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.

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 Compact wavefunctions from compressed imaginary time evolution

RSC Advances ◽  
2015 ◽  
Vol 5 (124) ◽  
pp. 102277-102283 ◽  
Author(s):  
Jarrod R. McClean ◽  
Alán Aspuru-Guzik
Keyword(s):  
Time Evolution ◽  
Quantum Systems ◽  
Imaginary Time ◽  
Efficient Modeling

Compact wavefunctions built through compressed imaginary time evolution enable more efficient modeling of quantum systems.

scholarly journals THE TACHYON FIELD BELOW THE MASS BARRIER

1994 ◽  
Vol 09 (20) ◽  
pp. 3497-3502 ◽  
Author(s):  
D.G. BARCI ◽  
C.G. BOLLINI ◽  
M.C. ROCCA
Keyword(s):  
Green Function ◽  
Eigenvalue Problem ◽  
Plane Wave ◽  
Time Evolution ◽  
Mass Parameter ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Tachyon Field ◽  
Expectation Value ◽  
Wave Solutions

We consider a tachyon field whose Fourier components correspond to spatial momenta with modulus smaller than the mass parameter. The plane wave solutions have then a time evolution which is a real exponential. The field is quantized and the solution of the eigenvalue problem for the Hamiltonian leads to the evaluation of the vacuum expectation value of products of field operators. The propagator turns out to be half-advanced and half-retarded. This completes the proof4 that the total propagator is the Wheeler Green function.4,7

FRUSTRATED TRANSVERSE ISING MODELS: A CLASS OF FRUSTRATED QUANTUM SYSTEMS

1992 ◽  
Vol 06 (14) ◽  
pp. 2439-2469 ◽  
Author(s):  
P. SEN ◽  
B. K. CHAKRABARTI
Keyword(s):  
Excited States ◽  
Transverse Field ◽  
Ising Models ◽  
Quantum Systems ◽  
Nearest Neighbour ◽  
Competing Interactions ◽  
Annni Model ◽  
Kirkpatrick Model ◽  
Transverse Fields ◽  
Exact Diagonalisation

The analytical and numerical (Monte Carlo and exact diagonalisation) estimates of phase diagrams of frustrated Ising models in transverse fields are discussed here. Specifically we discuss the Sherrington–Kirkpatrick model in transverse field and the Axial Next-Nearest Neighbour Ising (ANNNI) model in transverse field. The effects of quantum fluctuations (induced by the transverse field) on the ground and excited states of such systems with competing interactions (frustration) are also discussed. The results are compared to those available for other frustrated quantum systems.

Sign in / Sign up

Export Citation Format

Share Document