Limit Of Large Energy Research Articles

Charge filling factors in clean and disordered arrays of tunnel junctions.

We simulate one-dimensional arrays of tunnel junctions using the kinetic Monte Carlo method to study charge filling behaviour in the large charging energy limit. By applying a small fixed voltage bias and varying the offset voltage, we investigate this behaviour in clean and disordered arrays (both weak and strong disorder effects). The offset voltage dependent modulation of the current is highly sensitive to background charge disorder and exhibits substantial variation depending on the strength of the disorder. We show that while small fractional charge filling factors are likely to be washed out in experimental devices due to strong background charge disorder, larger factors may be observable.

Pinball Dynamics: Unlimited Energy Growth in Switching Hamiltonian Systems

A family of discontinuous symplectic maps arising naturally in the study of nonsmooth switched Hamiltonian systems is considered. This family depends on two parameters and is a canonical model for the study of bounded and unbounded behavior in discontinuous area-preserving transformations due to nonlinear resonances. This paper provides a general description of the map and a construction of nontrivial unbounded solutions for the special case of the pinball transformation. An asymptotic expansion of the pinball map in the limit of large energy is derived and used for the construction of unbounded solutions. For the generic values of the parameters, in the large energy limit, the map behaves similarly to another one considered earlier by Kesten (Acta Arith 1966).

Equilibration of Small and Large Subsystems in Field Theories and Matrix Models

It has been recently shown that small subsystems of finite quantum systems generically equilibrate. We extend these results to infinite-dimensional Hilbert spaces of field theories and matrix models. We consider a quench setup, where initial states are chosen from a microcanonical ensemble of finite energy in free theory, and then evolve with an arbitrary non-perturbative Hamiltonian. Given a dynamical assumption on the expectation value of particle number density, we prove that small subsystems reach equilibrium at the level of quantum wave-function, and with respect to all observables. The picture that emerges is that at higher energies, larger subsystems can reach equilibrium. For bosonic fields on a lattice, in the limit of large number of bosons per site, all subsystem smaller than half equilibrate. In the Hermitian matrix model, by contrast, this occurs in the limit of large energy per matrix element, emphasizing the importance of the $O(N^2)$ energy scale for the fast scrambling conjecture. Applying our techniques to continuum field theories on compact spaces, we show that the density matrix of small momentum-space observables equilibrate. Finally, we discuss the connection with scrambling, and provide a sufficient condition for a time-independent Hamiltonian to be a scrambler in terms of the entanglement entropy of its energy eigenstates.

Determinant quantum Monte Carlo study ofd-wave pairing in the plaquette Hubbard hamiltonian

Determinant Quantum Monte Carlo (DQMC) is used to determine the pairing and magnetic response for a Hubbard model built up from four-site clusters -a two-dimensional square lattice consisting of elemental 2x2 plaquettes with hopping $t$ and on-site repulsion $U$ coupled by an inter-plaquette hopping $t' \leq t$. Superconductivity in this geometry has previously been studied by a variety of analytic and numeric methods, with differing conclusions concerning whether the pairing correlations and transition temperature are raised near half-filling by the inhomogeneous hopping or not. For $U/t=4$, DQMC indicates an optimal $t'/t \approx 0.4$ at which the pairing vertex is most attractive. The optimal $t'/t$ increases with $U/t$. We then contrast our results for this plaquette model with a Hamiltonian which instead involves a regular pattern of site energies whose large site energy limit is the three band CuO$_2$ model; we show that there the inhomogeneity rapidly, and monotonically, suppresses pairing.

Harmonic Oscillator Trap and the Phase-Shift Approximation

The energy-spectrum of two point-like particles interacting in a 3-D isotropic Harmonic Oscillator (H.O.) trap is related to the free scattering phase-shifts $\delta$ of the particles by a formula first published by Busch et al. It is here used to find an expression for the \it shift \rm of the energy levels, caused by the interaction, rather than the perturbed spectrum itself. In the limit of high energy (large quantum number $n$ of the H.O.) this shift is shown to be given by $-2\frac{\delta}{\pi}$, also valid in the limit of infinite as well as zero scattering length at all H.O. energies. Numerical investigation shows that the shifts differ from the exact result of Busch et al, by less than $<\frac{1}{2}\%$ except for $n=0$ when it can be as large as $\approx 2.5\%$. This approximation for the energy-shift is well known from another exactly solvable model, namely that of two particles interacting in a spherical infinite square-well trap (or box) of radius $R$ in the limit $R\rightarrow \infty$, and/or in the limit of large energy. It is in this context referred to as the \it phase-shift approximation \rm. It can be (and has been) used in (infinite) nuclear matter calculations to calculate the two-body effective interaction in situations where in-medium effects can be neglected. It has also been used in expressing the energy of free electrons in a metal.

