相关论文: q-combinatorics and quantum integrability
There being no precise definition of the quantum integrability, the separability of variables can serve as its practical substitute. For any quantum integrable model generated by the Yangian Y[sl(3)] the canonical coordinates and the…
Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Both the difference systems in bond variables and the…
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 $N=2,3$.
Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…
Basic concepts of quantum integrable systems (QIS) are presented stressing on the unifying structures underlying such diverse models. Variety of ultralocal and nonultralocal models is shown to be described by a few basic relations defining…
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar…
We consider the simplest classical integrable model corresponding to a non-hyperelliptic spectral curve. We show that a certain complicated integral occurs when computing the average of observables in this model. This integral does not…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
Various physical constraints limit the number of qubits that can be implemented in a single quantum processor, and thus it is necessary to connect multiple quantum processors via quantum interconnects. While several compiler implementations…
We propose an approach to quantum cosmology of integrable models. To analyze the models with two dynamical variables, we introduce equivalent Hamiltonians in reduced phase spaces, which are obtained with the aid of the Faddeev--Jackiw…
This review provides a gentle introduction to one-way quantum computing in distributed architectures. One-way quantum computation shows significant promise as a computational model for distributed systems, particularly those architectures…
The computational power of a quantum computer is limited by the number of qubits available for information processing. Increasing this number within a single device is difficult; it is widely accepted that distributed modular architectures…
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
Cubic invariants for two-dimensional degenerate Hamiltonian systems are considered by using variables of separation of the associated St\"ackel problems with quadratic integrals of motion. For the superintegrable St\"ackel systems the cubic…
In [1] was considered the superintegrable system which describes the magnetic dipole with spin 1/2 (neutron) in the field of linear current. Here we present its generalization for any spin which preserves superintegrability. The dynamical…
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…
It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In [PRL,93 (2004) 254102] statistical properties of a certain…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
For some involutive maps $\Phi:{\mathbb C}P^1 \times {\mathbb C}P^1 \to {\mathbb C}P^1 \times {\mathbb C}P^1$ we find all invariants with separated variables. We investigate a link of the maps and their invariants with separated variables…