Article
Chemistry, Physical
Jan-Niklas Boyn, Aleksandr O. Lykhin, Scott E. Smart, Laura Gagliardi, David A. Mazziotti
Summary: Hybrid quantum-classical algorithms offer a promising pathway to achieve quantum advantage by leveraging both quantum and classical computing resources. A novel combination of quantum and classical algorithms has been developed to compute the energy of strongly correlated molecular systems with experimental accuracy on noisy intermediate-scale quantum devices, demonstrating chemically relevant and accurate results.
JOURNAL OF CHEMICAL PHYSICS
(2021)
Article
Mathematics
Houwang Li, Wenming Zou
Summary: We study the normalized solutions for quasilinear Schrödinger equations and prove the existence of ground state normalized solutions and infinitely many normalized solutions using perturbation method and index theory. We also obtain new existence results for the mass-critical case and discuss the concentration behavior of ground state solutions.
PACIFIC JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Andrea Sacchetti
Summary: In this paper, the authors propose a method of treating the nonlinear term of the Gross-Pitaevskii nonlinear Schrodinger equation as a perturbation of an isolated discrete eigenvalue of the linear problem. They prove the convergence of the power series and show that it provides a stationary solution to the nonlinear Schrodinger equation.
Article
Mathematics, Applied
Chen Yang, Shu-Bin Yu, Chun-Lei Tang
Summary: In this paper, the authors study the fractional Schrӧdinger equations with a prescribed L-2-norm constraint. They prove the multiplicity of normalized solutions when the mass is subcritical and the exponent e is small enough. They also establish new results on the existence of normalized ground states for nonautonomous elliptic equations.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Interdisciplinary Applications
Alberto Bueno-Guerrero
Summary: In this paper, we propose a model-free axiomatic formulation for option pricing theory and establish a connection between the discounted zero-coupon bond price and the wave function, similar to axiomatic quantum mechanics. By linking the theory to term structure models through the Hamiltonian operator, we demonstrate the consistency between its associated Schrödinger equation and the [25] model. We also identify the quantum mechanical equivalent of the standard risk-neutral option pricing formula and apply a time-dependent perturbation theory to derive an approximate closed-form expression for call option pricing under the [26] model with a small local volatility perturbation.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Milena Stanislavova, Atanas G. Stefanov
Summary: The classical Schrodinger equation for the quantum harmonic oscillator with a harmonic trap potential has been extensively studied over the past 20 years. Ground states are bell-shaped, unique, non-degenerate, and strongly orbitally stable among localized positive solutions. The results are based on ODE methods designed for the Laplacian and power function potential, and this article provides a generalization of these results.
JOURNAL OF EVOLUTION EQUATIONS
(2021)
Article
Mathematics
Iraj Dehsari, Nemat Nyamoradi
Summary: In this paper, we consider a modified fractional Schrödinger system of Choquard type and obtain ground state solutions to the system using the variational method.
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
(2022)
Article
Chemistry, Physical
Pablo E. E. Videla, Lidor Foguel, Patrick H. H. Vaccaro, Victor S. S. Batista
Summary: Understanding the dynamics of proton transfer along low-barrier hydrogen bonds remains a fundamental challenge with practical implications in chemical and biological reactions. This study combines ab initio calculations with a semiclassical ring-polymer instanton method to investigate tunneling processes in 6-hydroxy-2-formylfulvene (HFF), a neutral molecule with low-barrier hydrogen bonding. The results show that the tunneling process involves a multidimensional reaction pathway, with concerted reorganization of the heavy-atom framework to facilitate proton transfer.
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
(2023)
Article
Physics, Multidisciplinary
A. J. Sous, Ibsal Assi, Nasser Saad
Summary: In this study, a zeroth-order perturbation theory is presented to solve the Schrodinger equation for spherically symmetric singular potentials using the asymptotic iteration method (AIM). Exponential and hyperbolic potential ansatz substitutions are employed to handle the difference between the original and new potential as a small perturbation. Each potential ansatz is chosen to have a small enough free parameter to provide an accurate zeroth-order perturbative wave equation solution. This approach avoids the oscillatory behavior observed in AIM solutions for such problems. We illustrate our method by solving problems involving quartic and sextic singular potentials and compare the results with those obtained from other methods, showing good agreement.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics
Bartosz Bieganowski, Jaroslaw Mederski
Summary: In this study, a new simplification method is proposed to demonstrate the existence of solutions to a normalized problem by directly minimizing the energy functional on a linear combination of specific constraints. This method allows for general growth assumptions, covering various physical examples and nonlinear growth considered in the literature.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mathematics, Applied
Guoyuan Chen
Summary: This paper studies the nondegeneracy of ground states of the Hartree equation and constructs multiple semiclassical solutions based on this result.
RESULTS IN MATHEMATICS
(2021)
Article
Multidisciplinary Sciences
Sirilak Sriburadet, Yin-Tzer Shih, B-W Jeng, C-H Hsueh, C-S Chien
Summary: This study explores the existence of nontrivial solution branches of three-coupled Gross-Pitaevskii equations (CGPEs) as a mathematical model for rotating spin-1 Bose-Einstein condensates (BEC). Utilizing the Lyapunov-Schmidt reduction and a multilevel continuation method, the efficiency of computing ground state solutions under rapid rotation for spin-1 Rb-87 and Na-23 is demonstrated. Additionally, the impact of magnetization on CGPEs is investigated.
SCIENTIFIC REPORTS
(2021)
Article
Physics, Multidisciplinary
Anurag Anshu, Aram W. Harrow, Mehdi Soleimanifar
Summary: This study identifies the structural property of ground-state entanglement in gapped local Hamiltonians and captures it using the entanglement spread, a quantum information quantity. The main result shows that gapped ground states have limited entanglement spread across any partition of the system, exhibiting an area-law scaling.
Article
Engineering, Mechanical
Jingli Wang, Jingsong He
Summary: We investigated the robustness of rogue wave solutions in two reductions of the generalized nonlinear Schrodinger equation. The perturbed equations, which include a third-order dispersion term, have practical applications but lack exact solutions by analytical methods due to non-integrability. Numerical simulations and quantitative analysis were used to assess the robustness of rogue wave solutions. Results showed that the rogue wave solutions in both reductions are robust under the perturbation, with the solution in the second-type derivative nonlinear Schrodinger equation being more sensitive than that in the nonlinear Schrodinger equation.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Chang-En Du, Ching-Sung Liu
Summary: In this paper, a Newton-Noda iteration (NNI) method is proposed to find the ground state of nonlinear Schrodinger equations. Numerical experiments are performed to validate the performance of the method.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)