scholarly journals Electronic states and optical transitions in a graphene quantum dot in a normal magnetic field

2011 ◽  
Vol 8 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Marko Grujic ◽  
Milan Tadic
Keyword(s):  
Magnetic Field ◽  
Quantum Dot ◽  
Boundary Conditions ◽  
Zero Energy ◽  
Graphene Quantum Dot ◽  
Infinite Mass ◽  
Infinite Mass Boundary Conditions ◽  
The Magnetic Field ◽  
Normal Magnetic Field ◽  
Weyl Equation

An analytical approach using the Dirac-Weyl equation is implemented to obtain the energy spectrum and optical absorption of a circular graphene quantum dot in the presence of an external magnetic field. The results are obtained for the infinite-mass and zigzag boundary conditions. We found that the energy spectra of a dot with zigzag boundary condition exhibit a zero energy band regardless of the value of the magnetic field, while for the infinite mass boundary conditions, the zero energy states appear only for high magnetic fields.

scholarly journals Quasi-bound states in an NPN-type nanometer-scale graphene quantum dot under a magnetic field

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Yueting Pan ◽  
Haijiao Ji ◽  
Xin-Qi Li ◽  
Haiwen Liu
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Quantum Dot ◽  
State Energy ◽  
Bound State ◽  
Scanning Tunneling ◽  
Bound State Energy ◽  
Graphene Quantum Dot ◽  
The Magnetic Field ◽  
Quasi Bound State

AbstractWe solve the quasi-bound state-energy spectra and wavefunctions of an NPN-type graphene quantum dot under a perpendicular magnetic field. The evolution of the quasi-bound state spectra under the magnetic field is investigated using a Wentzel–Kramers–Brillouin approximation. In numerical calculations, we also show that the twofold energy degeneracy of the opposite angular momenta breaks under a weak magnetic field. As the magnetic field strengthens, this phenomenon produces an observable splitting of the energy spectrum. Our results demonstrate the relation between the quasi-bound state-energy spectrum in graphene quantum dots and magnetic field strength, which is relevant to recent measurements in scanning tunneling microscopy.

scholarly journals On the differential system govering flows in magnetic field with data inLp

1998 ◽  
Vol 21 (2) ◽  
pp. 299-305 ◽  
Author(s):  
Fengxin Chen ◽  
Ping Wang ◽  
Chaoshun Qu
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Boundary Conditions ◽  
Differential System ◽  
Existence And Uniqueness ◽  
Mhd Equations ◽  
The Earth ◽  
Initial And Boundary Conditions ◽  
Time Existence ◽  
The Magnetic Field

In this paper we study the system governing flows in the magnetic field within the earth. The system is similar to the magnetohydrodynamic (MHD) equations. For initial data in spaceLp, we obtained the local in time existence and uniqueness ofweak solutions of the system subject to appropriate initial and boundary conditions.

scholarly journals Investigation of Light Absorption in a ZnS Quantum Dot

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Hojjatollah K. Salehani ◽  
Maedeh Zakeri
Keyword(s):  
Magnetic Field ◽  
Optical Absorption ◽  
Quantum Dot ◽  
Excited States ◽  
Light Absorption ◽  
Blue Shift ◽  
Optical Absorption Coefficient ◽  
Parabolic Confinement ◽  
Parabolic Confinement Potential ◽  
The Magnetic Field

The light absorption of a ZnS quantum dot with a parabolic confinement potential is studied in this paper in the presence of magnetic field perpendicular to dot plane. The Schrodinger equation of a single electron is solved numerically, and energy spectra and wave functions are obtained. Then, the optical absorption coefficients in transition from ground state to different excited states are calculated. The effects the magnetic field and quantum dot width on the optical absorption are investigated. It is found that the optical absorption coefficient has a blue shift by increasing of magnetic field or confinement strength of quantum dot.

scholarly journals Effect of confinement potential shape on the electronic, thermodynamic, magnetic and transport properties of a GaAs quantum dot at finite temperature

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
K. Luhluh Jahan ◽  
Bahadir Boyacioglu ◽  
Ashok Chatterjee
Keyword(s):  
Magnetic Field ◽  
Heat Capacity ◽  
Quantum Dot ◽  
Transport Properties ◽  
Average Energy ◽  
Persistent Current ◽  
Confinement Potential ◽  
Potential Shape ◽  
Gaas Quantum Dot ◽  
The Magnetic Field

Abstract The effect of the shape of the confinement potential on the electronic, thermodynamic, magnetic and transport properties of a GaAs quantum dot is studied using the power-exponential potential model with steepness parameter p. The average energy, heat capacity, magnetic susceptibility and persistent current are calculated using the canonical ensemble approach at low temperature. It is shown that for soft confinement, the average energy depends strongly on p while it is almost independent of p for hard confinement. The heat capacity is found to be independent of the shape and depth of the confinement potential at low temperatures and for the magnetic field considered. It is shown that the system undergoes a paramagnetic-diamagnetic transition at a critical value of the magnetic field. It is furthermore shown that for low values of the potential depth, the system is always diamagnetic irrespective of the shape of the potential if the magnetic field exceeds a certain value. For a range of the magnetic field, there exists a window of p values in which a re-entrant behavior into the diamagnetic phase can occur. Finally, it is shown that the persistent current in the present quantum dot is diamagnetic in nature and its magnitude increases with the depth of the dot potential but is independent of p for the parameters considered.

