Billiards in magnetic fields: A molecular dynamics approach

Aichinger, Michael; Janecek, S.; Räsänen, E.

doi:10.1103/physreve.81.016703

Cited by 10 publications

(10 citation statements)

References 41 publications

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“…Our first-principles model works in the spirit of molecular dynamics 11 by using microscopic equations for the motion of electrons in a charge-field and highlights the importance of electron-electron interactions together with the boundary conditions at particle reservoirs. In the classical microscopic model, the force F k on the kth electron consists of the forces F C k due to all other N = N e + N d electrons and donors, the confining potential V w , and the velocity dependent Lorentz force F L k ,…”

Section: Interacting Particles Simulation Of Semiconductor Devicesmentioning

confidence: 99%

Self-consistent calculation of electric potentials in Hall devices

et al. 2010

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Using a first-principles classical many-body simulation of a Hall bar, we study the necessary conditions for the formation of the Hall potential: (i) Ohmic contacts with metallic reservoirs, (ii) electron-electron interactions, and (iii) confinement to a finite system. By propagating thousands of interacting electrons over million time-steps we capture the build-up of the self-consistent potential. The microscopic model sheds light on the the current injection process and directly links the Hall effect to specific boundary conditions at the particle reservoirs.

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Section: Interacting Particles Simulation Of Semiconductor Devicesmentioning

confidence: 99%

Self-consistent calculation of electric potentials in Hall devices

et al. 2010

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“…With a magnetic field the system is no longer trivial, and no analytic solution is known. Another interesting feature of this system is that the corresponding classical system shows chaotic behavior [12,13], making the particle in a box with magnetic field an interesting testbed for quantum chaos studies.…”

Section: High Energy Eigenstates Of a Particle In A Box With A Magnetmentioning

confidence: 99%

Imaginary time propagation code for large-scale two-dimensional eigenvalue problems in magnetic fields

Luukko

Räsänen

2013

Computer Physics Communications

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We present a code for solving the single-particle, time-independent Schrödinger equation in two dimensions. Our program utilizes the imaginary time propagation (ITP) algorithm, and it includes the most recent developments in the ITP method: the arbitrary order operator factorization and the exact inclusion of a (possibly very strong) magnetic field. Our program is able to solve thousands of eigenstates of a two-dimensional quantum system in reasonable time with commonly available hardware. The main motivation behind our work is to allow the study of highly excited states and energy spectra of two-dimensional quantum dots and billiard systems with a single versatile code, e.g., in quantum chaos research. In our implementation we emphasize a modern and easily extensible design, simple and user-friendly interfaces, and an open-source development philosophy. Nature of problem: Numerical calculation of the lowest energy solutions (up to a few thousand, depending on available memory), of a single-particle, time-independent Schrödinger equation in two dimensions with or without a homogeneous magnetic field. Solution method: Imaginary time propagation (also known as the diffusion algorithm), with arbitrary even order factorization of the imaginary time evolution operator. Additional comments: Please see the README file distributed with the program for more information. The source code of our program is also available at https: //bitbucket.org/luukko/itp2d. Running time: Seconds to hours, depending on system size. Keywords

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“…The main distinction here from other works on annular billiards is that in the rotating frame the electron moves along curved paths between successive wall collisions. The introduction of a Coriolis term into the Hamiltonian upon the transformation to the rotating frame is, of course, akin to introducing an effective uniform magnetic field (and another frequency, the Larmor frequency) in which an electron moves on a curved path [15][16][17][18][19]. The laser wavelength is taken as 780 nm (corresponding to a frequency of 0.0584 a.u.)…”

Section: Introductionmentioning

confidence: 99%

Annular billiard dynamics in a circularly polarized strong laser field

et al. 2012

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We analyze the dynamics of a valence electron of the buckminsterfullerene molecule (C60) subjected to a circularly polarized laser field by modeling it with the motion of a classical particle in an annular billiard. We show that the phase space of the billiard model gives rise to three distinct trajectories: "whispering gallery orbits," which hit only the outer billiard wall; "daisy orbits," which hit both billiard walls (while rotating solely clockwise or counterclockwise for all time); and orbits that only visit the downfield part of the billiard, as measured relative to the laser term. These trajectories, in general, maintain their distinct features, even as the intensity is increased from 10(10) to 10(14) Wcm-2. We attribute this robust separation of phase space to the existence of twistless tori.

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Billiards in magnetic fields: A molecular dynamics approach

Cited by 10 publications

References 41 publications

Self-consistent calculation of electric potentials in Hall devices

Self-consistent calculation of electric potentials in Hall devices

Imaginary time propagation code for large-scale two-dimensional eigenvalue problems in magnetic fields

Annular billiard dynamics in a circularly polarized strong laser field

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