相关论文: On transfer operators for C*-dynamical systems
We study a system of partial differential equations defined by commuting family of differential operators with regular singularities. We construct ideally analytic solutions depending on a holomorphic parameter. We give some explicit…
We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…
We present a different way to study the C*-algebra associated with an injective endomorphism of a group G of infinite cokernel. We follow the work of Boava and Exel to construct a partial crossed product representation of that C*-algebra…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
A C*-algebra formulation of Quantum Mechanics is derived from purely operational axioms in which the primary role is played by the "transformations" that the system undergoes in the course of an "experiment". The notion of the {\em adjoint}…
By a physical system we recognize a set of propositions about a given system with their truth-values depending on the states of the system. Since every physical system can go from one state in another one, there exists a binary relation on…
We study Translation functors and Wall-Crossing functors on infinite dimensional representations of a complex semisimple Lie algebra using D-modules. This functorial machinery is then used to prove the Endomorphism-theorem and the…
Let $\mathcal{B}_d$ be the unital $C^*$-algebra generated by the elements $u_{jk}, \, 0 \le i, j \le d-1$, satisfying the relations that $[u_{j,k}]$ is a unitary operator, and let $C^*(\mathbb{F}_{d^2})$ be the full group $C^*$-algebra of…
We discuss the interplay between K-theoretical dynamics and the structure theory for certain C*-algebras arising from crossed products. For noncommutative C*-systems we present notions of minimality and topological transitivity in the…
We construct C*-dynamical systems for the dynamics of classical infinite particle systems describing harmonic oscillators interacting with arbitrarily many neighbors on lattices, as well on more general structures. Our approach allows…
An automorphism defined on an evolution algebra can provide both a finite number and an infinite number of evolution operators on it. This question is dealt with in the paper, as well as others more related to the evolution operators of…
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
For a fixed C*-algebra A, we consider all noncommutative dynamical systems that can be generated by A. More precisely, an A-dynamical system is a triple (i,B,\alpha) where $\alpha$ is a *-endomorphism of a C*-algebra B, and i: A --> B is…
In this paper we consider families of mutually commuting endomorphisms of the generalized tangent bundle. We identify natural tensorial constraints extending the notion of a generalized K\"ahler structure to endomorphisms that are not…
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…
We consider applications of transfer operators (also known as Ruelle operators) to completely positive maps (CPT) in quantum information theory. It is described a correspondence between fixed points of CPT maps and certain Markov-invariant…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…
The paper presents a criterion for a C*-algebra to be a coefficient algebra associated with a given endomorphism