Order Perturbation Research Articles

Gas phase proton affinities of proline-containing peptides. 1: ProGly, ProAla, ProVal, ProLeu, ProIle, and ProPro

The gas-phase proton affinities (PA) for a series of proline-containing dipeptides have been measured in an ESI triple quadrupole instrument using the extended kinetic method. Proton affinities for ProGly (1), ProAla (2), ProVal (3), ProLeu (4), ProIle (5), and ProPro (6) were determined to be 969.6 ± 7.8, 990.4 ± 7.7, 987.6 ± 7.9, 982.8 ± 8.0, 988.8 ± 10.1, and 996.5 ± 12.2 kJ/mol, respectively. Predictions for the proton affinities for 1–6 were also obtained through isodesmic calculations at the B3LYP/6-311++G(d,p)//B3LYP/6-31+G(d) level of theory. The predicted proton affinities for 1 and 6 of 966.9 and 991.0 kJ/mol are in agreement with the experimental values. However, the predicted proton affinities for 2–5 of 973.5, 975.9, 975.7, and 975.9 are between 8 and 15 kJ/mol lower than the experimental values. Additional calculations with a larger basis set (B3LYP/6-311++G(2df,2p), inclusion of dispersion (B3LYP-D3/6-311++G(d,p)), switching to second order perturbation theory (MP2/6-31++G(d,p) and MP2/6-311++G(2df,2p), or switching density functional (M06-2x/6-311++G(d,p) and M06-2x/6-311++G(2df,2p) show only modest changes in derived thermochemistry lending support to the original calculations. We recommend using the experimental proton affinities for ProGly and ProPro and using the calculated values for ProAla, ProVal, ProLeu, and ProIle with the experimental proton affinities as upper limits.

Uncertainty quantification of 3D acoustic shape sensitivities with generalized [formula omitted]-order perturbation boundary element methods

This paper presents a novel perburbation-based method for uncertainty quantification of acoustic fields and their shape sensitivities. In this work, the frequencies of impinging acoustic waves are regarded as random variables. Taylor’s series expansions of acoustic boundary integral equations are derived to obtain nth-order derivatives of acoustic state functions with respect to frequencies. Acoustic shape sensitivity is obtained by directly differentiating acoustic boundary integral equation with respect to shape design variables, and then the nth-order derivatives of shape sensitivity with respect to random frequencies are formulated with Taylor’s series expansions. Based on the nth-order perturbation theory, the statistical characteristics of acoustic state functions and their shape sensitivities can be evaluated. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed algorithm.

High precision accelerator for our hybrid model of the redshift space power spectrum

Abstract Upcoming Large Scale Structure surveys aim to achieve an unprecedented level of precision in measuring galaxy clustering. However, accurately modelling these statistics may require theoretical templates that go beyond two-loop order perturbation theory, especially for achieving precision at smaller scales. In our previous work, we introduced a hybrid model for the redshift space power spectrum of galaxies. This model combines two-loop order templates with N-body simulations to capture the influence of scale-independent parameters on the galaxy power spectrum. However, the impact of scale-dependent parameters was addressed by precomputing a set of input statistics derived from computationally expensive N-body simulations. As a result, exploring the scale-dependent parameter space was not feasible in this approach. To address this challenge, we present an accelerated methodology that utilizes Gaussian processes, a machine learning technique, to emulate these input statistics. Our emulators exhibit remarkable accuracy, achieving reliable results with just 13 N-body simulations for training. Our emulators can reproduce the set of statistics we are interested in with less than 0.1% error in the parameter space within 5σ of the Planck ΛCDM predictions, specifically for scales around k > 0.1 h Mpc−1. Following the training of our emulators, we can predict all inputs for our hybrid model in approximately 0.2 seconds at a specified redshift. Given that performing 13 N-body simulations is a manageable task, our present methodology enables us to construct efficient and highly accurate models of the galaxy power spectra within a manageable time frame.

