The Quantum Hydrodynamic Description of Tunneling

Conference · Fri Jun 15 00:00:00 EDT 2012

OSTI ID:1044084

Kendrick, Brian K ^[1]

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1. Los Alamos National Laboratory

The quantum hydrodynamic approach is based on the de Broglie-Bohm formulation of quantum mechanics. The resulting fluid-like equations of motion describe the flow of probability and an accurate solution to these equations is equivalent to solving the time-dependent Schroedinger equation. Furthermore, the hydrodynamic approach provides new insight into the mechanisms as well as an alternative computational approach for treating tunneling phenomena. New concepts include well-defined 'quantum trajectories', 'quantum potential', and 'quantum force' all of which have classical analogues. The quantum potential and its associated force give rise to all quantum mechanical effects such as zero point energy, tunneling, and interference. A new numerical approach called the Iterative Finite Difference Method (IFDM) will be discussed. The IFDM is used to solve the set of non-linear coupled hydrodynamic equations. It is 2nd-order accurate in both space and time and exhibits exponential convergence with respect to the iteration count. The stability and computational efficiency of the IFDM is significantly improved by using a 'smart' Eulerian grid which has the same computational advantages as a Lagrangian or Arbitrary Lagrangian Eulerian (ALE) grid. The IFDM is also capable of treating anharmonic potentials. Example calculations using the IFDM will be presented which include: a one-dimensional Gaussian wave packet tunneling through an Eckart barrier, a one-dimensional bound-state Morse oscillator, and a two-dimensional (2D) model collinear reaction using an anharmonic potential energy surface. Approximate treatments of the quantum hydrodynamic equations will also be discussed which could allow scaling of the calculations to hundreds of degrees of freedom which is important for treating tunneling phenomena in condensed phase systems.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: DOE/LANL
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 1044084
• Report Number(s): LA-UR-12-22223; TRN: US201214%%298
• Resource Relation: Conference: 16th International Workshop on Quantum Atomic and Molecular Tunneling in Solids and other Condensed Phases (QAMTS) ; 2012-06-10 - 2012-06-14 ; Santa Fe, New Mexico, United States
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
74 ATOMIC AND MOLECULAR PHYSICS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
77 NANOSCIENCE AND NANOTECHNOLOGY
BOUND STATE
CONVERGENCE
DEGREES OF FREEDOM
EFFICIENCY
EQUATIONS OF MOTION
FINITE DIFFERENCE METHOD
HYDRODYNAMICS
LAGRANGIAN FUNCTION
MECHANICAL PROPERTIES
POTENTIAL ENERGY
PROBABILITY
QUANTUM MECHANICS
SCHROEDINGER EQUATION
STABILITY
TRAJECTORIES
TUNNELING
WAVE PACKETS