Quartic Terms Research Articles

Dynamics of Lanthanide(III) complexes from crystallographic data and computational studies

In this study we take advantage of the large body of X-ray data reported for lanthanide complexes, as well as their similar coordination chemistry properties, to gain insight on the dynamic processes involving λ ↔ δ configurational changes leading to isomer interconversion. The analysis of X-ray data reveals that different donor groups are characterized by Gaussian distributions of the dihedral N–C–X–Y angles ϕ. In the case of ethylenediamine groups (X = C; Y = N) Gaussian distributions are very narrow, while acetates (X = C; Y = O) provide very broad distributions. The analysis of the potential energy surfaces (PESs) using DFT reveals that ethylenediamine groups are characterised by well-defined deep energy minima, while those of acetate groups are rather swallow. Other donor groups like acetamide, pyridine or phosphinate show intermediate Gaussian distributions with respect to ethylenediamine and acetates. The PESs were fitted to a potential incorporating quadratic, cubic and quartic terms. The quadratic force constants k11 obtained for the different donor types follow the trend of the full width at half maxima (FWHM) of Gaussian distributions obtained from X-ray data. The k11 values are very similar for a given donor group, while the anharmonic cubic (k111) and quartic (k1111) force constants vary significantly depending on the environment of the donor group. Overall, this work demonstrates that the analysis of X-ray crystallographic data in lanthanide complexes can provide very useful information on their coordination chemistry preferences and dynamic processes.

Two types of series expansions valid at strong coupling

It is known that perturbative expansions in powers of the coupling in quantum mechanics (QM) and quantum field theory (QFT) are asymptotic series. This can be useful at weak coupling but fails at strong coupling. In this work, we present two types of series expansions valid at strong coupling. We apply the series to a basic integral as well as a QM path integral containing a quadratic and quartic term with coupling constant λ. The first series is the usual asymptotic one, where the quartic interaction is expanded in powers of λ. The second series is an expansion of the quadratic part where the interaction is left alone. This yields an absolutely convergent series in inverse powers of λ valid at strong coupling. For the basic integral, we revisit the first series and identify what makes it diverge even though the original integral is finite. We fix the problem and obtain, remarkably, a series in powers of the coupling which is absolutely convergent and valid at strong coupling. We explain how this series avoids Dyson’s argument on convergence. We then consider the QM path integral (discretized with time interval divided into N equal segments). As before, the second series is absolutely convergent and we obtain analytical expressions in inverse powers of λ for the nth order terms by taking functional derivatives of generalized hypergeometric functions. The expressions are functions of N and we work them out explicitly up to third order. The general procedure has been implemented in a Mathematica program that generates the expressions at any order n. We present numerical results at strong coupling for different values of N starting at N = 2. The series matches the exact numerical value for a given N (up to a certain accuracy). The continuum is formally reached when N → ∞ but in practice this can be reached at small N.

Quantum backreactions in (A)dS3 massive gravity and logarithmic asymptotic behavior

We study the interplay between higher-curvature terms and the backreaction of quantum fluctuations in three-dimensional massive gravity in asymptotically (anti–)de Sitter space. We focus on the theory at the special point of the parameter space where the two maximally symmetric vacua coincide. In the case of positive cosmological constant, this corresponds to the partially massless point, at which the classical theory admits de Sitter black holes and exhibits an extra conformal symmetry at linear level. We explicitly find the quantum corrected black hole geometry in the semiclassical approximation and show that it induces a relaxation of the standard asymptotic conditions. Nonetheless, the new asymptotic behavior is still preserved by an infinite-dimensional algebra, which, in addition to Virasoro, contains logarithmic supertranslations. Finally, we show that all the results we obtain for the quadratic massive gravity theory can be extended to theories including cubic and quartic terms in the curvature. Published by the American Physical Society 2024

Hairy black holes by spontaneous symmetry breaking

We study hairy black hole solutions in Einstein(-Maxwell)-scalar-Gauss-Bonnet theory. The complex scalar coupling function includes quadratic and quartic terms, so the gravitational action has a U(1) symmetry. We argued that when the effective mass of the scalar field is at the critical value, the black holes without hairs transform into hairy black holes in a symmetry-broken vacuum via spontaneous symmetry breaking. These hairy black holes are stable under scalar perturbations, and the Goldstone bosons are trivial. Moreover, we found that the spontaneous symmetry breaking associated with local U(1) is unlikely to occur in this theory. Published by the American Physical Society 2024

Tracing Prebiotic Molecules: Rotational Spectroscopy of Deuterated Glycolaldehyde and (Z)-1,2-Ethenediol.