Energy change and Landauer’s principle in the interaction between qubit and quantum field theory

We give a general description of the system evolution under the interaction between qubit and quantum field theory up to the second order perturbation, which is also referred to as the simplified model of light-matter interaction. The results are classified into rotating and counter-rotating wave terms, the former corresponding to stimulated absorption and emission, and the latter to Unruh and anti-Unruh effects. We obtain not only the reduced density matrix of the qubit, but also the backreaction obtained by quantum field theory as the environment. The result shows that the energy variation of the quantum field theory is related to trajectory and the initial state of the qubit, the expectation values of the linear and quadratic field operators, and the temporal order product operator. When the qubit is in accelerated motion, the conventional Unruh effect causes the vacuum state to possess a “temperature”, which raises some doubts about the validity of Landauer’s principle. We prove that Landauer’s principle still holds for any state of motion.

Information theoretic measures for Lifshitz system

In this work, we have studied various mixed state information theoretic quantities for an excited state of Lifshitz spacetime in 3 + 1-dimensions. This geometry is the gravity dual to a class of 2 + 1-dimensional quantum field theories having Lifshitz symmetry. We have holographically calculated mutual information, entanglement wedge cross section, entanglement negativity and mutual complexity for strip like subsystems at the boundary. For this we have used the results of holographic entanglement entropy and complexity present in the literature. We first calculate all of these mentioned quantities for the pure state of Lifshitz spacetime. Then we have moved on to calculate all these quantities for excited state of the Lifshitz spacetime. The gravity dual of excited state of Lifshitz systems in field theory can be obtained by applying constant perturbations along the boundary direction. Further, we would like to mention that for the simplicity of calculation we are only considering results up to the first order in perturbation. The change in the obtained holographic information theoretic quantities are then related to entanglement entropy, entanglement pressure, entanglement chemical potential and charge using the stress tensor complex. These relations are analogous to the first law of entanglement thermodynamics given earlier in the literature. All the calculations are carried out for both values of dynamical scaling exponent (z) present in the Lifshitz field theory.

The renormalization group for large-scale structure: origin of galaxy stochasticity

The renormalization group equations for large-scale structure (RG-LSS) describe how the bias and stochastic (noise) parameters — both of matter and biased tracers such as galaxies — evolve as a function of the cutoff Λ of the effective field theory. In previous work, we derived the RG-LSS equations for the bias parameters using the Wilson-Polchinski framework. Here, we extend these results to include stochastic contributions, corresponding to terms in the effective action that are higher order in the current J. We derive the general local interaction terms that describe stochasticity at all orders in perturbations,and a closed set of nonlinear RG equations for their coefficients. These imply thata single nonlinear bias term generates all stochastic moments through RG evolution. Further, theevolution is controlled by a different, lower scale than the nonlinear scale. This has implications for the optimal choice of the renormalization scale when comparing the theory with data to obtain cosmological constraints.

Growth of cosmic perturbations in the modified [formula omitted] gravity

We explore the generalized f(R,T) modified theory of gravity, where the gravitational Lagrangian is a function of Ricci scalar R and the trace of the energy–momentum tensor T. We derive modified field equations to the linear order of perturbations in the context of f(R,T) model. We then investigate the growth of perturbations in the context of f(R,T) modified gravity. Primary numerical investigations based on matter power spectra diagrams indicate a structure growth suppression in f(R,T) gravity, which exhibits consistency with local measurements. Also, we notice that matter-geometry interaction in f(R,T) model would results in the specific feature named as ”matter acoustic oscillations” appeared in matter power spectra diagrams. Moreover, we put constraints on the cosmological parameters of f(R,T) model, utilizing current observations, chiefly cosmic microwave background (CMB), weak lensing, supernovae, baryon acoustic oscillations, and redshift-space distortions data. Numerical results based on MCMC calculations imply that f(R,T) is a qualified theory of modified gravity in reconciling Planck CMB data with local probes of large scale structures, by reporting lower values for the structure growth parameter σ8 compared to the standard model of cosmology.

