On quantum analogue of instable oscillating states of an inverted oscillator in external poly-harmonic field

Nonstationary Schroedinger equation (NSE) is solved analytically and numerically to study a phenomenon of dynamical stabilization of the inverted oscillator driven by polyharmonic in time and spatially uniform force with specially chosen phase shifts. It is shown that for Gaussian wave packet asymptotically fitting the initial condition (IC) it occurs temporary delay of the packet center about top of the parabolic potential for about 2 fundamental time periods followed by the center bifurcation.

Scalar scattering amplitude in the Gaussian wave-packet formalism

We compute an $s$-channel $2\to2$ scalar scattering $\phi\phi\to\Phi\to\phi\phi$ in the Gaussian wave-packet formalism at the tree level. We find that wave-packet effects, including shifts of the pole and the width of the propagator of $\Phi$, persist even when we do not take into account the time boundary effect for $2\to2$ proposed earlier. An interpretation of the result is that a heavy scalar $1\to2$ decay $\Phi\to\phi\phi$, taking into account the production of $\Phi$, does not exhibit the in-state time boundary effect unless we further take into account in-boundary effects for the $2\to2$ scattering. We also show various plane-wave limits.

The frame bundle picture of Gaussian wave packet dynamics in semiclassical mechanics

Recently Ohsawa (Lett Math Phys 105:1301–1320, 2015) has studied the Marsden–Weinstein–Meyer quotient of the manifold $$T^*\mathbb {R}^n\times T^*\mathbb {R}^{2n^2}$$T∗Rn×T∗R2n2 under a $$\mathrm {O}(2n)$$O(2n)-symmetry and has used this quotient to describe the relationship between two different parametrisations of Gaussian wave packet dynamics commonly used in semiclassical mechanics. In this paper, we suggest a new interpretation of (a subset of) the unreduced space as being the frame bundle $${\mathcal {F}}(T^*\mathbb {R}^n)$$F(T∗Rn) of $$T^*\mathbb {R}^n$$T∗Rn. We outline some advantages of this interpretation and explain how it can be extended to more general symplectic manifolds using the notion of the diagonal lift of a symplectic form due to Cordero and de León (Rend Circ Mat Palermo 32:236–271, 1983).