Final Activity Report Summary - STOCH-EQ (Stochastic differential equations in Hilbert spaces and application to collapse models)
1) Development of an independent research career: An independent research career has been started by the researcher at the Department of Theoretical Physics of the University of Trieste, in collaboration with Prof. GianCarlo Ghirardi from the same University. Other collaborations include Prof. D. Duerr (Munich) and S.L. Adler (Princeton). The researcher is supervising a Ph.D. student working on topics related to the ERG research project.
2) Research activity:
A) The mathematical formalism of Collapse Models, i.e. stochastic differential equations, has been generalised in order to include also non white noises as the source of the reduction mechanism. This result is important in view of the possibility of identifying the collapsing field with some physical field already existing in nature.
B) The possibility of extending the formalism of Collapse Models to include also relativistic quantum field theories has been analysed. A stimulating and fruitful debate is going on with Profs. Conway and Kochen from Princeton University.
C) In a paper still in preparation, we are working on significantly improving recent proofs about the long time behavior of the solutions of certain stochastic differential equations.
D) Stochastic differential equations have been applied to study the effect of the environment on quantum algorithms. It has been shown that such an approach has the advantaged (with respect to the other ones) that the environmental noise can be effectively treated as a linear gate acting on the state vector, more or less like any other standard quantum gate.
3) Participation to conferences: The above results have been publicised in several international meetings.
2) Research activity:
A) The mathematical formalism of Collapse Models, i.e. stochastic differential equations, has been generalised in order to include also non white noises as the source of the reduction mechanism. This result is important in view of the possibility of identifying the collapsing field with some physical field already existing in nature.
B) The possibility of extending the formalism of Collapse Models to include also relativistic quantum field theories has been analysed. A stimulating and fruitful debate is going on with Profs. Conway and Kochen from Princeton University.
C) In a paper still in preparation, we are working on significantly improving recent proofs about the long time behavior of the solutions of certain stochastic differential equations.
D) Stochastic differential equations have been applied to study the effect of the environment on quantum algorithms. It has been shown that such an approach has the advantaged (with respect to the other ones) that the environmental noise can be effectively treated as a linear gate acting on the state vector, more or less like any other standard quantum gate.
3) Participation to conferences: The above results have been publicised in several international meetings.