The shape complexity of a particle confined in the circular quantum well with an external homogeneous perpendicular magnetic field is investigated. First, the Shannon entropy and the averaging electron probability density, as well as the shape complexities in the position and momentum spaces for several quantum states, are computed and discussed. The quantum confinement effect on the shape complexity of this system is extensively explored. Then, the influence of the magnetic field on the shape complexities of the particle confined in the circular quantum well is discussed. It is demonstrated that the shape complexity exhibits scaled invariance under the influence of the magnetic field. However, when the radius of the quantum well is fixed, the shape complexity of the given quantum state changes with the magnetic field strength. Results suggest that the shape complexity of a particle confined in the quantum well can be changed by varying both the strength of the magnetic field and the size of the well. This study has some practical applications in quantum information measurement of the confined particle and can guide future researches for the disorder characteristics of confined particle in semiconductor quantum dots.
In magnets with strong quantum fluctuations, paramagnetic ground states with or without confinement of spinon excitations can be realized. Here we discuss the physics of the confined phase in the vicinity of a confinement-deconfinement transition: this regime, likely relevant to a multitude of frustrated spin systems, is characterized by multiple length scales. In addition to the magnetic correlation length, a confinement length can be defined, which can be probed, e.g., by local static measurements near nonmagnetic impurities. We illustrate the ideas by explicit calculations for dimerized spin chains, but our qualitative results remain valid in higher dimensions as well. In particular, we study crossover from weak to strong confinement visible in the antiferromagnetic polarization cloud around a nonmagnetic impurity. We also discuss the effective magnetic interaction between impurities, relevant for impurity-induced magnetic order, and consequences for nuclear magnetic resonance and neutron-scattering experiments.
Monolayer tungsten diselenide (WSe
2) has become a suitable platform for quantum transport and spintronics and valleytronics applications because it possesses an intrinsic band gap and strong spin-orbit coupling and spin-valley coupling features. The electrostatic confinement of Dirac fermions proves challenging in graphene because of Klein tunneling, yet WSe
2 provides an environment that supports both carrier localization and the development of confined quantum states. In this work, we theoretically investigate the confinement of massive Dirac fermions in a WSe
2 quantum dot generated by a localized magnetic field. Using the effective Dirac Hamiltonian in the presence of a magnetic flux, we derive the exact wave functions and scattering coefficients by employing Kummer's confluent hypergeometric functions together with Bessel and Hankel functions. Our results show that the localized magnetic field provides an efficient mechanism to suppress Klein tunneling and promote the formation of stable quasibound states. We systematically examine the scattering efficiency and carrier density distributions as functions of the incident energy, magnetic field strength, and quantum dot radius. We find that low-energy carriers are strongly confined by the magnetic barrier, while the interplay between magnetic localization and geometric confinement gives rise to sharp and tunable resonance peaks. These results provide valuable insight into the control of spin-valley transport in transition metal dichalcogenide nanostructures and establish a theoretical basis for the development of quantum confinement devices and quantum information technologies.