Non-interacting Systems

Lev Deych

M. Pollak

In some recent papers in which Monte Carlo methods have been used, it has been found that disordered Anderson insulators with Coulomb interactions may become glassy at low temperatures. This was indicated by a non-vanishing value of an order parameter. In the present paper, the transition to a glassy state is investigated analytically for systems with and without Coulomb interactions. For the purposes of the analysis, a system is taken to be in the glassy state if it fails to satisfy the ergodic hypothesis. A transition to non-ergodic behaviour is found for both interacting and non-interacting systems, but the transition for the interacting system is softer and occurs at a higher temperature. The results are subject to certain approximations and assumptions, which are specified.

Barış Çakmak, Marco Pezzutto, Mauro Paternostro +1 more

We consider the dynamics of a collisional model in which both the system and environment are embodied by spin-$1/2$ particles. In order to include non-Markovian features in our model, we introduce interactions among the environmental qubits and investigate the effect that different models of such interaction have on the degree of non-Markovianity of the system's dynamics. By extending that interaction beyond the nearest neighbor, we enhance the degree of non-Markovianity in the system's dynamics. A further significant increase can be observed if a collective interaction with the forthcoming environmental qubits is considered. However, the observed degree of non-Markovianity in this case is nonmonotonic with the increasing number of qubits included in the interaction. Moreover, one can establish a connection between the degree of non-Markovianity in the evolution of the system and the fading behavior of quantum coherence in its state as the number of collisions grows. We complement our study with an investigation of system-environment correlations and present an example of their importance on a physical upper bound on the trace distance derivative.

Asif Zaman, Muhammad Faryad, Adam Zaman Chaudhry

Non-Markovian effects are often significant when the system-environment coupling is not weak. Indeed, we find that the non-Markovianity is negligible for a single two-level system undergoing pure dephasing via a weak interaction with a harmonic-oscillator environment. In this paper, we show that, within the framework of pure dephasing, the non-Markovianity displayed by a two-level system can, in fact, be far more pronounced. To demonstrate that this is indeed the case, we consider a pure dephasing model where a collection of two-level systems interacts with a common environment. We obtain analytically the dynamics of the collection of the two-level systems, and then take a partial trace over all the two-level systems except one. This remaining single two-level system exhibits markedly non-Markovian dynamics, even when the system-environment coupling is weak. This is due to the indirect interaction between the two-level systems, induced by their interaction with the common environment. In fact, this indirect interaction can not only increase the non-Markovianity by orders of magnitude, but also qualitatively change the characteristics of the non-Markovian behavior. For instance, for a single two-level system undergoing pure dephasing, the dynamics are Markovian for both Ohmic and sub-Ohmic environments. This is markedly not the case when we consider multiple two-level systems. These findings provide insights into controlling decoherence in multi-qubit quantum systems and have implications for quantum technologies where non-Markovianity can be a resource rather than a limitation.