We calculate the electric dipolarizability of ⁷Li nucleus within the cluster model and estimate a value of about 0.0188 fm³. We also discuss the possibility of observing this in the scattering of ⁷Li from a ²⁰⁸Pb target at energies about 30 MeV.

We construct the expression for the ground state eigenfunction of the Schrödinger equation for a particle inside an arbitrary planar triangle under the influence of a potential.

It is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian of the quantum system for an arbitrary pseudo-unitary (and hence $\mathcal{PT}$ -) quantum evolution. The result generalizes the time– energy uncertainty principle for pseudo-unitary quantum evolutions. Further, employing random matrix theory developed for pseudo-Hermitian systems, time correlation functions are studied in the framework of linear response theory. The results given here provide a quantum brachistochrone problem where the system will evolve in a thermodynamic environment with spectral complexity that can be modelled by random matrix theory.

We discuss the relevance of random matrix theory for pseudo-Hermitian systems, and, for Hamiltonians that break parity 𝑃 and time-reversal invariance 𝑇. In an attempt to understand the random Ising model, we present the treatment of cyclic asymmetric matrices with blocks and show that the nearest-neighbour spacing distributions have the same form as obtained for the matrices with scalar entries. We also summarize the theory for random cyclic matrices with scalar entries. We have also found that for block matrices made of Hermitian and pseudo-Hermitian sub-blocks of the form appearing in Ising model depart from the known results for scalar entries. However, there is still similarity in trends even in log–log plots.

We argue that mass parameters appearing in the treatment of large-amplitude collective motion, be it fission or heavy-ion reactions, originate as a consequence of their relation with Lyapunov exponents coming from the classical dynamics, and, fractal dimension associated with diffusive modes coming from hydrodynamic description.

In this paper the classical evolution of a particle is studied which bounces back and forth in a 1D vibrating cavity such that the reflection from the wall does not change the speed of the particle. A peculiar behaviour of the particle motion can be seen where the time evolution of the motion shows superposition of linear and oscillatory behaviour. In particular, the parameter range is found in which the particle oscillates between the walls in steady state as if the wall was static and it is showed that for these parameter ranges the particle settles to this steady state for all initial conditions. It is proposed that this phenomenon can be used to bunch charged particles in short pulses where the synchronization proposed in our model should work against the space charge effect in the charged particle bunch.

We study the well-known one-dimensional problem of 𝑁 particles with nonlinear interaction. The 𝛽-Fermi–Pasta–Ulam model is the special case of quadratic and quartic interaction potential among nearest neighbours. We enumerate and classify the simple periodic orbits for this system and find the stability zones, employing Floquet theory. We quantize the nonlinear normal modes and construct a wavefunction for what we believe is a primitive nonlinear analogue of a `phonon’.