Survival probability of a local excitation in a non-Markovian environment: Survival collapse, Zeno and anti-Zeno effects

Fiori, Elena Rufeil; Pastawski, Horacio M.

doi:10.1016/j.physb.2009.06.109

Cited by 6 publications

(9 citation statements)

References 21 publications

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Section: B Emergence Of the Correlation Holementioning

confidence: 73%

“…In the vicinity of the point where the decay of the survival probability changes from Gaussian to power-law, there occurs an interference between the two contributions. This causes a phenomenon known as survival collapse [41,76,77] that often results in P ini (t) <P ini , as indeed confirmed for spin- 1 2 systems in [40]. It is for times even longer, t > 10, that the correlation hole finally develops, first for the NNN model, where the minimum occurs at t ∼ 111 for the parameters of figure 2, and later for the defect model, where the minimum is at t ∼ 564.…”

Section: (B) Emergence Of the Correlation Holementioning

confidence: 99%

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Dynamical manifestations of quantum chaos: correlation hole and bulge

Torres-Herrera

Santos

2017

Phil. Trans. R. Soc. A.

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A main feature of a chaotic quantum system is a rigid spectrum where the levels do not cross. We discuss how the presence of level repulsion in lattice many-body quantum systems can be detected from the analysis of their time evolution instead of their energy spectra. This approach is advantageous to experiments that deal with dynamics, but have limited or no direct access to spectroscopy. Dynamical manifestations of avoided crossings occur at long times. They correspond to a drop, referred to as correlation hole, below the asymptotic value of the survival probability and by a bulge above the saturation point of the von Neumann entanglement entropy and the Shannon information entropy. In contrast, the evolution of these quantities at shorter times reflect the level of delocalization of the initial state, but not necessarily a rigid spectrum. The correlation hole is a general indicator of the integrable-chaos transition in disordered and clean models and as such can be used to detect the transition to the many-body localized phase in disordered interacting systems.

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Section: B Emergence Of the Correlation Holementioning

confidence: 73%

Section: (B) Emergence Of the Correlation Holementioning

confidence: 99%

Dynamical manifestations of quantum chaos: correlation hole and bulge

Torres-Herrera

Santos

2017

Phil. Trans. R. Soc. A.

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“…In this sense a non-Markovian environment is controlling the decay dynamics of the local excitation in this case, where a "quantum diffusion" described by a return term brings out the details of the spectral structure of the environment. 39,40 Anderson showed that when ε a is below the Fermi energy ε F and the energy of the doubly occupied state ε a + U is larger than ε F , a magnetic state is possible if U is sufficiently large and/or σ a sufficiently small. 29 In the case of Li interacting with graphene the requirement of a hybridization width small enough to allow for a magnetic state is fulfilled.…”

Section: A Hamiltonian Termsmentioning

confidence: 99%

Localized description of band structure effects on Li atom interaction with graphene

2011

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We study theoretically the localized aspects of the interaction between an Li atom and graphene. To this end, we use an ab initio calculation of the Hamiltonian terms within the Anderson model that allows us to take into account the chemical properties of Li and C atoms and the two-dimensional band structure of graphene. In this way, physical magnitudes of interest such as the hybridization function, the adatom spectral density and valence occupation are calculated. We find that the interference between the adatom neighboring sites together with the pronounced energy gap around the point lead to negligible hybridization widths in a wide range of energies and are practically not dependent on the adsorption site. Consequently, this very weak coupling regime makes possible a local magnetic moment formation. Moreover, the strong suppression of the atom level broadening allows for an explanation of the unexpected neutralization measured at low energies in experiments of Li + scattering by a highly oriented pyrolytic graphite surface.

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“…If a suitable change of basis is applied (basically turning into symmetric and anti symmetric basis), then it is only necessary to analyze two semi infinite linear chains (a particular case treated in Ref. [28,72]). Since the initial condition has equal weight on both effective chains, the corresponding rates for them have to be added.…”

Section: Systemmentioning

confidence: 99%

“…This problem has been previously addressed in Refs. [28] and [72] and we recall the LDoS computed there. Thus in Fig.…”

Section: N=1mentioning

confidence: 99%

Non-Markovian decay and dynamics of decoherence in private and public environments

Dente

Zangara²,

Pastawski³

2011

Phys. Rev. A

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We study the decay process in an open system, emphasizing on the relevance of the environment's spectral structure. Non-Markovian effects are included to quantitatively analyze the degradation rate of the coherent evolution. The way in which a two level system is coupled to different environments is specifically addressed: multiple connections to a single bath (public environment) or single connections to multiple baths (private environments). We numerically evaluate the decay rate of a local excitation by using the Survival Probability and the Loschmidt Echo. These rates are compared to analytical results obtained from the standard Fermi Golden Rule (FGR) in Wide Band Approximation, and a Self-Consistent evaluation that accounts for the bath's memory in cases where an exact analytical solution is possible. We observe that the correlations appearing in a public bath introduce further deviations from the FGR as compared with a private bath.

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Survival probability of a local excitation in a non-Markovian environment: Survival collapse, Zeno and anti-Zeno effects

Cited by 6 publications

References 21 publications

Dynamical manifestations of quantum chaos: correlation hole and bulge

Dynamical manifestations of quantum chaos: correlation hole and bulge

Localized description of band structure effects on Li atom interaction with graphene

Non-Markovian decay and dynamics of decoherence in private and public environments

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