# Transient dynamics of double quantum dots coupled to two reservoirs

## TL;DR

This paper analyzes the transient behavior of double quantum dots connected to reservoirs, deriving expressions for electron density and currents under time-dependent biases, and exploring how system parameters influence relaxation times and oscillations.

## Contribution

It provides a comprehensive theoretical framework for understanding the time-dependent dynamics of double quantum dots coupled to reservoirs, including analytical and numerical results.

## Key findings

- Currents oscillate with bias voltage.
- Relaxation time becomes constant at strong dot coupling.
- Number of current crests varies with bias voltage.

## Abstract

We study the time-dependent properties of double quantum dots coupled to two reservoirs using the nonequilibrium Green function method. For an arbitrary time-dependent bias, we derive an expression for the time-dependent electron density of a dot and several currents, including the current between the dots in the wide-band-limit approximation. For the special case of a constant bias, we calculate the electron density and the currents numerically. As a result, we find that these quantities oscillate and that the number of crests in a single period of the current from a dot changes with the bias voltage. We also obtain an analytical expression for the relaxation time, which expresses how fast the system converges to its steady state. From the expression, we find that the relaxation time becomes constant when the coupling strength between the dots is sufficiently large in comparison with the difference of coupling strength between the dots and the reservoirs.