Related papers: Scaling Limit of Quantum Electrodynamics with Spat…
For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and $V(x) = g/x^2$ with the coefficient $g$ in a certain range ($x$ being a space coordinate in one or more dimensions), the corresponding…
It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the…
A set of exactly solvable one-dimensional quantum mechanical potentials is described. It is defined by a finite-difference-differential equation generating in the limiting cases the Rosen-Morse, harmonic, and P\"oschl-Teller potentials.…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
We investigate further the relationship between the entanglement spectrum of a composite many-body system and the energy spectrum of a subsystem making use of concepts of canonical thermodynamics. In many important cases the entanglement…
We suggest that low-lying eigenvalues of realistic quantum many-body hamiltonians, given, as in the nuclear shell model, by large matrices, can be calculated, instead of the full diagonalization, by the diagonalization of small truncated…
We present a quantum algorithm for the calculation of scattering amplitudes of massive charged scalar particles in scalar quantum electrodynamics. Our algorithm is based on continuous-variable quantum computing architecture resulting in…
We derive the effective one-dimensional Schrodinger-Pauli equation for electrons constrained to move on a space curve. The electrons are confined using a double thin-wall quantization procedure with adiabatic separation of fast and slow…
We present the saddle-point approximation for the effective Hamiltonian of the quantum kink in two-dimensional linear sigma models to all orders in the time-derivative expansion. We show how the effective Hamiltonian can be used to obtain…
Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
For many quantum systems of interest, the classical computational cost of simulating their time evolution scales exponentially in the system size. At the same time, quantum computers have been shown to allow for simulations of some of these…
Using the operator formulation we discuss the bosonization of the two-dimensional derivative-coupling model. The fully bosonized quantum Hamiltonian is obtained by computing the composite operators as the leading terms in the Wilson short…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, one which acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian…
Quantum thermodynamics is often formulated as a theory with constrained access to operations and resources. In this manuscript, we find a closed formula for the Gaussian ergotropy, i.e. the maximum energy that can be extracted from bosonic…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…
We discuss the semiclassical limit of Quantum Reduced Loop Gravity, a recently proposed model to address the quantum dynamics of the early Universe. We apply the techniques developed in full Loop Quantum Gravity to define the semiclassical…
The diagonalization of the metrical and canonical Hamilton operators of a scalar field with an arbitrary coupling, with a curvature in N-dimensional homogeneous isotropic space is considered in this paper. The energy spectrum of the…
We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY…