Coulomb blockade with dispersive interfaces

What quantity controls the Coulomb blockade oscillations if the dot-lead conductance is essentially frequency dependent? We argue that it is the conductance at the imaginary frequency given by the effective charging energy. The latter may be very different from the bare charging energy due to the interface-induced capacitance (or inductance). These observations are supported by a number of examples, considered from the weak and strong coupling (perturbation theory versus instanton calculus) perspectives.     

Dark soliton in one-dimensional Bose–Einstein condensate under a periodic perturbation of trap

The perturbation of a confining trap leads to the collective oscillation of a Bose--Einstein condensate, thereby the propagation of a dark soliton in the condensate is affected. In this study, periodic perturbation is employed to match the soliton oscillation. We find that the soliton dynamics depends sensitively on the coupling between the moving direction of the trap and that of the soliton. The soliton energy/depth evolves periodically, and a relevant shift in the soliton trajectory occurs as compared with the unperturbed case. Overall, the soliton oscillation frequency changes little even if the perturbation amplitude and frequency vary.     

Propagation of acoustic waves in a medium with the Rayleigh energy release mechanism

This research continues theoretical studies of propagation of acoustic waves in a plasma considering it in the context of a Rayleigh medium. For the first time, the solution to the problem with the boundary and not the initial conditions is examined. It is shown that for small values of the parameter characterizing the energy input in the plasma, the amplification coefficients of a harmonic acoustic wave in the problem of propagation of the initial perturbation and in the problem with the boundary conditions are close. However, if the energy input increases, the amplification of the wave propagating from the source is larger than in the problem of the initial perturbation propagation. The same concerns the amplification of waves with different frequencies for fixed parameters of the plasma; i.e., the difference between the amplification coefficients is larger, the lower the wave frequency. The resultant analytic dependences make it possible to determine exactly which of the problems (with the initial or boundary conditions) should be solved to compute the amplification coefficient of acoustic waves under specific experimental conditions.     

Response of a burning heterogeneous propellant to small pressure disturbances

A numerical code for the simulation of heterogeneous propellant burning is used to examine the response to the pressure field of an incident acoustic wave. It is shown that there are two natural response functions, one defined by the perturbation mass flux beyond the combustion field, the other by the perturbation energy flux beyond the combustion field. The first of these plays an essential role in L* instability (a coupled propellant–rocket-chamber phenomenon), and the second in whether the acoustic wave is amplified on reflection (a phenomenon exclusive to the propellant). We show, for several choices of parameter values and propellant morphology, that the two responses are qualitatively similar, albeit they differ in magnitude by modest amounts. We show that in some cases each response displays a single maximum or peak as a function of frequency, in other cases multiple peaks are obtained. A tentative hypothesis is proposed as a predictor of multiple peaks.     

Relative to the interpretation of terms of the Schrödinger perturbation theory series

An approach different from those ordinarily expounded is proposed for the construction of the Schrödinger perturbation theory. This approach sets up a functional dependence between the energy corrections and the coefficients characterizing the corrections to the wave functions. It is shown that within the framework of the Schrödinger theory these coefficients are determined by extremum conditions of fourth-order corrections to the energy. In the Schrödinger approximation the fourth-order energy corrections reach their extremal values. The approach developed includes a proof of the Dalgarno and Stewart theorem that says that the energy can be estimated to the order (2n + 1) if the wave function is known to n-th-order accuracy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 18–20, February, 1982.     

Frequency shift and pulse compression of an ultrashort pulse in a large-amplitude plasma wave

By calculating the momenta of a coupled set of nonlinear equations of laserpulse-plasma wave interaction in the weak relativistic approximation,the conditions for fre-quency up-shift have been found.That the energy change of the pulse due to frequency shiftis compensated by the change of plasma wave energy results in photon number conservation.Some factors that affect the frequency up-shift are studied.It is also found that the laser pulsecan be compressed when it is located near the valley of plasma density perturbation and ifsome threshold value of the plasma wave field is exceeded.     

