Scaled quantum theory. The bouncing ball problem

Abstract

Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is described by the linear scaled von Neumann equation for mixed states and after it has been particularized to the case of pure states. The main purpose of this work is to show how this theory works for conservative systems and the quantum-classical transition is carried out in a continuous and smooth way, being equivalent to a nonlinear differential wave equation which contains a transition parameter ranging continuously from one to zero and covering all dynamical regimes in-between the two extreme quantum and classical regimes. This parameter can be seen as a degree of quantumness where all intermediate dynamical regimes show quantum features but are fading gradually when approaching to the classical value.

Accepted for publication in Euro. Phys. J. Plus

References in corpus (13)

• Quantum wave packet revivals
• Study of the neutron quantum states in the gravity field
• Coherent Evolution of Bouncing Bose-Einstein Condensates
• A Nonlinear Schrödinger Wave Equation With Linear Quantum Behavior
• Expectation value analysis of wave packet solutions for the quantum bouncer: short-term classical and long-term revival behavior
• Tomograms in the Quantum-Classical transition
• Dissipative tunneling by means of scaled trajectories
• Exact results for `bouncing' Gaussian wave packets
• Quantum-classical transition in dissipative systems through scaled trajectories
• Stochastic Bohmian and Scaled Trajectories
• Quantum Classical Transition for Mixed States: The Scaled Von Neumann Equation
• Quantum effective force and Bohmian approach for time-dependent traps
• Quantum effective force in an expanding infinite square-well potential and Bohmian perspective