Magnetohydrodynamic Equilibria

2020 ◽  
Author(s):  
Thomas Wiegelmann
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Lorentz Force ◽  
Plasma Flow ◽  
Plasma Pressure ◽  
Mhd Equations ◽  
The Sun ◽  
Planetary Magnetospheres ◽  
Mhd Equilibria ◽  
The Magnetic Field

Magnetohydrodynamic equilibria are time-independent solutions of the full magnetohydrodynamic (MHD) equations. An important class are static equilibria without plasma flow. They are described by the magnetohydrostatic equations j×B=∇p+ρ∇Ψ,∇×B=μ0j,∇·B=0. B is the magnetic field, j the electric current density, p the plasma pressure, ρ the mass density, Ψ the gravitational potential, and µ0 the permeability of free space. Under equilibrium conditions, the Lorentz force j×B is compensated by the plasma pressure gradient force and the gravity force. Despite the apparent simplicity of these equations, it is extremely difficult to find exact solutions due to their intrinsic nonlinearity. The problem is greatly simplified for effectively two-dimensional configurations with a translational or axial symmetry. The magnetohydrostatic (MHS) equations can then be transformed into a single nonlinear partial differential equation, the Grad–Shafranov equation. This approach is popular as a first approximation to model, for example, planetary magnetospheres, solar and stellar coronae, and astrophysical and fusion plasmas. For systems without symmetry, one has to solve the full equations in three dimensions, which requires numerically expensive computer programs. Boundary conditions for these systems can often be deduced from measurements. In several astrophysical plasmas (e.g., the solar corona), the magnetic pressure is orders of magnitudes higher than the plasma pressure, which allows a neglect of the plasma pressure in lowest order. If gravity is also negligible, Equation 1 then implies a force-free equilibrium in which the Lorentz force vanishes. Generalizations of MHS equilibria are stationary equilibria including a stationary plasma flow (e.g., stellar winds in astrophysics). It is also possible to compute MHD equilibria in rotating systems (e.g., rotating magnetospheres, rotating stellar coronae) by incorporating the centrifugal force. MHD equilibrium theory is useful for studying physical systems that slowly evolve in time. In this case, while one has an equilibrium at each time step, the configuration changes, often in response to temporal changes of the measured boundary conditions (e.g., the magnetic field of the Sun for modeling the corona) or of external sources (e.g., mass loading in planetary magnetospheres). Finally, MHD equilibria can be used as initial conditions for time-dependent MHD simulations. This article reviews the various analytical solutions and numerical techniques to compute MHD equilibria, as well as applications to the Sun, planetary magnetospheres, space, and laboratory plasmas.

Effect of temperature on magnetic susceptibility and thermodynamic properties of an asymmetric quantum dot in tilted magnetic field

2015 ◽  
Vol 29 (23) ◽  
pp. 1550127 ◽  
Author(s):  
R. Khordad
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Quantum Dot ◽  
Specific Heat ◽  
Energy Levels ◽  
Effect Of Temperature ◽  
Magnetic Field Direction ◽  
Asymmetric Quantum ◽  
Gaas Quantum Dot ◽  
The Magnetic Field

In this paper, the specific heat, entropy and magnetic susceptibility of an asymmetric GaAs quantum dot (QD) are studied under the influence of temperature and a tilted external magnetic field. We first calculate the analytical wave functions and energy levels using a transformation to simplify the Hamiltonian of the system. Then, we obtain the analytical expressions for specific heat, entropy and magnetic susceptibility as the function of temperature, magnetic field and its direction for various anisotropy of the system. According to the results obtained from the present work, we find that (i) the specific heat and entropy are decreased when the magnetic field increases. (ii) When anisotropy is increased, the specific heat and entropy decrease. (iii) At large magnetic fields, the anisotropy has not important effect on specific heat and entropy. In briefly, the magnetic field, magnetic field direction and anisotropy play important roles in the specific heat, entropy and magnetic susceptibility of an asymmetric QD.

Theory of Lubrication With Ferrofluids: Application to Short Bearings

1982 ◽  
Vol 104 (4) ◽  
pp. 510-515 ◽  
Author(s):  
Nicolae Tipei
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Reynolds Equation ◽  
Viscous Fluids ◽  
Pressure Differential ◽  
Numerical Example ◽  
Bearing Stiffness ◽  
Pyromagnetic Coefficient ◽  
The Magnetic Field

The momentum equations are written for viscous fluids exhibiting magnetic stresses. The velocity profiles are deduced; then from continuity, a pressure differential equation, equivalent to Reynolds equation is obtained. This equation is discussed with emphasis on the case when magnetic stresses derive from a potential, also when the pyromagnetic coefficient vanishes. The boundary conditions for lubrication problems are then formulated. In particular, short bearings with ferromagnetic lubricants are considered. A numerical example yields the pressure diagrams at low and moderate eccentricity ratios and for different speeds. In conclusion, it is shown that ferromagnetic lubricants may improve substantially the performance of bearings operating under low loads and/or at low speeds. However, a correct variation of the magnetic field, toward the center of the lubricated area, is required. Under such conditions, the extent of the active area of the film is increased and bearing stiffness and stability are improved.

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