相关论文: Hartree-Fock Approximation for Inverse Many-Body P…
The one-body density matrix is derived within the Extended Thomas-Fermi approximation. This has been done starting from the Wigner-Kirkwood distribution function for a non-local single-particle potential. The links between this new approach…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
Recent developments of experimental techniques in the field of ultra-cold gases open a path to study the crossover from 'few' to 'many' on the quantum level. In this case, accurate description of inter-particle correlations is very…
We adopt the Hartree-Fock (HF) method in the proton-neutron-$\Lambda$ (p-n-$\Lambda$) formalism and the nucleon-$\Lambda$ Tamm-Dancoff Approximation (N$\Lambda$ TDA) to study the energy spectra of medium-mass hypernuclei. The formalism is…
An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient…
Inversion of the K-fold stochastic autoconvolution integral equation is an elementary nonlinear problem, yet there are no de facto methods to solve it with finite statistics. To fix this problem, we introduce a novel inverse algorithm based…
This paper focuses on inverse problems arising in studying multi-population aggregations. The goal is to reconstruct the diffusion coefficient, advection coefficient, and interaction kernels of the aggregation system, which characterize the…
The Hartree-Fock (HF) approximation has been an important tool for quantum-chemical calculations since its earliest appearance in the late 1920s, and remains the starting point of most single-reference methods in use today. Intuition…
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr\"odinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining…
Nanoscale engineered spin systems, ranging from spins on surfaces to nanographenes, provide flexible platforms to realize entangled quantum magnets from a bottom up approach. However, assessing the quantum many-body Hamiltonian realized in…
Modeling many-body quantum systems with strong interactions is one of the core challenges of modern physics. A range of methods has been developed to approach this task, each with its own idiosyncrasies, approximations, and realm of…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for…
We present unrestricted Hartree Fock method coupled with configuration interaction (CI) method (URHF-CI) suitable for the calculation of ground and excited states of large number of electrons localized by complex gate potentials in…
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
Efficient characterization of highly entangled multi-particle systems is an outstanding challenge in quantum science. Recent developments have shown that a modest number of randomized measurements suffices to learn many properties of a…
Quantum mechanical few-body systems in reduced dimensionalities can exhibit many interesting properties such as scale-invariance and universality. Analytical descriptions are often available for integer dimensionality, however, numerical…
Some calculations of parton distributions from first principles only give access to a limited range of Fourier modes of the function to reconstruct. We present a physically motivated procedure to regularize the inverse integral problem…
Quantum many-body control is among most challenging problems in quantum science, due to computational complexity of related underlying problems. We propose an efficient approach for solving a class of control problems for many-body quantum…