Forward–backward asymmetry study of semi-leptonic B decays

We study the resonant contributions in the process of B¯0→K−π+μ+μ− with the K−π+ invariant mass square mKπ2 involving strange mesons, K⁎(1410),K0⁎(1430),K2⁎(1430),K⁎(1680),K3⁎(1780) and K4⁎(2045). Applying the heavy quark expansion and the large energy limit, we derive the relations of form factors to cancel much of the hadronic uncertainties. Using the dependence of branching fractions on the mKπ, we find that the KJ⁎ resonance has a clear signature. Branching ratios, polarizations, forward–backward asymmetries and transversity amplitudes are predicted, from which we find a promising prospective to observe these channels in the future experiment. We update the constraints on effective Wilson coefficients and/or free parameters in these new physics scenarios by making use of the B→K⁎l+l− and b→sl+l− experimental data. Their impact on B→KJ⁎l+l− is subsequently explored and in particular the zero-crossing point for the forward–backward asymmetry in new physics scenarios can sizably deviate from the standard model.

Asymptotic structure of laminar diffusion flames at high pressure

We analyze the structure of laminar diffusion flames at high pressure in the limit of large activation energy for the particular configuration of a steady flame in counterflow. We consider a dense fluid in which normal Fickian diffusion of the fuel is limited, and thermal diffusion, i.e., the Soret effect, is the dominant mechanism for fuel mass transport. Temperature and species profiles, as well as flame temperature and location, are determined as a function of Damköhler number and Soret diffusion coefficient. In particular, we find that oxidant is entirely consumed by the flame, while some fuel leaks through. For light fuels, the fuel profile is found to have a local peak on the oxidant side as a result of thermal diffusion. Our analysis includes a description of extinction phenomena, including explicit criteria in terms of the Soret diffusion coefficient, ratio of temperature of the two streams, and the Damköhler number at extinction.

Determination of the Surface Corrugation Amplitude from Classical Atom Scattering

The energy landscape of an atomic or molecular projectile interacting with a surface is often described in terms of a corrugation function that gives the classical turning point as a function of position vector parallel to the surface. It is shown here that the relative height variation of the corrugation function for scattering of atoms under classical conditions can be determined by a measurement of the maximum intensity in energy-resolved scattering spectra as a function of surface temperature. This is demonstrated by developing a semiclassical quantum theory of atomic scattering from corrugated surfaces and then extending the theory to the classical limit of large incident energies and high surface temperatures. Comparisons of calculations with available data for Ar atom scattering determine the corrugation amplitude for a molten In surface to be about 29% of the mean interparticle spacing in the bulk liquid.

B→Kη(′)γdecays in the standard model and in scenarios with universal extra dimensions

We study the radiative $B\ensuremath{\rightarrow}K{\ensuremath{\eta}}^{(\ensuremath{'})}\ensuremath{\gamma}$ decays, which are important to investigate $CP$ violation, and are also relevant to assess the role of the exclusive modes induced by the $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$ transition to saturate the inclusive $B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ decay rate. Moreover, these channels do not display the same hierarchy as $B\ensuremath{\rightarrow}K{\ensuremath{\eta}}^{(\ensuremath{'})}$ modes, for which the decay into ${\ensuremath{\eta}}^{\ensuremath{'}}$ is enhanced with respect to one into $\ensuremath{\eta}$. The three-body radiative decays reverse the role: we find that this experimentally observed behavior (although affected by a large uncertainty in the case of the ${\ensuremath{\eta}}^{\ensuremath{'}}$) is reproduced in the theoretical analysis. We compute a ${B}^{*}\ensuremath{\rightarrow}K$ form factor, needed for this study, using light cone QCD sum rules, and discuss a relation expected to hold in the large energy limit for the light meson. Finally, we examine $B\ensuremath{\rightarrow}K\ensuremath{\eta}\ensuremath{\gamma}$ in two extensions of the standard model with universal extra dimensions, to investigate the sensitivity of this rare mode to such a kind of new physics effects.

