We address the question of how weak perturbations, which are quite ineffective in small many-body systems, can lead to decoherence and hence to irreversibility when they proliferate as the system size increases. This question is at the heart of solid-state NMR. There, an initially local polarization spreads all over due to spin-spin interactions that conserve the total spin projection, leading to an equilibration of the polarization. In principle, this quantum dynamics can be reversed by changing the sign of the Hamiltonian. However, the reversal is usually perturbed by nonreversible interactions that act as a decoherence source. The fraction of the local excitation recovered defines the Loschmidt echo (LE), here evaluated in a series of closed $N$ spin systems with all-to-all interactions. The most remarkable regime of the LE decay occurs when the perturbation induces proliferated effective interactions. We show that if this perturbation exceeds some lower bound, the decay is ruled by an effective Fermi golden rule (FGR). Such a lower bound shrinks as $N$ increases, becoming the leading mechanism for LE decay in the thermodynamic limit. Once the polarization stayed equilibrated longer than the FGR time, it remains equilibrated in spite of the reversal procedure.We address the question of how weak perturbations, which are quite ineffective in small many-body systems, can lead to decoherence and hence to irreversibility when they proliferate as the system size increases. This question is at the heart of solid-state NMR. There, an initially local polarization spreads all over due to spin-spin interactions that conserve the total spin projection, leading to an equilibration of the polarization. In principle, this quantum dynamics can be reversed by changing the sign of the Hamiltonian. However, the reversal is usually perturbed by nonreversible interactions that act as a decoherence source. The fraction of the local excitation recovered defines the Loschmidt echo (LE), here evaluated in a series of closed $N$ spin systems with all-to-all interactions. The most remarkable regime of the LE decay occurs when the perturbation induces proliferated effective interactions. We show that if this perturbation exceeds some lower bound, the decay is ruled by an effective Fermi golden rule (FGR). Such a lower bound shrinks as $N$ increases, becoming the leading mechanism for LE decay in the thermodynamic limit. Once the polarization stayed equilibrated longer than the FGR time, it remains equilibrated in spite of the reversal procedure.

arXiv:1412.4070Physical Review AApr 13, 201513 citations

Adiabatic Decoherence

Dima Mozyrsky, Vladimir Privman A

arXiv:quant-ph/9709020Journal of Statistical PhysicsMay 1, 199881 citations

Equilibration and thermalization in finite quantum systems

Vyacheslav I. Yukalov

Experiments with trapped atomic gases have opened novel possibilities for studying the evolution of nonequilibrium finite quantum systems, which revived the necessity of reconsidering and developing the theory of such processes. This review analyzes the basic approaches to describing the phenomena of equilibration, thermalization, and decoherence in finite quantum systems. Isolated, nonisolated, and quasi-isolated quantum systems are considered. The relations between equilibration, decoherence, and the existence of time arrow are emphasized. The possibility for the occurrence of rare events, preventing complete equilibration, are mentioned.Experiments with trapped atomic gases have opened novel possibilities for studying the evolution of nonequilibrium finite quantum systems, which revived the necessity of reconsidering and developing the theory of such processes. This review analyzes the basic approaches to describing the phenomena of equilibration, thermalization, and decoherence in finite quantum systems. Isolated, nonisolated, and quasi-isolated quantum systems are considered. The relations between equilibration, decoherence, and the existence of time arrow are emphasized. The possibility for the occurrence of rare events, preventing complete equilibration, are mentioned.

arXiv:1201.2781Laser Physics LettersMay 2, 2011157 citations

Decoherence for phase-sensitive relaxation

Dmitri S. Kilin, Michael Schreiber

Journal of LuminescenceDec 1, 20003 citations

Environment-induced super selection without pointer states

Christian Gogolin

We investigate decoherence and equilibration in the experimentally relevant situation of weak coupling to an environment. We consider small subsystems of large closed quantum systems that evolve according to the von Neumann equation. Without approximations and without making any special assumptions on the form of the interaction we prove that, for almost all initial states and almost all times, the off-diagonal elements of the density matrix of the subsystem in the eigenbasis of its local Hamiltonian must be small whenever the energy difference of the corresponding eigenstates is larger than the interaction energy. This proves that decoherence with respect to the local energy eigenbasis is a natural property of weakly interacting quantum systems.We investigate decoherence and equilibration in the experimentally relevant situation of weak coupling to an environment. We consider small subsystems of large closed quantum systems that evolve according to the von Neumann equation. Without approximations and without making any special assumptions on the form of the interaction we prove that, for almost all initial states and almost all times, the off-diagonal elements of the density matrix of the subsystem in the eigenbasis of its local Hamiltonian must be small whenever the energy difference of the corresponding eigenstates is larger than the interaction energy. This proves that decoherence with respect to the local energy eigenbasis is a natural property of weakly interacting quantum systems.

arXiv:0908.2921Physical Review EMay 20, 201033 citations

N

spin systems with all-to-all interactions. The most remarkable regime of the LE decay occurs when the perturbation induces proliferated effective interactions. We show that if this perturbation exceeds some lower bound, the decay is ruled by an effective Fermi golden rule (FGR). Such a lower bound shrinks as

N

increases, becoming the leading mechanism for LE decay in the thermodynamic limit. Once the polarization stayed equilibrated longer than the FGR time, it remains equilibrated in spite of the reversal procedure.