Resonant tunneling diode and quantum chaos

Short note and Related References added by Scholarpedia Editor D.Shepelyansky in May 2020

Resonant tunneling spectroscopy is used to study the energy-level spectrum of a chaotic dynamical system, an electron in a trapezoidal potential well in the presence of a high magnetic field tilted relative to the confining barriers. This system is now known as a resonant tunneling diode. Distinct series of quasiperiodic resonances are observed in the current-voltage characteristics which change dramatically with tilt angle. These resonances are related to unstable closed orbits within the chaotic domain. The experimental results are explained by identifying and studying the properties of periodic orbits accessible to the tunneling electrons [1],[2]. The experimental discovery of a transition from integrable to chaotic electron dynamics are also reported in [3]. The analytical reduction of this system to the kicked top model and conditions of chaos and dynamical localization are given in [4]. The analytical and numerical results of different theory groups are available at [5,6,7,8,9]. The observation of scarred wavefunctions in this system was reported in [10] even if this was questioned on the basis of numerical analysis in the discussion presented in [11].

## [edit] Related References

1. T.M.Fromhold, L.Eaves, F.W.Sheard, M.L.Leadbeater, T.J.Foster, P.C.Main, "Magnetotunneling spectroscopy of a quantum well in the regime of classical chaos", Phys. Rev. Lett. 72: 2608 (1994)
2. T.M.Fromhold, P.B.Wilkinson, F.W.Sheard, L.Eaves, J.Miao, G.Edwards, "Manifestations of classical chaos in the energy level spectrum of a quantum well", Phys. Rev. Lett. 75: 1142 (1995)
3. G.Muller, G.S.Boebinger, H.Mathur, L.N.Pfeiffer, K.W.West, "Presursors and transition to chaos in a quantum well in a tilted magnetic field", Phys. Rev. Lett. 75: 2875 (1995)
4. D.L.Shepelyansky, A.D.Stone, "Chaotic Landau level mixing in classical and quantum wells", Phys. Rev. Lett. 74: 2098 (1995)
5. T.S.Monteiro, D.Delande, A.J.Fisher, G.S.Boebinger, "Bifurcations and the transition to chaos in the resonant-tunneling diode", Phys. Rev. B 56: 3913 (1997)
6. E.E.Narimanov, A.D.Stone, "Origin of strong scarring of wave functions in quantum wells in a tilted magnetic field", Phys. Rev. Lett. 80: 49 (1998)
7. E.E.Narimanov, A.D.Stone, "Theory of the periodic orbits of a chaotic quantum well", Phys. Rev. B 57: 9807 (1998)
8. E.E.Narimanov, A.D.Stone, G.S.Boebinger, "Semiclassical theory of magnetotransport through a chaotic quantum well", Phys/ Rev. Lett. 80: 4024 (1998)
9. D.S.Sagara, T.S.Monteiro, "Quantum chaos with nonperiodic, complex orbits in the resonant tunneling diode", Phys. Rev. Lett. 81: 5796 (1998)
10. P.B.Wilkinson, T.M.Fromhold, L.Eaves, F.W.Sheard, N.Miura, T.Takamasu, "Observation of 'scarred' wavefunctions in a quantum well with chaotic electron dynamics", Nature 380: 608 (1996)
11. T.S.Monteiro, D.Delande, J.-P.Connerade, "Have quantum scars been observed?", Nature 387: 863 (1997)

## [edit] See also internal links

Quantum chaos, Quantum scars, Kicked top, Mesoscopic transport and quantum chaos