Related papers: Groups of Operators for Evolution Equations of Qua…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
In classical kinetic theory, the BBGKY hierarchy is an infinite chain of integro-differential equations that describes the full time-reversal-invariant (Liouville) system of interacting (quasi)-particles in terms of $N$-particle…
We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our projection operator based theory yields a highly efficient…
Entanglement in quantum many-body systems is the key concept for future technology and science, opening up a possibility to explore uncharted realms in an enormously large Hilbert space. The hybrid quantum-classical algorithms have been…
The particle algebras generated by the creation/annihilation operators for bosons and for fermions are shown to possess quantum invariance groups. These structures and their sub(quantum)groups are investigated.
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…
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers…
The Heisenberg evolution of a given unitary operator corresponds classically to a fixed canonical transformation that is viewed through a moving coordinate system. The operators that form the bases of the Weyl representation and its Fourier…
The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary…
In this chapter we present transformation semigroups and their applications. We begin with Klein's approach to geometry based on invariants of transformation groups. Then we present symmetry groups in chemistry and in classical mechanics.…
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…
The Stone-von Neumann Theorem is a fundamental result which unified the competing quantum mechanical models of matrix mechanics and wave mechanics. It's mechanism of proof ultimately involved the study of unitary group representations on a…
We propose solutions of the quantum Q-systems of types $B_N,C_N,D_N$ in terms of $q$-difference operators, generalizing our previous construction for the Q-system of type $A$. The difference operators are interpreted as $q$-Whittaker limits…
The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called…
The quantum dynamics of correlated fermionic or bosonic many-body systems following external excitation can be successfully studied using nonequilibrium Green functions (NEGF) or reduced density matrix methods. Approximations are introduced…
In this paper, building on a previous analysis [1] of exact diagonalization of the space-discretized evolution operator for the study of properties of non-relativistic quantum systems, we present a substantial improvement to this method. We…
Multipartite entanglement is an essential resource for quantum information tasks, but characterizing entanglement structures in continuous variable systems remains challenging, especially in multimode non-Gaussian scenarios. In this work,…
We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space…
We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…