TY - JOUR

T1 - Fractional Langevin equation: Overdamped, underdamped, and critical behaviors

AU - Borov, S.

AU - Barkai, E.

PY - 2008

Y1 - 2008

N2 - The dynamical phase diagram of the fractional Langevin equation is investigated for a harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents are found. (i)
α
c
=
0.402
±
0.002
marks a transition to a nonmonotonic underdamped phase, (ii)
α
R
=
0.441
…
marks a transition to a resonance phase when an external oscillating field drives the system, and (iii)
α
χ
1
=
0.527
…
and (iv)
α
χ
2
=
0.707
…
mark transitions to a double-peak phase of the “loss” when such an oscillating field present. As a physical explanation we present a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing over and underdamped regimes, with or without resonances, show behaviors different from normal.

AB - The dynamical phase diagram of the fractional Langevin equation is investigated for a harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents are found. (i)
α
c
=
0.402
±
0.002
marks a transition to a nonmonotonic underdamped phase, (ii)
α
R
=
0.441
…
marks a transition to a resonance phase when an external oscillating field drives the system, and (iii)
α
χ
1
=
0.527
…
and (iv)
α
χ
2
=
0.707
…
mark transitions to a double-peak phase of the “loss” when such an oscillating field present. As a physical explanation we present a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing over and underdamped regimes, with or without resonances, show behaviors different from normal.

UR - https://scholar.google.co.il/scholar?q=Fractional+Langevin+Equation%3A+Over-Damped%2C+Under-Damped+and+Critical+Behaviors&btnG=&hl=en&as_sdt=0%2C5

M3 - Article

VL - 78

JO - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

IS - 3

ER -