A mass-independent conformal quantum cloak

Lin, De-Hone

doi:10.1088/1367-2630/aa8a5d

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…A similar means to the construction of the invisibility cloak for the matter wave can interpret the transformation structure as the anisotropic mass parameter and an effective scalar potential [10]. Recently, it was reported that using conformal mapping to design a quantum device for splitting a matter wave only needs to offer a scalar potential in the controlling region without resorting to the modulation of mass [11] . It largely simplifies the construction of the transformation device.…”

Section: Physical Realization Of the Conformally Geometric Effectmentioning

confidence: 99%

On the magnetic Hooke-Newton transmutation of electrons

Lin

2019

J. Phys. Commun.

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The author investigates the Hooke-Newton transmutation of the electron in the uniform magnetic field. Two results are reported. First, the modulable quantum spectrum and spinor of the magnetic field are given. Spin exhibits its effect, even in the first order approximation of the power series expansion of the spectrum. Since the transmuted Coulomb interaction, attractive or repulsive, is determined by both the signatures of the charge and the total angular momentum, the pure spin states of different orientations experience the reverse Coulomb forces. This feature may be useful in grouping the pure spin states of the same orientation. Second, it is shown that the effect of the effective vector potential due to the geometry of conformal mapping can be generated by the vector potential of two fractional magnetic fluxes with the reverse directions which couple to the different components of the spinor. The equivalence shows the possibility of demonstrating the physics of the 2D electron in conformal space with an isotropic momentum modulation while interacting with the field of the magnetic fluxes.

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Section: Physical Realization Of the Conformally Geometric Effectmentioning

confidence: 99%

On the magnetic Hooke-Newton transmutation of electrons

Lin

2019

J. Phys. Commun.

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“…Through the reinterpretation of the geometric structure of the transformation as the material properties, the method enables novel devices such as invisibility cloaks (e.g., [4]). Recently, researchers have been interested in the applications of transformation design to the steering of matter waves (e.g., [5,6]). Due to the interaction nature of the quantum particle with external fields, the concept of the transformation design in quantum physics could exhibit more fertile content such as leading us to reveal new quantization systems (e.g., [7]) and more general monopole fields [8].…”

Section: Introductionmentioning

confidence: 99%

The Magnetic Hooke-Newton Transmutation in Momentum Space

Lin

2021

Symmetry

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The magnetic Hooke-Newton transmutation, which emerges from the transformation design of the quadratic conformal mapping for the system of charged particles moving in the uniform magnetic field, is investigated in the momentum space. It is shown that there are two ways to turn the linear interaction force of the system into the inverse square interaction. The first one, which involves simply applying the mapping to the system, has the spectrum with the Landau levels of even angular momentum quantum number. The second one considers the geometric structure of the mapping as an effective potential which leads us to the transmuted Coulomb system with the novel quantum spectrum. The wave functions of momentum for the bound and scattering states of the transmutation system are given. It is also shown that the effective potential due to the geometric structure can be generalized to a general 2D surface, and the Schrödinger equation of a particle moving on the surface while under the action of the potential can be solved by the form-invariant Schrödinger equation of the free particle. The solution of a particle moving on the hyperbolic surface under the potential is given with the conclusion. The presentation manifests the transformation design of the quantum state, depending mainly on the geometric structure of the representation space, not on the action of the specific potential field. This characteristic makes it possible for us to use the geometric structure of different representation spaces to explore some novel behaviors of quantum particles.

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The Conformal Image of the Electron

Lin

2024

Annalen der Physik

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The construction of a transformation image is pivotal to the transformation design method for steering waves around an object. Constructing the conformal images of an electron, however, remains a challenge, primarily due to the complexities involved in realizing the spin structure within the image space. This study proposes a novel solution in this regard of the electron's spin structure on a surface, leveraging on the interactions between the electron and a vector potential. By introducing a scalar potential to facilitate the generation of a conformal metric structure and differential operator in the Dirac equation, it is demonstrated that the conformal image of the electron can indeed be constructed within an appropriate electromagnetic field. Furthermore, an equivalence between the geometric effect of a conformal deformation on the electron and the action of an electromagnetic force is established. Electromagnetic fields are used to generate form‐invariant conformal images of the electron within a plane and on a sphere. These examples help showcase the effectiveness of the currently presented method in realizing the conformal images of the electron in various settings.

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A mass-independent conformal quantum cloak

Cited by 3 publications

References 20 publications

On the magnetic Hooke-Newton transmutation of electrons

On the magnetic Hooke-Newton transmutation of electrons

The Magnetic Hooke-Newton Transmutation in Momentum Space

The Conformal Image of the Electron

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