How do wave packets spread? Time evolution on Ehrenfest time scales
arXiv:1112.4056 · doi:10.1088/1751-8113/45/21/215307
Abstract
We derive an extension of the standard time dependent WKB theory which can be applied to propagate coherent states and other strongly localised states for long times. It allows in particular to give a uniform description of the transformation from a localised coherent state to a delocalised Lagrangian state which takes place at the Ehrenfest time. The main new ingredient is a metaplectic operator which is used to modify the initial state in a way that standard time dependent WKB can then be applied for the propagation. We give a detailed analysis of the phase space geometry underlying this construction and use this to determine the range of validity of the new method. Several examples are used to illustrate and test the scheme and two applications are discussed: (i) For scattering of a wave packet on a barrier near the critical energy we can derive uniform approximations for the transition from reflection to transmission. (ii) A wave packet propagated along a hyperbolic trajectory becomes a Lagrangian state associated with the unstable manifold at the Ehrenfest time, this is illustrated with the kicked harmonic oscillator.
30 pages, 3 figures
References in corpus (2)
Cited by in corpus (28)
- Scrambling and entanglement spreading in long-range spin chains
- Experimental Observation of Quantum Chaos in a Beam of Light
- Dynamics of the Dicke model close to the classical limit
- Classical and quantum chaos in a three-mode bosonic system
- Phase space geometry and optimal state preparation in quantum metrology with collective spins
- Quantum echo dynamics in the Sherrington-Kirkpatrick model
- Irrealism from fringe visibility in matter-wave double-slit interference with initial contractive states
- Chaos and magic in the dissipative quantum kicked top
- Quantum revival patterns from classical phase-space trajectories
- Wavepackets in inhomogeneous periodic media: propagation through a one-dimensional band crossing
- Lindblad dynamics of Gaussian states and their superpositions in the semiclassical limit
- Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature
- Schrödinger-type 2D coherent states of magnetized uniaxially strained graphene
- Probing Dynamical Sensitivity of a Non-KAM System Through Out-of-Time-Order Correlators
- Semiclassical evolution of quantum wave packets on the torus beyond the Ehrenfest time in terms of Husimi distributions
- Quantum-Chaotic Evolution Reproduced from Effective Integrable Trajectories
- Symplectic Semiclassical Wave Packet Dynamics II: Non-Gaussian States
- Rotating Gaussian wave packets in weak external potentials
- Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians
- A unified time scale for quantum chaotic regimes
- Quantum Enhancement of Thermalization
- Distinguishing quantum features in classical propagation
- Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems
- Computing Quantum Mean Values in the Deep Chaotic Regime
- Asymptotic Approximations for the Phase Space Schrodinger Equation
- An estimation of the logarithmic timescale in an ergodic dynamics
- Interscale entanglement production in a quantum system simulating classical chaos
- Information acquisition, scrambling, and sensitivity to errors in quantum chaos