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Center for Nonlinear Studies |
Rudolf Clausius first derived the virial theorem in classical mechanics in 1870, [Phil. Mag. (1870)]. This has been applied to a variety of problems over the last fourteen decades in classical and quantum mechanics. In the 1960’s the virial theorem was extended to quantum many-body systems and in particular to the d (= 1, 2 and 3) dimensional electron gas, dDEG. This has provided considerable insight into the role of interactions in the calculation of the ground state energy, E, in, for example, the 2DEG but it does not give an explicit form for E. We have recently derived the virial theorem for graphene and other Dirac Materials for systems close to the Dirac point where the dispersion relation is linear. What we find is that the ground state energy of the d (= 1, 2 and 3) dimensional Dirac gas, dDDG, is given by the remarkably simple result, E = B/rs, where rsa0 is proportional to the average distance between particles, with a0 the Bohr radius, and B is a constant independent of rs. With the energy we can derive the compressibility and other thermodynamic quantities for all values of rs and for all dimensions. Our calculation of the compressibility for the 2DDG agrees with experiments done on graphene. One of the most interesting/controversial aspects of our result is that the ground state energy expression we find for the interacting Dirac gas is the same as that of a free Dirac gas. This leads to one of the big questions in graphene physics: Do interactions matter in graphene? With these results can we answer this question? Come to the colloquium to find the answer!
Host: Cristian Batista