TY - JOUR

T1 - Effective classical stochastic theory for quantum tunneling

AU - Heifetz, Eyal

AU - Plochotnikov, Igor

N1 - Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/7/27

Y1 - 2020/7/27

N2 - The ensemble mean equations for a classical particle moving stochastically obtain the form of fluid equations. When applying the Madelung transformation to write the Schrödinger equation in a fluid-like form we find that the equations are equivalent to the classical ensemble mean equations if an additional force is added to the equations. The latter can be expressed as a pressure gradient force of a fluctuating pressure with zero mean. Here we analyze the mechanism of quantum tunneling through a rectangular potential barrier from this perspective. We find that despite of the vanishing of the mean of the pressure fluctuations their local non zero gradients enable the tunneling by balancing the counter external potential gradients at the two sides of the potential barrier. Consequently, for stationary solutions, the ensemble mean kinetic energy remains unchanged across the boundaries of the barrier.

AB - The ensemble mean equations for a classical particle moving stochastically obtain the form of fluid equations. When applying the Madelung transformation to write the Schrödinger equation in a fluid-like form we find that the equations are equivalent to the classical ensemble mean equations if an additional force is added to the equations. The latter can be expressed as a pressure gradient force of a fluctuating pressure with zero mean. Here we analyze the mechanism of quantum tunneling through a rectangular potential barrier from this perspective. We find that despite of the vanishing of the mean of the pressure fluctuations their local non zero gradients enable the tunneling by balancing the counter external potential gradients at the two sides of the potential barrier. Consequently, for stationary solutions, the ensemble mean kinetic energy remains unchanged across the boundaries of the barrier.

KW - Ensemble mean dynamics

KW - Madelung equations

UR - http://www.scopus.com/inward/record.url?scp=85084262790&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2020.126511

DO - 10.1016/j.physleta.2020.126511

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AN - SCOPUS:85084262790

SN - 0375-9601

VL - 384

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 21

M1 - 126511

ER -