Deformed C λ-Extended Heisenberg Algebra in Noncommutative Phase-Space

We construct a deformed C _λ-extended Heisenberg algebra in two-dimensional space using noncommuting coordinates which close an algebra depends on statistical parameter characterizing exotic particles. The obtained symmetry is nothing but an exotic particles algebra interpolating between bosonic and deformed fermionic algebras. PACS numbers: 03.65.Fd, 02.40.Gh, 05.30.Pr     

Isometric Actions of Heisenberg Groups on Compact Lorentz Manifolds

We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions – those for which the dimension of the Heisenberg group is one less than the dimension of the manifold. The main result is a classification of codimension-one actions, under the assumption they are real-analytic.     

Stopping times for quantum Markov chains

In the paper we introduce stopping times for quantum Markov states. We study algebras and maps corresponding to stopping times, give a condition of strong Markov property and give classification of projections for the property of accessibility. Our main result is a new recurrence criterium in terms of stopping times (Theorem 1 and Corollary 2). As an application of the criterium we study how, in Section 6, the quantum Markov chain associated with the one-dimensional Heisenberg (usually non-Markovian) process, obtained from this quantum Markov chain by restriction to a diagonal subalgebra, is such that all its states are recurrent. We were not able to obtain this result from the known recurrence criteria of classical probability.Supported by GNAFA-CNR, Bando n. 211.01.25.     

Explicit Runge-Kutta-like schemes to solve certain quantum operator equations of motion

We propose a kind of explicit sympletic Runge-Kutta-like scheme to solve operator equations of motion in quantum mechanics and in a quantum scalar field theory.     

On the local and asymptotic behavior of Brownian motion on simply connected nilpotent Lie groups

The aim of this paper is to study the local and asymptotic behavior of Brownian motion on simply connected nilpotent Lie groups. We carry over a qualitative version of the Erdös-Rényi law of large numbers for Brownian motion to simply connected step 2-nilpotent Lie groups. The method applied gives rise to a proof for qualitative results concerning the modulus of continuity of Brownian motion on simply connected step 3-resp. step 2-nilpotent Lie groups without using the Ventsel-Freidlin theory as in Baldi.     

Magnetic single-component molecular conductors exhibiting strong π-d interactions

Single-component molecular conductors [M(tmdt)₂] (tmdt = trimethylenetetrathiafulvalenedithiolate; M = Ni, Au, Pt, Cu), exhibit a variety of electromagnetic properties, which originate from the differences of the metal’s d-orbitals role in the band structure formation. The [Au(tmdt)₂] crystal undergoes an antiferromagnetic transition at 110 K, while maintaining a metallic state at lower temperatures. The Au analog has a high magnetic transition temperature as compared to traditional magnetic molecular conductors due to the strong three-dimensional (3-D) structure and the contribution of the metal d-orbitals. The single-component molecular conductor, [Cu(tmdt)₂], with π- and d-like frontier orbitals is isostructural with other metallic [M(tmdt)₂] systems (M = Ni, Pt, Au). The Cu(tmdt)₂ molecule is planar, which strikingly contrasts the tetrahedral coordination of Cu(dmdt)₂ (dmdt = dimethyltetrathiafulvalenedithiolate) with similarly extended TTF type ligands. Interestingly, unlike other [M(tmdt)₂] with metallic behavior, [Cu(tmdt)₂] shows semiconducting behavior at room temperature (σ(RT) = ∼7 S cm⁻¹). The RT conductivity increased linearly with increased pressure to 110 S cm⁻¹ at 15 kbar despite the compressed pellet sample. The magnetic susceptibility indicates one-dimensional (1-D) Heisenberg behavior with J = 117 cm⁻¹ and shows antiferromagnetic ordering at 13 K. The [Cu(tmdt)₂] is a new multi-frontier π-d system, which introduces a d(σ)-type frontier orbital around the Fermi level of the π-like metal bands.     

Random attractors for a stochastic hydrodynamical equation in Heisenberg paramagnet

This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in˙ H 1 .     

A restriction theorem for the quaternion Heisenberg group

We prove that the restriction operator for the sublaplacian on the quaternion Heisenberg group is bounded from L p to L p if 1 ≤ p ≤ 4 3 . This is different from the Heisenberg group, on which the restriction operator is not bounded from L p to L p unless p = 1.