相关论文: (p,q)-Sheaves and the Representability Problem

We recast quantum entanglement as a cohomological obstruction to reconstructing a global quantum state from locally compatible information. We address this by considering presheaf cohomologies of states and entanglement witnesses.…

An original approach is suggested to analysis of full quantum Liouville equation for single electron (quantum particle) interacting with ideal phonon gas (harmonic boson thermostat). It is shown that under the thermodynamic limit this…

By expressing the electronic wavefunction in an explicitly-correlated (Jastrow-factorised) form, a similarity-transformed effective Hamiltonian can be derived. The effective Hamiltonian is non-Hermitian and contains three-body interactions.…

The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured…

The purpose of the current paper is to introduce some new methods for studying the $p$-adic Banach spaces introduced by Emerton \cite{emerton}. We first relate these spaces to more familiar sheaf cohomology groups. As an application, we…

We study certain moduli spaces of sheaves on Enriques surfaces thereby obtaining, in every odd dimension, new examples of Calabi-Yau manifolds. We describe the geometry (canonical bundle, fundamental group, second Betti number and certain…

We introduce two families of symmetric functions generalizing the factorial Schur $P$- and $Q$- functions due to Ivanov. We call them $K$-theoretic analogues of factorial Schur $P$- and $Q$- functions. We prove various combinatorial…

We study the \'etale sheafification of algebraic K-theory, called \'etale K-theory. Our main results show that \'etale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is defined at the level of categories.…

Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…

Representative wave functions, which encode the topological properties of the spin polarized fractional quantum Hall states in the lowest Landau level, can be expressed in terms of correlation functions in conformal field theories. Until…

In modeling low-dimensional electronic nanostructures, the evaluation of the electron-electron interaction is a challenging task. Here we present an accurate and practical density-functional approach to the two-dimensional many-electron…

Inspired by earlier work on the band-gap problem in insulators, we reexamine the treatment of strongly correlated Hubbard-type models within density-functional theory. In contrast to previous studies, the density is fully parametrized by…

This is an up-to-date survey of the p-mechanical construction (see funct-an/9405002, quant-ph/9610016, math-ph/0007030, quant-ph/0212101, quant-ph/0303142), which is a consistent physical theory suitable for a simultaneous description of…

Early work extending the Kohn-Sham theory to excited states utilized an ensemble average of the Hamiltonian considered as a functional of the corresponding average density. We propose and develop an alternative that utilizes the matrix…

This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $\alpha$, and $\nu$. The time-independent Schr\"{o}dinger equation for the induced deformed harmonic oscillator is solved; explicit analytic…

Single-electron capacitance spectroscopy precisely measures the energies required to add individual electrons to a quantum dot. The spatial extent of electronic wavefunctions is probed by investigating the dependence of these energies on…

Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…

We describe the $(p,q)$ Fock--Carleson measures for weighted Fock--Sobolev spaces in terms of the objects $(s,t)$-Berezin transforms, averaging functions, and averaging sequences on the complex space $\mathbb{C}^n$. The main results show…

In the state-vector space for relativistic quantum fields a new set of basis vectors are introduced, which are taken to be eigenstates of the field operators themselves. The corresponding eigenvalues are then interpreted as representing…

This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finite-difference or finite-element formulations. The relationship of real-space approaches to linear-scaling…