Supersharp resonances in chaotic wave scattering

Wave scattering in chaotic systems can be characterized by its spectrum of resonances, z(n)=E(n)-iΓ(n)/2, where E(n) is related to the energy and Γ(n) is the decay rate or width of the resonance. If the corresponding ray dynamics is chaotic, a gap is believed to develop in the large-energy limit: almost all Γ(n) become larger than some γ. However, rare cases with Γ<γ may be present and actually dominate scattering events. We consider the statistical properties of these supersharp resonances. We find that their number does not follow the fractal Weyl law conjectured for the bulk of the spectrum. We also test, for a simple model, the universal predictions of random matrix theory for density of states inside the gap and the hereby derived probability distribution of gap size.

Analysis ofB→K*J(→Kπ)μ+μ−in the higher kaon resonance region

We study the resonant contributions in the process of ${\overline{B}}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ with the ${K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ invariant mass square ${m}_{K\ensuremath{\pi}}^{2}\ensuremath{\in}[1,5]\text{ }\text{ }{\mathrm{GeV}}^{2}$. Width effects of the involved strange mesons, ${K}^{*}(1410)$, ${K}_{0}^{*}(1430)$, ${K}_{2}^{*}(1430)$, ${K}^{*}(1680)$, ${K}_{3}^{*}(1780)$ and ${K}_{4}^{*}(2045)$, are incorporated. In terms of helicity amplitudes, we derive a compact form for the full angular distributions, through which the branching ratios, forward-backward asymmetries and polarizations are attained. We propose that the uncertainties in the $B\ensuremath{\rightarrow}{K}_{J}^{*}$ form factors can be pinned down by the measurements of a set of SU(3)-related processes. Using results from the large energy limit, we derive the dependence of branching fractions on the ${m}_{K\ensuremath{\pi}}$, and find that the ${K}_{2}^{*}$ resonance has a clear signature, in particular, in the transverse polarizations.

Form factors forΛb→Λtransitions in the soft-collinear effective theory

We present a systematic discussion of Lambda_b -> Lambda transition form factors in the framework of soft-collinear effective theory (SCET). The universal soft form factor, which enters the symmetry relations in the limit of large recoil energy, is calculated from a sum-rule analysis of a suitable SCET correlation function. The same method is applied to derive the leading corrections from hard-collinear gluon exchange at first order in the strong coupling constant. We present numerical estimates for form factors and form-factor ratios and their impact on decay observables in Lambda_b -> Lambda mu^+ mu^- decays.

Heavy-to-light baryonic form factors at large recoil

We analyze heavy-to-light baryonic form factors at large recoil and derive the scaling behavior of these form factors in the heavy quark limit. It is shown that only one universal form factor is needed to parameterize Lambda_b to p and Lambda_b to Lambda matrix elements in the large recoil limit of light baryons, while hadronic matrix elements of Lambda_b to Sigma transition vanish in the large energy limit of Sigma baryon due to the space-time parity symmetry. The scaling law of the soft form factor eta(P^{\prime} \cdot v), P^{\prime} and v being the momentum of nucleon and the velocity of Lambda_b baryon, responsible for Lambda_b to p transitions is also derived using the nucleon distribution amplitudes in leading conformal spin. In particular, we verify that this scaling behavior is in full agreement with that from light-cone sum rule approach in the heavy-quark limit. With these form factors, we further investigate the Lambda baryon polarization asymmetry alpha in Lambda_b to Lambda gamma and the forward-backward asymmetry A_{FB} in Lambda_b to Lambda l^{+} l^{-}. Both two observables (alpha and A_{FB}) are independent of hadronic form factors in leading power of 1/m_b and in leading order of alpha_s. We also extend the analysis of hadronic matrix elements for Omega_b to Omega transitions to rare Omega_b to Omega gamma and Omega_b to Omega l^{+} l^{-} decays and find that radiative Omega_b to Omega gamma decay is probably the most promising FCNC b to s radiative baryonic decay channel. In addition, it is interesting to notice that the zero-point of forward-backward asymmetry of Omega_b to Omega l^{+} l^{-} is the same as the one for Lambda_b to Lambda l^{+} l^{-} to leading order accuracy provided that the form factors \bar{\zeta}_i (i=3, 4, 5) are numerically as small as indicated from the quark model.

