相关论文: A Dynamical Systems Approach to the Kadison-Singer…

We study one-dimensional systems of $N$ particles in a one-dimensional harmonic trap with an inverse power law interaction $\sim|x|^{-d}$. Within the framework of the harmonic approximation we derive, in the strong interaction limit, the…

Extending the work of Cuntz and Vershik, we develop a general notion of independence for commuting group endomorphisms. Based on this concept, we initiate the study of irreversible algebraic dynamical systems, which can be thought of as…

The weak-strong uniqueness of solutions to a broad class of cross-diffusion systems with volume filling is established. In general, the diffusion matrices are neither symmetric nor positive definite. This issue is overcome by supposing that…

Given a dynamical system $(X, \Gamma)$, the corresponding crossed product $C^*$-algebra $C(X)\rtimes_{r}\Gamma$ is called reflecting, when every intermediate $C^*$-algebra $C^*_r(\Gamma)<\mathcal{A} < C(X)\rtimes_{r}\Gamma$ is of the form…

Inclusions and extensions lie at the heart of physics and mathematics. The most relevant kind of inclusion in quantum systems is that of a von Neumann subalgebra, which is the focus of this work. We propose an object intrinsic to a given…

It is shown that a unital C*-algebra A has the Dixmier property if and only if it is weakly central and satisfies certain tracial conditions. This generalises the Haagerup-Zsido theorem for simple C*-algebras. We also study a uniform…

In the framework of the Lindblad theory for open quantum systems, expressions for the density operator, von Neumann entropy and effective temperature of the damped harmonic oscillator are obtained. The entropy for a state characterized by a…

The theme of the paper is the question of existence and basic structure of transfer operators for endomorphisms of a unital C*-algebra. We establish a complete description of non-degenerate transfer operators, characterize complete transfer…

We show that the the shift on the reduced C*--algebras of RD--groups, including the free group on infinitely many generators, and the amalgamated free product C*--algebras, enjoys the very strong ergodic property of the convergence to the…

We develop the theory of quasi--invariant (resp. strongly quasi--invariant) states under the action of a group $G$ of normal $*$--automorphisms of a $*$--algebra (or von Neumann alegbra) $\mathcal{A}$. We prove that these states are…

We study the problem of determining when the reduced twisted group C*-algebra associated with a discrete group G is simple and/or has a unique tracial state, and present new sufficient conditions for this to hold. One of our main tools is a…

A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical characterization of C*-simplicity was recently…

All self-adjoint extensions of minimal linear relation associated with the discrete symplectic system are characterized. Especially, for the scalar case on a finite discrete interval some equivalent forms and the uniqueness of the given…

A discrete analogue of the dressing method is presented and used to derive integrable nonlinear evolution equations, including two infinite families of novel continuous and discrete coupled integrable systems of equations of nonlinear…

This paper explores the intriguing connections between the invariant subspace problem, the Kadison-Singer problem, and the Borel conjecture. The Kadison-Singer problem, originally formulated in terms of pure states on C*-algebras, was later…

We generalize to the setting of Arveson's maximal subdiagonal subalgebras of finite von Neumann algebras, the Szeg\"o $L^p$-distance estimate, and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. In so doing, we…

We construct a pure state on the C*-algebra $\mathcal B(\ell_2)$ of all bounded linear operators on $\ell_2$ which is not diagonalizable, i.e., it is not of the form $\lim_u\langle T(e_k), e_k\rangle$ for any orthonormal basis $(e_k)_{k\in…

We consider converses to the density theorem for irreducible, projective, unitary group representations restricted to lattices using the dimension theory of Hilbert modules over twisted group von Neumann algebras. We show that under the…

In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of…