Path integrals for dissipative systems by tensor multiplication. Condensed phase quantum dynamics for arbitrarily long time

1994 ◽  
Vol 221 (5-6) ◽  
pp. 482-491 ◽  
Author(s):  
Dmitrii E. Makarov ◽  
Nancy Makri
Keyword(s):  
Condensed Phase ◽  
Quantum Dynamics ◽  
Path Integrals ◽  
Dissipative Systems ◽  
Long Time ◽  
Tensor Multiplication

scholarly journals Real-time quantum dynamics, path integrals and the method of thimbles

2019 ◽  
Vol 2019 (6) ◽  
Author(s):  
Zong-Gang Mou ◽  
Paul M. Saffin ◽  
Anders Tranberg ◽  
Simon Woodward
Keyword(s):  
Real Time ◽  
Quantum Dynamics ◽  
Path Integrals ◽  
Time Quantum

scholarly journals Electron-Induced Chemistry in the Condensed Phase

Atoms ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 33
Author(s):  
Jan Hendrik Bredehöft
Keyword(s):  
Gas Phase ◽  
Cross Sections ◽  
Condensed Phase ◽  
Theoretical Understanding ◽  
The Past ◽  
Long Time ◽  
The Difference ◽  
Molecule Interactions ◽  
Multi Body ◽  
Molecule Interaction

Electron–molecule interactions have been studied for a long time. Most of these studies have in the past been limited to the gas phase. In the condensed-phase processes that have recently attracted attention from academia as well as industry, a theoretical understanding is mostly based on electron–molecule interaction data from these gas phase experiments. When transferring this knowledge to condensed-phase problems, where number densities are much higher and multi-body interactions are common, care must be taken to critically interpret data, in the light of this chemical environment. The paper presented here highlights three typical challenges, namely the shift of ionization energies, the difference in absolute cross-sections and branching ratios, and the occurrence of multi-body processes that can stabilize otherwise unstable intermediates. Examples from recent research in astrochemistry, where radiation driven chemistry is imminently important are used to illustrate these challenges.

Phase space path integrals in Monte Carlo quantum dynamics

1996 ◽  
Vol 104 (16) ◽  
pp. 6265-6277 ◽  
Author(s):  
Stavros Caratzoulas ◽  
Philip Pechukas
Keyword(s):  
Monte Carlo ◽  
Phase Space ◽  
Quantum Dynamics ◽  
Path Integrals

scholarly journals Long-time Dynamics of Spontaneous Parametric Down-conversion and Quantum Limitations of Conversion Efficiency

1999 ◽  
Vol 54 (1) ◽  
pp. 57-62 ◽  
Author(s):  
Michael Fleischhauer ◽  
Oliver Veits
Keyword(s):  
Quantum Dynamics ◽  
Equations Of Motion ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Time Dynamics ◽  
Pendulum Equation ◽  
Parametric Down Conversion ◽  
Long Time ◽  
Down Conversion

Abstract We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motion fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined. A numerical integration of the 2-mode Schrödinger equation using a dynamically optimized basis of displaced and squeezed number states verifies the characteristic times predicted by the mean-field approximation. In contrast to semiclassical and mean-field predictions it is found that quantum fluctuations of the pump mode lead to a substantial limitation of the efficiency of parametric down-conversion.

Convergence of exponential Lawson-multistep methods for the MCTDHF equations

2019 ◽  
Vol 53 (6) ◽  
pp. 2109-2119 ◽  
Author(s):  
Othmar Koch
Keyword(s):  
Quantum Dynamics ◽  
Multistep Methods ◽  
Equations Of Motion ◽  
Time Integration ◽  
Time Intervals ◽  
Numerical Illustration ◽  
Hartree Fock ◽  
Long Time ◽  
Long Time Integration ◽  
Adaptive Time

We consider exponential Lawson multistep methods for the time integration of the equations of motion associated with the multi-configuration time-dependent Hartree–Fock (MCTDHF) approximation for high-dimensional quantum dynamics. These provide high-order approximations at a minimum of evaluations of the computationally expensive nonlocal potential terms, and have been found to enable stable long-time integration. In this work, we prove convergence of the numerical approximation on finite time intervals under minimal regularity assumptions on the exact solution. A numerical illustration shows adaptive time propagation based on our methods.

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