Related papers: Projector-based renormalization method (PRM) and i…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation…
Relevant metrological scenarios involve the simultaneous estimation of multiple parameters. The fundamental ingredient to achieve quantum-enhanced performances is based on the use of appropriately tailored quantum probes. However, reaching…
The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving…
The Fermi polaron refers to a system of free fermions interacting with an impurity particle by means of two-body contact forces. Motivated by the physicists' approach to this system, the present article develops a general mathematical…
We apply the well known Rayleigh-Ritz method (RRM) to the projection of a Hamiltonian operator chosen recently for the extension of the Rayleigh-Ritz variational principle to ensemble states. By means of a toy model we show that the RRM…
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…
Renormalization group procedure for effective particles in the front form of Hamiltonian dynamics is applied to an elementary quantum field theory for two species of particles mixed through a mass-like interaction term. The model…
We present a method to accelerate the numerical evaluation of spatial integrals of Feynman diagrams when expressed on the real frequency axis. This can be realized through use of a renormalized perturbation expansion with a constant but…
A variational method is discussed, based on the principle of minimal variance. The method seems to be suited for gauge interacting fermions, and the simple case of quantum electrodynamics is discussed in detail. The issue of renormalization…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We derive functional renormalization group schemes for Fermi systems which are based on the two-particle irreducible approach to the quantum many-body problem. In a first step, the cutoff is introduced in the non-interacting propagator as…
Quantum state tomography (QST) is essential for validating quantum devices but suffers from exponential scaling in system size. Neural-network quantum states, such as Restricted Boltzmann Machines (RBMs), can efficiently parameterize…
Multiple quantum (MQ) NMR methods \cite{Baum} are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian \cite{Baum} describing MQ NMR dynamics is related to the…
We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians. In particular, we include the predictive…
The ground state of a many body Hamiltonian considered in the quasiparticle representation is redefined by accounting for the quasiparticle quadrupole pairing interaction. The residual interaction of the newly defined quasiparticles is…
This chapter gives a self-contained review of the how standard open quantum system Hamiltonians can be mapped analytically onto representations in which the environments appear as one dimensional harmonic chains with nearest neighbour…
We present a theoretical method to generate a highly accurate {\em time-independent} Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which…