Drastic facilitation of the onset of global chaos

We show that the onset of global chaos in a time periodically perturbed Hamiltonian system may occur at unusually small magnitudes of perturbation if the unperturbed system possesses more than one separatrix. The relevant scenario is the combination of the overlap in the phase space between resonances of the same order and their overlap in energy with chaotic layers associated with separatrices of the unperturbed system. We develop the asymptotic theory and verify it in simulations.     

Determinant Bounds and the Matsubara UV Problem of Many-Fermion Systems

It is known that perturbation theory converges in fermionic field theory at weak coupling if the interaction and the covariance are summable and if certain determinants arising in the expansion can be bounded efficiently, e.g. if the covariance admits a Gram representation with a finite Gram constant. The covariances of the standard many–fermion systems do not fall into this class due to the slow decay of the covariance at large Matsubara frequency, giving rise to a UV problem in the integration over degrees of freedom with Matsubara frequencies larger than some Ω (usually the first step in a multiscale analysis). We show that these covariances do not have Gram representations on any separable Hilbert space. We then prove a general bound for determinants associated to chronological products which is stronger than the usual Gram bound and which applies to the many–fermion case. This allows us to prove convergence of the first integration step in a rather easy way, for a short–range interaction which can be arbitrarily strong, provided Ω is chosen large enough. Moreover, we give – for the first time – nonperturbative bounds on all scales for the case of scale decompositions of the propagator which do not impose cutoffs on the Matsubara frequency.     

Stability of the curvature perturbation in dark sectors' mutual interacting models

We consider perturbations in a cosmological model with a small coupling between dark energy and dark matter. We prove that the stability of the curvature perturbation depends on the type of coupling between dark sectors. When the dark energy is of quintessence type, if the coupling is proportional to the dark matter energy density, it will drive the instability in the curvature perturbations; however if the coupling is proportional to the energy density of dark energy, there is room for the stability in the curvature perturbations. When the dark energy is of phantom type, the perturbations are always stable, no matter whether the coupling is proportional to the one or the other energy density.     

Measures of vocal function during changes in vocal effort level

The purpose of this article is to present the results of a controlled study of the day-to-day variabilities of three acoustic parameters (jitter, shimmer, and normalized noise energy), and two electroglottographic parameters (contact quotient and contact quotient perturbation) for vowels produced at three vocal efforts (low, normal, high). Data were obtained with use of a sophisticated bilinear interpolation pitch detection method. A repeated measures design required subjects to produce the vowels // and /a/ five times a day over 3 days at each vocal effort level. The jitter, shimmer, and normalized noise energy values from acoustic measures and contact quotient and contact quotient perturbation values varied significantly among the three vocal effort levels. The clinical implication of this finding is that vocal effort must be controlled in order to obtain consistent clinical measures. Furthermore, day-to-day variability must be taken into account if representative measures are to be obtained for clinical use.     

Degenerate approach to the mean field Bose-Hubbard Hamiltonian

A degenerate variant of mean field perturbation theory for the on-site Bose-HubbardHamiltonian is presented. We split the perturbation into two terms and perform exactdiagonalization in the two-dimensional subspace corresponding to the degenerate states.The final relations for the second order ground state energy and first order wave functiondo not contain singularities at integer values of the chemical potentials. The resultingequation for the phase boundary between superfluid and Mott states coincides with theprediction from the conventional mean field perturbation approach.     

Second-order effects in chiral-invariant pion Lagrangians and the use of superpropagators

We examine the second-order corrections to the scattering amplitude and to the vector currents for chiral-invariant Lagrangians of massless pions. Standard renormalization theory leads to three undetermined parameters. We discuss the possibility of choosing definite values for these parameters by applying the technique of superpropagators. In an appendix we investigate the restrictions which follow if localizability of the perturbation expansion in powers of the interaction Lagrangian is required. It is shown that this condition determines the pion-field coordinates uniquely.     

