Relationships between power-law long-range interactions and fractional mechanics

2012 ◽  
Vol 391 (23) ◽  
pp. 5827-5838 ◽  
Author(s):  
Ryosuke Ishiwata ◽  
Yūki Sugiyama
Keyword(s):  
Long Range ◽  
Power Law ◽  
Long Range Interactions ◽  
Fractional Mechanics

scholarly journals RESTRICTIONS ON THE HYPOTHETICAL LONG RANGE INTERACTIONS FROM THE CASIMIR-TYPE NULL EXPERIMENT WITH THREE TEST BODIES

1994 ◽  
Vol 09 (29) ◽  
pp. 2671-2680 ◽  
Author(s):  
M. BORDAG ◽  
V. M. MOSTEPANENKO ◽  
I. YU. SOKOLOV
Keyword(s):  
Long Range ◽  
Power Law ◽  
Casimir Force ◽  
Power Laws ◽  
Gravitational Attraction ◽  
Spherical Lens ◽  
Plane Plate ◽  
Wide Range ◽  
Long Range Interactions

A realistic null experiment is suggested in which the Casimir force between a plane plate and a spherical lens is compensated by the force of gravitational attraction. This configuration is shown to be very sensitive to the existence of additional hypothetical forces of Yukawa-type or power laws. From the suggested null experiment the restrictions on the Yukawa constant α can be strengthened by a factor up to 1000 in a wide range 10−8 m < λ < 10−4 m and by a factor of 10 for λ from several centimeters to several meters. For power law interactions the strengthening of restrictions by a factor of 20 is possible for the force decreasing as r−5.

LONG-RANGE INTERACTIONS IN THE HELICOIDAL DNA DYNAMICS

2013 ◽  
Vol 27 (24) ◽  
pp. 1350143 ◽  
Author(s):  
MIRABEAU SAHA ◽  
TIMOLEON C. KOFANÉ
Keyword(s):  
Rna Polymerase ◽  
Long Range ◽  
Power Law ◽  
Dna Dynamics ◽  
Extended Version ◽  
Range Interaction ◽  
Dna Molecule ◽  
Long Range Interactions ◽  
Long Range Interaction

In this paper, the comparison between power-law long-range interaction and Kac–Baker long-range interaction in the DNA molecule is investigated. This is done by employing an extended version of spin-like model of the DNA molecule with long-range interaction between intra-strand nucleotides and helicoidal coupling between inter-strand nucleotides when an RNA-polymerase binds to the DNA at biological temperature. Results show that LRIs have an undeniable effect on the DNA dynamics and that one is free to use either PLLRI or KBLRI to study DNA behaviors.

Solitons in anharmonic chains with power-law long-range interactions

1998 ◽  
Vol 58 (3) ◽  
pp. 3833-3842 ◽  
Author(s):  
Serge F. Mingaleev ◽  
Yuri B. Gaididei ◽  
Franz G. Mertens
Keyword(s):  
Long Range ◽  
Power Law ◽  
Long Range Interactions

scholarly journals Metastability and discrete spectrum of long-range systems

2021 ◽  
Vol 118 (30) ◽  
pp. e2101785118
Author(s):  
Nicolò Defenu
Keyword(s):  
Discrete Spectrum ◽  
Long Range ◽  
Power Law ◽  
System Size ◽  
Many Body ◽  
Internal Parameters ◽  
Quantum Ising Model ◽  
Long Range Interactions ◽  
Interacting Systems ◽  
Chaotic Nature

Long-lived quasi-stationary states (QSSs) are a signature characteristic of long-range interacting systems both in the classical and in the quantum realms. Often, they emerge after a sudden quench of the Hamiltonian internal parameters and present a macroscopic lifetime, which increases with the system size. Despite their ubiquity, the fundamental mechanism at their root remains unknown. Here, we show that the spectrum of systems with power-law decaying couplings remains discrete up to the thermodynamic limit. As a consequence, several traditional results on the chaotic nature of the spectrum in many-body quantum systems are not satisfied in the presence of long-range interactions. In particular, the existence of QSSs may be traced back to the finiteness of Poincaré recurrence times. This picture justifies and extends known results on the anomalous magnetization dynamics in the quantum Ising model with power-law decaying couplings. The comparison between the discrete spectrum of long-range systems and more conventional examples of pure point spectra in the disordered case is also discussed.

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