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We consider the dynamics of a spin-1/2 particle constrained to move in an arbitrary space curve with an external electric and magnetic field applied. With the aid of gauge theory, we successfully decouple the tangential and normal dynamics…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
We derive the effective field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be…
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical…
Information geometry provides differential geometric concepts like a Riemannian metric, connections and covariant derivatives on spaces of probability distributions. We discuss here how these concepts apply to quantum field theories in the…
The behavior of a quantum test particle satisfying the Klein-Gordon equation in a certain class of 4 dimensional stationary space-times is examined. In a space-time of a spinning cosmic string, the wave function of a particle in a box is…
Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the…
We study the quantum Hall effect in a monolayer graphene by using an approach based on thermodynamical properties. This can be done by considering a system of Dirac particles in an electromagnetic field and taking into account of the edges…
In this article, the quantum representation of the algebra among reduced twisted geometries (with respect to the Gauss constraint) is constructed in the gauge invariant Hilbert space of loop quantum gravity. It is shown that the reduced…
This work discusses the effect of topology in the frame of direct Coulomb interactions, considering two distinct geometries, namely the Hall bar and the Corbino disc. In the mainstream approaches to the quantized Hall effect, the…
A particle that is constrained to freely move on a hyperspherical surface in an $N\left( \geq 2\right) $ dimensional flat space experiences a curvature-induced gauge potential, whose form was given long ago (J. Math. Phys.…
One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of…
We analyze the mechanical deformations that are required to create uniform pseudomagnetic fields in graphene. It is shown that, if a ribbon is bent in-plane into a circular arc, this can lead to fields exceeding 10T, which is sufficient for…
A scanning probe technique was used to obtain a high-resolution map of the random electrostatic potential inside the quantum Hall liquid. A sharp metal tip, scanned above a semiconductor surface, sensed charges in an embedded…
The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…
We demonstrate theoretically how a two-dimensional electron gas can be used to probe local potential profiles using the Hall effect. For small magnetic fields, the Hall resistance is inversely proportional to the average potential profile…
Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…
We study the quantum Hall effect inside a gravitational field. First, we review the influence of the gravitational field of the Earth on the quantum Hall effect. Taking the gravitational field of the Earth to be uniform along the vertical…
We consider the quantum dynamics of a charged particle in Euclidean space subjected to electric and magnetic fields under the presence of a potential that forces the particle to stay close to a compact surface. We prove that, as the…
We study magnetic Schrodinger operators with random or almost periodic electric potentials on the hyperbolic plane, motivated by the quantum Hall effect in which the hyperbolic geometry provides an effective Hamiltonian. In addition we add…