Light scalar quarkonia from Laplace sum rule at NLO

We review our results on light scalar quarkonia (q¯q and four-quark states) from (inverse) QCD Laplace sum rules (LSR) and their ratios R within stability criteria and including higher order perturbative (PT) corrections up to the (estimated) O(αs5). As the Operator Product Expansion (OPE) usually converges for D⩽6−8, we evaluated the QCD spectral functions at Lowest Order (LO) of PT QCD and up to the D=6 dimension vaccum condensates. We request that the optimal results obey the constraint: Pole (Resonance) contribution to the spectral integral is larger than the QCD continuum one which excludes an on-shell mass around (500−600)MeV obtained for values of the QCD continuum threshold tc⩽(1∼1.5)GeV2. Our results for the different assignments of the scalar mesons are compiled in Tables 1 to 3.

Analysis of an iterative reconstruction method in comparison of the standard reconstruction method

ABSTRACT We present a detailed analysis of a new iterative density reconstruction algorithm. This algorithm uses a decreasing smoothing scale to better reconstruct the density field in Lagrangian space. We implement this algorithm to run on the quijote simulations, and extend it to (a) include a smoothing kernel that smoothly goes from anisotropic to isotropic, and (b) a variant that does not correct for redshift space distortions. We compare the performance of this algorithm with the standard reconstruction method. Our examinations of the methods include cross-correlation of the reconstructed density field with the linear density field, reconstructed two-point functions, and BAO parameter fitting. We also examine the impact of various parameters, such as smoothing scale, anisotropic smoothing, tracer type/bias, and the inclusion of second order perturbation theory. We find that the two reconstruction algorithms are comparable in most of the areas we examine. In particular, both algorithms give consistent fittings of BAO parameters. The fits are robust over a range of smoothing scales. We find the iterative algorithm is significantly better at removing redshift space distortions. The new algorithm will be a promising method to be employed in the ongoing and future large-scale structure surveys.

Vibrational spectroscopic interpretation, solvent effect and molecular docking studies of TAAR1 partial agonist RO5263397

Density functional theory studies of TAAR1 (trace amine associated receptor 1) partial agonist RO5263397 carried out with precise and detailed spectroscopic investigation as well as validated experimentally. FT-IR, confocal Raman and UV–visible spectroscopic techniques were used to characterize the compound and corresponding theoretical calculations were carried out using DFT/B3LYP method with 6-311++G (d,p) basis set. Estimated and observed vibrational wavenumbers of the compound were assigned. UV–visible spectrum and FMOs (frontier molecular orbital) analysis reveals that the polarity affects the molecular reactivity and stability of the compound. Donor – acceptor interaction and second order perturbation energy have been explained using natural bond orbital analysis clarify the presence hydrogen bonds in the system. ELF and LOL studies visualises the localized and delocalized electrons in the title compound. RDG analysis evidences the various interactions present in the monomer and dimer of RO5263397. The structural importance of the compound were clearly examined using NMR spectral analysis. The existence of hydrogen bonding is validated by reactive site findings from Mulliken atomic charge distribution and molecule electrostatic potential surface studies. Information about distinct drug-receptor interactions obtained from molecular docking investigation offers the path of further study of molecular activity in various drug-receptor mechanism.

