Inverse Dynamics in the Classical Fermi Accelerator

Quantum Trajectory Description of the Time-Independent (Inverse) Fermi Accelerator

“…This will be useful, not only for establishing a connection with the fully classical treatment of Ref. [5] but also for explaining the limiting case described therein, wherein m → 0 as the particle kinetic energy remains constant. Also, in the molecular QCD context, as per Section 3.3, a bipolar treatment of the particle would serve as an accurate quantum description of the time-dependent dynamics of the electron.…”

“…In previous studies, either or both subsystems-i.e., particle and wall-were treated either classically or quantum mechanically [4][5][6]. TISE solutions were presumed for the quantum subsystems, as will be the case here as well.…”

“…That said, however, a bipolar QTM treatment of the particle also offers an interesting perspective, and in any event is necessary to connect with the fully classical treatment of Ref. [5]. This direction will be explored in a future publication, as discussed further in Section 4.…”

“…Hussein, a nuclear physicist, realized that a very similar model could be used to exploit energy loss in quantum systems. This would then lead to a microscopic, albeit simplified, derivation of what may be called the "quantum friction force" [4][5][6].…”

“…In an Annals of Physics article [4], M. Hussein and V. Kharchenko solved the fully quantum (inverse) Fermi accelerator system exactly-and also approximately, using the adiabatic (Born-Oppenheimer, BO) and mixed quantumclassical (mixed QC) approximations. Later, with M. Pato, they solved the same problem classically [5] and critically analyzed the manner in which the friction force depends on the velocity of the particle or wall. The problem was revisited in 2008, while Hussein was visiting the Max-Planck Institute for the Physics of Complex Systems (MPIPKS) in Dresden, Germany.…”