Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?

The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy is given for the rolling ellipsoid of revolution problem in two cases, namely, on a smooth and on a rough plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no difference between the two systems, and thus disprove the conjecture by Cushman and Duistermaat stating that the topological monodromy gives a topological obstruction for Hamiltonization of the rolling ellipsoid of revolution on a rough plane.Comment: 31 pages, 11 figure

Kramers Degenerated Spin Systems "NV Center + Few Proximal 13C Nuclei" in Diamond for Single-Spin Magnetometry

Spin systems consisted of single electronic spin S=1 of the NV center and few nearby carbon-13 nuclei spins I=1/2 in diamond lattice which can be used as a small register of a quantum computer or as a sensor of a magnetic field are studied both numerically and analytically using spin Hamiltonian method. At odd number of carbon-13 nuclei the eigenstates of the spin system at zero external magnetic field are twofold degenerated (Kramers degeneration) due to time reversal invariance of the spin Hamiltonian. This degeneracy is lifted only by external magnetic field regardless of the presence of any electric (crystal) field which also lifts the degeneracy thus hindering measurement of external magnetic field. Therefore the Kramers-degenerated spin systems are especially perspective for measurement of a local magnetic field by the NV-based single-spin quantum magnetometer. Here we discussed spin properties of such spin systems using the parameters of hyperfine NV-13C interactions taken from electron paramagnetic resonance EPR experiments on NV ensemble or from optically detected magnetic resonance (ODMR) experiments on single NV centers as well as from ab initio (Density Functional Theory (DFT)) simulation of H-terminated carbon clusters hosting NV centers. Moreover, we calculated by DFT the zero-field splitting parameters D and E for the NV center. For the simplest spin system "NV+single carbon-13" we got simple approximate analytical expressions for energy levels and eigenstates

Kramers Degenerated Spin Systems "NV Center + Few Proximal 13C Nuclei" in Diamond for Single-Spin Magnetometry

Spin systems consisted of single electronic spin S=1 of the NV center and few nearby carbon-13 nuclei spins I=1/2 in diamond lattice which can be used as a small register of a quantum computer or as a sensor of a magnetic field are studied both numerically and analytically using spin Hamiltonian method. At odd number of carbon-13 nuclei the eigenstates of the spin system at zero external magnetic field are twofold degenerated (Kramers degeneration) due to time reversal invariance of the spin Hamiltonian. This degeneracy is lifted only by external magnetic field regardless of the presence of any electric (crystal) field which also lifts the degeneracy thus hindering measurement of external magnetic field. Therefore the Kramers-degenerated spin systems are especially perspective for measurement of a local magnetic field by the NV-based single-spin quantum magnetometer. Here we discussed spin properties of such spin systems using the parameters of hyperfine NV-13C interactions taken from electron paramagnetic resonance EPR experiments on NV ensemble or from optically detected magnetic resonance (ODMR) experiments on single NV centers as well as from ab initio (Density Functional Theory (DFT)) simulation of H-terminated carbon clusters hosting NV centers. Moreover, we calculated by DFT the zero-field splitting parameters D and E for the NV center. For the simplest spin system "NV+single carbon-13" we got simple approximate analytical expressions for energy levels and eigenstates