INVESTIGATION OF NON-MAGNETIC AND FERROMAGNETIC PHASES OF 3D ELECTRON CRYSTAL WITH NaCl AND CsCl STRUCTURES

2008 ◽  
Vol 22 (21) ◽  
pp. 3627-3640
Author(s):  
R. RAJESWARA PALANICHAMY ◽  
M. ANANDAJOTHI ◽  
A. JAWAHAR ◽  
K. IYAKUTTI
Keyword(s):  
Ground State ◽  
State Energy ◽  
Correlation Energy ◽  
Magnetic Phase ◽  
Ferromagnetic Phase ◽  
Density Region ◽  
Wannier Functions ◽  
Ground State Energies ◽  
Electron Crystal

The non-magnetic and ferromagnetic phases of 3D Wigner electron crystal are investigated using a localized representation of the electrons with NaCl and CsCl structures. The ground state energies of ferromagnetic and non-magnetic phases of Wigner electron crystal are computed in the range 10 ≤ rs ≥ 130. The role of correlation energy is suitably taken into account. The low density region favorable for the ferromagnetic phase is found to be 4.8 × 1020 electrons/cm3 and for the non-magnetic phase, it is 2.03 × 1020 electrons/cm3. It is found that the ground state energy of ferromagnetic phase is less than that of the non-magnetic phase of the Wigner electron crystal. The structure-dependent Wannier functions, which give proper localized representation for Wigner electrons, are employed in the calculation.

INVESTIGATION OF THE FERROMAGNETIC PHASE OF WIGNER ELECTRON CRYSTAL

2002 ◽  
Vol 16 (09) ◽  
pp. 1353-1361 ◽  
Author(s):  
R. RAJESWARA PALANICHAMY ◽  
K. IYAKUTTI
Keyword(s):  
Correlation Energy ◽  
Ferromagnetic Phase ◽  
Low Density ◽  
Density Region ◽  
Wannier Functions ◽  
Fcc Lattice ◽  
Low Density Limit ◽  
The Stability ◽  
Ground State Energies

The ground state energies of the ferromagnetically ordered electron crystals corresponding to sc, bcc, fcc, diamond and perovskite structures are computed. The stability of these structures is analyzed. In each case, the possibility of the Wigner electrons having cubic or spherical constant energy surface (the region of integration in momentum space) is considered for the range of r s values corresponding to low densities. The role of correlation energy is suitably taken into account. The range of low density region favourable for Wigner crystallization is found to be above r s = 30. It is found that, the ferromagnetically ordered electrons crystallize into fcc lattice in the low density limit. The structure dependent Wannier functions, which give proper localized representation for the Wigner electrons in the crystal, are employed in the calculation.

EFFECT OF POSITIVE BACKGROUND ON THE FERROMAGNETIC PHASE OF 3D WIGNER ELECTRON CRYSTAL

2004 ◽  
Vol 18 (26) ◽  
pp. 3399-3408 ◽  
Author(s):  
R. RAJESWARA PALANICHAMY ◽  
K. IYAKUTTI
Keyword(s):  
Correlation Energy ◽  
Electron System ◽  
Ferromagnetic Phase ◽  
Low Density ◽  
Density Region ◽  
Wannier Functions ◽  
Fcc Lattice ◽  
Low Density Limit ◽  
The Stability ◽  
Ground State Energies

In the ferromagnetic phase of the 3D electron system, it is assumed that the spins of all the electrons are arranged in a parallel manner. The ferromagnetically ordered electrons are represented by the structure dependent Wannier functions. The ground state energies of the ferromagnetically ordered electron crystals corresponding to sc, bcc, fcc, diamond and perovskite structures are computed with Gaussian type and Yukawa type positive backgrounds. The stability of these structures is analyzed. In each case, the possibility of the Wigner electrons having cubic or spherical constant energy surface (the region of integration in momentum space) is considered for the range of rs values corresponding to low densities. The effect of correlation energy is suitably taken into account. The range of low density region favorable for Wigner crystallization is found to be at 6.0×1019/ cm 3. It is found that the ferromagnetically ordered electrons crystallize into fcc lattice in the low density limit with Yukawa type positive background.

STUDY OF STRUCTURAL STABILITY OF WIGNER ELECTRON CRYSTAL

2000 ◽  
Vol 14 (17) ◽  
pp. 1767-1779 ◽  
Author(s):  
R. RAJESWARA PALANICHAMY ◽  
K. IYAKUTTI
Keyword(s):  
Ground State ◽  
Energy Surface ◽  
Three Dimensional ◽  
Present Calculation ◽  
Wannier Functions ◽  
Constant Energy ◽  
Bcc Lattice ◽  
The Stability ◽  
Ground State Energies ◽  
Electron Crystal

The ground state energies of the non-magnetic Wigner electron crystals corresponding to sc, bcc, fcc, diamond and perovskite structures are estimated and it is found that the bcc lattice still remains to be the stable known arrangement for three-dimensional Wigner electron crystal. Perovskite structure is not the stablest as claimed in a previous work, it is preferred only after fcc and sc. The stability is analysed taking different structures and assuming the possibility of the Wigner electrons having cubic or spherical constant energy surface, the region of occupation in momentum space, for a whole range of rs values (rs=20 to 200). The structure dependent Wannier functions, which give a proper localized representation for the Wigner electrons in the crystals are constructed and employed in the present calculation.

