Internal degrees of freedom, long-range interactions and nonlocal effects in perturbed Klein–Gordon equations

2012 ◽  
Vol 391 (3) ◽  
pp. 515-527 ◽  
Author(s):  
J.A. González ◽  
S. Jiménez ◽  
A. Bellorín ◽  
L.E. Guerrero ◽  
L. Vázquez
Keyword(s):  
Long Range ◽  
Degrees Of Freedom ◽  
Nonlocal Effects ◽  
Long Range Interactions ◽  
Klein Gordon ◽  
Internal Degrees Of Freedom

scholarly journals A novel class of translationally invariant spin chains with long-range interactions

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
B. Basu-Mallick ◽  
F. Finkel ◽  
A. González-López
Keyword(s):  
Long Range ◽  
Degrees Of Freedom ◽  
Spin Chains ◽  
Open Chain ◽  
New Class ◽  
Spin Interactions ◽  
Long Range Interactions ◽  
Spin Reversal ◽  
Twisted Yangian ◽  
Internal Degrees Of Freedom

Abstract We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular degenerate case. The new class is characterized by the fact that the Hamiltonian is invariant under “twisted” translations, combining an ordinary translation with a spin flip at one end of the chain. It includes a remarkable model with elliptic spin-spin interactions, smoothly interpolating between the XXX Heisenberg model with anti-periodic boundary conditions and a new open chain with sites uniformly spaced on a half-circle and interactions inversely proportional to the square of the distance between the spins. We are able to compute in closed form the partition function of the latter chain, thereby obtaining a complete description of its spectrum in terms of a pair of independent su(1|1) and su(m/2) motifs when the number m of internal degrees of freedom is even. This implies that the even m model is invariant under the direct sum of the Yangians Y (gl(1|1)) and Y (gl(0|m/2)). We also analyze several statistical properties of the new chain’s spectrum. In particular, we show that it is highly degenerate, which strongly suggests the existence of an underlying (twisted) Yangian symmetry also for odd m.

scholarly journals Internal degrees of freedom in perturbed nonlinear Klein-Gordon equations

2011 ◽  
pp. 527-553
Author(s):  
L. Vázquez ◽  
S. Jiménez ◽  
A. Bellorín ◽  
L. E. Guerrero ◽  
J. A. González
Keyword(s):  
Degrees Of Freedom ◽  
Klein Gordon ◽  
Internal Degrees Of Freedom

scholarly journals The world of long-range interactions: A bird’s eye view

2017 ◽  
Vol 32 (09) ◽  
pp. 1741018 ◽  
Author(s):  
Shamik Gupta ◽  
Stefano Ruffo
Keyword(s):  
Statistical Mechanics ◽  
Long Range ◽  
Degrees Of Freedom ◽  
Large Deviation ◽  
Mean Field ◽  
Coulomb Systems ◽  
Two Dimensions ◽  
Slow Relaxation ◽  
Long Range Interactions ◽  
Non Equilibrium

In recent years, studies of long-range interacting (LRI) systems have taken center stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as kinetic theory, non-equilibrium statistical mechanics, and large deviation theory, but also due to new and exciting experimental realizations of LRI systems. In the first, introductory, Section 1, we discuss the general features of long-range interactions, emphasizing in particular the main physical phenomenon of non-additivity, which leads to a plethora of distinct effects, both thermodynamic and dynamic, that are not observed with short-range interactions: Ensemble inequivalence, slow relaxation, broken ergodicity. In Section 2, we discuss several physical systems with long-range interactions: mean-field spin systems, self-gravitating systems, Euler equations in two dimensions, Coulomb systems, one-component electron plasma, dipolar systems, free-electron lasers. In Section 3, we discuss the general scenario of dynamical evolution of generic LRI systems. In Section 4, we discuss an illustrative example of LRI systems, the Kardar–Nagel spin system, which involves discrete degrees of freedom, while in Section 5, we discuss a paradigmatic example involving continuous degrees of freedom, the so-called Hamiltonian mean-field (HMF) model. For the former, we demonstrate the effects of ensemble inequivalence and slow relaxation, while for the HMF model, we emphasize in particular the occurrence of the so-called quasistationary states (QSSs) during relaxation towards the Boltzmann–Gibbs equilibrium state. The QSSs are non-equilibrium states with lifetimes that diverge with the system size, so that in the thermodynamic limit, the systems remain trapped in the QSSs, thereby making the latter the effective stationary states. In Section 5, we also discuss an experimental system involving atoms trapped in optical cavities, which may be modelled by the HMF system. In Section 6, we address the issue of ubiquity of the quasistationary behavior by considering a variety of models and dynamics, discussing in each case the conditions to observe QSSs. In Section 7, we investigate the issue of what happens when a long-range system is driven out of thermal equilibrium. Conclusions are drawn in Section 8.

Reversibly Sampling Conformations and Binding Modes Using Molecular Darting

2020 ◽  
Author(s):  
Samuel C. Gill ◽  
David Mobley
Keyword(s):  
Monte Carlo ◽  
Ligand Binding ◽  
Binding Sites ◽  
Degrees Of Freedom ◽  
Dynamics Simulation ◽  
Hiv Integrase ◽  
Binding Modes ◽  
System A ◽  
Multiple Binding ◽  
Internal Degrees Of Freedom

<div>Sampling multiple binding modes of a ligand in a single molecular dynamics simulation is difficult. A given ligand may have many internal degrees of freedom, along with many different ways it might orient itself a binding site or across several binding sites, all of which might be separated by large energy barriers. We have developed a novel Monte Carlo move called Molecular Darting (MolDarting) to reversibly sample between predefined binding modes of a ligand. Here, we couple this with nonequilibrium candidate Monte Carlo (NCMC) to improve acceptance of moves.</div><div>We apply this technique to a simple dipeptide system, a ligand binding to T4 Lysozyme L99A, and ligand binding to HIV integrase in order to test this new method. We observe significant increases in acceptance compared to uniformly sampling the internal, and rotational/translational degrees of freedom in these systems.</div>

scholarly journals Structural Changes in the Acceptor Site of Photosystem II upon Ca2+/Sr2+ Exchange in the Mn4CaO5 Cluster Site and the Possible Long-Range Interactions

Biomolecules ◽  
2019 ◽  
Vol 9 (8) ◽  
pp. 371
Author(s):  
Koua
Keyword(s):  
Crystal Structure ◽  
Photosystem Ii ◽  
Long Range ◽  
Electron Acceptor ◽  
Structural Changes ◽  
Acceptor Site ◽  
Oxygen Evolving Complex ◽  
Long Range Interactions ◽  
Structural Perturbations ◽  
Oxygen Evolving

The Mn4CaO5 cluster site in the oxygen-evolving complex (OEC) of photosystem II (PSII) undergoes structural perturbations, such as those induced by Ca2+/Sr2+ exchanges or Ca/Mn removal. These changes have been known to induce long-range positive shifts (between +30 and +150 mV) in the redox potential of the primary quinone electron acceptor plastoquinone A (QA), which is located 40 Å from the OEC. To further investigate these effects, we reanalyzed the crystal structure of Sr-PSII resolved at 2.1 Å and compared it with the native Ca-PSII resolved at 1.9 Å. Here, we focus on the acceptor site and report the possible long-range interactions between the donor, Mn4Ca(Sr)O5 cluster, and acceptor sites.

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