Analytic Expression for Exact Ground State Energy Based on an Operator Method for a Class of Anharmonic Potentials

A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic expressions for the exact ground state energy have also been derived specifically for a large class of the one-dimensional oscillator with cubic-quartic anharmonic terms. Our analytical results can be used to check the accuracy of existing numerical methods, for instance the method of state-dependent diagonalization. Our results also agree with the asymptotic behavior in the divergent pertubative expansion of quartic harmonic oscillator.Comment: LaTeX with six figure (gif) files; Submitted to Phys. Rev.

A unified approach for exactly solvable potentials in quantum mechanics using shift operators

We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new class of solvable potentials.Comment: RevTex, 8 page

General Approach to Functional Forms for the Exponential Quadratic Operators in Coordinate-Momentum Space

In a recent paper [Nieto M M 1996 Quantum and Semiclassical Optics, 8 1061; quant-ph/9605032], the one dimensional squeezed and harmonic oscillator time-displacement operators were reordered in coordinate-momentum space. In this paper, we give a general approach for reordering multi-dimensional exponential quadratic operator(EQO) in coordinate-momentum space. An explicit computational formula is provided and applied to the single mode and double-mode EQO through the squeezed operator and the time displacement operator of the harmonic oscillator.Comment: To appear in J. Phys. A: Mathematics and Genera

Vertical Moist Thermodynamic Structure and Spatial–Temporal Evolution of the MJO in AIRS Observations

The atmospheric moisture and temperature profiles from the Atmospheric Infrared Sounder (AIRS)/Advanced Microwave Sounding Unit on the NASA Aqua mission, in combination with the precipitation from the Tropical Rainfall Measuring Mission (TRMM), are employed to study the vertical moist thermodynamic structure and spatial–temporal evolution of the Madden–Julian oscillation (MJO). The AIRS data indicate that, in the Indian Ocean and western Pacific, the temperature anomaly exhibits a trimodal vertical structure: a warm (cold) anomaly in the free troposphere (800–250 hPa) and a cold (warm) anomaly near the tropopause (above 250 hPa) and in the lower troposphere (below 800 hPa) associated with enhanced (suppressed) convection. The AIRS moisture anomaly also shows markedly different vertical structures as a function of longitude and the strength of convection anomaly. Most significantly, the AIRS data demonstrate that, over the Indian Ocean and western Pacific, the enhanced (suppressed) convection is generally preceded in both time and space by a low-level warm and moist (cold and dry) anomaly and followed by a low-level cold and dry (warm and moist) anomaly. The MJO vertical moist thermodynamic structure from the AIRS data is in general agreement, particularly in the free troposphere, with previous studies based on global reanalysis and limited radiosonde data. However, major differences in the lower-troposphere moisture and temperature structure between the AIRS observations and the NCEP reanalysis are found over the Indian and Pacific Oceans, where there are very few conventional data to constrain the reanalysis. Specifically, the anomalous lower-troposphere temperature structure is much less well defined in NCEP than in AIRS for the western Pacific, and even has the opposite sign anomalies compared to AIRS relative to the wet/dry phase of the MJO in the Indian Ocean. Moreover, there are well-defined eastward-tilting variations of moisture with height in AIRS over the central and eastern Pacific that are less well defined, and in some cases absent, in NCEP. In addition, the correlation between MJO-related midtropospheric water vapor anomalies and TRMM precipitation anomalies is considerably more robust in AIRS than in NCEP, especially over the Indian Ocean. Overall, the AIRS results are quite consistent with those predicted by the frictional Kelvin–Rossby wave/conditional instability of the second kind (CISK) theory for the MJO

Adiabatic Fidelity for Atom-Molecule Conversion in a Nonlinear Three-Level \Lambda-system

We investigate the dynamics of the population transfer for atom-molecule three-level $\Lambda$-system on stimulated Raman adiabatic passage(STIRAP). We find that the adiabatic fidelity for the coherent population trapping(CPT) state or dark state, as the function of the adiabatic parameter, approaches to unit in a power law. The power exponent however is much less than the prediction of linear adiabatic theorem. We further discuss how to achieve higher adiabatic fidelity for the dark state through optimizing the external parameters of STIRAP. Our discussions are helpful to gain higher atom-molecule conversion yield in practical experiments.Comment: 4 pages, 5 figure

Properties of a beam splitter entangler with Gaussian input states

An explicit formula is given for the quantity of entanglement in the output state of a beam splitter, given the squeezed vacuum states input in each mode.Comment: To appear in Phys. Rev.

Hawking Radiation of Black Rings from Anomalies

We derive Hawking radiation of 5-dimensional black rings from gauge and gravitational anomalies using the method proposed by Robinson and Wilczek. We find as in the black hole case, the problem could reduce to a (1+1) dimensional field theory and the anomalies result in correct Hawking temperature for neutral,dipole and charged black rings.Comment: 15 pages,Latex; revised version, typos corrected, reference added

Deduction of Pure Spin Current from Spin Linear and Circular Photogalvanic Effect in Semiconductor Quantum Wells

We study the spin photogalvanic effect in two-dimensional electron system with structure inversion asymmetry by means of the solution of semiconductor optical Bloch equations. It is shown that a linearly polarized light may inject a pure spin current in spin-splitting conduction bands due to Rashba spin-orbit coupling, while a circularly polarized light may inject spin-dependent photocurrent. We establish an explicit relation between the photocurrent by oblique incidence of a circularly polarized light and the pure spin current by normal incidence of a linearly polarized light such that we can deduce the amplitude of spin current from the measured spin photocurrent experimentally. This method may provide a source of spin current to study spin transport in semiconductors quantitatively

The Impact of Perceived Lottery Knowledge on Problem Lottery Playing: A Moderated Mediation Model

The study explored the mechanism of perceived lottery knowledge in predicting problem in lottery playing through a Moderated Mediation Model centering on overconfidence. A total of 972 Chinese football bettors from nine provinces completed a questionnaire survey. The result showed that: (1) perceived lottery knowledge could positively predict problem lottery playing; (2) perceived lottery knowledge influenced problem lottery playing directly and indirectly through overconfidence; (3) risk perception moderated the mediated path. The indirect effect was stronger for football bettors with low-risk perception than for those with high-risk perception. Implications of consumption and intervention for problem lottery players were discussed.     Keywords: football bettors, problem lottery playing, perceived lottery knowledge, overconfidence, risk perceptio