On the formation of cavitylike small-polaronic states in solid deuterium

1985 ◽  
Vol 63 (1) ◽  
pp. 94-98 ◽  
Author(s):  
S. K. Bose ◽  
J. D. Poll
Keyword(s):  
Ground State ◽  
Continuum Model ◽  
State Energy ◽  
Stark Shift ◽  
Localized State ◽  
Solid Deuterium ◽  
Vibrational Levels ◽  
Radiation Induced ◽  
Absorption Features ◽  
Ground State Energies

Certain infrared absorption features in tritiated as well as proton-irradiated samples of solid deuterium have been attributed to the formation of bubblelike electronic states localized in the lattice. These bubblelike states are shown to be energetically stable in the Wigner–Seitz model of the crystal and the gap between the ground-state energies in the bubble and the quasi-free states of the electron is calculated. An initial trapping of the electron by a vacancy is assumed in calculating the localized state energy. Calculations based on a continuum model of the solid yield the radius of such bubbles to close agreement with that obtained from the observed Stark shift of the vibrational levels of the neighbouring molecules due to the localized electrons. The model is used to interpret the radiation-induced absorption in proton-irradiated solid deuterium in the spectral region 4000–7500 cm−1.

Spin-polarized hydrogen, deuterium, and tritium: II. Pressure and compressibility calculated by a lowest order constrained-variation method

1989 ◽  
Vol 67 (7) ◽  
pp. 649-656 ◽  
Author(s):  
Magne Haugen ◽  
Erlend Østgaard
Keyword(s):  
Molar Volume ◽  
Ground State ◽  
Particle Density ◽  
Variation Method ◽  
Density Region ◽  
Spin Polarized ◽  
Hydrogen Deuterium ◽  
Constrained Variation ◽  
Ground State Energies ◽  
Theoretical Results

The pressure and the compressibility of spin-polarized H↓, D↓, and T↓ are obtained from ground-state energies calculated by means of a modified variational lowest order constrained-variation method. The pressure and the compressibility are calculated or estimated from the dependence of the ground-state energy on density or molar volume, generally in a density region from 0 to 1.5σ−3 corresponding to a molar volume of more than 20 cm3/mol, where σ = 3.69 Å (1Å = 10−10 m); the calculations are done for five different two-body potentials. Theoretical results for the pressure are 54.1–57.9 atm for spin-polarized H↓ 18.4–23.4 atm for spin-plolarized D↓, and 5.6–12.9 atm for spin-polarized T↓ at a particle density of 0.50σ−3 or a molar volume of 60 cm3/mol (1 atm = 101 kPa). Theoretical results for the compressibility are 51 × 10−4 −54 × 10−4 atm−1 for spin-polarized H↓, 108 × 10−4 −120 × 10−4 atm−1 for spin-polarized D↓, and 162 × 10−4 −224 × 10−4 atm−1 for spin-polarized T↓ at a particle density of 0.50σ−3 for a molar volume of 60 cm3/mol. The relative agreement between results for different potentials is somewhat better for higher densities.

scholarly journals Remarks on the boundary set of spectral equipartitions

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120492 ◽  
Author(s):  
P. Bérard ◽  
B. Helffer
Keyword(s):  
Riemannian Manifold ◽  
Lower Bound ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Two Dimensional ◽  
Nodal Sets ◽  
Nodal Domains ◽  
Open Set ◽  
Ground State Energies

Given a bounded open set in (or in a Riemannian manifold), and a partition of Ω by k open sets ω j , we consider the quantity , where λ ( ω j ) is the ground state energy of the Dirichlet realization of the Laplacian in ω j . We denote by ℒ k ( Ω ) the infimum of over all k -partitions. A minimal k -partition is a partition that realizes the infimum. Although the analysis of minimal k -partitions is rather standard when k =2 (we find the nodal domains of a second eigenfunction), the analysis for higher values of k becomes non-trivial and quite interesting. Minimal partitions are in particular spectral equipartitions, i.e. the ground state energies λ ( ω j ) are all equal. The purpose of this paper is to revisit various properties of nodal sets, and to explore if they are also true for minimal partitions, or more generally for spectral equipartitions. We prove a lower bound for the length of the boundary set of a partition in the two-dimensional situation. We consider estimates involving the cardinality of the partition.

