Adiabatic theorems for quantum resonances

We study the adiabatic time evolution of quantum resonances over time scales which are small compared to the lifetime of the resonances. We consider three typical examples of resonances: The first one is that of shape resonances corresponding, for example, to the state of a quantum-mechanical particle in a potential well whose shape changes over time scales small compared to the escape time of the particle from the well. Our approach to studying the adiabatic evolution of shape resonances is based on a precise form of the time-energy uncertainty relation and the usual adiabatic theorem in quantum mechanics. The second example concerns resonances that appear as isolated complex eigenvalues of spectrally deformed Hamiltonians, such as those encountered in the N-body Stark effect. Our approach to study such resonances is based on the Balslev-Combes theory of dilatation-analytic Hamiltonians and an adiabatic theorem for nonnormal generators of time evolution. Our third example concerns resonances arising from eigenvalues embedded in the continuous spectrum when a perturbation is turned on, such as those encountered when a small system is coupled to an infinitely extended, dispersive medium. Our approach to this class of examples is based on an extension of adiabatic theorems without a spectral gap condition. We finally comment on resonance crossings, which can be studied using the last approach.Comment: 35 pages. One remark added in section 3, and references updated. To appear in Commun. Math. Phy

Cyclic thermodynamic processes and entropy production

We study the time evolution of a periodically driven quantum-mechanical system coupled to several reserviors of free fermions at different temperatures. This is a paradigm of a cyclic thermodynamic process. We introduce the notion of a Floquet Liouvillean as the generator of the dynamics on an extended Hilbert space. We show that the time-periodic state to which the true state of the coupled system converges after very many periods corresponds to a zero-energy resonance of the Floquet Liouvillean. We then show that the entropy production per cycle is (strictly) positive, a property that implies Carnot's formulation of the second law of thermodynamics.Comment: version accepted for publication in J. Stat. Phy

Status of the Fundamental Laws of Thermodynamics

We describe recent progress towards deriving the Fundamental Laws of thermodynamics (the 0th, 1st and 2nd Law) from nonequilibrium quantum statistical mechanics in simple, yet physically relevant models. Along the way, we clarify some basic thermodynamic notions and discuss various reversible and irreversible thermodynamic processes from the point of view of quantum statistical mechanics.Comment: 23 pages. Some references updated. To appear in J. Stat. Phy

Reaction Rates and Nuclear Properties Relevant for Nucleosynthesis in Massive Stars and Far From Stability

Explosive nuclear burning in astrophysical environments produces unstable nuclei which again can be targets for subsequent reactions. In addition, it involves a large number of stable nuclides which are not fully explored by experiments, yet. Thus, it is necessary to be able to predict reaction cross sections and thermonuclear rates with the aid of theoretical models. Such predictions are also of interest for investigations at radioactive ion beam facilities. An extended library of theoretical cross sections and reaction rates is presented. The problem of alpha+nucleus potentials is addressed and new parametrizations presented. The problem of properly predicting cross sections at low level densities is illustrated by the 62Ni(n,gamma) reaction.Comment: 7 pages, invited talk, to appear in proceedings of CGS11 (Prague), World Scientific (new version: fixed typo in potential parameters; note: they will still be incorrect in the printed version

Time-resolved charge translocation by the Ca-ATPase from sarcoplasmic reticulum after an ATP concentration jump

