Related papers: Uncertainty relations for the Hohenberg-Kohn theor…
Density-functional theory for superfluid systems is developed in the framework of the functional renormalization group based on the effective action formalism. We introduce the effective action for the particle-number and nonlocal pairing…
The hypothesis of molecular chaos plays the central role in kinetic theory, which provides a closure leading to the Boltzmann equation for quantitative description of classic fluids. Yet how to properly extend it to active systems is still…
A generalization of the Kohn--Sham approach is derived where the correlation-energy functional depends on the one-particle density matrix of noninteracting states and on the external potential from the interacting target-state. The…
Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical…
We consider the extended Hubbard model and introduce a corresponding Heisenberg-like problem written in terms of spin operators. The derived formalism is reminiscent of Anderson's idea of the effective exchange interaction and takes into…
Despite recent advances and focus on rigorous uncertainty quantification for microscopic models of quantum many-body systems, the uncertainty on the dynamics of those systems has been under-explored. To address this, we have used…
We prove the existence of extensive many-body Hamiltonians with few-body interactions and a many-body mobility edge: all eigenstates below a nonzero energy density are localized in an exponentially small fraction of "energetically allowed…
We demonstrate the existence of different density-density functionals designed to retain selected properties of the many-body ground state in a non-interacting solution starting from the standard density functional theory ground state. We…
Collective electronic fluctuations in correlated materials give rise to various important phenomena, such as existence of the charge ordering, superconductivity, Mott insulating and magnetic phases, plasmon and magnon modes, and other…
In this paper, I give an overview of some selected results in quantum many body theory, lying at the interface between mathematical quantum statistical mechanics and condensed matter theory. In particular, I discuss some recent results on…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
The Hofstadter-Hubbard model captures the physics of strongly correlated electrons in an applied magnetic field, which is relevant to many recent experiments on Moir\'e materials. Few large-scale, numerically exact simulations exists for…
Free classical particles have well-defined momentum and position, while free quantum particles have well-defined momentum but a position fully delocalized over the sample volume. We develop a many-body formalism based on wave-packet…
The structure of nuclei far off beta-stability is investigated by nuclear many-body theory. In-medium interactions for asymmetric nuclear matter are obtained by (Dirac-) Brueckner theory thus establishing the link of nuclear forces to free…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
We investigate the density instabilities present in the infinite-U Hubbard-Holstein model both at zero and finite momenta as well as the occurrence of Cooper instabilities with a specific emphasis on the role of long-range Coulomb forces.…
One of the most powerful strategies to address properties of real many-body systems is to incorporate data obtained for models, for example, to use data of the homogeneous electron gas in order to build the Local Density Approximation for…
A detailed analysis of density-functional theory for quantum-electrodynamical model systems is provided. In particular, the quantum Rabi model, the Dicke model, and a generalization of the latter to multiple modes are considered. We prove a…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
We study a system in which the quantum dynamics of electrons depend on the particle density in their neighborhood. For any on-site repulsive interaction, we show that the exact two-body and three-body ground states are bound states. We also…