Scaling behaviour of the relaxation in quantum chains

Thierry Platini, Dragi Karevski

We study the relaxation behaviour of the quantum Ising chain, focusing our attention onto the non-equilibrium dynamics of the transverse magnetization. The initial states, from which the magnetization relaxes, are product states such as those generated by setting in contact several systems, each initially equilibrated at a given temperature. Due to the free fermionic structure of the chain, the dynamics of the transverse magnetization is easily expressed in a compact form. In the completely factorized initial state, corresponding to a situation where all the spins are thermalized independently, we obtain in the scaling limit the Green function associated to the transverse magnetization. The relaxation behaviour is also considered in the system-bath case, where part of the chain called the system is thermalized at a temperature Ts and the remaining part is at a temperature Tb. The magnetization profiles show a scaling behaviour. Moreover, in the extreme case Tb=∞ and Ts=0, it is shown that the magnetization relaxes in quantized steps in the strong transverse field region.

Adithya Kandhadai, Antony Valentini

Thierry Platini, Dragi Karevski

In this paper we present the results obtained concerning the relaxation behaviour of a non equilibrium Ising quantum chain. In particular, we have focues our attention into the transverse magnetization. The out-of-equilibriumness is generated by setting up an initial thermal inhomogeneity. We present two different initial conditions: a completely factorized state, where all the spins are thermalized independently and second a system-bath case, where half of the chain called the system is thermalized at a temperature T s and the remaining half is at a temperature T b . In both cases, the magnetization profiles are calculated either analytically or numerically and show a scaling behaviour. It is also found that in the two-temperature case the magnetization relaxes in quantized steps in the strong transverse field region.

A.S. Davydov

Thierry Platini, Dragi Karevski

We present the results obtained on the magnetization relaxation properties of an XX quantum chain in a transverse magnetic field. We first consider an initial thermal kink-like state where half of the chain is initially thermalized at a very high temperature T b while the remaining half, called the system, is put at a lower temperature T s . From this initial state, we derive analytically the Green function associated with the dynamical behaviour of the transverse magnetization. Depending on the strength of the magnetic field and on the temperature of the system, different regimes are obtained for the magnetic relaxation. In particular, with an initial droplet-like state, that is a cold subsystem of the finite size in contact at both ends with an infinite temperature environment, we derive analytically the behaviour of the time-dependent system magnetization.