Quantum Zeno effect: Quantum shuffling and Markovianity
ABSTRACT The behavior displayed by a quantum system when it is perturbed by a series of von Neumann measurements along time is analyzed. Because of the similarity between this general process with giving a deck of playing cards a shuffle, here it is referred to as quantum shuffling, showing that the quantum Zeno and anti-Zeno effects emerge naturally as two time limits. Within this framework, a connection between the gradual transition from anti-Zeno to Zeno behavior and the appearance of an underlying Markovian dynamics is found. Accordingly, although a priori it might result counterintuitive, the quantum Zeno effect corresponds to a dynamical regime where any trace of knowledge on how the unperturbed system should evolve initially is wiped out (very rapid shuffling). This would explain why the system apparently does not evolve or decay for a relatively long time, although it eventually undergoes an exponential decay. By means of a simple working model, conditions characterizing the shuffling dynamics have been determined, which can be of help to understand and to devise quantum control mechanisms in a number of processes from the atomic, molecular and optical physics.Graphical abstractHighlights► The concept of quantum shuffling process is introduced. ► The quantum Zeno and anti-Zeno effects are seen as time limits of this process. ► The quantum shuffling induces a Markovian dynamics in the quantum Zeno limit. ► Analytical results are found for a non-stationary Gaussian wave packet. ► A link between the two Zeno regimes and the wave-packet natural time scales is found.
Full-textDOI: · Available from: Octavio Roncero, May 30, 2015
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ABSTRACT: As an application of the polymer quantization scheme, in this work we investigate the one dimensional quantum mechanical tunneling phenomenon from the perspective of polymer representation of a non-relativistic point particle and derive the transmission and reflection coefficients. Since any tunneling phenomenon inevitably evokes a tunneling time we attempt an analytical calculation of tunneling times by defining an operator well suited in discrete spatial geometry. The results that we come up with hint at appearance of the Quantum Zeno Effect in polymer framework.Physics Letters A 09/2014; 378(44). DOI:10.1016/j.physleta.2014.09.044 · 1.63 Impact Factor
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ABSTRACT: In spite of its apparent simplicity, the dynamics of single wave packets contains valuable physical information to understand more complex quantum-mechanical time-dependent problems and phenomena. In this chapter, an analysis of wave packet dynamics stressing different aspects of physical interest is presented, such as the role of translational motion and spreading, and how they influence its subsequent evolution are widely discussed. Diffraction will be considered in the context of how boundaries influence the subsequent wave-packet evolution, and the concepts of nonlocality and classical limit will be revisited. Going beyond standard treatments, phenomena such as space localization under the influence of a (quantum) viscid or viscous medium, or the quantum Zeno (and anti-Zeno) effect arising after a series of frequently repeated measurements will be considered. In this regard, the concept of quantum stochastic trajectory will also be introduced, discussing its connection to the so-called weak measurements.