SBFEM with perturbation method for solving the Reynolds equation

AbstractRotordynamic simulations with nonlinear hydrodynamic bearing forces require a solution of the Reynolds equation at every time step. As a computationally efficient alternative to the standard numerical methods, a semi‐analytical solution based on the scaled boundary finite element method (SBFEM) was developed recently. Through a discretization of the hydrodynamic pressure (dependent variable) along the circumferential but not the axial coordinate, the partial differential equation is transformed into a system of ordinary differential equations. This system of differential equations is referred to as SBFEM equation and can be solved exactly if the influence of shaft tilting is neglected. In common numerical models, this influence can be taken into account without difficulties, but as far as this semi‐analytical approach is concerned, shaft tilting complicates the equations substantially. Therefore, previous studies on the SBFEM solution of the Reynolds equation were conducted without consideration of this effect. The formulation presented in the work at hand no longer requires this simplification. The terms representing the influence of shaft tilting in the SBFEM equation are handled by the perturbation method. The pressure field is expressed by a series expansion, where the solution of order correlates to the power of a perturbation parameter chosen proportional to the tilting angle. The differential equation governing the solution contains lower‐order solutions on its right‐hand side, implying a recursive computation of the series from lowest to highest order. A universal expression for the general solution is formulated, where only the coefficients and the maximum power of the axial coordinate differ for every . This allows the implementation of a general algorithm with no inherent limitation regarding the maximum order of perturbation. For verification, the pressure fields computed by the proposed method are compared to a numerical reference solution, showing that the series converges to the correct result for the investigated set of parameters.

Dimuons from neutrino-nucleus collisions in the semi-inclusive DIS approach

We present a next-to-leading order perturbative QCD calculation of dimuon production in neutrino-nucleus collisions. This process is typically calculated by assuming it to be proportional to inclusive charm production, which requires an effective acceptance correction to take the experimental cuts on the decay-muon kinematics into account. Here, we instead compute the dimuon production cross section directly as a convolution of semi-inclusive deep inelastic scattering to produce charmed hadrons, and a decay function fitted to e+e− data to produce a muon from the charmed hadrons. The presented approach is in a good agreement with available experimental data and will serve as a starting point for higher-order QCD calculations without an external acceptance correction. The uncertainties arising from the decay function and scale dependence are sizeably smaller than those from the nuclear parton distribution functions. We also calculate the effective acceptances within our approach and compare them to those usually used in global fits of parton distribution functions, finding differences of the order of 10 %, depending on the kinematics, perturbative order, and applied parton distributions.

Analytical Inverse QCD Coupling Constant Approach and Its Result for αs

We propose a model for the QCD running coupling constant based on the analytical inverse QCD coupling constant concept with an additional regularization in the low momentum region. Analyticity in the q2-complex plane, where q is the four-momentum transfer, is imposed by methods of the Analytic Perturbation Theory. The model incorporates a peculiar low-momentum behavior for αs(q2) as a divergence at q2=0 to retrieve color confinement, without spoiling its correct high-momentum behavior. This was achieved by means of a two-parameter regularization function, for which we considered three possible analytic expressions. In fact, within the framework of the Analytic Perturbation Theory, αs(q2) assumes a finite value for q2=0, at all perturbative orders (infrared stability), hence the infrared divergence cannot be implemented. For this reason, we found it more straightforward to work with its reciprocal, namely, εs(q2)=1/αs(q2), imposing its vanishing at the origin of the q2-complex plane via the multiplication of the aforementioned regularizing functions and the spectral density. Once the two free parameters of the regularization functions were settled by fitting to the experimental values of αs(q2) at the momenta where these data were available and reliable, the model could reproduce the QCD running coupling constant at any other momentum transferred.

On positive solutions of the nonlocal Yamabe type equation in compact Riemannian manifold

In this paper we deal with a nonlocal curvature equation involving a critical nonlinearity and a lower order perturbation f on a compact Riemannian N-manifold (M,g) (with or without boundary):(−Δg)psu+a(x)up−1=K(x)ups⁎−1+f(x,u) in Mu>0 in Mu=0 on ∂M where (−Δg)ps is the fractional p-Laplacian on (M,g) for p>1 and the fractional exponent 0<s<1 with ps<N and ps⁎:=NpN−ps. Here a(x) is a non-trivial function in L∞(M) and K is a positive smooth function on M. Using critical point theory on the manifold, we prove the existence of a positive solution under certain assumptions.