Heat and mass fluxes in the presence of fast exothermic superficial reaction

In this paper heat and mass transfer phenomena are studied in a catalytic monolith with a fast exothermic reaction taking place at the walls at fully developing laminar flow for different values of the kinetic parameters. A two-dimensional model has been adopted to simulate the behaviour of the monolith reactor. The unsteady Navier–Stokes equations have been discretized by adopting the control volume approach and solved by means of the CFD-ACE+ package. The model surface reaction is parametrically varied to account for the effects of the perturbation generated by heat production associated with the reaction on flow field, temperature and concentration profiles and then on transport. Results show that Nu and Sh trends are not monotonic functions but that there exists a transfer enhancement due to the perturbation of the flow field. This increase is shown to be dependent on the kinetics parameters of the surface reaction. We show that the definition of the new driving force we previously proposed, which relates the transfer coefficients to the adiabatic temperature rise, is also able to describe the effect of the kinetic parameters if the pre-exponential factor and the activation energy are included in the correlation.     

Perturbative analysis of the divergent contributions to the Casimir energy

We investigate the divergence structure of the Casimir energy for the case that ?(x) and μ(x) are general functions ofx and of the frequency. The analysis is done in perturbation theory up to second order. The degree of divergence is found to be lowered by one unit if the usual approximation of sharp boundaries is relaxed. This introduces the inverse width of the boundary layer as another physical cutoff for the divergent integrals, besides the cutoffs related to retardation and spatial nonlocality of the dielectric response.     

Dynamic polarizability,dispersion coefficient C6 and dispersion energy in the effective fragment potential method

The development of a fragment–fragment dispersion energy expression, for the general effective fragment potential (EFP2) method is presented. C₆ dispersion coefficients, expressed in terms of the dynamic polarizabilties over the imaginary frequency range (α(iν)), were calculated for a set of homo and hetero dimers. Using these coefficients the dispersion energy has been calculated. The dispersion energy is expressed using a simple London series expansion terminated after the n=6 term and implemented using distributed localized molecular orbitals (LMOs). The EFP2 dispersion energy is compared to symmetry adapted perturbation theory (SAPT) values. From this comparison, it is apparent that one needs to include higher order terms in the dispersion energy. Adding an estimated C₈ term to the C₆ energy greatly improves the agreement with the benchmark SAPT energies.     

Phase transition and thermodynamic stability in extended phase space and charged Hořava–Lifshitz black holes

For charged black holes in Ho?ava–Lifshitz gravity, a second order phase transition takes place in extended phase space where the cosmological constant is taken as thermodynamic pressure. We relate the second order nature of phase transition to the fact that the phase transition occurs at a sharp temperature and not over a temperature interval. Once we know the continuity of the first derivatives of the Gibbs free energy, we show that all the Ehrenfest equations are readily satisfied. We study the effect of the perturbation of the cosmological constant as well as the perturbation of the electric charge on thermodynamic stability of Ho?ava–Lifshitz black hole. We also use thermodynamic geometry to study phase transition in extended phase space. We investigate the behavior of scalar curvature of Weinhold, Ruppeiner, and Quevedo metric in extended phase space of charged Ho?ava–Lifshitz black holes. It is checked if these curvatures could reproduce the result of specific heat for the phase transition.     

Disturbing synchronization: Propagation of perturbations in networks of coupled oscillators

We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the interaction network underlying the ensemble. The overall response of the system is resonant, exhibiting a maximum when the perturbation frequency coincides with the natural frequency of the phase oscillators. The individual response, on the other hand, can strongly depend on the distance to the place where the perturbation is applied. For small distances on a random network, the system behaves as a linear dissipative medium: the perturbation propagates at constant speed, while its amplitude decreases exponentially with the distance. For larger distances, the response saturates to an almost constant level. These different regimes can be analytically explained in terms of the length distribution of the paths that propagate the perturbation signal. We study the extension of these results to other interaction patterns, and show that essentially the same phenomena are observed in networks of chaotic oscillators.     

