arXiv subjects

M. K. Balasubramanya

Publications and source records attributed to M. K. Balasubramanya.

4 recordsLinked to original sources

arXiv2007

Frequencies and energy levels of the weakly relativistic harmonic oscillator from the action variable

The frequency of a classical periodic system and the energy levels of the corresponding quantum system can both be obtained using action variables. We demonstrate the construction of two forms of the action variable for a one dimensional harmonic oscillator in classical, relativistic and quantum regimes. The relativistic effects are considered as perturbative, within the context of a non-relativistic quantum formalism. The transition of the relativistic quantum system to both classical relativistic and classical non-relativistic regimes is illustrated in a unified framework. Formulas for the frequency of a classical relativistic oscillator and the energy eigenvalues of the corresponding quantum oscillator for the weak relativistic case are derived. Also studied are the non-relativistic and classical limits of these formulas which provide valuable insights on the parallels between relativistic and non-relativistic systems on the one hand and between classical and quantum systems on the other.

quant-ph↗

arXiv2007

Two forms of the action variable for the relativistic harmonic oscillator

The frequency of a classical periodic system can be obtained using action variables without solving the dynamical equations. We demonstrate the construction of two equivalent forms of the action variable for a one dimensional relativistic harmonic oscillator and obtain its energy dependent frequency. This analysis of oscillation is compared with the traditional solution of the problem which requires the use of hypergeometric series.

math-ph↗

arXiv2006

Molecular dynamics simulations of noble gas release from endohedral fullerene clusters

We report the results of molecular dynamics simulations of the release of five species of noble gas atoms trapped inside a small cluster of fullerenes in the temperature range 4000K < T < 5000K. We find that larger noble gas atoms are generally released at a slower rate and that helium is released considerably more rapidly than any of the other noble gases. The differing release rates are due not only to the differences in the size and mass of a given endohedral species but also because larger trapped atoms tend to stabilize the fullerene cage against thermal fluctuations. Unlike with the case of atoms entering fullerenes, we find that any atom escaping from the cage results in a window which does not close. Escape rate constants are reported and comparisons with experiment are discussed.

cond-mat.mtrl-sci↗

arXiv2005

Simulated Dynamics and Endohedral Relesase of Ne from Ne@C60 Clusters

Molecular Dynamics (MD) computer simulations are utilized to better understand the escape of neon from small (N=5) endohedral Ne@C60 clusters. Multiple runs at various temperatures are used to increase the reliability of our statistics. The cluster holds together until somewhere between T = 1150K and T = 1200K, where it dissociates, showing no intermediate sign of melting or fullerene disintegration. When the temperature is increased to around T = 4000K, the encapsulated neon atoms begin to leave the cluster, with the fullerene molecules still remaining intact. At temperatures near T = 4400K, thermal disintegration of the fullerenes pre-empts the cluster dissociation. The neon atoms are then more quickly released and the fullerenes form a larger connected structure, with bonding taking place in atom pairs from different original fullerene molecules. Escape constants and half lives are calculated for the temperature range 4000K < T < 5000K. The agreements and disagreements of results of this work with experiments suggest that classical MD simulations are useful in describing fullerene systems at low temperatures and near disintegration, but require more thought and modification before accurately modeling windowing at temperatures below T = 3000K.

cond-mat.mtrl-sci↗