In quantum optics, unitary transformations of arbitrary states are evaluated by using the Taylor series expansion. However, this traditional approach can become cumbersome for the transformations involving non-commuti...In quantum optics, unitary transformations of arbitrary states are evaluated by using the Taylor series expansion. However, this traditional approach can become cumbersome for the transformations involving non-commuting operators. Addressing this issue, a nonstandard unitary transformation technique is highlighted here with new perspective. In a spirit of “quantum” series expansions, the transition probabilities between initial and final states, such as displaced, squeezed and other nonlinearly transformed coherent states are obtained both numerically and analytically. This paper concludes that, although this technique is novel, its implementations for more extended systems are needed.展开更多
The electrochemical oxidation of sulfide on a polycrystalline platinum electrode was studied under potentiostatic condition when an external resistor is in series with the working electrode. Only two os- cillatory reg...The electrochemical oxidation of sulfide on a polycrystalline platinum electrode was studied under potentiostatic condition when an external resistor is in series with the working electrode. Only two os- cillatory regions can be obtained in the absence of the external resistance, but four oscillatory regions, including two new current oscillations, were found in this system by controlling the external resistance. It is demonstrated that three oscillatory regimes, which arise on the positive branch of current-potential curve, can be classified as HN-NDR (Hidden N-shaped Negative Differential Resistance) oscillators. For the first oscillatory region, various transient complex phenomena, which result from the change of the electrode/electrolyte interface by accumulation of adsorbed element sulfur on the electrode, have been observed. The dynamic behavior of NDR (Negative Differential Resistance) oscillations, appearing along with negative branch of polarization curve, can transform from oscillations into bistability with a sufficient large external resistance in series. Two oscillatory regions in high-potential region classified as HN-NDR type oscillations are separated by a saddle-loop bifurcation. They displayed a sequence of bursting oscillations and irregular oscillations, respectively. The electrochemical oxidation of sulfide provides a model system for studying complex dynamics and possible application in sulfur removal.展开更多
文摘In quantum optics, unitary transformations of arbitrary states are evaluated by using the Taylor series expansion. However, this traditional approach can become cumbersome for the transformations involving non-commuting operators. Addressing this issue, a nonstandard unitary transformation technique is highlighted here with new perspective. In a spirit of “quantum” series expansions, the transition probabilities between initial and final states, such as displaced, squeezed and other nonlinearly transformed coherent states are obtained both numerically and analytically. This paper concludes that, although this technique is novel, its implementations for more extended systems are needed.
基金Supported by the National Natural Science Foundation of China (Grant No. 20573134)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20050290512)Program for New Century Excellent Talents in Univer-sity (Grant No. 05-0477)
文摘The electrochemical oxidation of sulfide on a polycrystalline platinum electrode was studied under potentiostatic condition when an external resistor is in series with the working electrode. Only two os- cillatory regions can be obtained in the absence of the external resistance, but four oscillatory regions, including two new current oscillations, were found in this system by controlling the external resistance. It is demonstrated that three oscillatory regimes, which arise on the positive branch of current-potential curve, can be classified as HN-NDR (Hidden N-shaped Negative Differential Resistance) oscillators. For the first oscillatory region, various transient complex phenomena, which result from the change of the electrode/electrolyte interface by accumulation of adsorbed element sulfur on the electrode, have been observed. The dynamic behavior of NDR (Negative Differential Resistance) oscillations, appearing along with negative branch of polarization curve, can transform from oscillations into bistability with a sufficient large external resistance in series. Two oscillatory regions in high-potential region classified as HN-NDR type oscillations are separated by a saddle-loop bifurcation. They displayed a sequence of bursting oscillations and irregular oscillations, respectively. The electrochemical oxidation of sulfide provides a model system for studying complex dynamics and possible application in sulfur removal.
