scholarly journals Gaussian-based techniques for quantum propagation from the time-dependent variational principle: Formulation in terms of trajectories of coupled classical and quantum variables

2008 ◽  
Vol 129 (8) ◽  
pp. 084104 ◽  
Author(s):  
Dmitrii V. Shalashilin ◽  
Irene Burghardt
Keyword(s):  
Variational Principle ◽  
Time Dependent

scholarly journals Effects of entanglement on vortex dynamics in the hydrodynamic representation of quantum mechanics

2020 ◽  
Vol 18 (06) ◽  
pp. 2050030
Author(s):  
Satoya Imai
Keyword(s):  
Quantum Mechanics ◽  
Variational Principle ◽  
Quantum System ◽  
Quantum Entanglement ◽  
Vortex Dynamics ◽  
Ritz Method ◽  
Hamiltonian Formalism ◽  
Time Dependent ◽  
Nodal Points ◽  
As If

The hydrodynamic representation of quantum mechanics describes virtual flow as if a quantum system were fluid in motion. This formulation illustrates pointlike vortices when the phase of a wavefunction becomes nonintegrable at nodal points. We study the dynamics of such pointlike vortices in the hydrodynamic representation for a two-particle wavefunction. In particular, we discuss how quantum entanglement influences vortex–vortex dynamics. For this purpose, we employ the time-dependent quantum variational principle combined with the Rayleigh–Ritz method. We analyze the vortex dynamics and establish connections with Dirac’s generalized Hamiltonian formalism.

scholarly journals Parallel time-dependent variational principle algorithm for matrix product states

2020 ◽  
Vol 101 (23) ◽  
Author(s):  
Paul Secular ◽  
Nikita Gourianov ◽  
Michael Lubasch ◽  
Sergey Dolgov ◽  
Stephen R. Clark ◽  
...  
Keyword(s):  
Variational Principle ◽  
Time Dependent ◽  
Matrix Product ◽  
Matrix Product States ◽  
Parallel Time

scholarly journals Polaron dynamics with off-diagonal coupling: beyond the Ehrenfest approximation

2017 ◽  
Vol 19 (2) ◽  
pp. 1655-1668 ◽  
Author(s):  
Zhongkai Huang ◽  
Lu Wang ◽  
Changqin Wu ◽  
Lipeng Chen ◽  
Frank Grossmann ◽  
...  
Keyword(s):  
Variational Principle ◽  
Molecular Crystal ◽  
Time Dependent ◽  
Phonon Coupling ◽  
One Dimensional ◽  
Crystal Model ◽  
Polaron Dynamics ◽  
Diagonal Coupling

Treated traditionally by the Ehrenfest approximation, the dynamics of a one-dimensional molecular crystal model with off-diagonal exciton–phonon coupling is investigated in this work using the Dirac–Frenkel time-dependent variational principle with the multi-D2Ansatz.

Time-dependent Hartree-Fock phase: Unique implication of variational principle

1979 ◽  
Vol 88 (3-4) ◽  
pp. 221-225 ◽  
Author(s):  
Peter C. Lichtner ◽  
James J. Griffin ◽  
Hildegard Schultheis ◽  
Rainer Schultheis ◽  
Anatole B. Volkov
Keyword(s):  
Variational Principle ◽  
Time Dependent ◽  
Hartree Fock

scholarly journals Gaussian Time-Dependent Variational Principle for Bosons

1997 ◽  
Vol 260 (2) ◽  
pp. 250-274 ◽  
Author(s):  
Arthur K. Kerman ◽  
Paolo Tommasini
Keyword(s):  
Variational Principle ◽  
Time Dependent ◽  
Gaussian Time
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