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Research Fellows Directory

Christof Sparber

Dr Christof Sparber

Research Fellow

Organisation

University of Cambridge

Research summary

Ever since the pioneering work of Sir Isaac Newton, the language of modern physics is largely based on the mathematical description via partial differential equations (PDEs). These equations describe the variations of certain physical observables, like energy, momentum, etc. with respect to more basic variables like space and time. A particularly important feature of such a mathematical descriptions is that problems with rather diverse scientific backgrounds can often be described by (classes of) mathematically similar equations. My URF project deals with the analysis and numerical simulation of nonlinear PDEs modeling collective phenomena in quantum many particle systems. Modern experimental techniques have made it possible to design, manipulate, and closely monitor quantum mechanical systems involving many particles interacting with each other. An important example, are so-called Bose-Einstein condensates, whose experimental realization has been rewarded by a Nobel prize in 2001. These are ultra-cold gases of, say, several thousand atoms, which, below a critical temperature, form a collective state of matter that can only be explained through quantum mechanics. Surprisingly, this collective behavior can be very well described by a single, yet nonlinear, PDE, the so-called Gross- Pitaevskii equation. This mathematical model describes the time-evolution of the collective wave function of the condensate, from which all relevant physical observables can be derived. From a mathematical point of view, the appearance of nonlinearities brings up fundamental new difficulties which are highly intriguing. A good understanding of these nonlinear effects is particularly important for the accurate (and efficient) numerical simulation of these systems, which is often needed to guide physicists and engineers in the design of new experiments and devices. To this end, physical applications will drive the development of new mathematical techniques and vice versa.

Grants awarded

Partial differential equations modeling collective dynamics in quantum systems

Scheme: University Research Fellowship

Dates: Oct 2009 - Aug 2011

Value: £450,949.60