Discrete lattice model for the large polaron

1991 ◽  
Vol 69 (5) ◽  
pp. 635-640 ◽  
Author(s):  
V. V. Paranjape ◽  
P. V. Panat
Keyword(s):  
Ground State ◽  
Weak Coupling ◽  
State Energy ◽  
Zero Point ◽  
Weak Coupling Limit ◽  
Point Energy ◽  
Model Based ◽  
Discrete Nature ◽  
Polaron Energy ◽  
Polaron Radius

The energy states of a polaron in the weak-coupling limit were first obtained by Fröhlich and co-workers, assuming that the polarization of the lattice due to the electron is continuous. If the polaron radius is comparable to the lattice constant then the assumption is inappropriate. A model based on the discrete nature of the lattice is more suitable. Such a model, based on the semiclassical zero-point energy, is proposed. We have calculated the ground-state energy of the polaron and the energy of the polaron near the bottom of the conduction band. The first discussion of the effect of lattice discreteness on the polaron energy was presented by Lepine and Frongillo who used for their calculations, a method based on the "kq" representation. Our method differs from the method of these earlier authors but the results of the two approaches are similar. Some differences exist nevertheless. The main aim of this paper is, therefore, to provide an alternate method for calculating the effect of discreteness on the polaron energy. The differences arising between the results of the two methods are discussed.

scholarly journals Ground-state energy of thed=1,2,3 dimensional Hubbard model in the weak-coupling limit

1989 ◽  
Vol 39 (7) ◽  
pp. 4462-4466 ◽  
Author(s):  
Walter Metzner ◽  
Dieter Vollhardt
Keyword(s):  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
Weak Coupling ◽  
State Energy ◽  
Weak Coupling Limit

scholarly journals Ground-State Energy of a Bose System in the Weak Coupling Limit

1975 ◽  
Vol 54 (2) ◽  
pp. 308-315 ◽  
Author(s):  
K. Hiroike
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Weak Coupling ◽  
State Energy ◽  
Weak Coupling Limit ◽  
Bose System

CONTINUOUS UPPER BOUND ON THE GROUND-STATE ENERGY OF THE FRÖHLICH POLARON

1994 ◽  
Vol 08 (08n09) ◽  
pp. 553-560 ◽  
Author(s):  
A. V. SOLDATOV
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behavior ◽  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
Coherent States ◽  
Weak Coupling ◽  
State Energy ◽  
Coupling Parameter ◽  
Weak Coupling Limit

The upper bound on the ground-state energy for the Fröhlich polaron is derived by means of a new version of variational principle based on the Wick symbols formalism and the coherent states theory. The bound is continuous in some respect, i.e. it is valid for all values of coupling parameter including the intermediate regions. Asymptotic behavior of the bound for the weak coupling limit and for the strong coupling limit provides, in general, lower values than well-known existing bounds. The bound can be readily generalized for the case of nonzero magnetic field.

FISSION HALF LIVES OF FERMIUM ISOTOPES WITHIN SKYRME HARTREE-FOCK-BOGOLIUBOV THEORY

2011 ◽  
Vol 20 (02) ◽  
pp. 557-564 ◽  
Author(s):  
A. BARAN ◽  
A. STASZCZAK ◽  
W. NAZAREWICZ
Keyword(s):  
Ground State ◽  
Spontaneous Fission ◽  
Zero Point ◽  
Nuclear Fission ◽  
Point Energy ◽  
Generator Coordinate Method ◽  
Hartree Fock ◽  
Bogoliubov Theory ◽  
Generator Coordinate ◽  
Fission Barriers

Nuclear fission barriers, mass parameters and spontaneous fission half lives of fermium isotopes calculated in a framework of the Skyrme Hartree-Fock-Bogoliubov model with the SkM* force are discussed. Zero-point energy corrections in the ground state are determined for each nucleus using the Gaussian overlap approximation of the generator coordinate method and in the cranking formalism. Results of spontaneous fission half lives are compared to experimental data.

INFLUENCE OF LATTICE VIBRATION ON THE GROUND STATE OF MAGNETOPOLARON IN A PARABOLIC QUANTUM DOT

2010 ◽  
Vol 24 (27) ◽  
pp. 2705-2712 ◽  
Author(s):  
EERDUNCHAOLU ◽  
WEI XIN ◽  
YUWEI ZHAO
Keyword(s):  
Magnetic Field ◽  
Strong Coupling ◽  
Ground State Energy ◽  
Vibration Frequency ◽  
Ground State ◽  
Weak Coupling ◽  
State Energy ◽  
Cyclotron Frequency ◽  
Lattice Vibration ◽  
The Magnetic Field

Influence of the lattice vibration on the properties of the magnetopolaron in the parabolic quantum dots (QDs) is studied by using the Huybrechts' linear combination operator and Lee–Low–Pines (LLP) transformation methods. The expressions for the vibration frequency and the ground-state energy of the magnetopolaron as functions of the confinement strength of the QDs, the magnetic field and temperature are derived under the strong and weak coupling, respectively. The results of the numerical calculations show that the changes of the vibration frequency and ground-state energy of the magnetopolaron with the confinement strength of the QDs, the magnetic field and temperature are different under different couplings. The vibration frequency and the ground-state energy of the weak-coupling magnetopolaron and the vibration frequency of the strong-coupling magnetopolaron will increase with increase of the confinement strength of the QDs and cyclotron frequency, the vibration frequency and ground-state energy of the strong-coupling magnetopolaron. However, the ground-state energy of the weak-coupling magnetopolaron will decrease with increase of the temperature. The dependence of the ground-state energy of the strong-coupling magnetopolaron on the confinement strength of the QDs and cyclotron frequency is strongly influenced by the temperature. The remarkable influence of the temperature on the ground-state energy of the magnetopolaron arises when the temperature is relatively higher.

