Related papers: Intrinsic operators for the translationally-invari…
One-body multipole operators are defined as irreducible representations of rotational symmetry together with spatial-inversion and time-reversal symmetries, providing a systematic framework for classifying electronic internal degrees of…
The one-body and two-body density matrices in coordinate space and their Fourier transforms in momentum space are studied for a nucleus (a nonrelativistic, self-bound finite system). Unlike the usual procedure, suitable for infinite or…
Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing…
We present the symplectic no-core configuration interaction (SpNCCI) framework, in which the nuclear many-body problem is solved a symmetry-adapted basis that explicitly encodes approximate symmetries associated with nuclear collectivity…
Unitary transformations play a fundamental role in many-body physics, and except for special cases, they are not expressible in closed form. We present closed-form expressions for unitary transformations generated by a single fermionic…
The dynamics of many-body fermionic systems are important in problems ranging from catalytic reactions at electrochemical surfaces, to transport through nanojunctions, and offer a prime target for quantum computing applications. Here we…
We consider the two body problem with central interaction on two point homogeneous spaces from point of view of the invariant differential operators theory. The representation of the two particle Hamiltonian in terms of the radial…
The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schr\"odinger equation. The associated working equations at play in…
The past two decades have seen a revolution in ab initio calculations of nuclear properties. One key element has been the development of a rigorous effective interaction theory, applying unitary transformations to soften the nuclear…
We introduce two-body nuclear conditional probabilities that allow the definition of an intrinsic reference frame and the multipole moments of angular-momentum-$J$-conserving states. This enables the characterization of quadrupole…
The computational cost of ab initio nuclear structure calculations is rendered particularly acute by the presence of (at least) three-nucleon interactions. This feature becomes especially critical now that many-body methods aim at extending…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
A brief excursion into the three-body problem in quantum mechanics is presented for graduate students or researchers in nuclear physics. Starting from single-particle coordinates, the three-body Schr\"{o}dinger equation is systematically…
Non-perturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster…
We study the quantization of three-dimensional many-body systems in rotating coordinate frames defined implicitly by frame conditions. We carry out the elimination of orientational degrees of freedom in general, giving the Hamiltonian for…
The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. As a consequence,…
The many-body states in an extended Fermionic Molecular Dynamics approach are flexible enough to allow the description of nuclei with shell model nature as well as nuclei with cluster and halo structures. Different many-body configurations…
The kinematics of a robot manipulator are described in terms of the mapping connecting its joint space and the 6-dimensional Euclidean group of motions $SE(3)$. The associated Jacobian matrices map into its Lie algebra $\mathfrak{se}(3)$,…
We propose new dipole and quadrupole indices for interacting insulators with point group symmetries. The proposed indices are defined in terms of many-body quantum multipole operators combined with the generator of the point group symmetry.…
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…