scholarly journals Ground and excited states of spherically symmetric potentials through an imaginary-time evolution method: application to spiked harmonic oscillators

2014 ◽  
Vol 52 (10) ◽  
pp. 2645-2662 ◽  
Author(s):  
Amlan K. Roy
Keyword(s):  
Time Evolution ◽  
Excited States ◽  
Harmonic Oscillators ◽  
Spherically Symmetric ◽  
Imaginary Time

scholarly journals Quantum confinement in 1D systems through an imaginary-time evolution method

2015 ◽  
Vol 30 (37) ◽  
pp. 1550176 ◽  
Author(s):  
Amlan K. Roy
Keyword(s):  
Time Evolution ◽  
Excited States ◽  
Quantum Confinement ◽  
Global Minimum ◽  
Quantum Systems ◽  
Attractive Potential ◽  
Imaginary Time ◽  
Expectation Values ◽  
Expectation Value ◽  
Orthogonality Constraint

Quantum confinement is studied by numerically solving time-dependent (TD) Schrödinger equation (SE). An imaginary-time evolution technique is employed in conjunction with the minimization of an expectation value, to reach the global minimum. Excited states are obtained by imposing the orthogonality constraint with all lower states. Applications are made on three important model quantum systems, namely, harmonic, repulsive and quartic oscillators; enclosed inside an impenetrable box. The resulting diffusion equation is solved using finite-difference method. Both symmetric and asymmetric confinement are considered for attractive potential; for others only symmetrical confinement. Accurate eigenvalue, eigenfunction and position expectation values are obtained, which show excellent agreement with existing literature results. Variation of energies with respect to box length is followed for small, intermediate and large sizes. In essence, a simple accurate and reliable method is proposed for confinement in quantum systems.

Imaginary-Time Time-Dependent Density Functional Calculation of Excited States of Atoms Using CWDVR Approach

2021 ◽  
Vol 323 ◽  
pp. 14-20
Author(s):  
Naranchimeg Dagviikhorol ◽  
Munkhsaikhan Gonchigsuren ◽  
Lochin Khenmedekh ◽  
Namsrai Tsogbadrakh ◽  
Ochir Sukh
Keyword(s):  
Excited States ◽  
Density Functional ◽  
Time Dependent ◽  
Discrete Variable ◽  
Coulomb Wave Function ◽  
Discrete Variable Representation ◽  
Density Functional Calculation ◽  
Imaginary Time ◽  
Sham Equation ◽  
Variable Representation

We have calculated the energies of excited states for the He, Li, and Be atoms by the time dependent self-consistent Kohn Sham equation using the Coulomb Wave Function Discrete Variable Representation CWDVR) approach. The CWDVR approach was used the uniform and optimal spatial grid discretization to the solution of the Kohn-Sham equation for the excited states of atoms. Our results suggest that the CWDVR approach is an efficient and precise solutions of excited-state energies of atoms. We have shown that the calculated electronic energies of excited states for the He, Li, and Be atoms agree with the other researcher values.

scholarly journals Geometry of variational methods: dynamics of closed quantum systems

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Lucas Hackl ◽  
Tommaso Guaita ◽  
Tao Shi ◽  
Jutho Haegeman ◽  
Eugene Demler ◽  
...  
Keyword(s):  
Variational Methods ◽  
Time Evolution ◽  
Coherent States ◽  
Geometric Approach ◽  
Quantum Systems ◽  
Imaginary Time ◽  
Excitation Spectra ◽  
Spectral Functions ◽  
Geometric Framework ◽  
Gaussian States

We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: Kähler and non-Kähler. Traditional variational methods typically require the variational family to be a Kähler manifold, where multiplication by the imaginary unit preserves the tangent spaces. This covers the vast majority of cases studied in the literature. However, recently proposed classes of generalized Gaussian states make it necessary to also include the non-Kähler case, which has already been encountered occasionally. We illustrate our approach in detail with a range of concrete examples where the geometric structures of the considered manifolds are particularly relevant. These go from Gaussian states and group theoretic coherent states to generalized Gaussian states.

scholarly journals Publisher Correction: Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

2020 ◽  
Vol 16 (2) ◽  
pp. 231-231 ◽  
Author(s):  
Mario Motta ◽  
Chong Sun ◽  
Adrian T. K. Tan ◽  
Matthew J. O’Rourke ◽  
Erika Ye ◽  
...  
Keyword(s):  
Time Evolution ◽  
Quantum Computer ◽  
Imaginary Time ◽  
Thermal States
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