### Abstract

We consider discrete potentials as controls in systems of finite difference equations which are discretizations of a 1-D Schrödinger equation. We give examples of palindromic potentials which have corresponding steerable initial-terminal pairs which are not mirror-symmetric. For a set of palindromic potentials, we show that the corresponding steerable pairs that satisfy a localization property are mirror-symmetric. We express the initial and terminal states in these pairs explicitly as scalar multiples of vector-valued functions of a parameter in the control.

Original language | English (US) |
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Pages (from-to) | 1601-1621 |

Number of pages | 21 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 23 |

Issue number | 4 |

DOIs | |

State | Published - Jun 2018 |

### Fingerprint

### Keywords

- Complex-valued matrix
- Control
- Mirror
- Palindromic
- Potential
- Schrödinger
- Symmetry

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

**Palindromic control and mirror symmetries in finite difference discretizations of 1-D schrödinger equations.** / Kime, Katherine A.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Palindromic control and mirror symmetries in finite difference discretizations of 1-D schrödinger equations

AU - Kime, Katherine A.

PY - 2018/6

Y1 - 2018/6

N2 - We consider discrete potentials as controls in systems of finite difference equations which are discretizations of a 1-D Schrödinger equation. We give examples of palindromic potentials which have corresponding steerable initial-terminal pairs which are not mirror-symmetric. For a set of palindromic potentials, we show that the corresponding steerable pairs that satisfy a localization property are mirror-symmetric. We express the initial and terminal states in these pairs explicitly as scalar multiples of vector-valued functions of a parameter in the control.

AB - We consider discrete potentials as controls in systems of finite difference equations which are discretizations of a 1-D Schrödinger equation. We give examples of palindromic potentials which have corresponding steerable initial-terminal pairs which are not mirror-symmetric. For a set of palindromic potentials, we show that the corresponding steerable pairs that satisfy a localization property are mirror-symmetric. We express the initial and terminal states in these pairs explicitly as scalar multiples of vector-valued functions of a parameter in the control.

KW - Complex-valued matrix

KW - Control

KW - Mirror

KW - Palindromic

KW - Potential

KW - Schrödinger

KW - Symmetry

UR - http://www.scopus.com/inward/record.url?scp=85046773603&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85046773603&partnerID=8YFLogxK

U2 - 10.3934/dcdsb.2018063

DO - 10.3934/dcdsb.2018063

M3 - Article

AN - SCOPUS:85046773603

VL - 23

SP - 1601

EP - 1621

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 4

ER -