Anomalous diffusion of a quantum Brownian particle in a one-dimensional molecular chain.

We discuss anomalous relaxation processes of a quantum Brownian particle which interacts with an acoustic phonon field as a thermal reservoir in one-dimensional chain molecule. We derive a kinetic equation for the particle using the complex spectral representation of the Liouville-von Neumann operator. Due to the one-dimensionality, the momentum space separates into infinite sets of disjoint irreducible subspaces dynamically independent of one another. Hence, momentum relaxation occurs only within each subspace toward the Maxwell distribution. We obtain a hydrodynamic mode with transport coefficients, a sound velocity, and a diffusion coefficient, defined in each subspace. Moreover, because the sound velocity has momentum dependence, phase mixing affects the broadening of the spatial distribution of the particle in addition to the diffusion process. Due to the phase mixing, the increase rate of the mean-square displacement of the particle increases linearly with time and diverges in the long-time limit.

Nonequilibrium transport on a quantum molecular chain in terms of the complex Liouvillian spectrum.

The transport process in a molecular chain in a nonequilibrium stationary state is theoretically investigated. The molecule is interacting at both ends with thermal baths of different temperatures, while no dissipation mechanism is contained inside the molecular chain. We have first obtained the nonequilibrium stationary state outside the Hilbert space in terms of the complex spectral representation of Liouvillian. The nonequilibrium stationary state is obtained as an eigenstate of the Liouvillian, which is constructed through the collision invariant of the kinetic equation. The eigenstate of the Liouvillian contains information on the spatial correlation between the molecular chain and the thermal baths. While energy flow in the nonequilibrium state which is due to the first-order correlation can be described by the Landauer formula, the particle current due to the second-order correlation cannot be described by the Landauer formula. The present method provides a simple way to evaluate the energy transport in a molecular chain in a nonequilibrium situation.

Quasibound states in the continuum in a two channel quantum wire with an adatom.

We report the prediction of quasibound states (resonant states with very long lifetimes) that occur in the eigenvalue continuum of propagating states for certain systems in which the continuum is formed by two overlapping energy bands. We illustrate this effect using a quantum wire system with two channels and an attached adatom. When the energy bands of the two channels overlap, a would-be bound state that lays just below the upper energy band is slightly destabilized by the lower energy band and thereby becomes a resonant state with a very long lifetime (a second such state lays above the lower energy band). Unlike the bound states in continuum predicted by von Neumann and Wigner, these states occur for a wide region of parameter space.

Resonance overlap, secular effects, and nonintegrability: an approach from ensemble theory.

The time evolution of a classical multiresonance nonintegrable Hamiltonian system with few degrees of freedom is analyzed on the ensemble level. Time-dependent perturbation analysis is applied to the Liouville equation to determine the most secular series for the time evolution of the expectation value of some physical observables. In contrast to the so-called lambda(2) t expansion for thermodynamic systems, which is well known in nonequilibrium statistical physics, we find a square root of lambda t expansion in small nonintegrable systems with few degrees of freedom. This asymptotic expansion exists only on the level of ensemble but not on the level of trajectories. Moreover, the time symmetry of this expansion is broken as in nonequilibrium statistical mechanics. The relation of the Chirikov overlapping criterion to our approach is discussed.