相关论文: Exact solution for low energy quantum anharmonic v…
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different…
Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious…
We obtain the eigenvalues and eigenfunctions of the singular harmonic oscillator $V(x)=\alpha/(2x^2)+x^2/2$ by means of the simple and straightforward Frobenius (power-series) method. From the behaviour of the eigenfunctions at origin we…
We introduce a quantum information analysis of vibrational wave functions to understand complex vibrational spectra of molecules with strong anharmonic couplings and vibrational resonances. For this purpose, we define one- and two-modal…
An approximate scaling relation is found for the transition temperature to a charge-density-wave instability in the anharmonic electron-phonon problem, which maps a wide range of interaction strengths, anharmonicities, and phonon…
Time symmetry in quantum mechanics, where the current quantum state is determined jointly by both the past and the future, offers a more comprehensive description of physical phenomena. This symmetry facilitates both forward and backward…
We introduce various optimization schemes for highly accurate calculation of the eigenvalues and the eigenfunctions of the one-dimensional anharmonic oscillators. We present several methods of analytically fixing the nonlinear variational…
We expand iterative numerically-exact influence functional path-integral tools and present a method capable of following the nonequilibrium time evolution of subsystems coupled to multiple bosonic and fermionic reservoirs simultaneously.…
The problem of detecting specific features of microscopic dynamics in the macroscopic behavior of a many-degrees-of-freedom system is investigated by analyzing the position and momentum time series of a heavy impurity embedded in a chain of…
A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights since they are often amenable to exact methods. However, no exact solution is…
Hybrid quantum-classical algorithms have been proposed to circumvent noise limitations in quantum computers. Such algorithms delegate only a calculation of the expectation value to the quantum computer. Among them, the Variational Quantum…
It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…
We quantize the \beta-Fermi-Pasta-Ulam (FPU) model with nearest and next-nearest neighbour interactions using a number conserving approximation and a numerical exact diagonalization method. Our numerical mean field bi-phonon spectrum shows…
Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Understanding the vibrational and thermal properties of amorphous solids is one of the most discussed and long-standing issues in condensed matter physics. Recent works have made significant steps towards understanding harmonic vibrational…
The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in [1]. Specifically, we examine the system when expressed in terms of commutative variables, utilizing a…
We study a chain of infinitely many particles coupled by nonlinear springs, obeying the equations of motion [\ddot{q}_n = V'(q_{n+1}-q_n) - V'(q_n-q_{n-1})] with generic nearest-neighbour potential $V$. We show that this chain carries exact…