Evidence for quantum states corresponding to families of stable and chaotic classical orbits in a wide potential well

Fromhold, T.M.; Fogarty, A.; Eaves, L.; Sheard, F. W.; Henini, M.; Foster, T.J.; Main, P. C.; Hill, G.

doi:10.1103/physrevb.51.18029

Cited by 24 publications

(7 citation statements)

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“…We note that this system has been extensively studied numerically, both classically via the Surfaceof-Section method 8,3,12 , and quantum-mechanically by analysis of scaled spectra 10,11 and tunneling current 6,7,10,11 . In addition to our own semiclassical treatment of the problem 5 , recently there has been an independent work by Bogomolny and Rouben which presents two possible semiclassical tunneling formulas for this system 13 .…”

mentioning

confidence: 99%

Quantum chaos in quantum wells

Narimanov

Stone

1999

Physica D: Nonlinear Phenomena

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mentioning

confidence: 99%

Quantum chaos in quantum wells

Narimanov

Stone

1999

Physica D: Nonlinear Phenomena

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“…As V is varied, resonant tunnelling into the energy levels ε n of the QW might be expected to produce an irregular sequence of peaks in the current-voltage characteristic I(V). Previous measurements on RTDs with 60 nm and 120 nm wide QWs in magnetic fields up to 11 T, revealed quasiperiodic series of resonant peaks, which were attributed to Gutzwiller fluctuations in the density of levels associated with distinct unstable closed orbits in the QW [19,21]. In these studies, the QWs were too wide for individual energy levels to be resolved.…”

Section: Analysis Of the Data And Discussionmentioning

confidence: 65%

“…According to the uncertainty principle, this leads to an energy level broadening of the quantum well states by about 5-6 meV. In our original experiments, we employed wide quantum wells of width 60 and 120 nm [19][20][21]. In this case, the mean level separation is less than the linewidth.…”

Section: Quantum Chaos In Semiconductor Heterostructuresmentioning

confidence: 99%

“…However, the magnetic field can induce chaotic motion when it is tilted at an angle to the barriers [18][19][20][21][22][23][24]. In this case, the cyclotron motion becomes "scrambled up" with successive bounces off the barrier walls.…”

Section: Quantum Chaos In Semiconductor Heterostructuresmentioning

confidence: 99%

“…It is easy to demonstrate the existence of completely chaotic motion in this situation by generating Poincaré sections. This involves plotting successive values of the in-plane velocity components, v, v,, as points in 2D space for successive hits on one of the barrier walls [18,21]. At a sufficiently large angle of tilt, 8, from the normal to the barriers, the Poincaré sections have a "dusty" appearance due to a random distribution of points [20].…”

Section: Quantum Chaos In Semiconductor Heterostructuresmentioning

confidence: 99%

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Resonant Tunnelling Studies of Chaos in Quantised Systems

et al. 1997

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This paper gives a brief introductory overview of quantum chaology, with particular reference to recent experimental work involving the use of semiconductor heterostructures. In the presence of a tilted magnetic field, a double-barrier resonant-tunnelling device incorporating a quantum well produces a chaotic stadium for electron motion. The basic properties of this system are described. It is shown how resonant magnetotunnelling spectroscopy provides firm experimental evidence for the effect of scarred wave functions on a physically-measurable property, in this case the measured current-voltage characteristics of the device. The paper concludes with some speculations concerning for the development of this field.PACS numbers: 72.20.Μy, 73.40.Gk, 85.30.Μn, 05.45.+b Quantum biHiards, unstable orbits and scarred wave functionsQuantum chaology has been defined by Berry [1] as the "study of semiclassical, but non-classical, behaviour of systems whose classical motion exhibits chaos". Much of the theoretical work in this field has focused on the classical motion and corresponding eigenstates of particles which are confined to move within a twodimensional stadium (also commonly referred to as a billiard) [1][2][3]. Particles are assumed to bounce elastically off the walls of the stadium, with specular reflection. The motion within the confines of the stadium is normally assumed to be free and frictionless. Particles moving in square-and circular-shaped stadia have regular motion, with one or two characteristic periods; in mathematical terms, this means that the equation of motion is separable into two one-dimensional parts. Examples of stadia which give rise to chaotic motion are the Bunimovich stadium (a square area with two semicircular areas adjoined to opposite sides; for experimental stadia see Ref. [4]) and the Sinai billiard [5] (a square with a hard-walled circular "nogo" area in the centre). The properties of unstable but periodic classical orbits are of fundamental importance for the quantum chaology of these types of billiard [1,2]. These orbits are associated with regular clustering of the quantised energy levels of the system, which gives rise to energy-periodic fluctuations in the density of states. This effect is described in terms of the well-known (609)

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