Related papers: Significant Conditions on the Two-electron Reduced…
In this article, we present a set of hierarchy Bloch equations for the reduced density operators in either canonical or grand canonical ensembles in the occupation number representation. They provide a convenient tool for studying the…
Explicitly separable density matrices are constructed for all separable two-qubits states based on Hilbert-Schmidt (HS) decompositions. For density matrices which include only two-qubits correlations the number of HS parameters is reduced…
The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices.…
Two-Body Dirac equations of constraint dynamics provide a covariant framework to investigate the problem of highly relativistic quarks in meson bound states. This formalism eliminates automatically the problems of relative time and energy,…
Supersymmetry and Compositeness are two prevalent paradigms providing both a solution to the hierarchy problem and a motivation for a light Higgs boson state. As the latter has now been found, its dynamics can hold the key to disentangle…
We present an alternative approach to decompose non-negative tensors, called many-body approximation. Traditional decomposition methods assume low-rankness in the representation, resulting in difficulties in global optimization and target…
We introduce QRDM-NEVPT2: a hybrid quantum-classical implementation of strongly-contracted N-electron Valence State $2^{nd}$-order Perturbation Theory (SC-NEVPT2), in which the Complete Active Space Configuration Interaction (CASCI) step,…
Systematic description of a spin one-half system endowed with magnetic moment or any other two-level system (qubit) interacting with the quantized electromagnetic field is developed. This description exploits a close analogy between a…
The model of a two-electron quantum dot, confined to move in a two dimensional flat space, is revisited. Generally, it is argued that the solutions of this model obtained by solving a biconfluent Heun equation have some limitations. In…
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…
We formulate N-fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of N-fold supersymmetry, namely, almost isospectrality and weak…
A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and is presented here for U_q(sl(n)). First a…
We use the density matrix renormalization group (DMRG) to perform a detailed study of the critical properties of the two dimensional Q state Potts model, including the magnetization and energy-density profiles, bulk and surface critical…
We establish necessary and sufficient conditions for the boundedness of the relativistic Schr\"odinger operator $\mathcal{H} = \sqrt{-\Delta} + Q$ from the Sobolev space $W^{1/2}_2 (\R^n)$ to its dual $W^{-1/2}_2 (\R^n)$, for an arbitrary…
The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…
We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which…
Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents…
Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest "atoms"? In the following paper we answer these…
The partial separability of multipartite qubit density matrixes is strictly defined. We give a reduction way from N-partite qubit density matrixes to bipartite qubit density matrixes, and prove a necessary condition that a N-partite qubit…
We revisit the power spectrum analysis of the complete sample of the two degree field (2dF) QSO redshift (2QZ) survey, as a complementary test of the work by Outram et al. (2003). A power spectrum consistent with that of the 2QZ group is…