Related papers: Alternative linear structures for classical and qu…
A new version of Farkas lemma of alternative linear systems is proposed. One and the same matrix $A$ and vector $b$ have always been used in alternative linear systems. The paper shows a different way of alternative systems involving…
The problem of quantum equivalence between non-linear sigma models related by Abelian or non-Abelian T-duality is studied in perturbation theory. Using the anomalous Ward identity for Weyl symmetry we derive a relation between the Weyl…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists…
The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of…
Quantum information and computation may serve as a source of useful axioms and ideas for the quantum logic/quantum structures project of characterizing and classifying types of physical theories, including quantum mechanics and classical…
Motivated by recent proposals (Bialynicki-Birula, Mycielski; Haag, Bannier; Weinberg; Doebner, Goldin) for nonlinear quantum mechanical evolution equations for pure states some principal difficulties in the framework of usual quantum…
We study the equivalence/duality between various non-commutative gauge models at the classical and quantum level. The duality is realised by a linear Seiberg-Witten-like map. The infinitesimal form of this map is analysed in more details.
It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree. We formulate a fixed-point-theoretic framework for the…
We sketch a group-theoretical framework, based on the Heisenberg-Weyl group, encompassing both quantum and classical statistical descriptions of mechanical systems. We re-define in group-theoretical terms the kinematical arena and the…
Controllable systems relying on quantum behavior to simulate distinctly quantum models so far rely on increasingly challenging classical computing to verify their results. We develop a general protocol for confirming that an arbitrary…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
We develop a general approach to setting up and studying classes of quantum dynamical systems close to and structurally similar to systems having specified properties, in particular detailed balance. This is done in terms of transport plans…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
Linear time-translation-invariant (LTI) models offer simple, yet powerful, abstractions of complex classical dynamical systems. Quantum versions of such models have so far relied on assumptions of Markovianity or an internal state-space…
We define the notion of Weyl anomalies, measuring the violation of local scale invariance, in interacting quantum field theory on curved spacetimes in the framework of locally covariant field theory. We discuss some general properties of…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…
In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian…
We clarify the correspondence between the two approaches to quantum graphs: via quantum adjacency matrices and via quantum relations. We show how the choice of a (possibly non-tracial) weight manifests itself on the quantum relation side…