23.9.2011
There will be a symposium from 25 to 28 September 2011 at the University of
Heidelberg on a new field of physics called PT quantum mechanics. Thirty invited
speakers from eight countries will present their theoretical and experimental discoveries in this rapidly developing area. The symposium is organized by Carl M Bender, Maarten DeKieviet, and Sandra P Klevansky and is funded by the "Joint Appointment" funds of the Excellenziniative and the Heidelberg Graduate School of Fundamental Physics..
Every undergraduate physics major knows that the properties of a physical system are governed by a single mathematical object called a Hamiltonian, and, in every introductory undergraduate quantum mechanics course one is taught that the Hamiltonian has a crucial mathematical property called Dirac Hermiticity. (As a mathematical equation Dirac Hermiticity is expressed as H=H†; the
symbol † represents complex conjugation and matrix transposition.) The mathematical requirement of Dirac Hermiticity has been an accepted and unquestioned axiom of quantum mechanics for eight decades, and for good reason: If a Hamiltonian is Dirac Hermitian, then a rigorous mathematical consequence is that the energy levels of the physical system will be real and that probability will be conserved. These are the two crucial features that any physical quantum
system must possess.
In 1998, however, there was a surprising discovery. It was found that it is possible for a physical system to have a Hamiltonian is not Dirac Hermitian. The energy levels of such a system can be real as long as the Hamiltonian has a symmetry called PT symmetry. (The term PT symmetry means space-time symmetry. A physical system is said to be PT symmetric if it behaves the same way in a mirror world in which right becomes left and time flows backward.) Several years later it was established that for such a PT-symmetric system the probability is conserved. Thus, one can have a physically realistic PT quantum-mechanical system whose Hamiltonian is not Dirac Hermitian.
The condition of PT symmetry is weaker than the requirement of Dirac Hermiticity. This means that there are many more PT-symmetric Hamiltonians than Dirac Hermitian Hamiltonians. Replacing Dirac Hermiticity by PT symmetry does not contradict quantum mechanics; rather, it generalizes it, in just the same way that the complex number system is a generalization of the real number system.
Within a few months after the discovery that a PT-symmetric Hamiltonian could describe physically realistic systems, there was an explosion of researchby theoretical physicists investigating the properties of various kinds of PT quantum systems. To date, there have been over 1000 published papers. In the past 7 or 8 years there have been over a dozen international physics conferences
entirely devoted to the subject of non-Hermitian and PT-symmetric Hamiltonians. In Europe these conferences have taken place in London, Bologna, and Prague, and conferences have also been held in Turkey, South Africa, Israel, China, India, and Japan.
The most remarkable recent development in PT quantum mechanics is that in the past two years experimental physicists have begun to verify the theoretical predictions of PT quantum mechanics. Experiments involving optical wave guides, microwave cavity resonators, atomic diffusion, graphene, nuclear magnetic resonance, lasers, and superconductivity have been published. Further experiments involving atomic beams, nuclear magnetic resonance, and Bose-Einstein condensates are being done. The symposium that will take place next week in Heidelberg is special in that it will provide an opportunity for theoreticians and experimentalists to interact with one another.
While theories defined by non-Hermitian PT-symmetric Hamiltonians do not contradict any of the essential features of conventional quantum mechanics, PT quantum theories can exhibit strange and unexpected properties. For example, PT-symmetric optical systems can exhibit unidirectional invisibility. (From the left an object may be visible, but from the right it may be invisible.) PT quantum mechanics offers the possibility of developing new kinds of devices, such as optical switches, and new kinds of synthetic materials, such as PT graphene. PT quantum mechanics may also provide new analytical tools for attacking some of the current puzzles in physics: Is there a Higgs particle, is there dark matter, how can one quantize gravity, why is there more matter than antimatter in the universe?
