相关论文: Yangians, Integrable Quantum Systems and Dorey's r…
We describe the construction of trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two irreducible representations of a quantum algebra $U_q(\G)$. Our method is a generalization of the tensor product…
Quantum correlations, crucial for the advantage and advancement of quantum science and technology, arise from the impossibility of expressing a quantum state as a tensor product over a given set of parties. In this work, a generalized…
The Jordan totient $J_k(n)$ can be defined by $J_k(n)=n^k\prod_{p\mid n}(1-p^{-k})$. In this paper, we study the average behavior of fractions $P/Q$ of two products $P$ and $Q$ of Jordan totients, which we call Jordan totient quotients. To…
Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang-Baxter equations, and second by solving a linear intertwining relation between a finite…
We propose alternative definitions of classical states and quantumness witnesses by focusing on the algebra of observables of the system. A central role will be assumed by the anticommutator of the observables, namely the Jordan product.…
Completely entangled quantum states are shown to factorize into tensor products of entangled states whose dimensions are powers of prime numbers. The entangled states of each prime-power dimension transform among themselves under a finite…
We give an explicit formula for the exchange matrix correponding to the tensor product of two copies of the natural (standard) evaluation representation of the quantum group associated to the affine Lie algebra of sl(n+1). Then we calculate…
The distribution of canonical determinants in QCD is determined by means of chiral perturbation theory. For a non-zero quark charge the canonical determinants take complex values. In the dilute pion gas approximation, we compute all moments…
We consider a tensor product $V(b)= \otimes_{i=1}^n\C^N(b_i)$ of the Yangian $Y(gl_N)$ evaluation vector representations. We consider the action of the commutative Bethe subalgebra $B^q \subset Y(gl_N)$ on a $gl_N$-weight subspace…
We determine the degree of entanglement for two indistinguishable particles based on the two-qubit tensor product structure, which is a framework for emphasizing entanglement founded on observational quantities. Our theory connects…
The properties of a prescription for the inner products of the resonance (Gamow states), scattering (Dirac kets), and bound states for 1-dimensional quantum barriers are worked out. The divergent asypmtotic behaviour of the Gamow states is…
For a large class of finite W algebras, the defining relations of a Yangian are proved to be satisfied. Therefore such finite W algebras appear as realisations of Yangians. This result is useful to determine properties of such W algebra…
Let G_1,...,G_q be algebraic varieties over a finite field k. We show that, if q >1, the finiteness of the tensor product of G_1, ...,G_q as Mackey functors. We apply this to prove the finiteness of a relative Chow group and an abelian…
The transition from unitary, reversible von Neumann-Everett quantum processes to non-unitary, irreversible processes and measurements is explored through infinite tensor products interpreted as nested, chained, or iterated Wigner's friend…
We calculate factorizing twists in evaluation representations of the quantum affine algebra U_q(\hat sl_2). From the factorizing twists we derive a representation independent expression of the R-matrices of U_q(\hat sl_2). Comparing with…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
We show that in the theory of Daniell integration iterated integrals may always be formed, and the order of integration may always be interchanged. By this means, we discuss product integrals and show that the related Fubini theorem holds…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
We present a novel matrix product representation of the Laughlin and related fractional quantum Hall wavefunctions based on a rigorous version of the correlators of a chiral quantum field theory. This representation enables the quantitative…
Yang-Baxter system related to quantum doubles is introduced and large class of both continuous and discrete symmetries of the solution manifold are determined. Strategy for solution of the system based on the symmetries is suggested and…