Wave packet revivals and the energy eigenvalue spectrum of the quantum pendulum

The rigid pendulum, both as a classical and as a quantum problem, is an interesting system as it has the exactly soluble harmonic oscillator and the rigid rotor systems as limiting cases in the low- and high-energy limits, respectively. The energy variation of the classical periodicity (τ) is also dramatic, having the special limiting case of τ→∞ at the ‘top’ of the classical motion (i.e., the separatrix.) We study the time-dependence of the quantum pendulum problem, focusing on the behavior of both the (approximate) classical periodicity and especially the quantum revival and superrevival times, as encoded in the energy eigenvalue spectrum of the system. We provide approximate expressions for the energy eigenvalues in both the small and large quantum number limits, up to fourth order in perturbation theory, comparing these to existing handbook expansions for the characteristic values of the related Mathieu equation, obtained by other methods. We then use these approximations to probe the classical periodicity, as well as to extract information on the quantum revival and superrevival times. We find that while both the classical and quantum periodicities increase monotonically as one approaches the ‘top’ in energy, from either above or below, the revival times decrease from their low- and high-energy values until very near the separatrix where they increase to a large, but finite value.     

Geometry of a chaotic layer

An analysis is made of the dependence of the geometric shape of the chaotic layer near the separatrix of a nonlinear resonance of a Hamiltonian system on the parameters of this system. A separatrix algorithmic mapping, which describes the motion near the separatrix in the presence of an asymmetric perturbation having an arbitrary degree of asymmetry. The separatrix algorithmic mapping is an algorithm containing conditional transfer instructions, is considered. An analytic procedure is derived to reduce the separatrix algorithmic mapping to the unified surface of the cross section of the initial Hamiltonian system (mapping synchronization procedure). It is observed that in the case of the high-frequency perturbation λ → +∞ (where λ is the ratio of the perturbation frequency to the frequency of small phase oscillations at resonance), the chaotic layer is subjected to strong bending in the sense that during motion near the separatrix theamplitude of the energy deviations relative to the unperturbed separatrix value is much larger than the layer width. However, the synchronized separatrix algorithmic mapping ensures an accurate representation of the phase portrait of the layer for both low and high values of the parameter λ provided that the amplitude of the perturbation is fairly small. This is demonstrated by comparing the phase portraits obtained using the synchronized separatrix algorithmic mapping with the results of direct numerical integrations of the initial Hamiltonian system.     

Frequency modulation indicator, Arnold’s web and diffusion in the Stark-Quadratic-Zeeman problem

We notice that the fundamental frequencies of a slightly perturbed integrable Hamiltonian system are not time-constant inside a resonance but frequency modulated, as is evident from pendulum models and wavelet analysis. Exploiting an intrinsic imprecision inherent to the numerical frequency analysis algorithm itself, hence transforming a drawback into an opportunity, we define the Frequency Modulation Indicator, a very sensitive tool in detecting where fundamental frequencies are modulated, localizing so the resonances without having to resort, as in other methods, to the integration of variational equations. For the Kepler problem, the space of the orbits with a fixed energy has the topology of the product of two 2-spheres. The perturbation Hamiltonian, averaged over the mean anomaly, has surely a maximum and a minimum, to which correspond two periodic orbits in physical space. Studying the neighbourhood of these two elliptic stable points, we are able to define adapted action-angle variables, for example, the usual but “SO(4)-rotated” Delaunay variables. The procedure, implemented in the program KEPLER, is performed transparently for the user, providing a general scheme suited for generic perturbation. The method is then applied to the Stark-Quadratic-Zeeman problem, displaying very clearly the Arnold web of the resonances. Sectioning transversely one of the resonance strips so highlighted and performing a numerical frequency analysis, one is able to locate with great precision the thin stochastic layer surrounding a separatrix. Another very long (10⁸ revolutions) frequency analysis on an orbit starting here reveals, as expected, a well defined pattern, which ensures that the integration errors do not eject the point out of the layer, and moreover a very slow drift in the frequency values, clearly due to Arnold diffusion.