Glycolaldehyde, an important prebiotic molecule, along with its monodeuterated species and its higher energy tautomer, (Z)-1,2-ethenediol, has been detected in the interstellar medium. Although the elemental D/H ratio in the universe is only ∼1.6 × 10-5, the deuterium relative abundance in interstellar molecules might be by far larger than this. As such, it provides a remarkable and almost unique diagnostic tool. In particular, it might help elucidate the reaction mechanisms that lead to the formation of the so-called complex organic molecules. It is therefore crucial to extend the census of the interstellar deuterated molecules. To this aim, in this work, we present for the first time a spectroscopic investigation of the rotational spectra of the CHDOD-CHO bideuterated variant of glycolaldehyde and of mono- and bideuterated species of (Z)-1,2-ethenediol (CHOD═CHOD, CHOD═CHOH, and CHOH═CHOD rotamers). For each species, more than a hundred transitions have been assigned. Their analysis led to the accurate determination of all rotational constants as well as quartic and sextic centrifugal distortion terms, thus providing spectroscopic line catalogs suitable for supporting astronomical searches. In addition, the rotational constants of the bideuterated glycolaldehyde isotopologue studied in this work allowed us to improve the semiexperimental equilibrium structure determination for this molecule.

Tangleoids with quantum field theories in biosystems

Abstract The open question whether quantum field theories can be used in biological systems will be addressed in this study. Quantum effects were reported for certain biological systems like the magnetic orientation sense in migratory birds. In quantum field theories it is possible to derive effective quantum field theories with welded tangleoids including braid relations that describe composite particles based on the dynamics of microscopic particle where these composite particles are made of. We observe that the generators of the tangleoid category that will depict the Feynman graphs are X X for a scattering vertex. This arises after carrying out the integral over bosonic fields A μ {A}_{\mu } in the partition function (D) that will lead to an four-valent interaction vertex generated by a quartic term in the fermionic fields. With X + {X}_{+} and X − {X}_{-} we will depict order changes like that regarding time orderings. Ordinary propagators are depicted by ∪ \cup and ∩ \cap . Finally, the generators ! \! and ¡ \hspace{0.1em}\text{¡}\hspace{0.1em} come into play if other foreign fields are picked up.

Simulating a numerical UV completion of quartic Galileons

The Galileon theory is a prototypical effective field theory that incorporates the Vainshtein screening mechanism—a feature that arises in some extensions of general relativity, such as massive gravity. The Vainshtein effect requires that the theory contain higher order derivative interactions, which results in Galileons, and theories like them, failing to be technically well posed. While this is not a fundamental issue when the theory is correctly treated as an effective field theory, it nevertheless poses significant practical problems when numerically simulating this model. These problems can be tamed using a number of different approaches: introducing an active low-pass filter and/or constructing a UV completion at the level of the equations of motion, which controls the high momentum modes. These methods have been tested on cubic Galileon interactions, and have been shown to reproduce the correct low-energy behavior. Here we show how the numerical UV-completion method can be applied to quartic Galileon interactions, and present the first simulations of the quartic Galileon model using this technique. We demonstrate that our approach can probe physics in the regime of the effective field theory in which the quartic term dominates, while successfully reproducing the known results for cubic interactions. Published by the American Physical Society 2024