THERMAL PROPERTIES AND GROUND STATE ENERGY SHIFT OF CHARGED ANYONS

1994 ◽  
Vol 09 (20) ◽  
pp. 3683-3705
Author(s):  
J.Y. KIM ◽  
Y.S. MYUNG ◽  
S.H. YI
Keyword(s):  
Coulomb Interaction ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Correlation Energy ◽  
Virial Coefficients ◽  
Energy Shift ◽  
Second Order ◽  
Quantization Scheme ◽  
Coulomb Interactions

We derive the second and third virial coefficients and the ground state energy shift for charged anyons within the Hartree-Fock approximation. A second quantization scheme at finite temperature is introduced for this calculation up to the second order and the vertex is composed of anyonic, point, constant as well as Coulomb interactions. The thermodynamic potential for the second order correlation diagram of Coulomb interaction leads to the logarithmic divergence (V ln V). Hence, we find the heat capacity and the correlation energy of anyons without Coulomb-Coulomb interaction. Finally, we discuss the magnetic-field-induced localization at low filling ν, including the Wigner crystal phase.

GROUND STATE ENERGIES OF HYDROGEN-LIKE IMPURITY IN A LENS-SHAPED QD

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2529-2533 ◽  
Author(s):  
XIANGHUA ZENG ◽  
JIAFENG CHANG ◽  
PENGXIA ZHOU
Keyword(s):  
Magnetic Field ◽  
Quantum Dot ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Lateral Deviation ◽  
Mass Approximation ◽  
The Magnetic Field ◽  
Ground State Energies ◽  
Electronic Ground

In this paper,the ground state energies of hydrogen-like impurity in a lens-shaped quantum dot ( GaAs / In 1-x Ga x As ) under vertical magnetic field have been discussed by using effective mass approximation and variational method. It gives that for a lens-shaped quantum dot, due to the asymmetry of the vertical and lateral bound potentials, the electronic ground state energies are related not only with the deviation distance but also with the deviation direction; for the spherical quantum dot, the ground state energy is only related with the distance of the impurity deviation, neither with vertical nor lateral deviation. And with the increasing of the magnetic field, the ground state energy is increasing.

scholarly journals THE ROLE OF THE CARRIER MASS IN SEMICONDUCTOR QUANTUM DOTS

2000 ◽  
Vol 14 (17) ◽  
pp. 1753-1765 ◽  
Author(s):  
M. SINGH ◽  
V. RANJAN ◽  
VIJAY A. SINGH
Keyword(s):  
Quantum Dot ◽  
Effective Mass ◽  
Ground State ◽  
State Energy ◽  
Dimensionless Parameter ◽  
Theoretical Calculations ◽  
Dielectric Coating ◽  
Semiconductor Quantum Dot ◽  
Photoemission Data

In the present work we undertake a re-examination of effective mass theory (EMT) for a semiconductor quantum dot. We take into account the fact that the effective mass (mi) of the carrier inside the dot of radius R is distinct from the mass (m0) in the dielectric coating surrounding the dot. The electronic structure of the quantum dot is determined in crucial ways by the mass discontinuity factor β ≡mi/m0. In this connection we propose a novel quantum scale, σ, which is a dimensionless parameter proportional to β2V0R2, where V0 represents the barrier due to dielectric coating. The scale σ represents a mass modified " strength" of the potential. We show both by numerical calculations and asymptotic analysis that the charge density near the nanocrystallite surface, ρ(r=R), can be large and scales as 1/σ. This fact suggests a significant role for the surface in an EMT based model. We also show that the upshift in the ground state energy is weaker than quadratic, unlike traditional EMT based calculations, and chart its dependence on the proposed scale σ. Finally, we demonstrate that calculations based on our model compare favorably with valence band photoemission data and with more elaborate theoretical calculations.

USING EVOLUTIONARY ALGORITHM TO CALCULATE THE GROUND-STATE ENERGY OF DOUBLE-ELECTRON ATOMS IN A UNIFORM MAGNETIC FIELD (B ≤ 109G)

2000 ◽  
Vol 11 (01) ◽  
pp. 183-194 ◽  
Author(s):  
LIANJUN LIU ◽  
LI ZHAO ◽  
YOUDONG MAO ◽  
DONG YU ◽  
JINGWEN XU ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Evolutionary Algorithm ◽  
Ground State Energy ◽  
Ground State ◽  
Uniform Magnetic Field ◽  
State Energy ◽  
Electron System ◽  
Energy Calculation ◽  
Double Electron

It is very difficult to calculate the accurate ground-state energies of the double-electron atom like helium in a uniform magnetic field. By using the modified configuration interaction (MCI) method and the evolutionary algorithm (EA), we obtained highly accurate results. We discuss the role of magnetic field in the ground state of the double-electron system and the possibility of variational ground-state energy calculation by using evolutionary algorithm directly. Results show that compared with other algorithms, such as the simplex method, EA is more efficient in calculating atomic energies, and can be used in other fields of physics.

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