相关论文: A novel analytic spin chain model with fractional …
A systematic study of fractional revival at two sites in $XX$ quantum spin chains is presented and analytic models with this phenomenon are exhibited. The generic models have two essential parameters and a revival time that does not depend…
Analytic mass-spring chains with dispersionless pulse transfer and fractional revival are presented. These are obtained using the properties of the para-Racah polynomials. This provides classical analogs of the quantum spin chains that…
Analogs of Krawtchouk polynomials defined on a bi-lattice are introduced. They are shown to provide a (novel) spin chain with perfect transfer. Their characterization is given as well as their connection to the quadratic Hahn algebra
A new solvable two-dimensional spin lattice model defined on a regular grid of triangular shape is proposed. The hopping amplitudes between sites are related to recurrence coefficients of certain bivariate dual-Hahn polynomials. For a…
The occurrence of fractional revival in quantum spin chains is examined. Analytic models where this phenomenon can be exhibited in exact solutions are provided. It is explained that spin chains with fractional revival can be obtained by…
New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed…
New exactly solvable one-dimensional XX spin chain models that exhibit perfect state transfer are defined. These models have inhomogeneous couplings and magnetic fields determined from the three-term recurrence relations satisfied by the…
It is shown how choices based on the $q$-Racah polynomials for the masses and spring constants along a chain give new systems that exactly allow dispersionless end-to-end transmission of a pulse as well as periodic splitting of the initial…
Connections between the 1-excitation dynamics of spin lattices and quantum walks on graphs will be surveyed. Attention will be paid to perfect state transfer (PST) and fractional revival (FR) as well as to the role played by orthogonal…
Certain non-uniformly coupled spin chains can exhibit perfect transfer of quantum states from end to end. Motivated by recent experimental implementations, we extend the simplest such chain to next-to-nearest neighbour (NNN) couplings. It…
Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the characteristic vectors of the two vertices. This phenomenon is…
In [J. Phys. A: Math. Theor. 45 (2012)], while looking for spin chains that admit perfect state transfer, Vinet and Zhedanov found an apparently new sequence of orthogonal polynomials, that they called para-Krawtchouk polynomials, defined…
We introduce an analytical $XX$ spin chain with asymmetrical transport properties. It has an even number $N+1$ of sites labeled by $n=0,\cdots N$. It does not exhibit perfect state transfer (PST) from end-to-end but rather from the first…
We study the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. Some years ago it was discovered that when the spin chain data (the nearest neighbour interaction strengths…
New bispectral orthogonal polynomials are obtained from an unconventional truncation of the Askey-Wilson polynomials. In the limit $q \to 1$, they reduce to the para-Racah polynomials which are orthogonal with respect to a quadratic…
We find all the $XX$ spin chains with perfect state transfer (PST) that are connected with the dual -1 Hahn polynomials $R_n(x; \alpha,\beta,N)$. For $N$ odd we recover a model that had already been identified while for $N$ even, we obtain…
The production of quantum states required for use in quantum protocols & technologies is studied by developing the tools to re-engineer a perfect state transfer spin chain so that a separable input excitation is output over multiple sites.…
An extension with next-to-nearest neighbour interactions of the simplest XX spin chain with perfect state transfer (PST) is presented. The conditions for PST and entanglement generation (balanced fractional revival) can be obtained exactly…
Fractional revival, known as a quantum transport phenomenon, is essential for entanglement generation in quantum spin networks. The concept of fractional revival is a generalization of perfect state transfer and periodicity on graphs. In…
It is shown how to systematically construct the $XX$ quantum spin chains with nearest-neighbor interactions that allow perfect state transfer (PST). Sets of orthogonal polynomials (OPs) are in correspondence with such systems. The key…