Spontaneous breaking of the SO(2N) symmetry in the Gross-Neveu model

The canonical Gross-Neveu model for N two-component Dirac fermions in 2+1 dimensions suffers a continuous phase transition at a critical interaction gc1∼1/N at large N, at which its continuous symmetry SO(2N) is preserved and a discrete (Ising) symmetry becomes spontaneously broken. A recent mean-field calculation, however, points to an additional transition at a different critical gc2∼−Ngc1, at which SO(2N)→SO(N)×SO(N). To study the latter phase transition we rewrite the Gross-Neveu interaction g(ψ¯ψ)2 in terms of three different quartic terms for the single (L=1) 4N-component real (Majorana) fermion, and then extend the theory to L>1. This allows us to track the evolution of the fixed points of the renormalization group transformation starting from L≫1, where one can discern three distinct critical points which correspond to continuous phase transitions into (1) SO(2N)-singlet mass-order-parameter, (2) SO(2N)-symmetric-tensor mass-order-parameters, and (3) SO(2N)-adjoint nematic-order-parameters, down to L=1 value that is relevant to the standard Gross-Neveu model. Below the critical value of Lc(N)≈0.35N for N≫1 only the Gross-Neveu critical point (1) still implies a diverging susceptibility for its corresponding (SO(2N)-singlet) order parameter, whereas the two new critical points that existed at large L ultimately become equivalent to the Gaussian fixed point at L=1. We interpret this metamorphosis of the SO(2N)-symmetric-tensor fixed point from critical to spurious as an indication that the transition at gc2 in the original Gross-Neveu model is turned first-order by fluctuations. Published by the American Physical Society 2024

Counting \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 black holes as algebraic varieties

We calculate the helicity trace index B14 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 pure D-brane black holes using various techniques of computational algebraic geometry and find perfect agreement with the existing results in the literature. For these black holes, microstate counting is equivalent to finding the number of supersymmetric vacua of a multi-variable supersymmetric quantum mechanics which in turn is equivalent to solving a set of multi-variable polynomial equations modulo gauge symmetries. We explore four different techniques to solve a set of polynomial equations, namely Newton Polytopes, Homotopy continuation, Monodromy and Hilbert series. The first three methods rely on a mixture of symbolic and high precision numerics whereas the Hilbert series is symbolic and admit a gauge invariant analysis. Furthermore, exploiting various exchange symmetries, we show that quartic and higher order terms are absent in the potential, which if present would have spoiled the counting. Incorporating recent developments in algebraic geometry focusing on computational algorithms, we have extended the scope of one of the authors previous works [1, 2] and presented a new perspective for the black hole microstate counting problem. This further establishes the pure D-brane system as a consistent model, bringing us a step closer to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 2 black hole microstate counting.

Study of boson stars with wormhole

In this paper, we study the mixed system of boson stars (BSs) with wormholes at their center. The boson star is obtained by employing a complex scalar field without self-interaction or a complex scalar field with quartic self-interaction and the wormhole is obtained by employing a phantom field. Utilizing the numerical method, we successfully obtain both symmetric and asymmetric solutions within the two asymptotically flat regions. The key focus of our study involves the systematic exploration of variations in results by varying the throat parameter η0, and the parameter c, representing the quartic term in potential. In the ground state, we find the mass M and Noether charge Q versus the scalar field frequencies ω are multi-valued curves when the η0 is small or the self-interaction is strong, the multi-valued curves will turn into single-valued curves as η0 or c increases. Furthermore, we observe that asymmetric solutions can transition into symmetric solutions at specific scalar field frequencies ω for certain settings of η0 and c. In addition, when it comes to the excited state, the properties of symmetric solutions remain akin to those in the ground state, while asymmetrical results display different characteristics from the ground state. We also present the wormhole spacetime geometry to investigate the properties of this model.

First-Principles Anharmonic Infrared and Raman Vibrational Spectra of Materials: Fermi Resonance in Dry Ice.