Euler-Heisenberg lagrangians and asymptotic analysis in 1+1 QED. Part I: two-loop

We continue an effort to obtain information on the QED perturbation series at high loop orders, and particularly on the issue of large cancellations inside gauge invariant classes of graphs, using the example of the l - loop N - photon amplitudes in the limit of large photons numbers and low photon energies. As was previously shown, high-order information on these amplitudes can be obtained from a nonperturbative formula, due to Affleck et al., for the imaginary part of the QED effective lagrangian in a constant field. The procedure uses Borel analysis and leads, under some plausible assumptions, to a number of nontrivial predictions already at the three-loop level. Their direct verification would require a calculation of this `Euler-Heisenberg lagrangian' at three-loops, which seems presently out of reach. Motivated by previous work by Dunne and Krasnansky on Euler-Heisenberg lagrangians in various dimensions, in the present work we initiate a new line of attack on this problem by deriving and proving the analogous predictions in the simpler setting of 1+1 dimensional QED. In the first part of this series, we obtain a generalization of the formula of Affleck et al. to this case, and show that, for both Scalar and Spinor QED, it correctly predicts the leading asymptotic behaviour of the weak field expansion coefficients of the two loop Euler-Heisenberg lagrangians.

Triple-flame propagation in a parallel flow: an analytical study

We present an analytical study of triple-flame propagation in a two-dimensional mixing layer against a parallel flow. The problem is formulated within a constant density thermo-diffusive model, and solved analytically in the asymptotic limit of large activation energy of the chemical reaction for flames thin compared with their typical radius of curvature. Explicit expressions are obtained in this limit, describing the influence of the flow on the triple-flame. The results are expected to be applicable when the ratio between the flow-scale and the flame-front radius of curvature (which is mainly dictated by concentration gradients) is of order unity, or larger. When this ratio is large, as in the illustrative case of a Poiseuille flow in a porous channel considered here, the flow is found to negligibly affect the flame structure except for a change in its speed by an amount which depends on the stoichiometric conditions of the mixture. On the other hand, when this ratio is of order unity, the flow is able to significantly wrinkle the flame-front, modify its propagation speed, and shift its leading edge away from the stoichiometric line. The latter situation is investigated in the illustrative case of spatially harmonic flows. The results presented describe, in particular, how the leading-edge of the flame-front can be determined in terms of the flow amplitude A which is critical in determining the flame speed. The latter is found to depend linearly on A in the first approximation with a correction proportional to the flame thickness multiplied by , for |A| sufficiently large. The effect of varying the flow-scale on flame propagation in this context is also described, with explicit formulae provided, and interesting behaviours, such as non-monotonic dependence on the scale, identified.

Critical Slow Dynamics of Detonation in a Gas with Non-Uniform Initial Temperature and Composition: A Large-Activation-Energy Analysis

We study the dynamic conditions of existence of the self-sustained detonation regime in gases with non-uniform initial temperature and dilution in the case where the gradients of initial state are parallel to the propagation direction. We analyze the slow dynamics of the detonation supposing that the initial variations have the same order of smallness as the unsteadiness and curvature of the leading shock of the detonation front. We obtain a hyperbolic evolution law for the detonation shock front as a solution to an eigenvalue problem solved in the asymptotic limit of large activation energies for which the induction time of the chemical decomposition process is considered much larger than the heat-release time. We study the effect of the shock dynamics of this self-sustained detonation front on the induction time and we integrate the evolution law for some examples of distinct or combined, dispersive or localized, initial variations in the temperature and diluent mass fraction. We show the existence of a bifurcation set of initial conditions that separates the self-sustained detonations that will continuously achieve the CJ regime from those whose dynamics eventually fail to initiate the chemical decomposition because the dynamic induction length becomes too long. We find that the characteristic critical lengths associated with the initial or boundary conditions are larger than the reference CJ characteristic chemical length by several orders of magnitude, a well-established experimental feature of gaseous detonations. We identify subcritical and supercritical limits which, respectively, give necessary and sufficient conditions for detonation. Below the subcritical limit, the combustion front cannot be coupled to the shock front because the volumetric expansion rate behind the shock is too large. Above the supercritical limit, the relaxation from an overdriven detonation regime to the self-sustained regime is a continuous process, without decoupling and recoupling of the combustion and shock fronts. We interpret the critical domain between these limits as the parametric zone in which experiments show successive decouplings and transverse recouplings of the combustion and shock fronts before the final self-sustained CJ regime.

