

The mutual coupling between neurons in a realistic neuronal system is much complex, and a two-layer neuronal network is designed to investigate the transition of electric activities of neurons. The Hindmarsh-Rose neuron model is used to describe the local dynamics of each neuron, and neurons in the two-layer networks are coupled in dislocated type. The coupling intensity between two-layer networks, and the coupling ratio (Pro), which defines the percentage involved in the coupling in each layer, are changed to observe the synchronization transition of collective behaviors in the two-layer networks. It is found that the two-layer networks of neurons becomes synchronized with increasing the coupling intensity and coupling ratio (Pro) beyond certain thresholds. An ordered wave in the first layer is useful to wake up the rest state in the second layer, or suppress the spatiotemporal state in the second layer under coupling by generating target wave or spiral waves. And the scheme of dislocation coupling can be used to suppress spatiotemporal chaos and excite quiescent neurons.     

On the relation between the interacting boson model of Arima and Iachello and the collective model of Bohr and Mottelson. II

The generator coordinate method is used to relate the interacting boson model of Arima and lachello and the collective model of Bohr and Mottelson through an isometric transformation. It associates complex parameters to the original boson operators whereas the ultimate collective variables are real. The absolute squares of the collective wave functions can be given a direct probability interpretation. The lowest order Bohr-Mottelson hamiltonian is obtained in the harmonic approximation to the interacting boson model; unharmonic coupling terms render the collective potential to be velocity dependent. The mapping of operators of the interacting boson model onto those of the Bohr-Mottelson model turns out to be of Holstein-Primakoff type.     

Environment induced entanglement in cavity-QED

The effects of dissipative dynamics on the magnitude of entanglement generated In atom-photon interactions inside cavities is studied. We present some concrete examples of environment Induced entanglement in alom-photon interactions. We consider various dissipative atom-cavity systems and show that their collective dynamics can be used to maximize entanglement for intermediate values of the cavity leakage parameter κ. We first consider the interaction of a single two-level atom with one of two coupled microwave cavities and show analytically that the atom-cavity entanglement increases with cavity leakage. We next consider a system of two atoms passing successively through a cavity and derive the expression for the maximum value of in terms of the Rabi angle gt, for which the two-atom entanglement can be Increased. Finally, numerical investigation of micromaser dynamics also reveals the increase of two-atom entanglement with stronger cavity-environment coupling for experimentally attainable values of the micromaser parameters.     

Level density and collective enhancement factor of a compound nucleus in non-adiabatic approach

In this paper a simple statistical formalism that takes into account the diabatic motion of a compound system to calculate total level density is given. The diabatic motion is introduced by coupling the adiabatic collective motion to an environment consisting of intrinsic degrees of freedom. The collective enhancement of level density is studied. It has anadiabatical coefficient that depends only on the excitation energy and adynamical one that depends on the excitation energy and the coupling between intrinsic and collective modes. Qualitatively, the coefficients of the vibrational enhancement factor forA=240 have been studied. The coupling is understood as the initial effect of the oscillatory motion of the mass asymmetry of fragments on the nucleonic motion. The damping effect of the vibrational motion is taken into account considering the collective motion of the fragments as a zero-sound wave propagating in the Fermiliquid. The intrinsic state in the framework of the Fermi Gas Model (FGM) is described. The Pashkevich’s parametrization is used to describe the binary decay of the compound nucleus.     

Dicke Quantum Phase Transition for a Bose-Einstein Condensate in a Two-Mode Optical Cavity

In this paper we mainly discuss the ground state properties of the two-mode Dicke model, which is realized in an ensemble of two-level atoms interacting simultaneously with two quantized cavity fields. We reveal rich phase diagrams and discover the second-order quantum phase transition from the normal phase to the superradiant phase by means of the spin-coherent-state variational method. While the critical phase transition point can be shifted by the detuning of the cavity mode or the atom-field coupling imbalance parameter. The collective atom-field coupling imbalance parameter can make the phase transition point symmetrically shift left or right in the resonance or non-resonance. If the two collective atom-photon coupling strengths are not equal in the resonance, the system may be in different phases, while the phases occupied are completely symmetrical. When one of the coupling constants vanishes or two couplings are equal, the ground-states’s properties and related QPT reduce to that of a standard or an ordinary Dicke model.

     

Microscopic theory of particle-vibration coupling

A microscopic theory of the coupling between collective vibrations and independent-particle excitations is developed, in which generator coordinates are used in order to describe the collective modes. Formulae for the coupling are derived and compared with the standard theory. The method applies to any Hamiltonian with two-body interactions that has a stable Hartree-Fock solution. It is found that the strength of some of the coupling terms depends on energy, and that second-order coupling, which does not figure in the standard treatment, can be important.     

Collective states of odd nuclei in a model with quadrupole-octupole degrees of freedom

We apply the collective axial quadrupole—octupole Hamiltonian to describe the rotation—vibration motion of odd nuclei with Coriolis coupling between the even-even core and the unpaired nucleon.We consider that the core oscillates coherently with respect to the quadrupole and octupole axialdeformation variables. The coupling between the core and the unpaired nucleon provides a split paritydoublet structure of the spectrum. The formalism successfully reproduces the parity-doublet splitting in a wide range of odd-A nuclei. It provides model estimations for the third angular-momentum projection K on the intrinsic symmetry axis and the related intrinsic nuclear structure. The text was submitted by the authors in English.