Lifshitz singularities in random harmonic chains: Periodic amplitudes near the band edge and near special frequencies

Nieuwenhuizen, Th. M.; Luck, J. M.

doi:10.1007/bf01019680

Cited by 12 publications

(4 citation statements)

References 13 publications

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“…Along the lines of [61], let us parametrize the boundary conditions imposed by the rest of the sample as…”

Section: A Classical Particlementioning

confidence: 99%

“…Indeed it only misses an oscillatory prefactor of order unity. This prefactor has been shown to be a periodic function of π/ √ E with unit period, which reflects the discrete nature of the underlying chain, and can be expressed in terms of the distribution of the boundary parameters Y L and Y R at E = 0 [61].…”

Section: A Classical Particlementioning

confidence: 99%

“…In order to proceed, it is therefore necessary to determine the distribution of these boundary parameters. This can be done as follows, along the lines of [61]. In the theory of one-dimensional disordered systems (see e.g.…”

Section: A Quantum Particlementioning

confidence: 99%

“…In the classical situation, we review the predictions of the theory of Lifshitz tails. We thus introduce tools from the theory of one-dimensional disordered systems [61,62], which are also pertinent to the analysis of the quantum situation. In the latter case, for a large but finite system, the decay rate of the survival probability is a fluctuating quantity, whose distribution is investigated.…”

Section: Introductionmentioning

confidence: 99%

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Survival of Classical and Quantum Particles in the Presence of Traps

2014

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We present a detailed comparison of the motion of a classical and of a quantum particle in the presence of trapping sites, within the framework of continuous-time classical and quantum random walk. The main emphasis is on the qualitative differences in the temporal behavior of the survival probabilities of both kinds of particles. As a general rule, static traps are far less efficient to absorb quantum particles than classical ones. Several lattice geometries are successively considered: an infinite chain with a single trap, a finite ring with a single trap, a finite ring with several traps, and an infinite chain and a higher-dimensional lattice with a random distribution of traps with a given density. For the latter disordered systems, the classical and the quantum survival probabilities obey a stretched exponential asymptotic decay, albeit with different exponents. These results confirm earlier predictions, and the corresponding amplitudes are evaluated. In the one-dimensional geometry of the infinite chain, we obtain a full analytical prediction for the amplitude of the quantum problem, including its dependence on the trap density and strength.

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“…Along the lines of [61], let us parametrize the boundary conditions imposed by the rest of the sample as…”

Section: A Classical Particlementioning

confidence: 99%

Section: A Classical Particlementioning

confidence: 99%

Section: A Quantum Particlementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations