Energy Oscillations in a One Dimensional Crystal?

Question

Good day!

Can anyone help me find articles on similar topics "Energy Oscillations in a One Dimensional Crystal" (I have links to one article on this subject)?

article, that I have

Comments

Yes, you can just click on the category in the tree to chose it. The ones with a blue triangle have subcategories you can chose too be first expanding into the subcategories by clicking the triangle and click the subcategory you want to have.

Unfortunately, our hierarchical tree of categories for submissions is still rather rudimentary. So if you can not find a proper path your paper fits in, you can just temporary place it at an approximate place in the tree, and request the proper path to your paper to be created here. An administrator will then create it appropriately recategorize your paper.

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@sashavak I am sorry, I first misunderstand your points 1-3 a bit, it is actually good to specify what points should be adressed in the references you are looking for. So my advice to remove these points was not appropriate :-/, please feel free to put them back into the question ...

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What is Paper reference tag of http://mech.spbstu.ru/images/1/1e/Energy_Oscillations.pdf?

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I am not quite sure what it is in this case, the ISSN 1028-3358 at the upper left corner of the first page could be it.

Maybe @ArnoldNeumaier or @Dimension10 can have a look too what they would choose?

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Especially interested in issues (similar topics "Energy Oscillations in a One Dimensional Crystal"):

1. One of the theoretical questions in the mechanics of discrete media is associated with high frequency oscillations of the kinetic and potential energies, which are known well by the results of numerical modeling. In particular, if at the initial instant the particles are ordered into the ideal crystal lattice and their velocities are specified randomly, then the dynamic transition of the kinetic energy into the potential energy of the bonds deformation is initiated in the crystal. This transition leads to the distribution of the internal energy between the kinetic and deformation degrees of freedom, which are determined by the virial theorem. However, the transition is accompanied by high frequency oscillatory process with decreasing amplitude, which still has no theoretical interpretation.

Is last sentence true?

1. Thus, we derived an exact analytical solution, according to which the Lagrangian function for the chain with the stochastic initial conditions varies following the same law, according to which the central particle for the chain with the deterministic initial conditions moves.
2. The variation in the kinetic and potential energies of the system under consideration is described by the Bessel function, the oscillation period of which is T0/4, while the amplitude of oscillations is inversely proportional to the root of time.
3. It follows from the found solution that the damping of oscillations of energies is determined by excitation of correlations, which associates the motion of the particles remote from each other.

Points 1-3 are the original or they have already been described in scientific articles?

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Thank you for 

possibly related papers:

http://arxiv.org/abs/cond-mat/0004112
http://scholarworks.unist.ac.kr/bitstream/201301/7370/1/2-s2.0-56849118513.pdf

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But I need related paper with points:

1.  exact analytical solution, according to which the Lagrangian function for the chain with the stochastic initial conditions varies following the same law, according to which the central particle for the chain with the deterministic initial conditions moves.
2. The variation in the kinetic and potential energies of the system under consideration is described by the Bessel function, the oscillation period of which is T0/4, while the amplitude of oscillations is inversely proportional to the root of time.
3. It follows from the found solution that the damping of oscillations of energies is determined by excitation of correlations, which associates the motion of the particles remote from each other.