We introduce a computational tool for the quantum-mechanical simulation of anharmonic infrared and Raman vibrational spectra of materials. The approach, implemented in the CRYSTAL software, stems from Taylor's expansion of the potential energy surface (PES) on the basis of normal modes up to cubic and quartic terms. The PES can be sampled with four different numerical schemes at the level of density functional theory (DFT), with local, generalized-gradient, and hybrid density functional approximations. Anharmonic states are obtained by solving Shrödinger's nuclear equation with either the vibrational self-consistent field (VSCF) or vibrational configuration interaction (VCI) methods. Nuclear quantum effects (NQEs) are thus fully accounted for. Infrared intensities are computed numerically through a Berry phase approach or analytically through a coupled-perturbed (CP) approach. Raman intensities are computed analytically via the CP approach. A variety of anharmonic features of vibrational spectra of materials can be simulated, including band shifts, combination bands, overtones, resonances (first-order Fermi, second-order Darling-Dennison), and hot bands. We showcase the effectiveness of the approach on the description of a first-order Fermi resonance (FR) in CO2 dry ice: a challenging test-case given that the FR occurs in the Raman spectrum, requires NQEs, and involves two- and three-mode couplings. Fundamental mechanistic differences with respect to the well-known FR in molecular CO2 are addressed. This application represents the first quantum-mechanical, periodic description of FR in dry ice.

Vibrational bands of formaldoxime isotopologue 13CD2NOH in the 280–4000 cm−1 region and rovibrational analysis of its [formula omitted] band by Fourier transform infrared (FTIR) spectroscopy

A total of 11 fundamental and 3 overtone bands of the formaldoxime isotopologue 13CD2NOH were identified using its Fourier transform infrared (FTIR) spectra which were recorded with a low resolution (0.50 cm−1) in the 500–4000 cm−1 region, and high resolution (0.00096 cm−1) in the 280–500 cm−1 region. Their relative infrared (IR) band intensities were also measured. Furthermore, a rovibrational analysis of the IR transitions of the ν12 band of 13CD2NOH was carried out using its high-resolution FTIR spectrum which was recorded at the Australian Synchrotron. A total of 1077 IR transitions of the C-type ν12 band were assigned and fitted using the Watson's A-reduced Hamiltonian in the Ir representation to derive its band center and the v12 = 1 state rovibrational constants up to all 5 quartic centrifugal distortion terms for the first time, with a root-mean-square (rms) deviation of 0.00044 cm−1. The band center of the ν12 band of 13CD2NOH were found to be 391.054446(36) cm−1. The ground state rovibrational constants up to all 5 quartic terms were determined for the first time by fitting 407 ground state combination differences (GSCDs) derived from the assigned IR transitions of the ν12 band of 13CD2NOH of this work. The rms deviation of the GSCD fit was 0.00040 cm−1. Additionally, all 3 rotational constants and 5 quartic centrifugal distortion terms of the ground state and 3 rotational constants of the v12 = 1 state of 13CD2NOH were computed from theoretical anharmonic calculations at two different levels of theory, B3LYP and MP2 with the cc-pVTZ basis set, for comparison with the experimental results. Close agreement was found for the calculated and experimental rovibrational constants of 13CD2NOH for both ground and v12 = 1 states. The vibrational anharmonic frequencies of the 12 fundamental bands of 13CD2NOH in the 280–4000 cm−1 region, and their IR band intensities were also calculated using B3LYP and MP2 with the cc-pVTZ basis set, and they were compared with the respective experimental data. Finally, the ground state rotational constants and the band center of the ν12 band of the cis conformer of 13CD2NOH were calculated and compared with those of the trans conformer of this work.

On the dynamic characteristics of using track nonlinear energy sinks for structural vibration control

Nonlinear energy sinks (NESs) have emerged as a promising solution to overcome the narrow effective bandwidth of linear dynamic vibration absorbers such as the tuned mass damper (TMD). In particular, track NESs are increasingly attracting attention as they are capable of generating nonlinear restoring forces by the movement of an additional mass on the curved tracks. The present study aims to investigate and explore the versatile characteristics of track NESs in structural vibration control. To this end, three different track profiles are considered, namely the profiles designed by a quartic term only, by combined positive quadratic and quartic terms, and by combined negative quadratic and positive quartic terms. Their profiles and damping coefficients are analytically derived in closed form. The frequency response functions of standalone track NESs are constructed using the Harmonic Balance Method and compared with those obtained by the 4th-order Runge-Kutta method, and the dynamic responses, including the displacements, the phase planes, the nonlinear stiffness forces, and the vibrational frequencies, of the track NESs are presented and discussed under different excitation amplitudes and frequencies. The effectiveness and robustness of using track NESs for structural vibration control are also systematically investigated and compared with TMD under harmonic and white-noise ground excitations. Results show that the closed-form solutions of optimal profile and damping coefficients are sufficiently accurate for lightly damped structures, and the frequency response functions of track NESs can be accurately estimated using the Harmonic Balance Method for low and moderate excitations, although their dynamic responses are sensitive to the excitation amplitudes and frequencies. Furthermore, in comparison to TMD, the track NESs are superior in terms of decreased stiffness and smaller working strokes. In general, the present study demonstrates the potential of using track NESs as an effective and robust alternative for structural vibration control.

