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.
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.
This paper explores the influence of complex magnetic fields on the quantum information properties of graphene, using Shannon and Fisher information measures. Due to its distinctive electronic characteristics, graphene is an ideal platform for investigating how quantum information can be modulated by varying magnetic field configurations. Through theoretical analysis and computational simulations, we study the effects of these complex fields on the electronic states and information entropy of graphene. Shannon information is employed to measure the uncertainty or entropy associated with the electronic states, while Fisher information evaluates their sensitivity to magnetic field variations. Our results show that complex magnetic fields can significantly reshape the quantum information dynamics of graphene, highlighting potential applications in quantum computing and information processing.
Abstract Influence of the transverse uniform magnetic field B on position (subscript ρ ) and momentum ( γ ) Shannon quantum-information entropies S ρ , γ Fisher informations I ρ , γ and informational energies O ρ , γ is studied theoretically for the 2D circular quantum dots (QDs) whose circumference supports homogeneous either Dirichlet or Neumann boundary condition (BC). Comparative analysis reveals similarities and differences of the influence on the properties of the structure of the surface interaction with the magnetic field. A conspicuous distinction between the two spectra are crossings at the increasing induction of the Neumann energies with the same radial quantum number n and adjacent non-positive angular indices m . At the growing B , either system undergoes Landau condensation when its characteristics turn into their uniform field counterparts. It is shown that for the Dirichlet system this transformation takes place at the smaller magnetic intensities; e.g. the Dirichlet sum S ρ 00 + S γ 00 on its approach from above to a fundamental limit 2 ( 1 + ln π ) is at any B smaller than the corresponding Neumann quantity what physically means that the former geometry provides more total information about the position and motion of the particle. It is pointed out that the widely accepted disequilibrium uncertainty relation O ρ O γ ≤ 2 π − d , with d being a dimensionality of the system, is violated by the Neumann QD in the magnetic field. Comparison with electrostatic harmonic confinement is performed; in particular, contrary to the hard-wall QDs, for this configuration the sums S ρ + S γ and the products I ρ I γ and O ρ O γ do not depend on the field. Physical interpretation is based on the different roles of the two BCs and their interplay with the field: Dirichlet (Neumann) surface is a repulsive (attractive) interface.
Abstract The effect of the spatially inhomogeneous electric field on the quantum thermodynamic property of the particle confined in a quantum well has been investigated theoretically. The Schrodinger equation was solved for the particle subjected to a spatial confinement by an inhomogeneous electric field and energy eigen-values were obtained. Using the energy eigen-values, we have calculated the average energy, free energy, entropy, and heat capacity of this system. As an important parameter in the inhomogeneous electric field, the inhomogeneity gradient of the field plays an important role. Compared with the spatially homogenous electric field, some novel quantum effect appears. The energy eigen-value for the particle corresponding to each bound state increases as the inhomogeneity gradient increases, resulting in the increase of the average energy, free energy, and heat capacity; however, the entropy, which measures the disorder of the particle confined in the inhomogeneous field, gradually decreases with the increase of the inhomogeneity gradient. In addition, the confinement effect of the quantum well on the thermodynamic properties of this system has also investigated in great detail. The results show that the larger size of the quantum well is, the stronger the influence of inhomogeneous field becomes, which makes the thermodynamic properties of the particle in the spatially inhomogeneous field quite different from those in the homogeneous field. Our work may provide some references for the future research on the thermodynamic property of the confined atom and molecule in the inhomogeneous field and has some practical applications in statistical physics, chemical physics, and condensed physics, etc.
This research examines the influence of a particle in a quantum-mechanical system constrained in a time-dependent magnetic field and the strengths of a Calogero-like potential. Analytical expressions for the expectation values of the relevant observables were first derived from the exact energy spectrum using the total confinement frequency, which incorporates both the intrinsic confinement and cyclotron frequencies. These expectation values were subsequently employed to evaluate the Fisher information (FI) in both position space (PS) and momentum space (MS), and to assess the effects of the external magnetic fields and the strength of the Calogero-like potential on quantum localization and uncertainty. The expectation values increase with increasing magnetic field strength, resulting in spatial compression and enhanced localization, while stronger Calogero-like potential strengths mimic centrifugal confinement. The examination of FI for both ground and first-excited states across magnetic quantum numbers highlights that localization sharpens with increasing field strength and potential, with observable divergences between quantum states and magnetic quantum numbers. However, the product of the FI was evaluated as the Cramér-Rao bound, showcasing the interplay between quantum uncertainty and information content. A comparison of the ground and first excited states for two magnetic quantum numbers reveals whether the FI product obeys or violates the Cramér-Rao bound, offering insight into quantum stability and control. These results reinforce the controllability of quantum state localization via external field modulation, with implications for quantum control and confinement in potential applications. To the best of our understanding, this is the first time that the analysis of FI for a quantum system governed by a Calogero-like potential in the presence of a varying magnetic field, specifically using a total confinement frequency, is reported. The results provide new insights into quantum localization, information-theoretic uncertainty, and the controlled manipulation of confined quantum states, with potential applications in quantum control, quantum information processing, and nanoscale confinement technologies.
We consider a simple model for two-electron quantum dots (QDs) in the perpendicular magnetic field. With the aid of this model we study the degree of the orbital entanglement as a function of the magnetic field strength and the QD shape. We found that the circular QD exhibits no entanglement in the magnetic field. Although the entanglement increases with the increase of the QD deformation at a fixed value of the magnetic field, it approaches the constant value at the fixed deformation with the increase of the magnetic field.
The internal disorder of the two-dimensional confined hydrogenic atom is numerically studied in terms of the confinement radius for the 1 s , 2 s , 2 p and 3 d quantum states by means of the statistical Crámer-Rao complexity measure. First, the confinement dependence of the variance and the Fisher information of the position and momentum spreading of its electron distribution are computed and discussed. Then, the Crámer-Rao complexity measure (which quantifies the combined balance of the charge concentration around the mean value and the gradient content of the electron distribution) is investigated in position and momentum spaces. We found that confinement does disentangle complexity of the system for all quantum states by means of this two component measure.