We are studying the off-equilibrium state of a one dimensional quantum system.
Primarily we consider the Ising chain of N spins initially in a canonical
state($e^{-eta mathcal{hat{H}}}$), at constant inverse temperature
$eta$. The system is driven out of equilibrium by a transverse magnetic
field h(t).The evolution is calculated numerically by a Suzuki Trotter
decomposition along the protocol h(t). At time $ au$ we determine the
probability distribution $P(W)$ of the work transferred to the system.
The distribution P(W) is analysed when the protocol h(t) is repeated until
P(W) converges towards a stationnary distribution $P^infty(W)$. We will
discuss the influence of parameters as the amplitude of the field and or the
duration of the protocol $ au$ to the shape of the distribution. |
