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Journal of Physics Conference Series

Fast-Forward of Local-Phased-Regularized Spinor in Massless 2+1-Dimensions Adiabatic Dirac Dynamics

Ryan Sugihakim, Iwan Setiawan, Bobby Eka Gunara

Published Jun 1, 2021• 6 citations
Publisher

Abstract

Abstract We discuss a method of controlling Dirac dynamics in (2+1)-dimensions using adiabatic fast-forward method proposed by Masuda-Nakamura. Due to infinitely large amount of time of adiabaticity, we have to use an infinitely large scaling factor to shorten the time interval. Thus, we need a regularization to remove this infinity. Our strategy is analogue to adiabatic fast-forward of Schrodinger equation. That is using an auxiliary Hamiltonian but now we use two phase factors applied to the components of spinor. We applied to a case where a system is controlled by uniform magnetic field.

DOI
10.1088/1742-6596/1951/1/012068

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Abstract We discuss a method of controlling Dirac dynamics in (2+1)-dimensions using adiabatic fast-forward method proposed by Masuda-Nakamura. Due to infinitely large amount of time of adiabaticity, we have to use an infinitely large scaling factor to shorten the time interval. Thus, we need a regularization to remove this infinity. Our strategy is analogue to adiabatic fast-forward of Schrodinger equation. That is using an auxiliary Hamiltonian but now we use two phase factors applied to the components of spinor. We applied to a case where a system is controlled by uniform magnetic field.
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We study a scheme of fast-forward adiabatic quantum dynamics of a (2 + 1) Dirac particle. This scheme was originally proposed by Masuda and Nakamura. In this scheme, we include the adiabatic parameter that maintains the adiabatic motion of the particle and fast forward its motion by introducing a time scaling parameter. The fast forward adiabatic state is obtained by determining the regularization term and driving potential. We introduce the proposed method to the system with the Dirac particle using a (2 + 1) dimensiontime- dependent Dirac equation and obtain the regularization term, the driving scalar potential VFF and the driving vector potential AFF . By tuning the driving electric field, this method can accelerate the adiabatic dynamics of an electron as a Dirac particle trapped in the ground state in the plane xy and an electric field in the x direction and a constant magnetic field in the y direction. This acceleration will preserve the ground state of the wave function from the initial time to the final time.
Abstract We discussed a method to accelerate an adiabatic quantum dynamics of XY spin model by using the fast-forward method proposed by Masuda and Nakamura. The Accelerated scheme is constructed by adding the driving Hamiltonian to the original Hamiltonian and speeding it up with a large time-scaling factor and an adiabatic parameter that realizes adiabatic quantum dynamics in a shortened time. Accelerated adiabatic dynamics start by assuming the candidate of driving Hamiltonian consists of the pair-wise exchange interaction and magnetic field. The driving Hamiltonian terms multiplied by the velocity function together with the original Hamiltonian give fast-forward driving for adiabatic states. We apply our method to XY spin model by considering three spin systems on the Kagome lattice. In this model, we obtained the XY pair-wise exchange interaction of nearest neighbors and next-nearest neighbors should be added to the original Hamiltonian as a driving interaction to accelerate the adiabatic motion. This pair-wise driving interaction in the fast-forward scheme guarantees the complete fidelity of accelerated states.
Abstract We study a scheme to accelerate adiabatic quantum dynamics of Dirac particle. This scheme using the strategy of combining two opposite ideas: infinitely-large time-magnification factor (𝛼̅) and infinitely-small growth rate (𝜖) of adiabatic parameter. The accelerated adiabatic state is obtained by obtaining the regularization term and driving potential. We introduce the proposed method to the system of two level systems of Dirac particle by using a (1 + 1) dimension time dependent Dirac equation and obtained the regularization term. By tuning the driving magnetic field, this method to be able to accelerate adiabatic dynamics of electron as a Dirac particle in the ground state that considered as a two level system. This acceleration will preserve the ground state of the wave function from initial to the final time.
This research examines the application of the fast forward method to single spin with Rabi frequency. In this study, the electron spin dynamics are examined by accelerating adiabatic quantum dynamics. Through the concept of adiabatic will be obtained unchanged state of the system, at the beginning and end of the evolution of the system. This study aims to obtain an additional Hamiltonian on the concept of accelerated adiabatic quantum dynamics on single spin. The method used is the fast forward method developed by Masuda and Nakamura. The result of this research is to obtain the additional Hamiltonian “equation 54” and the driving magnetic field through the fast forward method “equation 56”. The fast forward method is applied by first obtaining the eigenvalues of the Hamiltonian system. Furthermore, by reviewing the lowest energy state (ground state). It is concluded that this study obtained an additional Hamiltonian term with a driving magnetic field that ensures that a single spin can move from the initial state to the final state in a short time, while maintaining the characteristics of each energy level in the system.
This research examines the application of the fast forward method to single spin with Rabi frequency. In this study, the electron spin dynamics are examined by accelerating adiabatic quantum dynamics. Through the concept of adiabatic will be obtained unchanged state of the system, at the beginning and end of the evolution of the system. This study aims to obtain an additional Hamiltonian on the concept of accelerated adiabatic quantum dynamics on single spin. The method used is the fast forward method developed by Masuda and Nakamura. The result of this research is to obtain the additional Hamiltonian “equation 54” and the driving magnetic field through the fast forward method “equation 56”. The fast forward method is applied by first obtaining the eigenvalues of the Hamiltonian system. Furthermore, by reviewing the lowest energy state (ground state). It is concluded that this study obtained an additional Hamiltonian term with a driving magnetic field that ensures that a single spin can move from the initial state to the final state in a short time, while maintaining the characteristics of each energy level in the system.