Energy evolution in time-dependent harmonic oscillator

The theory of adiabatic invariants has a long history, and very important implications and applications in many different branches of physics, classically and quantally, but is rarely founded on rigorous results. Here we treat the general time-dependent one-dimensional harmonic oscillator, whose Newton equation $\ddot{q} + \omega^2(t) q=0$ cannot be solved in general. We follow the time-evolution of an initial ensemble of phase points with sharply defined energy $E_0$ at time $t=0$ and calculate rigorously the distribution of energy $E_1$ after time $t=T$, which is fully (all moments, including the variance $\mu^2$) determined by the first moment $\bar{E_1}$. For example, $\mu^2 = E_0^2 [(\bar{E_1}/E_0)^2 - (\omega (T)/\omega (0))^2]/2$, and all higher even moments are powers of $\mu^2$, whilst the odd ones vanish identically. This distribution function does not depend on any further details of the function $\omega (t)$ and is in this sense universal. In ideal adiabaticity $\bar{E_1} = \omega(T) E_0/\omega(0)$, and the variance $\mu^2$ is zero, whilst for finite $T$ we calculate $\bar{E_1}$, and $\mu^2$ for the general case using exact WKB-theory to all orders. We prove that if $\omega (t)$ is of class ${\cal C}^{m}$ (all derivatives up to and including the order $m$ are continuous) $\mu \propto T^{-(m+1)}$, whilst for class ${\cal C}^{\infty}$ it is known to be exponential $\mu \propto \exp (-\alpha T)$.Comment: 26 pages, 5 figure

Insect‐associated bacteria assemble the antifungal butenolide gladiofungin by non‐canonical polyketide chain termination

Genome mining of one of the protective symbionts ( Burkholderia gladioli ) of the invasive beetle Lagria villosa revealed a cryptic gene cluster that codes for the biosynthesis of a novel antifungal polyketide with a glutarimide pharmacophore. Targeted gene inactivation, metabolic profiling, and bioassays led to the discovery of the gladiofungins as previously‐overlooked components of the antimicrobial armory of the beetle symbiont, which are highly active against the entomopathogenic fungus Purpureocillium lilacinum . By mutational analyses, isotope labeling, and computational analyses of the modular polyketide synthase, we found that the rare butenolide moiety of gladiofungins derives from an unprecedented polyketide chain termination reaction involving a glycerol‐derived C3 building block. The key role of an A‐factor synthase (AfsA)‐like offloading domain was corroborated by CRISPR‐Cas‐mediated gene editing, which facilitated precise excision within a PKS domain

Time evolution, cyclic solutions and geometric phases for the generalized time-dependent harmonic oscillator

The generalized time-dependent harmonic oscillator is studied. Though several approaches to the solution of this model have been available, yet a new approach is presented here, which is very suitable for the study of cyclic solutions and geometric phases. In this approach, finding the time evolution operator for the Schr\"odinger equation is reduced to solving an ordinary differential equation for a c-number vector which moves on a hyperboloid in a three-dimensional space. Cyclic solutions do not exist for all time intervals. A necessary and sufficient condition for the existence of cyclic solutions is given. There may exist some particular time interval in which all solutions with definite parity, or even all solutions, are cyclic. Criterions for the appearance of such cases are given. The known relation that the nonadiabatic geometric phase for a cyclic solution is proportional to the classical Hannay angle is reestablished. However, this is valid only for special cyclic solutions. For more general ones, the nonadiabatic geometric phase may contain an extra term. Several cases with relatively simple Hamiltonians are solved and discussed in detail. Cyclic solutions exist in most cases. The pattern of the motion, say, finite or infinite, can not be simply determined by the nature of the Hamiltonian (elliptic or hyperbolic, etc.). For a Hamiltonian with a definite nature, the motion can changes from one pattern to another, that is, some kind of phase transition may occur, if some parameter in the Hamiltonian goes through some critical value.Comment: revtex4, 28 pages, no figur

Preparation of anti-vicinal amino alcohols: asymmetric synthesis of D-erythro-Sphinganine, (+)-spisulosine and D-ribo-phytosphingosine

Two variations of the Overman rearrangement have been developed for the highly selective synthesis of anti-vicinal amino alcohol natural products. A MOM-ether directed palladium(II)-catalyzed rearrangement of an allylic trichloroacetimidate was used as the key step for the preparation of the protein kinase C inhibitor D-erythro-sphinganine and the antitumor agent (+)-spisulosine, while the Overman rearrangement of chiral allylic trichloroacetimidates generated by asymmetric reduction of an alpha,beta-unsaturated methyl ketone allowed rapid access to both D-ribo-phytosphingosine and L-arabino-phytosphingosine

Comparative and functional genomics provide insights into the pathogenicity of dermatophytic fungi

ABSTRACT: BACKGROUND: Millions of humans and animals suffer from superficial infections caused by a group of highly specialized filamentous fungi, the dermatophytes, which exclusively infect keratinized host structures. To provide broad insights into the molecular basis of the pathogenicity-associated traits, we report the first genome sequences of two closely phylogenetically related dermatophytes, Arthroderma benhamiae and Trichophyton verrucosum, both of which induce highly inflammatory infections in humans. RESULTS: 97% of the 22.5 megabase genome sequences of A. benhamiae and T. verrucosum are unambiguously alignable and collinear. To unravel dermatophyte-specific virulence-associated traits, we compared sets of potentially pathogenicity-associated proteins, such as secreted proteases and enzymes involved in secondary metabolite production, with those of closely related onygenales (Coccidioides species) and the mould Aspergillus fumigatus. The comparisons revealed expansion of several gene families in dermatophytes and disclosed the peculiarities of the dermatophyte secondary metabolite gene sets. Secretion of proteases and other hydrolytic enzymes by A. benhamiae was proven experimentally by a global secretome analysis during keratin degradation. Molecular insights into the interaction of A. benhamiae with human keratinocytes were obtained for the first time by global transcriptome profiling. Given that A. benhamiae is able to undergo mating, a detailed comparison of the genomes further unraveled the genetic basis of sexual reproduction in this species. CONCLUSIONS: Our results enlighten the genetic basis of fundamental and putatively virulence-related traits of dermatophytes, advancing future research on these medically important pathogens