Dissipative quantum tunneling and magnetic response of a single electron in a four-well potential (Q1283541)

This paper studies dissipative tunneling of a charged spinless particle with effective mass \(m\) and charge \(e\) in a four-well semiconductor nanostructure subjected to an external electromagnetic field \(A\) and coupled to a heat bath is studied. More specifically the Hamiltonian of the model under study is given by \(H(x,y,z) = {1}/({2m})(p -(e/c)A)^2 + \lambda (x^2 - d^2)^2 + \lambda (y^2 - d^2)^2 + {1}/({2}m) \omega_0^2 z^2 - C \sum_{\vec{k}} \sqrt{|\vec{k} |} (b_{\vec{k}}(t) - b_{\vec{k}}^\dagger(t)) \exp(i \vec{k} \vec{r})\) where \(b^\dagger_{\vec{k}}, b_{\vec{k}}\) are the creation and annihilation operators of the acoustic phonons with wave vector \(\vec{k}\) respectively (dissipative environment), \(p\) is the momentum of the particle, \(C, d, \lambda\) are constants and \(\omega_0^2 = 8 \lambda d^2/m\). The limit of weak coupling to the heat bath and the weak magnetic field limit is studied. The spectral functions of the phonon heat bath are computed and the average magnetic moment of the electron and its relaxation time is determined. The existence of orbital paramagnetism is evidence for persistent electron tunneling between quantum dots as well as for the conservation of quantum coherence in the thermodynamic-equilibrium state.