Browsing by Subject "Quantum chaos"

Now showing 1 - 4 of 4

Atom optics experiments in quantum chaos
(2001-12) Oskay, Windell Haven; Raizen, Mark G.
Electronic transport under strong optical radiation and quantum chaos in semiconductor nanostructures
(2003) Li, Wenjun; Reichl, L. E.
Quantum chaos and electron transport properties in a quantum waveguide
(2008-05) Lee, Hoshik, 1975-; Reichl, L. E.
We numerically investigate electron transport properties in an electron waveguide which can be constructed in 2DEG of the heterostructure of GaAs and AlGaAs. We apply R-matrix theory to solve a Schrödinger equation and construct a S-matrix, and we then calculate conductance of an electron waveguide. We study single impurity scattering in a waveguide. A [delta]-function model as a single impurity is very attractive, but it has been known that [delta]-function potential does not give a convergent result in two or higher space dimensions. However, we find that it can be used as a single impurity in a waveguide with the truncation of the number of modes. We also compute conductance for a finite size impurity by using R-matrix theory. We propose an appropriate criteria for determining the cut-off mode for a [delta]-function impurity that reproduces the conductance of a waveguide when a finite impurity presents. We find quantum scattering echoes in a ripple waveguide. A ripple waveguide (or cavity) is widely used for quantum chaos studies because it is easy to control a particle's dynamics. Moreover we can obtain an exact expression of Hamiltonian matrix with for the waveguide using a simple coordinate transformation. Having an exact Hamiltonian matrix reduces computation time significantly. It saves a lot of computational needs. We identify three families of resonance which correspond to three different classical phase space structures. Quasi bound states of one of those resonances reside on a hetero-clinic tangle formed by unstable manifolds and stable manifolds in the phase space of a corresponding classical system. Resonances due to these states appear in the conductance in a nearly periodic manner as a function of energy. Period from energy frequency gives a good agreement with a prediction of the classical theory. We also demonstrate wavepacket dynamics in a ripple waveguide. We find quantum echoes in the transmitted probability of a wavepacket. The period of echoes also agrees with the classical predictions. We also compute the electron transmission probability through a multi-ripple electron waveguide. We find an effect analogous to the Dicke effect in the multi-ripple electron waveguide. We show that one of the S-matrix poles, that of the super-radiant resonance state, withdraws further from the real axis as each ripple is added. The lifetime of the super-radiant state, for N quantum dots, decreases as [1/N] . This behavior of the lifetime of the super-radiant state is a signature of the Dicke effect.
Quantum chaos, scattering, and BICs on smooth potentials
(2019-08-08) Porter, Maxwell Dare; Reichl, L. E.; Morrison, Philip J.; Niu, Qian; Dicus, Duane A.; La Cour, Brian R.
In this dissertation, quantum signatures of chaos and scattering dynamics on several smooth potential models are investigated. In the second chapter, we study chaos in a honeycomb lattice reminiscent of graphene [Phys. Rev. E 93, 012204 (2016)].We show classical chaos to exist in a wide energy range, identify key stable and unstable orbits, and find a quantum eigenstate with irregular nodal structure that’s suggestive of quantum chaos. Newer work for this dissertation shows this model can approximately reproduce the band structure of graphene with only two tuning parameters at low computational cost. In the third chapter, we study a square lattice of Gaussians with variable width [Phys. Rev. E 95, 052213 (2017)]. We find underlying classical chaos correlates with more avoided crossings in band structure, causing frequent mixing of eigenstates. We also find hints of eigenstate scarring. Newer work for this dissertation shows some similarity to the classic Sinai billiard, but with stronger chaos due to the smooth Gaussian peaks, and mixed dynamics due to the potential saddles. In the fourth chapter, we further study quantum chaos in a square lattice [Chaos 27, 104604 (2017)]. We give stronger evidence that underlying chaos causes avoided crossings in the band structure, both on and off the Brillouin zone symmetry lines, and give further examples of eigenstate mixing. We then provide stronger evidence of quantum chaos via energy level spacing distributions. In the fifth chapter, we study scattering from a chaotic triple Gaussian potential [Phys. Rev. E 97, 042206 (2018)]. We use Wigner-Eisenbud (W-E) reaction matrix scattering theory to find quasibound state resonances, and corroborate them with Wigner-Smith delay time plots, reaction region eigenstate plots, and the non-Hermitian Hamiltonian method. We also give evidence of classical and quantum chaos. In the sixth chapter, we use W-E scattering theory to demonstrate that quantum bound states called BICs and long-lived quasibound states exist in the scattering continuum of a quasi-1D Gaussian well lattice [Physica B 571, 15 (2019)]. The BICs come in two types: one protected from decaying by reflection symmetry, the other protected by discrete translational symmetry (conservation of Bloch momentum). The long-lived quasibound states come in odd-even pairs and exist to high energies. The reaction region eigenstates corresponding to these special scattering states are shown to be localized and largely independent of the reaction region boundary (often called the "channel radius").