Statistics of Resonances and of Delay Times in Quasiperiodic Schrödinger Equations

Steinbach, F.; Ossipov, A.; Geisel, Theo

doi:10.1103/physrevlett.85.4426

Cited by 32 publications

(33 citation statements)

References 27 publications

(41 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In all tunnelling phenomena, the concept of tunnelling time is a well-studied topic [1,[28][29][30][31][32][33][34]. However, relation between the tunnelling times and the decay time or mean lifetime τ =h/Γ r of QB states is not examined in detail in literature.…”

Section: Comparison Of Tunnelling Time and Decay Timementioning

confidence: 99%

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

et al. 2009

View full text Add to dashboard Cite

In analogy with the definition of resonant or quasi-bound states used in three-dimensional quantal scattering, we define the quasi-bound states that occur in onedimensional transmission generated by twin symmetric potential barriers and evaluate their energies and widths using two typical examples: (i) twin rectangular barrier and (ii) twin Gaussian-type barrier. The energies at which reflectionless transmission occurs correspond to these states and the widths of the transmission peaks are also the same as those of quasi-bound states. We compare the behaviour of the magnitude of wave functions of quasi-bound states with those for bound states and with the above-barrier state wave function. We deduce a Breit-Wigner-type resonance formula which neatly describes the variation of transmission coefficient as a function of energy at below-barrier energies. Similar formula with additional empirical term explains approximately the peaks of transmission coefficients at above-barrier energies as well. Further, we study the variation of tunnelling time as a function of energy and compare the same with transmission, reflection time and Breit-Wigner delay time around a quasi-bound state energy. We also find that tunnelling time is of the same order of magnitude as lifetime of the quasi-bound state, but somewhat larger.

show abstract

Section: Comparison Of Tunnelling Time and Decay Timementioning

confidence: 99%

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

et al. 2009

View full text Add to dashboard Cite

show abstract

“…The distribution of delay time in 1D system has been thoroughly studied both theoretically [11][12][13][14][15][16][17][18] and experimentally. 19,20 Texier and Comet 13 showed by various methods the universality of the distribution of τ in a 1D semi-infinite system, which has a τ −2 power-law tail at large τ in the localized regime.…”

Section: Introductionmentioning

confidence: 99%

“…This power law tail has also been confirmed by others. 12,14,16 It has been established that τ −2 behavior is valid for different types of disorder potential with δ, gaussian, box, and exponential decaying distributions. 11,12 For 2D systems with multichannels, most of the theoretical works are based on the random matrix theory (RMT).…”

Section: Introductionmentioning

confidence: 99%

Statistics of Wigner delay time in Anderson disordered systems

Wang

2011

Phys. Rev. B

View full text Add to dashboard Cite

We numerically investigate the statistical properties of Wigner delay time in Anderson disordered 1D, 2D and quantum dot (QD) systems. The distribution of proper delay time for each conducting channel is found to be universal in 2D and QD systems for all Dyson's symmetry classes and shows a piece-wise power law behavior in the strong localized regime. Two power law behaviors were identified with asymptotical scaling τ −1.5 and τ −2 , respectively that are independent of the number of conducting channels and Dyson's symmetry class. Two power-law regimes are separated by the relevant time scale τ0 ∼ h/∆ where ∆ is the average level spacing. It is found that the existence of necklace states is responsible for the second power-law behavior τ −2 , which has an extremely small distribution probability.

show abstract

“…7 Recently, several works have been devoted to deepen our understanding of the scattering properties of disordered systems by analyzing the distribution of resonance widths and Wigner delay times. 8,9,10,11,12,13,14,16,17 Both distribution functions have been shown to be closely related to the properties of the corresponding closed system, i.e., the fractality of the eigenstates and the critical features of the MIT. In this respect, detailed analysis have been performed for the three-dimensional (3D) Anderson model 14 and also for the power law band random matrix (PBRM) model.…”

Section: Introductionmentioning

confidence: 99%

Scattering at the Anderson transition: Power-law banded random matrix model

Méndez-Bermúdez

Varga

2006

Phys. Rev. B

View full text Add to dashboard Cite

We analyze the scattering properties of a periodic one-dimensional system at criticality represented by the so-called power-law banded random matrix model at the metal insulator transition. We focus on the scaling of Wigner delay times τ and resonance widths Γ. We found that the typical values of τ and Γ (calculated as the geometric mean) scale with the system size L as τ typ ∝ L D 1 and Γ typ ∝ L −(2−D 2 ) , where D1 is the information dimension and D2 is the correlation dimension of eigenfunctions of the corresponding closed system.

show abstract

Statistics of Resonances and of Delay Times in Quasiperiodic Schrödinger Equations

Cited by 32 publications

References 27 publications

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

Statistics of Wigner delay time in Anderson disordered systems

Scattering at the Anderson transition: Power-law banded random matrix model

Contact Info

Product

Resources

About