scholarly journals The Energy of the Ground State of the Two-Dimensional Hamiltonian of a Parabolic Quantum Well in the Presence of an Attractive Gaussian Impurity

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1561
Author(s):  
Silvestro Fassari ◽  
Manuel Gadella ◽  
Luis Miguel Nieto ◽  
Fabio Rinaldi
Keyword(s):  
Integral Operator ◽  
Quantum Well ◽  
Fourth Order ◽  
Ground State ◽  
Fredholm Determinant ◽  
Quantum Mechanical ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Gaussian Potential

In this article, we provide an expansion (up to the fourth order of the coupling constant) of the energy of the ground state of the Hamiltonian of a quantum mechanical particle moving inside a parabolic well in the x-direction and constrained by the presence of a two-dimensional impurity, modelled by an attractive two-dimensional isotropic Gaussian potential. By investigating the associated Birman–Schwinger operator and exploiting the fact that such an integral operator is Hilbert–Schmidt, we use the modified Fredholm determinant in order to compute the energy of the ground state created by the impurity.

2D ISING MODEL WITH COMPETING INTERACTIONS AND ITS APPLICATION TO CLUSTERS AND ARRAYS OF π-RINGS, GRAPHENE AND ADIABATIC QUANTUM COMPUTING

2009 ◽  
Vol 23 (20n21) ◽  
pp. 3951-3967 ◽  
Author(s):  
ANTHONY O'HARE ◽  
F. V. KUSMARTSEV ◽  
K. I. KUGEL
Keyword(s):  
Quantum Computing ◽  
Ising Model ◽  
Ground State ◽  
Honeycomb Lattice ◽  
Graphene Plane ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Competing Interactions ◽  
Adiabatic Quantum Computing ◽  
Ising Spins

We study the two-dimensional Ising model with competing nearest-neighbour and diagonal interactions and investigate the phase diagram of this model. We show that the ground state at low temperatures is ordered either as stripes or as the Néel antiferromagnet. However, we also demonstrate that the energy of defects and dislocations in the lattice is close to the ground state of the system. Therefore, many locally stable (or metastable) states associated with local energy minima separated by energy barriers may appear forming a glass-like state. We discuss the results in connection with two physically different systems. First, we deal with planar clusters of loops including a Josephson π-junction (a π-rings). Each π-ring carries a persistent current and behaves as a classical orbital moment. The type of particular state associated with the orientation of orbital moments in the cluster depends on the interaction between these orbital moments and can be easily controlled, i.e. by a bias current or by other means. Second, we apply the model to the analysis of the structure of the newly discovered two-dimensional form of carbon, graphene. Carbon atoms in graphene form a planar honeycomb lattice. Actually, the graphene plane is not ideal but corrugated. The displacement of carbon atoms up and down from the plane can be also described in terms of Ising spins, the interaction of which determines the complicated shape of the corrugated graphene plane. The obtained results may be verified in experiments and are also applicable to adiabatic quantum computing where the states are switched adiabatically with the slow change of coupling constant.

Comparison of O- and C-models on pseudosphere

2016 ◽  
Vol 31 (34) ◽  
pp. 1650179
Author(s):  
G. V. Grigoryan ◽  
R. P. Grigoryan ◽  
I. V. Tyutin
Keyword(s):  
Mechanical Treatment ◽  
Schrödinger Operators ◽  
Energy Coupling ◽  
Quantum Mechanical ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Nonrelativistic Quantum ◽  
Spectral Problems ◽  
Quantum Mechanical Treatment ◽  
One To One

We present a mathematically rigorous quantum-mechanical treatment of a two-dimensional nonrelativistic quantum dual theories (with oscillator- and Coulomb-like potentials) on pseudosphere. We construct all self-adjoint Schrödinger operators for these theories and present solutions of the corresponding spectral problems. We show, that there is one-to-one correspondence between spectral points of the energy-coupling constant planes not only for discrete, but also for continuous spectra and corresponding eigenfunctions forming the complete orthonormalized systems.

The effect of temperature on strong-coupling magnetopolaron in an asymmetrical Gaussian potential quantum well

2020 ◽  
Vol 34 (12) ◽  
pp. 2050114
Author(s):  
Xiu-Juan Miao ◽  
Yong Sun ◽  
Jing-Lin Xiao
Keyword(s):  
Magnetic Field ◽  
Quantum Well ◽  
Strong Coupling ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Cyclotron Frequency ◽  
Operator Method ◽  
Effect Of Temperature ◽  
Gaussian Potential

The influences of temperature and cyclotron frequency of a magnetic field on the ground state energy and mean number of phonons (MNP) of strong-coupling magnetopolarons in an asymmetric Gaussian potential quantum well(AGPQW) are researched by employing the linear-combination operator method and the unitary transformation. It was demonstrated through the numerical calculations that the ground state energy and the MNP increase with higher magnetic field cyclotron frequencies and temperature. In addition, increasing of the barrier of asymmetric Gaussian potential (AGP) causes the ground state energy to decrease while increasing the MNP of magnetopolarons.

scholarly journals A new application of the quantum mechanical hypervirial theorems technique

2020 ◽  
Vol 9 ◽  
pp. 210
Author(s):  
M. E. Grypeos ◽  
Th. E. Liolios
Keyword(s):  
Wide Class ◽  
Ground State ◽  
State Energy ◽  
Bound State ◽  
Quantum Mechanical ◽  
Bound State Energy ◽  
New Approach ◽  
Analytic Determination ◽  
Gaussian Potential

A new approach is proposed on the basis of the quantum mechanical hypervirial theorems technique for the approximate analytic (or semi-analytic) determination of bound state energy eigenfunctions for quite a wide class of central potentials. The accuracy of the method is tested for the Gaussian potential and is best for the ground state.

The temperature effect on ground state binding energy of a strong-coupling magnetopolaron in an asymmetrical Gaussian potential quantum well

2021 ◽  
pp. 2150273
Author(s):  
Saren Gaowa ◽  
Xiu-Juan Miao ◽  
Jing-Lin Xiao ◽  
Cui-Lan Zhao
Keyword(s):  
Binding Energy ◽  
Quantum Well ◽  
Strong Coupling ◽  
Ground State ◽  
Cyclotron Frequency ◽  
Gaussian Potential ◽  
Ground State Binding Energy ◽  
Quantum Statistical Theory ◽  
Quantum Statistical ◽  
Physical Quantities

This paper utilized the methods of linear combination and unitary transformation to evaluate the vibrational frequency (VF) and ground state binding energy (GSBE) of a strong-coupling magnetopolaron in an asymmetrical Gaussian potential quantum well (AGPQW), and the effects of the temperature on these physical quantities were studied through quantum statistical theory. The changes of the VF and GSBE versus temperature and cyclotron frequency (CF) in a magnetic field were discussed. The numerical calculations revealed that with the increase of temperature, the VF and GSBE also increased. Meanwhile, the numerical results show that the VF increases with the increase of the CF. However, the GSBE versus the CF has different changing properties.

Sign in / Sign up

Export Citation Format

Share Document