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)?
Hi sashavak, welcome to PhysicsOverflow.
It seems that your question consists of two rather different parts and goals: you are looking for references and you would like to get feedback on your paper.
I therefore would like to suggest suggest that in this question you concentrate on the reference request (the resources and references category is appropriate for this) and in addition submit your paper to PO s Reviews section, to obtain feedback and discussion on your work. Your points 1.-3. could then for example be used to summarize the paper in the body of the submission.
How to do it (addition submit paper to PO s Reviews section, to obtain feedback and discussion on your work)?
The Q&A section and the reviews section are two different parts of PO, you can see the top-level sturcture of PO for example here. So it is not possible to make s submission out of a Q&A question by recategorizing.
The simplest thing for you do would would be to state in an answer to this question, that you would like to submit your paper, and somebody would then create the submission for you. Alternatively, you can create the submission directly yourself by inserting the relevant information into this form.
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?
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.
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.
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.
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?