Related papers: Generalizing the exact quantization rule to multip…

For a single degree of freedom confined mechanical system with given energy, we know that the motion is always periodic and action-angle variables are convenient choice as conjugate phase-space variables. We construct action-angle coherent…

Stabilization is still a somewhat controversial issue concerning its very existence and also the precise conditions for its occurrence. The key quantity to settle these questions is the ionization probability, for which hitherto no…

Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…

An exact quantization rule for the bound states of the one-dimensional Schr\"{o}dinger equation is presented and is generalized to the three-dimensional Schr\"{o}dinger equation with a spherically symmetric potential.

Starting with the equivalence of the rest energy of a particle to an amount of the radiant energy characterized by a frequency, in addition to the usual relativistic transformation rules leading to the wave-particle duality, we investigate…

By using the WKB quantization we deduce an analytical formula for the energy splitting in a double--well potential which is the usual Landau formula with additional quantum corrections. Then we analyze the accuracy of our formula for the…

We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We…

An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the…

We present a numerical study of the quantum action previously introduced as a parametrisation of Q.M. transition amplitudes. We address the questions: Is the quantum action possibly an exact parametrisation in the whole range of transition…

We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…

Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we show that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the `probability' of the…

We prove the bijectivity of the constraints of normalization and of the Fermi-Coulomb hole charge sum rule at each electron position for approximate wave functions. This bijectivity is surprising in light of the fact that normalization…

The dynamics of a wave function describing a particle confined in a multiple quantum well potential is studied numerically. As a consequence of quantum mechanical tunneling, an initial wavefunction designed to be localized in one well can…

Affine variables, which have the virtue of preserving the positive-definite character of matrix-like objects, have been suggested as replacements for the canonical variables of standard quantization schemes, especially in the context of…

We proved two Three Circles Theorems for harmonic functions on manifolds in integral sense. As one application, on manifold with nonnegative Ricci curvature, whose tangent cone at infinity is the unique metric cone with unique conic…

We have recently proposed a quantum control method based on the knowledge of the energy spectrum as a function of an external control parameter [Phys. Rev. Lett. {\bf 99}, 036806 (2007)]. So far, our method has been applied to connect the…

We derive a general WKB energy splitting formula in a double-well potential by incorporating both phase loss and anharmonicity effect in the usual WKB approximation. A bare application of the phase loss approach to the usual WKB method…

We demonstrate that the multipoles associated with the density matrix are truly observable quantities that can be unambiguously determined from intensity moments. Given their correct transformation properties, these multipoles are the…

We introduce and validate a theoretical framework for coherent control of multichannel scattering of linear waves to route waves through complex geometries with multiple scattering. We show that steady-state perfect routing solutions are…

Coupled quantum dots are an example of the ubiquitous quantum double potential well. In a typical transport experiment, each quantum dot is also coupled to a continuum of states. Our approach takes this into account by using a Green's…