Analyses of the transmission of the disorder from a disturbed environment to a spin chain

Abstract

We study spin chains submitted to disturbed kick trains described by classical dynamical processes. The spin chains are described by Heisenberg and Ising models. We consider decoherence, entanglement and relaxation processes induced by the kick irregularity in the multipartite system (the spin chain). We show that the different couplings transmit the disorder along the chain differently and also to each spin density matrix with different efficiencies. In order to analyze and to interpret the observed effects we use a semi-classical analysis across the Husimi distribution. It consists to consider the classical spin orientation movements. A possibility of conserving the order into the spin chain is finally analyzed.

Schrödinger–Koopman quasienergy states of quantum systems driven by classical flow

“…As for the previous example, we consider three initial conditions: The dynamics are represented figure 8. We have a decoherence phenomenon for large but also for small initial dispersions of the kicks, in accordance with the chaotic behaviour (and with the sensibility to initial conditions of the flow, for a detailed discussion see [24,25]). As expected, the fundamental quasienergy state is a steady state of the quantum system for which the reduced density matrix is the microcanonical density matrix 1 (θ)).…”

Chaos, decoherence and emergent extradimensions in D-brane dynamics with fluctuations

“…This spin is subject to the entanglement with the string attachment degree of freedom, to the classical chaotic fluctuations of X and x, and to the quantum chaos induced by H eff after the thermalization. In previous works [9][10][11], we have shown that a quantum system submitted to a chaotic flow presents an horizon of coherence, an initial duration where the quantum system is preserved from the decoherence phenomenon induced by the chaos. This horizon of coherence is a quantum version of the horizon of predictability of the classical chaotic flows (see discussion in [12]).…”

“…The fermionic string is then driven by a chaotic system. In previous papers [9][10][11] we have shown that quantum systems driven by chaotic flows are distinguished from quantum systems driven by random noises by a phenomenon called horizon of coherence, i.e. a duration at the beginning of the dynamics in which the quantum coherence is sustained before to fall with an increase of the entropy.…”

Information transmission and control in a chaotically kicked spin chain

“…The classical entropy (the disorder of the kick bath) begins from the horizon of predictability and the quantum entropy (the disorder of the spin chain), begins from the horizon of coherence. Even if the interaction and the entanglement allow a better transmission of the disorder into the spin chain (see [18]), the time required for the transmission of the disorder from the classical bath to the quantum one is the same as without interaction. We also see that the entropy of the spin chain increases only if the cumulated classical entropy exceeds a threshold value, S max .…”

“…A central question is to know if the horizon of coherence remains in spite of the coupling between the spins and if it is possible to control the spins before this horizon using appropriate stationary kicks. In the paper [18] we have already seen the general behaviour of a ten spin chain coupled by a nearestneighbour Heisenberg, Ising-Z and Ising-X interaction and submitted to various ultrashort kick dynamics (stationary, drift, microcanonical and Markovian). It results from this model that the coupling between the spins of the chain allows a better transmission of the disorder (the disorder into a spin chain being defined as a large difference between the states of the different spins) whatever the coupling.…”