1 The single quantum rotor CH 3 B H ~ 650 µeV CD 3 B D ~ 325 µeV Tunnelling Spectroscopy A 0  E 0 << ħ  ph INS Quantum Rotation of Methyl Groups: Tunnelling

2 Nonlinearity in the quantum regime Quantum dynamics in complex environments Isolated dynamics: Quantum Rotation of Methyl Groups: Tunnelling Crystal Structure-Methyl dynamics

3 Experiments Neutron Diffraction: Powders, single X’stals Spectroscopy: Neutrons, Infrared, Raman Chemistry:Isotope substitutions

4 The isolated chain of coupled methyl groups Approximation Hamiltonian

5 4 Å 3.6Å 4-Methylpyridine: Infinite chains of Methyl groups

6 F. Fillaux et al., Phys. Rev. B 68, (2003)  -Picoline 10 K

7 4-Methylpyridine: Inelastic Neutron Scattering F.Fillaux, C. J. Carlile and G. J. Kearley, Phys. Rev. B 58 (1998) 11416

8  -Picoline

9 Isotopic mixtures of 4MP-h 7 (%) and 4MP-d 7 Intensity (arb. units) Energy Transfer (meV) 100% h 7 85% h 7 65% h 7 50% h 7 26% h 7 20% h 7 5% h F.Fillaux and C. J. Carlile, Phys. Rev. B 42 (1990) 5990

10 The infinite chain of coupled methyl groups Energy band Hamiltonian

11 4-Methylpyridine: Inelastic Neutron Scattering F.Fillaux, C. J. Carlile and G. J. Kearley, Phys. Rev. B 58 (1998) 11416

12 The isolated chain of coupled methyl groups Hamiltonian Approximation

13 Quantization (Semi-classical) Kink-mass renormalization Breather mass Threefold potential: only l=1 Dashen et al., Phys. Rev. D 11 (1975) 3424

14 Quantization (Semi-classical)

15 Kinetic energy Quantization rule The energy spectrum F.Fillaux and C. J. Carlile, Phys. Rev. B 42 (1990) 5990 Quantization

16 4-Methylpyridine Single X’stal

17 Quantum sine-Gordon Theory Free Breathers = Plane Waves Nonlocal Excitations in Nonlinear Complex Systems Quantum Rotation of Infinite Chains of Methyl Groups