Time-resolved measurements of currents generated by Ca-ATPase from fragmented sarcoplasmic reticulum (SR) are described. SR vesicles spontaneously adsorb to a black lipid membrane acting as a capacitive electrode. Charge translocation by the enzyme is initiated by an ATP concentration jump performed by the light-induced conversion of an inactive precursor (caged ATP) to ATP with a time constant of 2.0 ms at pH 6.2 and 24 degrees C. The shape of the current signal is triphasic, an initial current flow into the vesicle lumen is followed by an outward current and a second slow inward current. The time course of the current signal can be described by five relaxation rate constants, lambda1 to lambda5 plus a fixed delay D approximately 1–3 ms. The electrical signal shows that 1) the reaction cycle of the Ca-ATPase contains two electrogenic steps; 2) positive charge is moved toward the luminal side in the first rapid step and toward the cytoplasmic side in the second slow step; 3) at least one electroneutral reaction precedes the electrogenic steps. Relaxation rate constant lambda3 reflects ATP binding, with lambda(3,max) approximately 100 s(-1). This step is electroneutral. Comparison with the kinetics of the reaction cycle shows that the first electrogenic step (inward current) occurs before the decay of E2P. Candidates are the formation of phosphoenzyme from E1ATP (lambda2 approximately 200 s[-1]) and the E1P --> E2P transition (D approximately 1 ms or lambda1 approximately 300 s[-1]). The second electrogenic transition (outward current) follows the formation of E2P (lambda4 approximately 3 s[-1]) and is tentatively assigned to H+ countertransport after the dissociation of Ca2+. Quenched flow experiments performed under the conditions of the electrical measurements 1) demonstrate competition by caged ATP for ATP-dependent phosphoenzyme formation and 2) yield a rate constant for phosphoenzyme formation of 200 s(-1). These results indicate that ATP and caged ATP compete for the substrate binding site, as suggested by the ATP dependence of lambda3 and favor correlation of lambda2 with phosphoenzyme formation

Determining phase transitions of layered oxides via electrochemical and crystallographic analysis

The chemical diffusion coefficient in LiNi1/3Mn1/3Co1/3O2 was determined via the galvanostatic intermittent titration technique in the voltage range 3 to 4.2 V. Calculated diffusion coefficients in these layered oxide cathodes during charging and discharging reach a minimum at the open-circuit voltage of 3.8 V and 3.7 V vs. Li/Li+, respectively. The observed minima of the chemical diffusion coefficients indicate a phase transition in this voltage range. The unit cell parameters of LiNi1/3Mn1/3Co1/3O2 cathodes were determined at different lithiation states using ex situ crystallographic analysis. It was shown that the unit cell parameter variation correlates well with the observed values for chemical diffusion in NMC cathodes; with a notable change in absolute values in the same voltage range. We relate the observed variation in unit cell parameters to the nickel conversion into the trivalent state, which is Jahn-Teller active, and to the re-arrangement of lithium ions and vacancies

Differential spot-size focus servo

We describe performance of a differential spot-size (wax-wane) focus servo. Crosstalk from the tracks are analyzed in the single detector and differential focus circuits. Magnitude of the crosstalk is reduced by a factor of three in the differential circuit. A false focus-error signal (FES) is present when the spot crosses sector marks at an angle

Developmental stage-specific regulation of the circadian Clock by Temperature in Zebrafish

The circadian clock enables animals to adapt their physiology and behaviour in anticipation of the day-night cycle. Light and temperature represent two key environmental timing cues (zeitgebers) able to reset this mechanism and so maintain its synchronization with the environmental cycle. One key challenge is to unravel how the regulation of the clock by zeitgebers matures during early development. The zebrafish is an ideal model for studying circadian clock ontogeny since the process of development occurs ex utero in an optically transparent chorion and many tools are available for genetic analysis. However, the role played by temperature in regulating the clock during zebrafish development is poorly understood. Here, we have established a clock-regulated luciferase reporter transgenic zebrafish line (Tg (−3.1) per1b::luc) to study the effects of temperature on clock entrainment. We reveal that under complete darkness, from an early developmental stage onwards (48 to 72 hpf), exposure to temperature cycles is a prerequisite for the establishment of self-sustaining rhythms of zfper1b, zfaanat2, and zfirbp expression and also for circadian cell cycle rhythms. Furthermore, we show that following the 5–9 somite stage, the expression of zfper1b is regulated by acute temperature shifts

On the theory of resonances in non-relativistic QED and related models

We study the mathematical theory of quantum resonances in the standard model of non-relativistic QED and in Nelson's model. In particular, we estimate the survival probability of metastable states corresponding to quantum resonances and relate the resonances to poles of an analytic continuation of matrix elements of the resolvent of the quantum Hamiltonian.Comment: 28 page