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Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
We investigate compressibility of the dimension of positive semidefinite matrices while approximately preserving their pairwise inner products. This can either be regarded as compression of positive semidefinite factorizations of…
Recently obtained results on linear energy bounds are generalized to arbitrary spin quantum numbers and coupling schemes. Thereby the class of so-called independent magnon states, for which the relative ground-state property can be…
Methods for calculating the transmission coefficient are proposed, all of which arise from improved non-reflecting WKB boundary conditions at the edge of the computational domain in 1-dimensional geometries. In the first, the…
Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…
As is well-known, for plasmas of high density and modest temperature, the classical kinetic theory needs to be extended. Such extensions can be based on the Schr\"odinger Hamiltonian, applying a Wigner transform of the density matrix, in…
We exploit the connection between quantum dot Dirac operators and $\overline\partial$-Robin Laplacians. First, we find a graphical relation between their smallest positive eigenvalues, which allows us to deduce a recipe for translating…
The problem of Bloch electrons in two dimensions subject to magnetic and intense electric fields is investigated, the quantum Hall conductance is calculated beyond the linear response approximation. Magnetic translations, electric evolution…
A derivative nonlinear Schrodinger model is shown to support localized N-body bound states for several ranges (called bands) of the coupling constant eta. The ranges of eta within each band can be completely determined using number…
This work applies a reduced basis method to study the continuum physics of a finite quantum system -- either few or many-body. Specifically, I develop reduced-order models, or emulators, for the underlying inhomogeneous Schr\"{o}dinger…
We derive general lower energy bounds for the ground state energy of any translationally invariant quantum lattice Hamiltonian. The bounds are given by the ground state energy of renormalized Hamiltonians on finite clusters.
We construct a W^*-dynamical system describing the dynamics of a class of anharmonic quantum oscillator lattice systems in the thermodynamic limit. Our approach is based on recently proved Lieb-Robinson bounds for such systems on finite…
We study a quantum thermal engine model for which the heat transfer law is determined by Einstein's theory of radiation. The working substance of the quantum engine is assumed to be a two-level quantum systems of which the constituent…
We analyze the Schr\"{o}dinger dynamics and the Schr\"{o}dinger function (or the so-called wavefunction) in the following four aspects. (1) The Schr\"{o}dinger equation is reconstructed from scratch in the real field only, without referring…
A model Hamiltonian dynamical system has been derived to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger equation on the torus. Here, we explore the framework for exploring a canonical ensemble formulation of the…
We investigate the effect of deterministic analog control errors in the time-dependent Hamiltonian on isolated quantum dynamics. Deterministic analog control errors are formulated as time-dependent operators in the Schrodinger equation. We…
For a quantum many-body problem, effective Hamiltonians that give exact eigenvalues in reduced model space usually have different expressions, diagrams and evaluation rules from effective transition operators that give exact transition…
On the basis of analytic solutions of Schrodinger and Pauli equations for a uniform magnetic field and a single attractive $\delta({\bf r})$-potential the equations for the bound one-active electron states are discussed. It is vary…