Abstract
Echoes are ubiquitous phenomena in several branches of physics, ranging from acoustics, optics, condensed matter and cold atoms to geophysics. They are at the base of a number of very useful experimental techniques, such as nuclear magnetic resonance, photon echo and time-reversal mirrors. Particularly interesting physical effects are obtained when the echo studies are performed on complex systems, either classically chaotic, disordered or many-body. Consequently, the term Loschmidt echo has been coined to designate and quantify the revival occurring when an imperfect time-reversal procedure is applied to a complex quantum system, or equivalently to characterize the stability of quantum evolution in the presence of perturbations. Here, we present the articles which discuss the work that has shaped the field in the past few years.
Highlights
In memory of Patricia Levstein.Loschmidt echo and time reversal in complex systemsArseni Goussev1, Rodolfo A
Where |ψ0 is the state of the system at time 0, H1 is the Hamiltonian governing the forward evolution, H2 is the Hamiltonian governing the backward evolution and t is the instant at which the reversal takes place. This measure was initially proposed by Peres in 1984 [1] in his attempt to understand the origin of irreversibility in quantum mechanics. He focused on the differences in the long-time behaviour of the fidelity in a single-particle system stemming from the nature of the underlying classical dynamics, be it regular or chaotic
Technical aspects of the Loschmidt echo and the rich variety of regimes for fidelity decay have been described in [7], which addresses the role of the initial state and the type of dynamics
Summary
In memory of Patricia Levstein.Loschmidt echo and time reversal in complex systemsArseni Goussev1, Rodolfo A. He focused on the differences in the long-time behaviour of the fidelity in a single-particle system stemming from the nature of the underlying classical dynamics, be it regular or chaotic. Following a short-time parabolic decay, the Loschmidt echo exhibits an exponential decay, where two different regimes can be observed depending on the perturbation strength.
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