The scalar-product expression of boundary free energy for long-range interacting systems

1978 ◽  
Vol 68 (1) ◽  
pp. 119 ◽  
Author(s):  
Ryoichi Kikuchi
Keyword(s):  
Free Energy ◽  
Long Range ◽  
Scalar Product ◽  
Product Expression ◽  
Interacting Systems

scholarly journals Effects of energy extensivity on the quantum phases of long-range interacting systems

2021 ◽  
Vol 103 (15) ◽  
Author(s):  
T. Botzung ◽  
D. Hagenmüller ◽  
G. Masella ◽  
J. Dubail ◽  
N. Defenu ◽  
...  
Keyword(s):  
Long Range ◽  
Quantum Phases ◽  
Interacting Systems

scholarly journals Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions

Open Physics ◽  
2012 ◽  
Vol 10 (3) ◽  
Author(s):  
Bruno Marcos ◽  
Andrea Gabrielli ◽  
Michael Joyce
Keyword(s):  
Long Range ◽  
Asymptotic Form ◽  
Pair Interaction ◽  
Collision Integral ◽  
Stationary States ◽  
Long Range Interactions ◽  
Interacting Systems ◽  
Dynamical Properties ◽  
Number Of Particles

AbstractSystems of particles interacting with long range interactions present generically ”quasi-stationary states” (QSS), which are approximately time-independent out of equilibrium states. In this proceedings, we explore the generalization of the formation of such QSS and their relaxation from the much studied case of gravity to a generic pair interaction with the asymptotic form of the potential v(r) ∼ 1/r γ with γ > 0 in d dimensions. We compute analytic estimations of the relaxation time calculating the rate of two body collisionality in a virialized system approximated as homogeneous. We show that for γ < (d − 1/2), the collision integral is dominated by the size of the system, while for γ > (d − 1/2), it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles if γ < d − 1 (i.e. the force is not integrable) and decreases if γ > d − 1. Using numerical simulations we confirm our analytic results. A corollary of our work gives a ”dynamical” classification of interactions: the dynamical properties of the system depend on whether the pair force is integrable or not.

scholarly journals Operator Lévy Flight: Light Cones in Chaotic Long-Range Interacting Systems

2020 ◽  
Vol 124 (18) ◽  
Author(s):  
Tianci Zhou ◽  
Shenglong Xu ◽  
Xiao Chen ◽  
Andrew Guo ◽  
Brian Swingle
Keyword(s):  
Long Range ◽  
Lévy Flight ◽  
Levy Flight ◽  
Interacting Systems
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