scholarly journals On the Vanishing of the t-term in the Short-Time Expansion of the Diffusion Coefficient for Oscillating Gradients in Diffusion NMR

2017 ◽  
Vol 5 ◽  
Author(s):  
Frederik B. Laun ◽  
Kerstin Demberg ◽  
Armin M. Nagel ◽  
Micheal Uder ◽  
Tristan A. Kuder
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Nmr ◽  
Time Expansion ◽  
Short Time ◽  
Oscillating Gradients

CLASSICAL DIFFUSION AND QUANTAL LOCALIZATION OF A KICKED PARTICLE IN A WELL

1988 ◽  
Vol 02 (01) ◽  
pp. 103-120 ◽  
Author(s):  
AVRAHAM COHEN ◽  
SHMUEL FISHMAN
Keyword(s):  
Diffusion Coefficient ◽  
Classical Limit ◽  
Approximate Formula ◽  
Quantum Systems ◽  
Potential Well ◽  
Diffusive Growth ◽  
Classical Chaos ◽  
The One ◽  
Short Time ◽  
Infinite Potential Well

The classical and quantal behavior of a particle in an infinite potential well, that is periodically kicked is studied. The kicking potential is K|q|α, where q is the coordinate, while K and α are constants. Classically, it is found that for α > 2 the energy of the particle increases diffusively, for α < 2 it is bounded and for α = 2 the result depends on K. An approximate formula for the diffusion coefficient is presented and compared with numerical results. For quantum systems that are chaotic in the classical limit, diffusive growth of energy takes place for a short time and then it is suppressed by quantal effects. For the systems that are studied in this work the origin of the quantal localization in energy is related to the one of classical chaos.

scholarly journals SURVIVAL PROBABILITY (HEAT CONTENT) AND THE LOWEST EIGENVALUE OF DIRICHLET LAPLACIAN

2011 ◽  
Vol 25 (15) ◽  
pp. 1993-2007
Author(s):  
PAVOL KALINAY ◽  
LADISLAV ŠAMAJ ◽  
IGOR TRAVĚNEC
Keyword(s):  
Survival Probability ◽  
Heat Content ◽  
Simple Algorithm ◽  
Time Behavior ◽  
Dirichlet Laplacian ◽  
Geometric Characteristics ◽  
Long Time ◽  
Time Expansion ◽  
Short Time ◽  
Lowest Eigenvalue

We study the survival probability of a particle diffusing in a two-dimensional domain, bounded by a smooth absorbing boundary. The short-time expansion of this quantity depends on the geometric characteristics of the boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue of the Dirichlet Laplacian defined on the domain. We present a simple algorithm for calculation of the short-time expansion for an arbitrary "star-shaped" domain. The coefficients are expressed in terms of powers of boundary curvature, integrated around the circumference of the domain. Based on this expansion, we look for a Padé interpolation between the short-time and the long-time behavior of the survival probability, i.e., between geometric characteristics of the boundary and the lowest eigenvalue of the Dirichlet Laplacian.

scholarly journals Fast converging path integrals for time-dependent potentials: I. Recursive calculation of short-time expansion of the propagator

2011 ◽  
Vol 2011 (03) ◽  
pp. P03004 ◽  
Author(s):  
Antun Balaž ◽  
Ivana Vidanović ◽  
Aleksandar Bogojević ◽  
Aleksandar Belić ◽  
Axel Pelster
Keyword(s):  
Path Integrals ◽  
Time Dependent ◽  
Recursive Calculation ◽  
Time Expansion ◽  
Short Time

Short-time asymptotics of hydrodynamic dispersion in porous media

2013 ◽  
Vol 732 ◽  
pp. 687-705 ◽  
Author(s):  
Tyler R. Brosten
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Low Reynolds Number ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Number Flow ◽  
Flow Through ◽  
Time Expansion ◽  
Low Reynolds ◽  
Short Time

AbstractWe consider convection–diffusion transport of a passive scalar within porous media having a piecewise-smooth and reflecting pore–grain interface. The corresponding short-time expansion of molecular displacement time-correlation functions is determined for the generalized steady convection field. By interpreting the generalized short-time expansion of dispersion dynamics in the context of low-Reynolds-number flow through macroscopically homogeneous porous media, we demonstrate the connection between hydrodynamic permeability and short-time dynamics. The analytical short-time expansion is compared with numerical simulation data for steady low-Reynolds-number flow through a random close-pack array of mono-disperse spheres. The quadratic short-time expansion term of the dispersion coefficient closely predicts the numerical data for a mean displacement of at least 10 % of the sphere diameter for a Péclet number of 54.49.

Short time expansion of the relative motion of molecular pairs. Application to water

2000 ◽  
Vol 12 (24) ◽  
pp. 5121-5127 ◽  
Author(s):  
Alberto De Santis ◽  
Alessandro Ercoli ◽  
Dario Rocca
Keyword(s):  
Relative Motion ◽  
Time Expansion ◽  
Short Time
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