Simultaneous eigenstates of the number-difference operator and a bilinear interaction Hamiltonian derived by solving a complex differential equation

As a continuum work of Bhaumik et al who derived the common eigenvector of the number-difference operator Q and pair-annihilation operator ab (J. Phys. A9 (1976) 1507) we search for the simultaneous eigenvector of Q and (ab-a^{+}b^{+}) by setting up a complex differential equation in the bipartite entangled state representation. The differential equation is then solved in terms of the two-variable Hermite polynomials and the formal hypergeometric functions. The work is also an addendum to Mod. Phys. Lett. A 9 (1994) 1291 by Fan and Klauder, in which the common eigenkets of Q and pair creators are discussed

Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

Enhanced voltage generation through electrolyte flow on liquid-filled surfaces.

The generation of electrical voltage through the flow of an electrolyte over a charged surface may be used for energy transduction. Here, we show that enhanced electrical potential differences (i.e., streaming potential) may be obtained through the flow of salt water on liquid-filled surfaces that are infiltrated with a lower dielectric constant liquid, such as oil, to harness electrolyte slip and associated surface charge. A record-high figure of merit, in terms of the voltage generated per unit applied pressure, of 0.043 mV Pa-1 is obtained through the use of the liquid-filled surfaces. In comparison with air-filled surfaces, the figure of merit associated with the liquid-filled surface increases by a factor of 1.4. These results lay the basis for innovative surface charge engineering methodology for the study of electrokinetic phenomena at the microscale, with possible application in new electrical power sources