• Corpus ID: 252762633

# Particle Trajectories for Quantum Maps

@inproceedings{BornsWeil2022ParticleTF,
title={Particle Trajectories for Quantum Maps},
author={Yonah Borns-Weil and Izak Oltman},
year={2022}
}
• Published 6 October 2022
• Physics, Mathematics
. We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian prop-agators or metaplectic operators. We show in both cases the convergence in total variation of the quantum trajectory to its corresponding classical trajectory, as deﬁned by propagation of a semiclassical defect measure. This convergence holds up to the Ehrenfest time…

## References

SHOWING 1-10 OF 27 REFERENCES

Abstract.We study a toy model for “partially open” wave-mechanical system, like for instance a dielectric micro-cavity, in the semiclassical limit where ray dynamics is applicable. Our model is a
• Physics
• 2012
We analyze the paper “The wave mechanics of $$\alpha$$-ray tracks” Mott (Proc R Soc Lond A 126:79–84, 1929), published in 1929 by N. F. Mott. In particular, we discuss the theoretical context in
• Mathematics, Physics
• 2002
We prove here that the semiclassical asymptotic expansion for the propagation of quantum observables, for C -Hamiltonians growing at most quadratically at infinity, is uniformly dominated at any
• Physics, Mathematics
Chaos
• 1996
A new example of a quantum map is constructed, the quantized version of the D-transformation, which is the natural extension to two dimensions of the tent map, which includes the quantization of a horseshoe.
• Physics
• 2009
I General theory.- The Stochastic Schr#x00F6 dinger Equation.- The Stochastic Master Equation: Part I.- Continuous Measurements and Instruments.- The Stochastic Master Equation: Part II.- Mutual
First, exact definitions are supplied for the terms: position, velocity, energy, etc. (of the electron, for instance), such that they are valid also in quantum mechanics. Canonically conjugated
• Physics
Journal of Mathematical Physics
• 2022
The appearance of tracks, close to classical orbits, left by charged quantum particles propagating inside a detector, such as a cavity periodically illuminated by light pulses, is studied for a
• Physics
Communications in Mathematical Physics
• 2021
The phenomenon that a quantum particle propagating in a detector, such as a Wilson cloud chamber, leaves a track close to a classical trajectory is analyzed. We introduce an idealized
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum
• Mathematics
• 1970
In order to provide a mathmatical framework for the process of making repeated measurements on continuous observables in a statistical system we make a mathematical definition of an instrument, a