Invariants for normal completely positive maps on the hyperfinite II1 factor

Goswami, Debashish; Sahu, Lingaraj

doi:10.1007/bf02829699

Search citation statements

Order By: Relevance

Paper Sections

Select...

We Prove (I)1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2011

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 17 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consider the sequence of states φ zn := ev zn •E 1 . By [17], this is a sequence of pure states on C * (T 2 θ ) converging in the weak- * topology to φ 1 := ev 1 • E 1 . Following the discussion in the beginning, consider e(0), (φ zn ⊗ 1) • 0≤s≤t (j s (P n ))e(0) .…”

Section: We Prove (I)mentioning

confidence: 99%

Quantum Brownian Motion on Non-Commutative Manifolds: Construction, Deformation and Exit Times

Das

Goswami

2011

Commun. Math. Phys.

Self Cite

View full text Add to dashboard Cite

We begin with a review and analytical construction of quantum Gaussian process (and quantum Brownian motions) in the sense of [25],[10] and others, and then formulate and study in details (with a number of interesting examples) a definition of quantum Brownian motions on those noncommutative manifolds (a la Connes) which are quantum homogeneous spaces of their quantum isometry groups in the sense of [11]. We prove that bi-invariant quantum Brownian motion can be 'deformed' in a suitable sense. Moreover, we propose a noncommutative analogue of the well-known asymptotics of the exit time of classical Brownian motion. We explicitly analyze such asymptotics for a specific example on noncommutative two-torus A θ , which seems to behave like a one-dimensional manifold, perhaps reminiscent of the fact that A θ is a noncommutative model of the (locally one-dimensional) 'leaf-space' of the Kronecker foliation.

show abstract

Section: We Prove (I)mentioning

confidence: 99%