A Simply Modified Single Pole Scenario For B → K* Form Factors

We revisit the form factors of B → K* by using the heavy quark limit and large energy limit, assuming that the form factors have single pole forms near the zero recoil. The deviation from the single pole model is taken into account by adding a term proportional to (v·v′-1)2. On the other hand, we require the form factors to obey the large recoil symmetry relationships when v · v′ becomes very large. A self-consistent set of B → K* form factors is found. This set of form factors is checked to be consistent with the experimental data about B → K*ll modes.

Homogeneous ignition for a three-step chain-branching reaction model

Spatially homogeneous thermal explosions governed by a three-step chain-branching kinetic model are described in the asymptotic limit of large activation energy for a range of chain-branching cross-over temperatures. The model consists of a sequence of chain-initiation, chain-branching and chain-termination steps. Temperature-sensitive Arrhenius kinetics is employed for the initiation and branching steps, while the termination step has a temperature-independent rate. Marked distinctions in structure arise as the magnitude of the chain-branching cross-over temperature is increased relative to the initial system temperature. Attention is focused on the regime where the chain-branching cross-over temperature is close to the initial system temperature. Results are also obtained for the fast and slow explosion limits where the two temperatures are not close.

Non-Abelian energy loss in cold nuclear matter

We use a formal recurrence relation approach to multiple parton scattering to find the complete solution to the problem of medium-induced gluon emission from partons propagating in cold nuclear matter. The differential bremsstrahlung spectrum, where Landau-Pomeranchuk-Migdal destructive interference effects are fully accounted for, is calculated for three different cases: (i) a generalization of the incoherent Bertsch-Gunion solution for asymptotic on-shell jets, (ii) initial-state energy loss of incoming jets that undergo hard scattering, and (iii) final-state energy loss of jets that emerge out of a hard scatter. Our analytic solutions are given as an infinite opacity series, which represents a cluster expansion of the sequential multiple scattering. These new solutions allow, for the first time, direct comparison between initial- and final-state energy loss in cold nuclei. We demonstrate that, contrary to the naive assumption, energy loss in cold nuclear matter can be large. Numerical results to first order in opacity show that, in the limit of large jet energies, initial- and final-state energy losses exhibit different path length dependences, linear versus quadratic, in contrast to earlier findings. In addition, in this asymptotic limit, initial-state energy loss is considerably larger than final-state energy loss. These new results have significant implications for heavy-ion phenomenology in both $p+A$ and $A+A$ reactions.

The asymptotic structure of premixed tubular flames

The steady isobaric combustion of premixed tubular flames undergoing a direct one-step irreversible Arrhenius-type exothermic global reaction with a constant but general Lewis number is studied in the physically interesting limit of large activation energy. This analysis applies the combustion approximation and differs from previous asymptotic analyses of tubular flames by applying the Hirschfelder boundary condition at the burner exit for chemical species and the application of the delta-function closure scheme. The analysis yields a solution for flame sheet position, flame temperature, heat loss rate to the burner, temperature in the burned region, and stabilization limits as functions of the mass flow rate supplied to the burner and temperature of the burner surface in the near equidiffusional flame limit. Results predict the existence of dual flame behavior consistent with other investigations on the planar and cylindrical burner-stabilized flame. Two stabilization limits are identified, one for approaching flames, consistent with previous studies, and one for receding flames that has not been reported to date. Flame temperature profiles predict a nonmonotonic response, unique to the tubular flame. Consistent with the excess enthalpy of the tubular flame, the results demonstrate a strong dependence of a Lewis number differing from unity. Previous asymptotic analyses of tubular flames with a plug flow boundary condition for mass fraction are reanalyzed with the application of the delta-function closure scheme. Unlike previous results, the analysis predicts an interesting dual response for the temperature in the burned region.