Conductance fluctuations in the ballistic regime: A probe of quantum chaos?

Jalabert, Rodolfo A.; Baranger, Harold U.; Stone, A. Douglas

doi:10.1103/physrevlett.65.2442

Cited by 466 publications

(461 citation statements)

References 14 publications

Supporting

Mentioning

437

Contrasting

Order By: Relevance

“…As in disordered systems, certain transport properties are found to be universal, like conductance fluctuations and weak localization properties of transport through cavities. [6][7][8][9][10][11] In contrast, if the dynamics is integrable, these features are in general not universal but depend on the specific system. Semiclassical methods have been applied to explain universal properties of chaotic transport as well as the nongeneric behavior of integrable cavities.…”

Section: Introductionmentioning

confidence: 95%

“…Semiclassical methods have been applied to explain universal properties of chaotic transport as well as the nongeneric behavior of integrable cavities. 6,7,9,12,13 Other experiments have been concerned with revealing signatures of classical periodic orbits in quantum phenomena. Examples are orbital magnetism in ballistic microstructures 14 and transport through antidot superlattices.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Universal quantum signature of mixed dynamics in antidot lattices

2005

View full text Add to dashboard Cite

We investigate phase coherent ballistic transport through antidot lattices in the generic case where the classical phase space has both regular and chaotic components. It is shown that the conductivity fluctuations have a non-Gaussian distribution, and that their moments have a power-law dependence on a semiclassical parameter, with fractional exponents. These exponents are obtained from bifurcating periodic orbits in the semiclassical approximation. They are universal in situations where sufficiently long orbits contribute.

show abstract

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Universal quantum signature of mixed dynamics in antidot lattices

2005

View full text Add to dashboard Cite

show abstract

“…In realistic quantum devices, nonhyperbolic dynamics with mixed phase space [33][34][35][36][37][38][39][40][41][42][43] can be expected to arise typically. Here we investigate the tunneling dynamics in classically nonhyperbolic systems in the presence of electronelectron interactions.…”

Section: Regularization Of Tunneling By Chaosmentioning

confidence: 99%

“…In closed chaotic Hamiltonian systems, the basic phenomena that have been and continue to be studied include energy level-spacing statistics [3][4][5] and quantum scarring . In open Hamiltonian systems, quantum chaotic scattering [33][34][35][36][37][38][39][40][41][42][43] has been investigated extensively. Quite recently, due to the significant development of graphene physics [44][45][46][47][48][49][50], relativistic quantum manifestations of classical chaos have become an interesting area of study [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65].…”

Section: Introductionmentioning

confidence: 99%

Quantum chaotic tunneling in graphene systems with electron-electron interactions

et al. 2014

View full text Add to dashboard Cite

An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem using graphene systems described by the Hubbard Hamiltonian in the setting of resonant tunneling. Such a system consists of two symmetric potential wells separated by a potential barrier, and the geometric shape of the whole domain can be chosen to generate integrable or chaotic dynamics in the classical limit. Employing a standard mean-field approach to calculating a large number of eigenenergies and eigenstates, we uncover a class of localized states with near-zero tunneling in the integrable systems. These states are not the edge states typically seen in graphene systems, and as such they are the consequence of many-body interactions. The physical origin of the non-edge-state type of localized states can be understood by the one-dimensional relativistic quantum tunneling dynamics through the solutions of the Dirac equation with appropriate boundary conditions. We demonstrate that, when the geometry of the system is modified to one with chaos, the localized states are effectively removed, implying that in realistic situations where many-body interactions are present, classical chaos is capable of facilitating greatly quantum tunneling. This result, besides its fundamental importance, can be useful for the development of nanoscale devices such as graphene-based resonant-tunneling diodes.

show abstract

“…On the other hand, the diagonal terms with s = u do not oscillate. If one is not interested in mesoscopic fluctuations of the spin conductance, or quantum corrections to it, only the terms with s = u have to be retained 16 . On the basis of the ergodic hypothesis of Ref.…”

Section: Semiclassical Approximationmentioning

confidence: 99%

Aharonov-Casher oscillations of spin current through a multichannel mesoscopic ring

Shlyapin

Mal’shukov

2010

Phys. Rev. B

View full text Add to dashboard Cite

The Aharonov-Casher (AC) oscillations of spin current through a 2D ballistic ring in the presence of Rashba spin-orbit interaction and external magnetic field has been calculated using the semiclassical path integral method. For classically chaotic trajectories the Fokker-Planck equation determining dynamics of the particle spin polarization has been derived. On the basis of this equation an analytic expression for the spin conductance has been obtained taking into account a finite width of the ring arms carrying large number of conducting channels. It was shown that the finite width results in a broadening and damping of spin current AC oscillations. We found that an external magnetic field leads to appearance of new nondiagonal components of the spin conductance, allowing thus by applying a rather weak magnetic field to change a direction of the transmitted spin current polarization.

show abstract

Conductance fluctuations in the ballistic regime: A probe of quantum chaos?

Cited by 466 publications

References 14 publications

Universal quantum signature of mixed dynamics in antidot lattices

Universal quantum signature of mixed dynamics in antidot lattices

Quantum chaotic tunneling in graphene systems with electron-electron interactions

Aharonov-Casher oscillations of spin current through a multichannel mesoscopic ring

Contact Info

Product

Resources

About