1. Relaxation and Nonequilibrium Dynamics in Single-Molecule Devices In Collaboration with: Avi Schiller, The Hebrew University Natan Andrei, Rutgers Yuval Vinkler Racah Institute of Physics, The Hebrew University

2. Experimental Motivation: Vibrational Modes in Nano Devices Single-molecule Transistors electrode Molecule electrode Suspended nano-tubes electrode Nano-tube electrode

3. Displacement-Coupling Hamiltonian electrode Molecule V q Configurational coordinate Hopping term Interaction via displacement

4. Energy scales and limit of interest Conduction-electron Bandwidth Half the tunneling rate Polaronic shift We obtained an asymptotically exact solution, in the regime where

5. Solution of the Model Continuum Limit Abelian Bosonization Hamiltonian is quadratic in bosons Localized level is absorbed in the continuum Solving the Lippmann- Schwinger eq. Diagonalization allows exact calculation of dynamical response to abrupt change in the system parameters Exactly Solvable!

6. 1st Quenching Scenario: Turning on the interaction Interaction is turned on at time t=0 Vibrational mode softens with increasing coupling Characteristic decay time depends both on coupling and vibrational energy

7. 1st Quenching Scenario: Turning on the interaction Thermalization to equilibrium Equilibrium expectation value independent of the initial state of the vibrational mode

8. 2nd Quenching Scenario: Abrupt Change of Frequency At t=0 the phonon frequency is abruptly changed by Relaxation time and amplitude of oscillations depend on Equilibrium expectation value independent of quench scenario Thermalization to a new equilibrium

9. Response to AC Drive Transient oscillations are governed by Long-time oscillations at frequency. No linear harmonic with frequency ! For t > 0, phonon position is forced by an AC drive

10. Conclusions Outlook Analytical, non-perturbative, and asymptotically exact solution of quench and ac dynamics of a single-molecule device. Complete real-time dynamics of the localized phonon was calculated under different quenching scenarios and ac drive. Relaxation to new thermal equilibrium independent of the initial phonon state and details of the quench scenario. Relaxation time is linear in the frequency, quadratic in the coupling, and inversely proportional to the tunneling rate squared. Nonequilibrium steady state and I-V characteristics