Quantum dynamics of wave packets in a non-stationary parabolic potential and the Kramers escape rate theory

At sufficiently low temperatures, the reaction rates in solids are controlled by quantum rather than by thermal fluctuations. We solve the Schrödinger equation for a Gaussian wave packet in a non-stationary harmonic oscillator and derive simple analytical expressions for the increase of its mean energy with time induced by the time-periodic modulation. Applying these expressions to the modified Kramers theory, we demonstrate a strong increase of the rate of escape out of a potential well under the time-periodic driving, when the driving frequency of the well position equals its eigenfrequency, or when the driving frequency of the well width exceeds its eigenfrequency by a factor of [Formula: see text]. Such regimes can be realized near localized anharmonic vibrations (LAVs), in which the amplitude of atomic oscillations greatly exceeds that of harmonic oscillations (phonons) that determine the system temperature. LAVs can be excited either thermally or by external triggering, which can result in strong catalytic effects due to amplification of the Kramers rate.

Asymptotic entropy of transformed random walks

We consider general transformations of random walks on groups determined by Markov stopping times and prove that the asymptotic entropy (respectively, rate of escape) of the transformed random walks is equal to the asymptotic entropy (respectively, rate of escape) of the original random walk multiplied by the expectation of the corresponding stopping time. This is an analogue of the well-known Abramov formula from ergodic theory; its particular cases were established earlier by Kaimanovich [Differential entropy of the boundary of a random walk on a group. Uspekhi Mat. Nauk38(5(233)) (1983), 187–188] and Hartman et al [An Abramov formula for stationary spaces of discrete groups. Ergod. Th. & Dynam. Sys.34(3) (2014), 837–853].

Behavioural response of larval sea lamprey (Petromyzon marinus) in a laboratory environment to potential damage-released chemical alarm cues

Sea lampreys (Petromyzon marinus L., 1758) invaded the Great Lakes early in the 20th century and have caused economic and ecological damage to native fish species. The integrated sea lamprey control program involves low-head barrier dams, lampricides, and trapping. The search for low cost and less toxic alternatives to lampricides could involve the use of repellents in the form of chemical alarm cues. The objective of this study was to determine whether larval sea lamprey showed a behavioural response when exposed to damage-released chemical alarm cues by increasing their swimming time, rate of direction changes, or rate of escape attempts in an artificial stream channel experiment. Larval sea lampreys were exposed to conspecific larval sea lamprey extract, heterospecific swordtail (Xiphophorus hellerii Heckel, 1848) extract, or a distilled water control. The larvae increased their rate of escape attempts after exposure to both swordtail and larval lamprey extracts and their rate of direction changes after exposure to sea lamprey extract. However, larvae did not increase their swimming time in response to any experimental stimuli. This is the first study to suggest that larval sea lamprey respond to potential chemosensory risk assessment cues.

The Influence of Dimensionality on the Rate of Diffusive Escape From an Energy Well

A commonly used idealization when describing separation of a chemical bond between molecules is that of an energy well which prescribes the dependence of energy of interaction between the molecules in terms of a reaction coordinate. The energy difference between the peak to be overcome and the root of the well is the so-called activation energy, and the overall shape of the well dictates the kinetics of separation through a constitutive assumption concerning transport. An assumption tacit in this description is that the state of the bond evolves with only a single degree of freedom—the reaction coordinate—as the system explores its energy environment under random thermal excitation. In this discussion we will consider several bonds described by one and the same energy profile. The cases differ in that the energy profile varies along a line extending from the root of the well in the first case, along any radial line in a plane extending from the root of the well in a second case, and along any radial line in space extending from the root of the well in a third case. To focus the discussion we determine the statistical rate of escape of states from the well in each case, requiring that the profile of the well is the same in all three cases. It is found that the rates of escape each depend exponentially on the depth of the well but that the coefficients of the exponential vary with depth of the well differently in the three cases considered.

Impaired immune evasion in HIV through intracellular delays and multiple infection of cells

With its high mutation rate, HIV is capable of escape from recognition, suppression and/or killing by CD8 + cytotoxic T lymphocytes (CTLs). The rate at which escape variants replace each other can give insights into the selective pressure imposed by single CTL clones. We investigate the effects of specific characteristics of the HIV life cycle on the dynamics of immune escape. First, it has been found that cells in HIV-infected patients can carry multiple copies of proviruses. To investigate how this process affects the emergence of immune escape, we develop a mathematical model of HIV dynamics with multiple infections of cells. Increasing the frequency of multiple-infected cells delays the appearance of immune escape variants, slows down the rate at which they replace the wild-type variant and can even prevent escape variants from taking over the quasi-species. Second, we study the effect of the intracellular eclipse phase on the rate of escape and show that escape rates are expected to be slower than previously anticipated. In summary, slow escape rates do not necessarily imply inefficient CTL-mediated killing of HIV-infected cells, but are at least partly a result of the specific characteristics of the viral life cycle.