Study of collective excitations in a one-dimensional system. Consider a set of rotors Sn = (cos( n

Study of collective excitations in a one-dimensional system. Consider a set of rotors Sn = (cos(φ_n), sin(φ_n)) located at positions xn = na with n = 1,2, . . . ,N. Here φ ∈ [0,2π) is the phase of the rotor.

Transcribed Image Text:

The energy of the system is given by N H=-J cos(on - On+1)-hcos on]. n=1 Assume periodic boundary conditions, i.e. SN+1 = S. We confine our analysis to the limit where on, is slowly varying and consider the continuum limit cos(on - On+1)~1 - (non+1) 1 In this approximation the Hamiltonian is given by - a (do 2 dx