Related papers: Quantum current operators (III): Commutative quant…
A scenario for realization of a quantum computer is proposed consisting of spatially distributed q-bits fabricated in a host structure where nuclear spin-spin coupling is mediated by laser pulse controlled electron-nuclear transferred…
We construct a commutative ring with identity which extends the ring of characters of finite dimensional representations of sl(3). It is generated by characters with values in the group ring $Z[\tilde{W}]$ of the extended affine Weyl group…
Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open…
Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(R^n)$ with Gaussican kernel bounds, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0<\alpha<n.$ For any locally integrable function $b$, The…
Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
In recent years there has been an increasing interest on the theoretical and experimental investigation of space-time dual quantum circuits. They exhibit unique properties and have applications to diverse fields. Periodic space-time dual…
A new model for calculating the structure of bound states of interacting particles is considered. The model takes into account the noncommutativity of the space and impulse operators plus the correlation equations for the indeterminacy of…
We prove a generalization of the quantum Markovian equation for observables. In this generalized equation, we use superoperators that are fractional powers of completely dissipative superoperators. We prove that the suggested superoperators…
The construction approach proposed in the previous paper Ref. 1 allows us there and in the present paper to construct at generic deformation parameter $q$ all finite--dimensional representations of the quantum Lie superalgebra…
We construct a representation of $U_q(\widehat{sl}_2)$ at level $-1/2$ by using the bosonic Fock spaces. The irreducible modules are obtained as the kernel of a certain operator, in contrast to the construction by Feingold and Frenkel for…
We describe the generators and prove a number of relations for the construction of a planar algebra from the restricted quantum group $\bar{U}_{q}(\mathfrak{sl}_{2})$. This is a diagrammatic description of…
Previously we have shown that open groups whose generators are in arbitrary involutions may be quantized within a ghost extended framework in terms of the nilpotent BFV-BRST charge operator. Here we show that they may also be quantized…
We construct explicit generators of the K-theory and K-homology of the coordinate algebra of `functions' on quantum projective spaces. We also sketch a construction of unbounded Fredholm modules, that is to say Dirac-like operators and…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
Decoupling the chiral dynamics in the canonical approach to the WZNW model requires an extended phase space that includes left and right monodromy variables. Earlier work on the subject, which traced back the quantum qroup symmetry of the…
Form factors of composite operators in the SL(2) sector of N=4 SYM theory are studied up to two loops via the on-shell unitarity method. The non-compactness of this subsector implies the novel feature and technical challenge of an unlimited…
In this paper we construct separated variables for quantum integrable models related to the algebra $U_q(\hat{sl}_N)$. This generalizes the results by Sklyanin for $N=2,3$.
In this work we uncover the mathematical structure of the Schwinger algebra and introduce an almost unitary Schwinger operators which are derived by considering translation operators on a finite lattice. We calculate mathematical relations…