相关论文: Exact solution and perturbation theory in a genera…

A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…

We transform the time-dependent Schroedinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time-evolution of exact wave functions of generalized harmonic oscillators is…

We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different…

A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several…

The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…

The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…

We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…

We provide sufficient conditions for the approximate controllability of infinite-dimensional quantum control systems corresponding to form perturbations of the drift Hamiltonian modulated by a control function. We rely on previous results…

The Cayley-Hamilton problem of expressing functions of matrices in terms of only their eigenvalues is well-known to simplify to finding the inverse of the confluent Vandermonde matrix. Here, we give a highly compact formula for the inverse…

Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…

We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…

It is shown that for the one-dimensional anharmonic oscillator with potential $V(x)= a x^2 + b g x^3 +\ldots=\frac{1}{g^2}\,\hat{V}(gx)$, as well as for the radial oscillator $V(r)=\frac{1}{g^2}\,\hat{V}(gr)$ and for the perturbed Coulomb…

Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…

An interacting spin-fermion model is exactly solved on an open chain. In a certain representation, it is the nearest-neighbor Hubbard model in the limit of infinite $U$ (local interaction). Exact solution of its complete energy…

Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. In the variational quantum eigensolver, a decomposition of the target Hamiltonian into exactly solvable fragments can be used for…

A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. A direct unitary block encoding of the explicit time-marching operator is constructed, resulting in the intrinsic…

This work presents an exactly soluble scheme to address the problem of optimal transfer of quantum states through a set of $s$ harmonic oscillators composing a network with connected ends as a closed quantum circuit. For this purpose we…

This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case…

Functional evolution equations are used in the modeling of numerous physical processes. In this work, our main tool is perturbation theory of strongly continuous semigroups. The advantage of this technique is that one can provide functional…

Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some…