Molecular dynamics study of diffusionless phase transformations in HMX: β\beta-HMX twinning and β\beta-ϵ\epsilon phase transition

We use molecular dynamics to study mechanism of deformation twinning of $\beta$-1,3,5,7-tetranitro-1,3,5,7-tetrazocane ($\beta$-HMX) in the $P2_1/n$ space group setting for the twin system specified by $K_1=(101)$, $\eta_1=[10\overline{1}]$, $K_2=(10\overline{1})$, and $\eta_2=[101]$ at $T=1$ K and 300 K. Twinning of a single perfect crystal was induced by imposing increasing stress. The following three forms of stress were considered: uniaxial compression along $[001]$, shear stress in $K_1$ plane along $\eta_1$ direction, and shear stress in $K_2$ plane along $\eta_2$ direction. In all cases the crystal transforms to its twin by the same mechanism: as the stress increases, the $a$ and $c$ lattice parameters become, respectively, longer and shorter; soon after the magnitude of $a$ exceeds that of $c$ the system undergoes a quick phase-transition-like transformation. This transformation can be approximately separated into two stages: glide of the essentially intact $\{101\}$ crystal planes along $\langle10\overline{1}\rangle$ crystal directions followed by rotations of all HMX molecules accompanied by N-NO$_2$ and CH$_2$ group rearrangements. The overall process corresponds to a military transformation. If uniaxial compression along $[001]$ is applied to a $\beta$-HMX crystal which is already subject to a hydrostatic pressure $\gtrsim 10$ GPa, the transformation described above proceeds through the crystal-plane gliding stage but only minor molecular rearrangements occurs. This results in a high-pressure phase of HMX which belongs to the $P2_1/n$ space group. The coexistence curve for this high-pressure phase and $\beta$-HMX is constructed using the harmonic approximation for the crystal Hamiltonians

Quantum transport in chains with noisy off-diagonal couplings

We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time-evolution of the system reduces to the Lindblad equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfy discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear.Comment: 6 pages, to appear in J. Chem. Phy

Exactly solvable approximating models for Rabi Hamiltonian dynamics

The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable Hamiltonians that approximate the Rabi Hamiltonian and compare our results to the Jaynes-Cummings model which neglects the so-called counter-rotating term in the Rabi Hamiltonian. Through a unitary transformation that diagonlizes the Jaynes-Cummings model, we transform the counter-rotating term into separate terms representing several different physical processes. By keeping only certain terms, we can achieve an excellent approximation to the exact dynamics within specified parameter ranges

Hamiltonian approach for the wave packet dynamics: Beyond Gaussian wave functions

It is well known that the Gaussian wave packet dynamics can be written in terms of Hamilton equations in the extended phase space that is twice as large as in the corresponding classical system. We construct several generalizations of this approach that include non-Gausssian wave packets. These generalizations lead to the further extension of the phase space while retaining the Hamilton structure of the equations of motion. We compare the Gaussian dynamics with these non-Gaussian extensions for a particle with the quartic potential.Comment: 5 pages, 3 figure