Asymptotics for some logistic maps and the renormalization group

Abstract We explain the relation between the r = 1 case of the logistic map x i+1 = r x i (1 − x i ), x i ∈ R , i = 0, 1, 2, …, r &gt; 0 and x 0 ≥ 0, and the renormalization group flow arising in the multiscale analysis of interesting zero fixed point, asymptotic free quantum field theory models such as the ultraviolet (1 + 1)-dimensional Gross-Neveu model and QCD, and the infrared ϕ 4 4 model . We obtain the asymptotics of the mapping, which shows an inverse power decay approach to the fixed point x * = 0, Gaussian fixed point, with additional logarithmic-like corrections. This asymptotic behavior is independent of the initial condition x 0 ∈ (0, 1) (hence, there is no constraint for x 0 to be small, as usual in quantum field models), and only depends on the lowest orders in a polynomial perturbation. In asymptotic free quantum field theory, this amounts to say that knowing the renormalization group β-function expansion in the coupling constant, up to higher orders, does not improve our knowledge of the asymptotics of the coupling flow. A comparison with a similar differential equation with continuous time is made by analyzing stability of this kind of solution and higher order monomial perturbations. We also obtain the detailed asymptotics for 0 &lt; r &lt; 1. As well, our methods can be applied when r ∈ (1, 3]. It is known, but without detailed asymptotics, that all trajectories with initial condition x 0 ∈ ( − 1, 1) converge to the fixed point x * = (r − 1)/r. For r = 2, the super attractive case, we obtain an explicit exact solution which exhibits an exploding, non-constant exponential decay rate approach to the x * = (1/2) fixed point. Our methods include the use of iterations, a discrete version of the Fundamental theorem of Calculus, a discrete version of the integrating factor method for first order linear ODEs and, sometimes, a scaling transformation. To obtain these results, we do not use the traditional Banach contraction mapping theorem, which only provides an upper bound on the asymptotics. We expect that our methods can be employed to determine the asymptotics of the logistic map for a wider range of parameters, where other fixed points are present.

Terahertz field generation in a self-sustained magnetic laser-plasma channel

We theoretically investigate the terahertz field excitation from a laser-driven self-sustained magnetized plasma channel. The expulsion of plasma electrons by the laser ponderomotive force modifies the plasma density, which self-focuses the laser pulse. For the optimized laser parameters, the laser propagates without diverging in plasma and a plasma channel is created. The magnetic field applied along the laser propagation enhances the channel formation efficiency. We utilize this magnetic plasma channel to excite the transverse radiation field by the self-focused laser via wakefield excitation. The magnetic plasma channel maintains the laser intensity over a larger propagation distance, exciting wakefields efficiently. The second order perturbation technique is applied to calculate the wakefield components excited by the laser pulse in a self-sustained magnetic plasma channel. The density perturbation associated with the low-frequency ponderomotive force derives the transverse nonlinear current at terahertz frequency. Our results show that the magnetic field plasma channel can significantly enhance the terahertz conversion efficiency. The tunable terahertz radiation fields of 20 THz frequency with about 10 GV/m may be obtained using one Tesla magnetic field. The efficiency of the process may be optimized and controlled by the laser and plasma parameters. These high-field THz may be useful in various applications such as ultra-fast technology.

Low-energy theorem revisited and OPE in massless QCD

We revisit a low-energy theorem (LET) of NSVZ type in SU(N) QCD with Nf massless quarks derived in [1] by implementing it in dimensional regularization. The LET relates n-point correlators in the l.h.s. to n + 1-point correlators with the extra insertion of TrF2 at zero momentum in the r.h.s. We demonstrate that, for 2-point correlators of an operator O in the l.h.s., the LET implies that, in general, the integrated 3-point correlator in the r.h.s. needs in perturbation theory an infinite additive renormalization in addition to the multiplicative one. We relate the above counterterm to a corresponding divergent contact term in a certain coefficient of the OPE of TrF2 with O in the momentum representation, thus extending to any operator O an independent argument that first appeared for O = TrF2 in [2]. Finally, we demonstrate that in the asymptotically free phase of QCD the aforementioned counterterm in the LET is actually finite nonperturbatively after resummation to all perturbative orders. We also briefly recall the implications of the LET in the gauge-invariant framework of dimensional regularization for the perturbative and nonperturbative renormalization in large-N QCD. The implications of the LET inside and above the conformal window of SU(N) QCD with Nf massless quarks will appear in a forthcoming paper.

