Lectures

ABSTRACT

Quantum trajectory models time evolution of a quantum system including a particular measurement strategy. In a quantum trajectory theory, the state of the system is a stochastic process depending on the measurement outputs. In this course, I will introduce quantum trajectories, describe their theory, and mention some experimental applications and mathematical open problems. The only prerequisite to follow the main part of the course is a basic knowledge of linear algebra and Markov processes, though a knowledge of quantum mechanics might be useful to follow some examples and applications.

SCHEDULE

REFERENCES

• T. Benoist, M. Fraas, J. Fröhlich, "The appearance of particle tracks in detectors -- II: the semi-classical realm", arXiv:2202.09558 [math-ph];

• M. Ballesteros, T. Benoist, M. Fraas, J. Fröhlich, "The appearance of particle tracks in detectors", Commun. Math. Phys. 385 (2021), 429 - 463, arXiv:2007.00785 [math-ph];

• T. Benoist, M. Fraas, Y. Pautrat, C. Pellegrini, "Invariant Measure for Quantum Trajectories", Probab. Theory Relat. Fields 174 (2019), 307 - 334, arXiv:1703.10773 [math.PR];

• M. Ballesteros, N. Crawford, M. Fraas, J. Fröhlich, B. Schubnel, "Perturbation Theory for Weak Measurements in Quantum Mechanics, I -- Systems with Finite-Dimensional State Space", arXiv:1709.03149 [math-ph];

• M. Ballesteros, N. Crawford, M. Fraas, J. Fröhlich, B. Schubnel, "Non-demolition measurements of observables with general spectra", arXiv:1706.09584 [math-ph];

• A.S. Holevo, Statistical Structure of Quantum Theory, Spinger, 2001;

• R. Figari, A. Teta, Quantum Dynamics of a Particle in a Tracking Chamber, Springer, 2014;

• R. Figari, A. Teta, "Emergence of classical trajectories in quantum systems: the cloud chamber problem in the analysis of Mott (1929)", Arch. Ist. Exact Sci. 67, 215-234 (2013).