The fundamental vibrational frequencies and spectroscopic constants of the C2O2H2 isomers: molecules known in simulated interstellar ice analogues.

While trans-glyoxal may not be easily observable in astronomical sources through either IR or radioastronomy due to its C2h symmetry, its cis conformer along with the cyc-H2COCO epoxide isomer should be ready targets for astrochemical detection. The present quantum chemical study shows that not only are both molecular isomers strongly polar, they also have notable IR features and low isomerisation energies of 4.1 kcal mol-1 and 10.7 kcal mol-1, respectively. These three isomers along with two other C2O2H2 isomers have had their full set of fundamental vibrational frequencies and spectroscopic constants characterised herein. These isomers have previously been shown to occur in simulated astrophysical ices making them worthy targets of astronomical search. Furthermore, the hybrid quartic force field (QFF) approach utilized herein to produce the needed spectral data has a mean absolute percent error compared to the experimentally-available, gas phase fundamental vibrational frequencies of 0.6% and rotational constants to better than 0.1%. The hybrid QFF is defined from explicitly correlated coupled cluster theory at the singles, doubles, and perturbative triples level [CCSD(T)-F12b] including core electron correlation and a canonical CCSD(T) relativity correction for the harmonic (quadratic) terms in the QFF and simple CCSD(T)-F12b/cc-pVDZ energies for the cubic and quartic terms, the so-called "F12-TcCR+DZ QFF." This method is producing spectroscopically-accurate predictions for both fundamental vibrational frequencies and principal spectroscopic constants. Hence, the values computed in this work should be notably accurate and, hence, exceptionally useful to the spectroscopy and astrochemistry communities.

Self-consistent phonon calculations and quartic anharmonic lattice thermal conductivity in 2D InS monolayer

Low lattice thermal conductivity (κl) is a crucial factor for higher figure-of merit and hence the efficiency of thermoelectric generators. There are several reports on intrinsically low κl values in two-dimensional (2D) van der Waals materials using density functional theory and molecular dynamics simulations. In general, phonon dispersions are studied at absolute zero temperature using the finite-displacement approach within harmonic approximations. In addition, the κlis calculated using the third-order cubic interatomic force constants (IFCs) by solving the Boltzmann transport equation for phonons. In these calculations, we use quartic IFCs to solve self-consistent phonon equations to obtain dynamical dispersion relations at a finite temperature of 300 K using finite-temperature Green’s function for Bosonic systems in 2D indium sulfide (InS) monolayer. The cubic and quartic IFCs are calculated using machine learning algorithms, namely, the ordinary least square fitting and the least absolute shrinkage and selection operator. It was found that there is a lowering of the renormalized anharmonic phonon frequencies in the dispersion relations at 300 K upon the inclusion of quartic IFCs and anharmonic terms in the case of the InS monolayer. Thus, the κlvalue is reduced to 0.6 W/mK as compared to 0.9 W/mK obtained using cubic IFCs.

Observable gravitational waves from hyperkination in Palatini gravity and beyond

We consider cosmology with an inflaton scalar field with an additional quartic kinetic term. Such a theory can be motivated by Palatini R+R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R+R^2$$\\end{document} modified gravity. Assuming a runaway inflaton potential, we take the Universe to become dominated by the kinetic energy density of the scalar field after inflation. Initially, the leading kinetic term is quartic and we call the corresponding period hyperkination. Subsequently, the usual quadratic kinetic term takes over and we have regular kination, until reheating. We study, both analytically and numerically, the spectrum of primordial gravitational waves generated during inflation and re-entering the horizon during the subsequent eras. We demonstrate that the spectrum is flat for modes re-entering during radiation domination and hyperkination and linear in frequency for modes re-entering during kination: kinetic domination boosts the spectrum, but hyperkination truncates its peak. As a result, the effects of the kinetic period can be extended to observable frequencies without generating excessive gravitational waves, which could otherwise destabilise the process of Big Bang Nucleosynthesis. We show that there is ample parameter space for the primordial gravitational waves to be observable in the near future. If observed, the amplitude and ‘knee’ of the spectrum will provide valuable insights into the background theory.

