Related papers: Density operator approach for Landau problem quant…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…
Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a…
We consider the entanglement entropy of an arbitrary subregion in a system of $N$ non-relativistic fermions in $2+1$ dimensions in Lowest Landau Level (LLL) states. Using the connection of these states to those of an auxiliary $1+1$…
The present manuscript was written in 1994 and was not published. It addresses the form that the quantum-mechanical current density must take in mesoscopic treatments of semiconductor heterostructures, in which the electron dispersion…
Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the…
An analysis of the thermodynamic behavior of quantum systems can be performed from a geometrical perspective investigating the structure of the state space. We have developed such an analysis for nonextensive thermostatistical frameworks,…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
The quantum entanglement for the two electrons in three-body atomic systems such as the helium atom, the hydrogen negative ion and the positronium negative ion are investigated by employing highly correlated Hylleraas functions to represent…
The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter…
We introduce the Markovian matrix product density operator, which is a special subclass of the matrix product density operator. We show that the von Neumann entropy of such ansatz can be computed efficiently on a classical computer. This is…
The requirement of Hermiticity of a Quantum Mechanical Hamiltonian, for the description of physical processes with real eigenvalues which has been challenged notably by Carl Bender, is examined for the case of a Fock space Hamilitonian…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
We introduce and systematically develop the theory of \emph{quantum doubly stochastic operators}, i.e. positive, trace-preserving maps on non-commutative $L_p$-spaces associated to semifinite von Neumann algebras. After establishing basic…
This paper presents a general method for producing randomly perturbed density operators subject to different sets of constraints. The perturbed density operators are a specified "distance" away from the state described by the original…
We will study rigorously the notion of mixed states and their density operators (or matrices.) We will also discuss the quantum-mechanical consequences of possible variations of Planck's constant h. This Review has been written having in…
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative…
Density-functional theory is used to study the electronic structure of quantum dots in a magnetic field. New series of magic numbers are found for the total angular momentum of electrons. The empirical formula for the plateau width is…
For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
Following recent work on the quantum Hall effect on $S^4$, we solve the Landau problem on the complex projective spaces ${\bf C}P^k$ and discuss quantum Hall states for such spaces. Unlike the case of $S^4$, a finite spatial density can be…