Objective
Within Quantum Mechanics, stochastic differential equations find useful applications in the following research fields:
- collapse models, to describe spontaneous localizations of the wave function;
- decoherence theory, to mimic the effect of the environment on an open system;
- the theory of continuous quantum measurement, to describe the action of a measuring device on a quantum system.
In the past years, in particular during his experience as a Marie-Curie fellow in Germany, the researcher has started to study, both analytically and numerically, classes of stochastic equations which are of particular physical relevance; the time evolution of specific solutions (e.g. Gaussian solutions), which are of interest in all applications, have been analyzed, together with the reduction mechanism and its stability, and the localization probabilities; applications to experiments have also been considered.
We now wish to pursue this line of research. In particular, we wish to focus on the following topics:
Problem 1. Analysis of the general solution and its properties (in particular the asymptotic behaviour) of the stochastic differential equation for the free quantum particle subject to spontaneous localization in space.
Problem 2. Analysis of the general solution and of the asymptotic behaviour of the stochastic differential equations for more complex systems, e.g. the harmonic oscillator and the hydrogen atom.
Problem 3. If there is time left, we will tackle the problem of formulating collapse models which are relativistically invariant.
Since stochastic differential equations are becoming an essential tool in the study of many physical phenomena (from non-equilibrium statistical mechanics, to biology, to mathematical finance, ...) the results of our analysis has the potentialities of being important also for research areas other than the one related to collapse models.
Fields of science (EuroSciVoc)
- natural sciences mathematics pure mathematics algebra linear algebra
- natural sciences mathematics pure mathematics mathematical analysis differential equations
- natural sciences physical sciences quantum physics quantum field theory
- natural sciences physical sciences classical mechanics statistical mechanics
- natural sciences physical sciences theoretical physics
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2004-MOBILITY-11
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Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
TRIESTE
Italy
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.