Relaxation and Nonequilibrium Dynamics in SingleMolecule Devices Yuval

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

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

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

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

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

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

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

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

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

Conclusions 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. Outlook Nonequilibrium steady state and I-V characteristics