Zero-Point Effects in Heisenberg Antiferromagnets with Arbitrary Range of Interaction

1972 ◽  
Vol 50 (23) ◽  
pp. 2991-2996 ◽  
Author(s):  
M. F. Collins ◽  
V. K. Tondon
Keyword(s):  
Ground State ◽  
State Energy ◽  
Correction Term ◽  
Zero Point ◽  
Face Centered Cubic ◽  
Heisenberg Antiferromagnet ◽  
Body Centered Cubic ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Face Centered

The ground state energy, spin-wave energy, and sublattice magnetization have been calculated for a Heisenberg antiferromagnet at the absolute zero of temperature. The treatment extends the earlier work of Anderson, Kubo, and Oguchi to apply for any two-sublattice antiferromagnet with arbitrary range of interaction. It is shown that for each exchange interaction there is a different characteristic correction term to the energies. Explicit calculations are made of these terms for the simple cubic, body-centered cubic, and face-centered cubic lattices, with both first- and second-neighbor interactions. Applications are also made to NiO and MnO. An extra term in the magnetization series beyond that given by earlier workers is derived.

On-the-fly Symmetrical Quasi-classical Dynamics with Meyer-Miller Mapping Hamiltonian for the Treatment of Nonadiabatic Dynamics at Conical Intersections

2020 ◽  
Author(s):  
Deping Hu ◽  
Yu Xie ◽  
Jiawei Peng ◽  
Zhenggang Lan
Keyword(s):  
Ground State ◽  
Zero Point ◽  
Classical Dynamics ◽  
Nonadiabatic Dynamics ◽  
Conical Intersections ◽  
Point Energy ◽  
Simulation Protocol ◽  
Polyatomic Systems ◽  
Dynamics Method ◽  
Better Than

The ‘on-the-fly’ version of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (SQC/MM) is implemented to study the nonadiabatic dynamics at conical intersections of polyatomic systems. The current ‘on-the-fly’ implementation of the SQC/MM method is based on the adiabatic representation and the dressed momentum. To include the zero-point energy (ZPE) correction of the electronic mapping variables, we employed both the γ-adjusted and γ-fixed approaches. Nonadiabatic dynamics of the methaniminium cation (CH2NH2+) and azomethane are simulated using the on-the-fly SQC/MM method. For CH2NH2+, both two ZPE correction approaches give reasonable and consistent results. However, for azomethane, the γ-adjusted version of the SQC/MM dynamics behaves much better than the γ-fixed version. The further analysis indicates that it is always recommended to use the γ-adjusted SQC/MM dynamics in the on-the-fly simulation of photoinduced dynamics of polyatomic systems, particularly when the excited-state is well separated from the ground state in the Frank-Condon region. This work indicates that the on-the-fly SQC/MM method is a powerful simulation protocol to deal with the nonadiabatic dynamics of realistic polyatomic systems.

scholarly journals The ground state tunneling splitting and the zero point energy of malonaldehyde: A quantum Monte Carlo determination

2007 ◽  
Vol 126 (2) ◽  
pp. 024308 ◽  
Author(s):  
Alexandra Viel ◽  
Maurício D. Coutinho-Neto ◽  
Uwe Manthe
Keyword(s):  
Monte Carlo ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Zero Point ◽  
Zero Point Energy ◽  
Point Energy ◽  
Tunneling Splitting

CAUSTICS IN A CUBIC SU(2) LATTICE MODEL WITH ANTIPERIODIC BOUNDARY CONDITIONS

1989 ◽  
Vol 04 (17) ◽  
pp. 4607-4626
Author(s):  
B. RAABE
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
Weak Coupling ◽  
Gauge Theories ◽  
Semiclassical Approximation ◽  
Hamiltonian Formalism ◽  
Weak Coupling Limit ◽  
Lattice Gauge ◽  
Classical Trajectories ◽  
Lattice Gauge Theories

In order to investigate the weak coupling limit of lattice gauge theories, it has been suggested recently to apply the semiclassical approximation to the Schrödinger equation in the Hamiltonian formalism. This method is used to study pure SU(2) gauge theory on a cube with sides of length one lattice constant and with antiperiodic boundary conditions. We show the existence of caustics, i.e. envelopes of families of classical trajectories where the ground state wave function peaks, and describe their shape.

Research on Information Applied Technology in the Study of Two-Layer Quantum Dots System

2013 ◽  
Vol 473 ◽  
pp. 133-136
Author(s):  
An Mei Wang
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Ground State ◽  
Weak Coupling ◽  
State Energy ◽  
Electron System ◽  
Exact Diagonalization ◽  
Hamiltonian Matrix ◽  
Applied Technology ◽  
The Magnetic Field

We study a two-electron system in a double-layer quantum dot under a magnetic field by means of the exact diagonalization of the Hamiltonian matrix. We find that discontinuous ground-state energy transitions are induced by an external magnetic field in the case of strong coupling. However, in the case of weak coupling, the angular momentum of the true ground state does not change in accordance with the change of the magnetic field B and remains = 0.

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