Related papers: Representability Conditions by Grassmann Integrati…

The eigenvalue PDF for some well known classes of non-Hermitian random matrices --- the complex Ginibre ensemble for example --- can be interpreted as the Boltzmann factor for one-component plasma systems in two-dimensional domains. We…

One plus two-body embedded Gaussian orthogonal ensemble of random matrices with parity [EGOE(1+2)-$\pi$] generated by a random two-body interaction (modeled by GOE in two particle spaces) in the presence of a mean-field, for spinless…

A consistent local approach to the study of interacting relativistic fermion systems with a condensation of bare particles in its ground or vacuum state, which may has a finite matter density, is developed. The attention is payed to some of…

Let H and K be Hilbert spaces and T be a coarse-graining from B(H) to B(K). Assume that density matrices D_1 and D_2 acting on H are given. In the paper the consequences of the existence of a coarse-graining S from B(K) to B(H) satisfying…

This paper studies quantum systems with a finite number of degrees of freedom in the context of non-extensive thermodynamics. A trial density matrix, obtained by heuristic methods, is proved to be the equilibrium density matrix. If the…

In the paper our aim was to study the properties of a new version of coherent states whose argument is a linear combination of two special singular square 2 x 2 matrix, having a single nonzero element, equal to 1, and two labeling complex…

The study of the entanglement properties of systems of N fermions has attracted considerable interest during the last few years. Various separability criteria for pure states of N identical fermions have been recently discussed but,…

In these notes I explain how to describe one-dimensional quantum systems that are simultaneously near to, but not exactly at, a critical point, and in a far-from-equilibrium steady state. This description uses a density matrix on scattering…

For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.

The density matrix of the 2D system of spinless electrons confined to the lowest Landau level is expressed using both basis of states parametrized by electron locations and basis of states parametrized by hole locations. In this…

A basic diagnostic of entanglement in mixed quantum states is known as the positive partial transpose (PT) criterion. Such criterion is based on the observation that the spectrum of the partially transposed density matrix of an entangled…

The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac…

We point out that the free single-fermion propagator which is used in the QFT equations for two-fermion systems, has a bosonic structure, transforms to the single-boson propagator for the Klein-Gordon equation in the nonrelativistic limit,…

We consider a quantum system A U B made up of degrees of freedom that can be partitioned into spatially disjoint regions A and B. When the full system is in a pure state in which regions A and B are entangled, the quantum mechanics of…

Fermionic reduced density matrices summarize the key observables in fermionic systems. In electronic systems, the two-particle reduced density matrix (2-RDM) is sufficient to determine the energy and most physical observables of interest.…

We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…

We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. The approach is…

A path integration formulation for the finite density and temperature problems is shown to be consistent with the thermodynamics using an 8 component ``real'' representation for the fermion fields by applying it to a free fermion system. A…

This article consists of two parts. The main objectives of Part 1 are to postulate a new principle of representation invariance (PRI), and to refine the unified field model of four interactions, derived using the principle of interaction…

We present in this report 1+1 dimensional nonlinear partial differential equation integrable through inverse scattering transform. The integrable system under consideration is a pseudo-Hermitian reduction of a matrix generalization of…