相关论文: On Some Open Problems in Many-Electron Theory
We review some topics in the theory of symmetric decreasing rearrangements with a particular focus on Lieb's fundamental contributions. Topics covered include the Brascamp--Lieb--Luttinger theorem, the sharp Young and…
Density functional theory together with the Kohn-Sham scheme represent an efficient framework to recover the ground state density and energy of a many-body quantum system from an auxiliary ``non-interacting'' system (one-body with a local…
In our comment we show that some of the very difficult problems have been successfully solved. We have to focus on the resolved problems, since the authors claims: Our hope, however, is that the topics we have presented will provide…
Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one…
Quantum Electrodynamics may be formulated as a Quantum Field Theory , and also as relativistic quantum mechanics by introduction of the Feynman-Stueckelberg parameter. As stated by M. Srednicki ({\it Quantum Field Theory}, Cambridge…
Much progress has been made in the last few decades in developing the necessary mathematics for understanding the full implications of the quantum-mechanical many-body problem and why the material world appears to be as stable as it is…
The author suggests an approach based on the separation of total energy of multielectron systems into the semi-classical Coulomb part and the non-classical additional part. This approach allows on the one hand to simplify calculations and…
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…
After a brief review of the theoretical description of nuclei based on nonrelativistic many-body theory and realistic hamiltonians, these lectures focus on its application to the analysis of the electroweak response. Special emphasis is…
We study the quantum tunneling of non-relativistic electrons for two dimensional condensed matter systems. We employ the Levy-Leblond equation (which is the analogue of the Dirac equation for non-relativistic fermions) and show that the…
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer…
With the recent rise of widely successful deep learning models, there is emerging interest among professionals in various math and science communities to see and evaluate the state-of-the-art models' abilities to collaborate on finding or…
Central to our understanding of quantum many particle physics are two ideas due to Landau. The first is the notion of the electron as a well-defined quasiparticle excitation in the many body state. The second is that of the order parameter…
Electron-electron interactions and correlations form the basis of difficulties encountered in the theoretical solution of problems dealing with multi-electron systems. Accurate treatment of the electron-electron problem is likely to unravel…
The theory for electron transport in simple liquids developed by Cohen and Lekner is extended to simple liquid mixtures. The focus is on developing benchmark models for binary mixtures of hard-spheres, using the Percus-Yevick model to…
The nonrelativistic many-electron system in the forward, exchange and BCS approximation is considered. In this approximation, which is still quartic in the annihilation and creation operators, the model is explicitly solvable for arbitrary…
For more than half a century, dualities have been at the heart of modern physics. From quantum mechanics to statistical mechanics, condensed matter physics, quantum field theory and quantum gravity, dualities have proven useful in solving…
Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…
Theoretical and experimental values to date for the resistances of single molecules commonly disagree by orders of magnitude. By reformulating the transport problem using boundary conditions suitable for correlated many-electron systems, we…
We state and prove four types of Lieb-Robinson bounds valid for many-body open quantum systems with power law decaying interactions undergoing out of equilibrium dynamics. We also provide an introductory and self-contained discussion of the…