Enhancing the electron pair approximation with measurements on trapped-ion quantum computers

The electron pair approximation offers an efficient variational quantum eigensolver (VQE) approach for chemistry simulations on quantum computers. With the number of entangling gates scaling quadratically with system size and a constant measurement overhead, the orbital optimized unitary pair coupled cluster double (oo-upCCD) ansatz strikes a balance between accuracy and efficiency. However, the electron pair approximation prevents the method from achieving quantitative accuracy. To improve it, we explore the theory of second order perturbation (PT2) correction to oo-upCCD. PT2 accounts for the missing broken-pair contributions in oo-upCCD, while retaining its efficiencies. For molecular bond stretching and chemical reactions, the method significantly improves the predicted energy accuracy, reducing oo-upCCD’s error by up to 90%. On IonQ’s quantum computers, we find that the PT2 energy correction is highly noise-resilient. The predicted VQE-PT2 reaction energies are in excellent agreement with noise-free simulators after applying simple error mitigations solely on the VQE energies.

Predicting phase coexistence and adsorption isotherms of classical and quantum fluids using the microcanonical-ensemble perturbation theory (MEPT)

The Microcanonical-Ensemble Perturbation Theory (MEPT) of Sastre et al. (2018) [7] has been extended to study the vapor-liquid phase coexistence of binary and ternary mixtures of fluids. The attractive interactions between chains of molecules are represented as monomer segments interacting via a square-well pair potential. Calculations for the thermodynamic properties and phase behavior of square-well monomer chains are considered and compared with experimental data. Molecular parameters have been obtained to model the phase behavior of real fluids such as n-alkanes (from C1 to C12), nitrogen, perfluoromethane, carbon dioxide, i-butane, i-pentane, neon, and hydrogen. Furthermore, the capability of the MEPT approach in predicting critical and azeotropic lines of binary and ternary mixtures is explored. The results demonstrate that the MEPT approach provides a robust description of the phase behavior of mixtures containing chains of fluids. Additionally, we have integrated the MEPT approach with the two-dimensional Statistical Associating Fluid Theory for fluids interacting via variable range potentials (SAFT-VR-2D) to investigate the effect of quantum contributions on both phase behavior and adsorption. Remarkable improvements are observed when both higher order perturbation terms of the Helmholtz free energy and quantum contributions are included in the predictions of the phase behavior of quantum fluids such as neon and hydrogen. In all cases, the theoretical results exhibit favorable comparisons with experimental data in a wide range of compositions, pressures, and temperatures.

Birefringence modulation via intense coherent phonons engineering with asymmetric VO2/TiO2 heterostructures

The ultrafast modulation of optical crystal birefringence, involving rapid deformations of crystalline lattices, holds significant scientific and technological importance. High-frequency coherent phonons, through transient perturbation of lattice order, have emerged as a powerful tool for modifying the properties of materials. Here, we systematically investigate coherent phonons in the asymmetric crystal directions [011], [110], and [100] of VO2/TiO2 heterostructures. Notably, in the (011)-VO2/TiO2 system, a remarkable shear mode coherent phonon signal was excited, exhibiting a marginally higher intensity compared to the longitudinal mode. By changing the probe light polarization, we observed a fascinating reversal in the birefringence sign induced by the giant coherent phonons. Density functional theory (DFT) calculations indicate that TiO2 possesses excellent photoelastic properties, with strong coherent phonons efficiently modulating refractive index anisotropy, accounting for this phenomenon. This finding provides novel insights into the development of ultrafast acousto-optic devices.