Related papers: Q-operator for the quantum NLS model
Several quantum systems have been used in the last few years to extend supersymmetry. In this paper we show all this systems fit into the picture of what we call "Number Operator Algebras".
Quantum state transfer is an important task in quantum information processing. It is known that one can engineer the couplings of a one-dimensional spin chain to achieve the goal of perfect state transfer. To leverage the value of these…
This paper is devoted to conditions defined in terms of the generalized shift operator for a rational number to be representable by certain positive generalizations of $q$-ary expansions.
We define and study the quantum equivariant $K$-theory of cotangent bundles over Grassmannians. For every tautological bundle in the $K$-theory we define its one-parametric deformation, referred to as quantum tautological bundle. We prove…
We introduce new $U_q\mathfrak{sl}_2$-invariant boundary conditions for the open XXZ spin chain. For generic values of $q$ we couple the bulk Hamiltonian to an infinite-dimensional Verma module on one or both boundaries of the spin chain,…
Integrable sl(N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of…
Q-operators for generalised eight vertex models associated to higher spin representations of the Sklyanin algebra are constructed by Baxter's first method and Fabricius's method, when the anisotropy parameter is rational.
In this paper, we give an interesting generalization of the Stancu type Baskakov-Kantorovich operators based on the q-integers and investigate their approximation properties. Also, we obtain the estimates for the rate of convergence for a…
Quantum synchronization (QS) in open many-body systems offers a promising route for controlling collective quantum dynamics, yet existing manipulation schemes often rely on dissipation engineering, which distorts limit cycles, lacks…
The paper considers some new properties of the so-called $A$-maximal numerical range of operators, denoted by $W_{\max}^A(\cdot)$, where $A$ is a positive bounded linear operator acting on a complex Hilbert space $\mathcal{H}$. Some…
We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to…
We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system,…
Inversion of operators is a fundamental concept in data processing. Inversion of linear operators is well studied, supported by established theory. When an inverse either does not exist or is not unique, generalized inverses are used. Most…
The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The…
Spinons are among the generic excitations in one-dimensional spin systems, they can be massless or massive. The quantitative description of massive spinons poses a considerable challenge in spite of various variational approaches. We show…
$V$ denotes arbitrary bounded bijection on Hilbert space $H$. We try to describe the sets of $V$-stable vectors, i.e. the set of elements $x$ of $H$ such that the sequence $\|V^N x\| (N=1,2,...)$ is bounded (we also consider some other…
We demonstrate a strategy for implementation a quantum full adder in a spin chain quantum computer. As an example, we simulate a quantum full adder in a chain containing 201 spins. Our simulations also demonstrate how one can minimize…
Averaged operators have played an important role in fixed point theory in Hilbert spaces. They emerged as a necessity to obtain solutions to fixed point problems where the underlying operator is not contractive and thus renders Banach fixed…
Using quantization in the Fock space of operators we compute the non-equilibrium steady state in an open Heisenberg XY spin 1/2 chain of finite but large size coupled to Markovian baths at its ends. Numerical and theoretical evidence is…
A model operator approach to calculations of the QED corrections to energy levels in relativistic many-electron atomic systems is developed. The model Lamb shift operator is represented by a sum of local and nonlocal potentials which are…