Related papers: Generalized James' effective Hamiltonian method
Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describing open quantum or wave systems have a variety of potential applications in particular in optics and photonics. However, the experimental realization is…
The ability to simulate one Hamiltonian with another is an important primitive in quantum information processing. In this paper, a simulation method for arbitrary $\sigma_z \otimes \sigma_z$ interaction based on Hadamard matrices…
The well known hypervirial perturbation method (HPM)\ based on hypervirial relations and the Hellmann-Feynman theorem is suitable for the calculation of perturbation corrections of large order for the two-dimensional hydrogen-like atom in a…
The idea of adaptive perturbation theory is to divide a Hamiltonian into a solvable part and a perturbation part. The solvable part contains the non-interacting sector and the diagonal elements of Fock space from the interacting terms. The…
The generalized-$\alpha$ time-marching method provides second-order accuracy in time and controls the numerical dissipation in the high-frequency region of the discrete spectrum. This method includes a wide range of time integrators. We…
We present a diagonalization method for generic matrix valued Hamiltonians based on a formal expansion in power of $\hbar $. Considering $\hbar $ as a running parameter, a differential equation connecting two diagonalization processes for…
Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants…
A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…
We present an efficient numerical method for simulating the low-energy properties of disordered many-particle systems. The method which is based on the quantum-chemical configuration interaction approach consists in diagonalizing the…
The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress…
Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasi-periodic solutions the issue of convergence of the series is plagued of the…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys.\ Rev.\ D {\bf 94}, 104015 (2016)].…
Black hole perturbation theory beyond second order is not well understood because typically one defines the meaning of gauge invariance order by order which is ambiguous. In this series of works we therefore developed a new approach which…
An approximation method which combines the perturbation theory with the variational calculation is constructed for quantum mechanical problems. Using the anharmonic oscillator and the He atom as examples, we show that the present method…
The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
We first use the quantum method to replicate the well-known results of a single atom relaxing, whilst demonstrating the intuitive picture it provides for dissipative dynamics. By use of individual "quantum trajectories", the method allows…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…