TY - JOUR

T1 - A probabilistic evolution approach trilogy, part 3

T2 - Temporal variation of state variable expectation values from Liouville equation perspective

AU - Demiralp, Metin

AU - Tunga, Burcu

PY - 2013/4

Y1 - 2013/4

N2 - This is the third and therefore the final part of a trilogy on probabilistic evolution approach. The work presented here focuses on the probabilistic evolution determination for the state variables of a many particle system from classical mechanical point of view. Probabilistic evolution involves the expected value evolutions for all natural number Kronecker powers of the state variables, positions and momenta. We use the phase space distribution of the Liouville equation perspective to construct the expected values of the state variables' Kronecker powers to define unknown temporal functions. The infinite number homogeneous linear ODEs with an infinite constant coefficient matrix are constructed by following the same steps as in the previous two works on quantum mechanics. The only difference is in the definitions of the expected values here. We also focus on a system of many harmonic oscillators to illustrate the block triangularity.

AB - This is the third and therefore the final part of a trilogy on probabilistic evolution approach. The work presented here focuses on the probabilistic evolution determination for the state variables of a many particle system from classical mechanical point of view. Probabilistic evolution involves the expected value evolutions for all natural number Kronecker powers of the state variables, positions and momenta. We use the phase space distribution of the Liouville equation perspective to construct the expected values of the state variables' Kronecker powers to define unknown temporal functions. The infinite number homogeneous linear ODEs with an infinite constant coefficient matrix are constructed by following the same steps as in the previous two works on quantum mechanics. The only difference is in the definitions of the expected values here. We also focus on a system of many harmonic oscillators to illustrate the block triangularity.

KW - Elastic spring forces

KW - Evolution matrix

KW - Expected value dynamics

KW - Phase space distribution

KW - Probabilistic evolution

UR - http://www.scopus.com/inward/record.url?scp=84874958434&partnerID=8YFLogxK

U2 - 10.1007/s10910-012-0081-z

DO - 10.1007/s10910-012-0081-z

M3 - Article

AN - SCOPUS:84874958434

SN - 0259-9791

VL - 51

SP - 1198

EP - 1210

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

IS - 4

ER -