Probability Current and a Simulation of Particle Separation

Tellander, Felix; Ulander, Johan E. M.; Yakimenko, I. I.; Berggren, Karl‐Fredrik

doi:10.22186/jyi.31.4.1-6

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…The nodal lines intersect at nodal points, ψ(x,y) = 0, around which the current density circulates in the form of a vortex [50]. Much of the current structure can be obtained by studying only the nodal lines and nodal points [51]. The nodal points may, e.g., also be used to determine if an open quantum system is chaotic, as done in [52], and they give a qualitative indication of the transmission through the cavity [53].…”

Section: Probability Current Densitymentioning

confidence: 99%

Spectra, current flow, and wave-function morphology in a modelPT-symmetric quantum dot with external interactions

Tellander

Berggren

2017

Phys. Rev. A

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In this paper we use numerical simulations to study a two-dimensional (2D) quantum dot (cavity) with two leads for passing currents (electrons, photons, etc.) through the system. By introducing an imaginary potential in each lead the system is made symmetric under parity-time inversion (PT symmetric). This system is experimentally realizable in the form of, e.g., quantum dots in low-dimensional semiconductors, optical and electromagnetic cavities, and other classical wave analogs. The computational model introduced here for studying spectra, exceptional points (EPs), wave-function symmetries and morphology, and current flow includes thousands of interacting states. This supplements previous analytic studies of few interacting states by providing more detail and higher resolution. The Hamiltonian describing the system is non-Hermitian; thus, the eigenvalues are, in general, complex. The structure of the wave functions and probability current densities are studied in detail at and in between EPs. The statistics for EPs is evaluated, and reasons for a gradual dynamical crossover are identified.

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Section: Probability Current Densitymentioning

confidence: 99%

Spectra, current flow, and wave-function morphology in a modelPT-symmetric quantum dot with external interactions

Tellander

Berggren

2017

Phys. Rev. A

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“…where the doublets have different charge under a U (1) symmetry may possess an axionà la Weinberg and Wilczek [43,44], however, we postpone this to a later paper [45].…”

Section: Discussionmentioning

confidence: 99%

Anomaly-free model building with algebraic geometry

Rathsman

Tellander

2019

Phys. Rev. D

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We present a method to find anomaly-free gauged Froggatt-Nielsen type models using results from algebraic geometry. These methods should be of general interest for model building beyond the Standard Model (SM) when rational charges are required. We consider models with a gauged U (1) flavor symmetry with one flavon and two Higgs doublets and three right-handed SM singlets to provide three model examples based on different physical assumptions. The models we study are: anomaly-free with no SM neutral heavy chiral fermions, anomaly-free with SM neutral heavy chiral fermions, and supersymmetric with SM neutral heavy chiral fermions where the anomalies cancel via the Green-Schwarz mechanism. With these different models we show how algebraic methods may be used in model building; both to reduce the charge constraints by calculation of Gröbner bases, and to find rational solutions to cubic equations using Mordell-Weil generators.Using these tools we find three phenomenologically viable models explaining the observed flavor structure.

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Probability Current and a Simulation of Particle Separation

Cited by 2 publications

References 9 publications

Spectra, current flow, and wave-function morphology in a modelPT-symmetric quantum dot with external interactions

Spectra, current flow, and wave-function morphology in a modelPT-symmetric quantum dot with external interactions

Anomaly-free model building with algebraic geometry

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