scholarly journals Quantum Mechanics and Nanotechnology

2021 ◽  
Author(s):  
Mulani Tabssum Tayyab
Keyword(s):  
Molecular Dynamics ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Quantum Physics ◽  
State Energy ◽  
Quantum Mechanical ◽  
Accurate Representation ◽  
Quantum Ground State ◽  
Ground State Energies

In quantum physics it is important that classical molecular dynamics studies of nanomachines may not give an accurate representation of their performance. Luckily another strategy, interior facilitate quantum Monte Carlo, a further developed method for processing quantum mechanical ground-state energies and wavefunctions, has the possible ability to demonstrate these frameworks. Some significant models show that the quantum ground state for some body frameworks like those of interest in nanotechnology has a subjectively unexpected construction in comparison to that got from a sub-atomic elements computation which displayed confusion and gross insecurities at energies of just a small amount of the ground-state energy. This outcome projects vulnerability on the unwavering quality of utilizing the sub-atomic elements strategy to ascertain the construction or some other dynamical amount pertinent to nanotechnology.

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.

Quantum Monte Carlo ground state energies for the singly charged ions from Li through Ar

2010 ◽  
Vol 133 (6) ◽  
pp. 064102 ◽  
Author(s):  
P. Maldonado ◽  
A. Sarsa ◽  
E. Buendía ◽  
F. J. Gálvez
Keyword(s):  
Monte Carlo ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Singly Charged ◽  
Charged Ions ◽  
Ground State Energies

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.

scholarly journals Contextual Subspace Variational Quantum Eigensolver

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 456
Author(s):  
William M. Kirby ◽  
Andrew Tranter ◽  
Peter J. Love
Keyword(s):  
Small Molecules ◽  
Ground State Energy ◽  
Ground State ◽  
Original Problem ◽  
State Energy ◽  
Quantum Devices ◽  
Intermediate Scale ◽  
Measurement Reduction ◽  
Quantum Processor

We describe the contextual subspace variational quantum eigensolver (CS-VQE), a hybrid quantum-classical algorithm for approximating the ground state energy of a Hamiltonian. The approximation to the ground state energy is obtained as the sum of two contributions. The first contribution comes from a noncontextual approximation to the Hamiltonian, and is computed classically. The second contribution is obtained by using the variational quantum eigensolver (VQE) technique to compute a contextual correction on a quantum processor. In general the VQE computation of the contextual correction uses fewer qubits and measurements than the VQE computation of the original problem. Varying the number of qubits used for the contextual correction adjusts the quality of the approximation. We simulate CS-VQE on tapered Hamiltonians for small molecules, and find that the number of qubits required to reach chemical accuracy can be reduced by more than a factor of two. The number of terms required to compute the contextual correction can be reduced by more than a factor of ten, without the use of other measurement reduction schemes. This indicates that CS-VQE is a promising approach for eigenvalue computations on noisy intermediate-scale quantum devices.

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