Linear and nonlinear optical absorption coefficients in InGaN/GaN quantum wells: Interplay between intense laser field and higher-order anharmonic potentials

This computational investigation delves into the electronic and optical attributes of InGaN/GaN nanostructures subjected to both harmonic and anharmonic confinement potentials, coupled with the influence of a nonresonant intense laser field (ILF). The theoretical framework incorporates higher-order anharmonic terms, specifically quartic and sextic terms. The solutions to the Schrödinger equation have been computed employing the finite element method and the effective mass theory. Moreover, linear and third-order nonlinear optical absorption coefficients are derived via a density matrix expansion. Our analysis reveals the feasibility of manipulating electronic and optical properties by adjusting confinement potential parameters, system attributes, and laser field intensity. In addition, the ILF induces remarkable modifications, characterized by reduced resonance peak amplitudes and a blue shift in absorption coefficients. Intriguingly, regardless of potential harmonicity, the impact of incident electromagnetic intensity is notably more pronounced in the absence of the ILF. These findings hold significant promise for advancing theoretical predictions, providing valuable insights into the intricate interplay between confinement potentials, laser fields, and their effects on electronic and optical behaviors within nanostructures.

Ground states of attractive Bose gases in rotating anharmonic traps

This paper is concerned with ground states of attractive Bose gases confined in an anharmonic trap V(x)=ω(|x|2+k|x|4) rotating at the velocity Ω>0, where ω>0 denotes the trapping frequency, and k>0 represents the strength of the quartic term. It is known that for any Ω>0, ground states exist in such traps if and only if 0<a<a⁎, where a⁎:=‖Q‖22 and Q>0 is the unique positive solution of ΔQ−Q+Q3=0 in R2. By analyzing the refined energies and expansions of ground states, we prove that there exists a constant C>0, independent of 0<a<a⁎, such that ground states do not have any vortex in the region R(a):={x∈R2:|x|≤C(a⁎−a)−1−6β20} as a↗a⁎, for the case where ω=3Ω24, k=16, and Ω=C0(a⁎−a)−β varies for some β∈[0,16) and C0>0.

The role of the Callan–Witten anomaly density as a Chern–Simons term in Skyrme model *

We consider axially symmetric solutions of the U(1) gauged Skyrme model supplemented with a Callan–Witten (CW) anomaly density term. The main properties of the solutions are studied, several specific features introduced by the presence of the CW term being identified. We find that the solitons possess a nonzero angular momentum proportional to the electric charge, which in addition to the usual Coulomb part, acquires an extra (topological) contribution from the CW term. Specifically, it is shown that the slope of mass/energy M electric charge Qe and angular momentum J can be both positive and negative. Furthermore, it is shown that the gauged Skyrmion persists even when the quartic (Skyrme) kinetic term disappears.

Application of QUBO model in credit score card combination optimization

Credit cards are a rule by which banks rate their customers. Different credit scoring cards have different thresholds, corresponding to different pass rates and bad debt rates, which have a crucial impact on the bank's revenue. To help banks choose the best combination of credit scoring cards, so as to maximize revenue. Based on the triple credit card combination strategy of the bank, this paper establishes a mathematical programming model for solving the optimal combination. Aiming at the particularity of the binary decision variables, a constraint method is proposed to transform the quartic and quartic terms in the model into quadratic terms. Then, in order to balance the relationship between the objective function and the constraint conditions, the weighted penalty coefficient is further introduced by combining the entropy weight method. The model is transformed into QUBO(quadratic unconstrained binary optimization) model, and then combined with the bank's credit score card data, the optimal combination is solved by quantum annealing algorithm and verified by experiment. The experimental results show that this method has high precision and strong applicability in solving combinatorial optimization problems.