Dynamics of the current-driven Josephson junction

The irreversible macroscopic dynamics of the Josephson junction coupled to external wires acting as a current source is derived rigorously from the underlying microscopic Hamiltonian quantum mechanics. The external systems are treated in the singular coupling limit. The use of this limit is explicitly justified via an interpretation of the singular coupling limit in terms of the relative magnitudes of system, reservoir, and coupling energies. The qualitative behavior of the macroscopic dynamical equations is shown to depend sensitively and crucially on the interaction between the wires and the superconductors and on the size of the wires: the dc Josephson effect only happens when one lets Cooper pairs be driven into the junction by collective (i.e., small) reservoirs.     

Phase space density representations in fluid dynamics

Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable.     

Invariants of chaotic Hamiltonian systems

The invariants of chaotic bounded Hamiltonian systems and their relation to the solutions of the first variational equations of the equations of motion are studied. We show that these invariants are characterized by the fact that they either lose the property of differentiability as functions on phase space or that a certain formal power series defined in terms of the derivatives of the invariants has zero radius of convergence. For a specific example, we show that the former possibility appears to apply.     

反转磁场处粒子运动分析

本文用解析方法分析了反转磁场位形中反转力线处粒子运动以及引导中心性质,从哈密顿函数出发,讨论了粒子在准势场中的束缚运动的特征以及x-px相空间上的周期性质;给出了引导中心坐标、绝热不变量、运动频率和漂移速度等物理量的表达式,从而描写了粒子二维运动图象。该工作为不稳定性理论和非线性动力学理论的进一步研究打下基础。     

Local Thermodynamic Equilibrium for some Stochastic Models of Hamiltonian Origin

We consider a class of 1-D stochastic models that are realizations of Hamiltonian models of heat conduction and prove that in the infinite volume limit local thermodynamic equilibrium is attained with linear energy profile.     

Coupling Integrable Couplings of an Equation Hierarchy

Based on a kind of Lie algebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using the methods proposed by Ma and Gao. With the help of variational identity, we get the Hamiltonian structure of the hierarchy.     

Radiation defects in Si of high purity

Abstract

Radiation defects created by γ-irradiation of Co⁶⁰ and fast neutrons in high purity p-Si (p = 5×10³ to 4 × 10⁴ Ω.cm) and n-Si (p = 4 × 10² to 5 × 10³ Ω.cm) are investigated by measurements of Hall effect, resistivity and minority carrier lifetime. The oxygen concentration in the crystals is in the range of 5 × 10¹⁴ to 5 × 10¹⁵ cm^?3.

It is shown that stable γ-defects at 300 °K are divacancies and complexes of vacancies with donor or acceptor impurities. Divacancies introduced by γ-irradiation are the secondary defects. They become predominant after ‘exhaustion’ of the dopant. When divacancies become the predominant defects the Fermi level occupies its boundary position E_v +0.39 eV in the gap. At low doses (Φ<10¹⁶ photons/cm²) vacancy-impurity complexes and at heavy doses (Φ>10¹⁷ photons/cm²) divacancies play the main role in the recombination process.

In neutron irradiation disordered regions are introduced and the level at E_v +0.35 eV is observed. The Fermi level in both n- and p-Si shifts to the middle of the gap. At the annealing of disordered regions in the interval 200 to 250 °C the level at E_v +0.27 eV appears and Fermi level occupies its boundary position at E_v +0.39 eV. This indicates that divacancies become the predominant defects which can be formed as secondary defects at the destruction of the disordered regions.     

Variational derivation of improved KP-type of equations

The Kadomtsev-Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg-de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 [1]) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.