Related papers: Second Quantized Reduced Bloch Equations and the E…
Starting from Bloch equation for a canonical ensemble, we deduce a set of hierarchy equations for the reduced statistical density operator for an identical many-body system with two-body interaction. They provide a law according to which…
We examine some properties of the non-normalized (or canonical) density matrix in the coherent states representation, by two equivalent ways. On the one hand by its definition, and on the other hand as a solution to Bloch's canonical…
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…
We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system+bath) is…
Motivated by recent quantum gas microscope experiments for fermions in optical lattices, we present proof of principle calculations showing that it is possible to obtain the complete information about the quantum state on a small subsystem…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
We provide a brief overview of approaches for calculating the density of states of quantum systems and random matrix Hamiltonians using the tools of free probability theory. For a given Hamiltonian of a quantum system or a generic random…
The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly-occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the…
We introduce an accurate non-Hermitian Schr\"odinger-type approximation of Bloch optical equations for two-level systems. This approximation provides a complete description of the excitation, relaxation and decoherence dynamics in both weak…
We obtain analytical lower bounds on the concurrence of bipartite quantum systems in arbitrary dimensions related to the violation of separability conditions based on local uncertainty relations and on the Bloch representation of density…
We review White's density matrix renormalisation group method, an increasingly popular method for the solution of low dimensional quantum Hamiltonians. We describe some applications to frustrated spin systems, quantum critical phenomena,…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
Recently, it has been shown how to perform the quantum hamiltonian reduction in the case of general $sl(2)$ embeddings into Lie (super)algebras, and in the case of general $osp(1|2)$ embeddings into Lie superalgebras. In another development…
In this paper we consider density matrices operator related to non-Hermitian Hamiltonians. In particular, we analyse two natural extensions of what is usually called a density matrix operator (DM), of pure states and of the entropy…
We introduce a framework suitable for describing pattern recognition task using the mathematical language of density matrices. In particular, we provide a one-to-one correspondence between patterns and pure density operators. This…
We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
It is shown how the canonical symmetry is used to look for the hierarchy of the Hamiltonian operators relevant to the system under consideration. It appears that only the invariance condition can be used to solve the problem.
For a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is…
We introduce a non-Hermitian approximation of Bloch optical equations. This approximation provides a complete description of the excitation, relaxation and decoherence dynamics of ensembles of coupled quantum systems in weak laser fields,…