Wick order, spreadability and exchangeability for monotone commutation relations

We exhibit a Hamel basis for the concrete $*$-algebra $\mathfrak{M}_o$ associated to monotone commutation relations realised on the monotone Fock space, mainly composed by Wick ordered words of annihilators and creators. We apply such a result to investigate spreadability and exchangeability of the stochastic processes arising from such commutation relations. In particular, we show that spreadability comes from a monoidal action implementing a dissipative dynamics on the norm closure $C^*$-algebra $\mathfrak{M} = \overline{\mathfrak{M}_o}$. Moreover, we determine the structure of spreadable and exchangeable monotone stochastic processes using their correspondence with sp\-reading invariant and symmetric monotone states, respectively.Comment: Ann. Henri Poincar\`e, to appea

C∗C^*-fermi systems and detailed balance

A systematic theory of product and diagonal states is developed for tensor products of $\mathbb Z_2$-graded $*$-algebras, as well as $\mathbb Z_2$-graded $C^*$-algebras. As a preliminary step to achieve this goal, we provide the construction of a {\it fermionic $C^*$-tensor product} of $\mathbb Z_2$-graded $C^*$-algebras. Twisted duals of positive linear maps between von Neumann algebras are then studied, and applied to solve a positivity problem on the infinite Fermi lattice. Lastly, these results are used to define fermionic detailed balance (which includes the definition for the usual tensor product as a particular case) in general $C^*$-systems with gradation of type $\mathbb Z_2$, by viewing such a system as part of a compound system and making use of a diagonal state.Comment: 44 page

Limits of Some Weighted Cesaro Averages

We investigate the existence of the limit of some high order weighted Cesaro averages

From discrete to continuous monotone C*-algebras via quantum central limit theorems

We prove that all finite joint distributions of creation and annihilation operators in monotone and anti-monotone Fock spaces can be realised as Quantum Central Limit of certain operators in a C*-algebra, at least when the test functions are Riemann integrable. Namely, the approximation is given by weighted sequences of creators and annihilators in discrete monotone C∗-algebras, the weights being related to the above cited test functions

Konsep Cara Pengolahan Pangan yang Baik (CPPB) di UKM Mumtaz Bakery Gondangrejo Karanganyar

Donat adalah roti yang digoreng yang berbentuk khas seperti cincin atau seperti bola jika diisi dengan sesuatu. Donat terbuat dari tepung terigu, ragi, gula, garam, telur, margarin, susu bubuk dan air. Konsep Cara Produksi Pangan Yang Baik (CPPB) yang dibuat oleh BPOM RI Nomor HK.03.1.23.04.12.2206 tahun 2012, menjelaskan bagaimana cara memproduksi pangan agar bermutu, aman dan layak konsumsi di Industri Rumah Tangga Pangan. Mengingat pentingnya mutu dan keamanan pangan, diperlukan upaya khusus dalam menerapkannya di industri. Oleh karena itu dilakukan penelitian terhadap Konsep Cara Produksi Pangan yang Baik (CPPB) di UKM Mumtaz Bakery sebagai upaya peningkatan mutu donat. Data diperoleh melalui observasi, wawancara dan studi pustaka. Proses pembuatan donat meliputi persiapan bahan baku, pencampuran, penimbangan adonan, pembulatan adonan, pengistirahatan adonan, pembentukan adonan, penggorengan dan penirisan. Pengujian karakteristik mutu pada produk akhir dilakukan dengan menganalisis kadar air, adar abu, kadar lemak, kadar NaCl dan Angka Lempeng Total (ALT). Hasil uji kimia dan mikrobiologi donat akan dibandingan dengan SNI 01-3840-1995 yang digunakan sebagai acuan. Hasil uji kadar air yaitu 23,34% sedangkan pada SNI 01-3840-1995 yaitu maksimal 40%, hasil uji kadar abu yaitu 0,75% sedangkan pada SNI 01-3840-1995 yaitu maksimal 3%, hasil uji kadar lemak yaitu 2,98% sedangkan pada SNI 01-3840-1995 yaitu maksimal 3%, hasil uji kadar NaCl yaitu 0,81% sedangkan pada SNI 01-3840-1995 yaitu maksimal 2,5%, dan hasil uji Angka Lempeng Total (ALT) yaitu 2,84 x 103 sedangkan menurut SNI 01-3840-1995 yaitu maksimal 1 x 10

On truncated tt-free Fock spaces: spectrum of position operators and shift-invariant states

The ergodic properties of the shift on both full and $m$-truncated $t$-free $C^*$-algebras are analyzed. In particular, the shift is shown to be uniquely ergodic with respect to the fixed-point algebra. In addition, for every $m\geq 1$, the invariant states of the shift acting on the $m$-truncated $t$-free $C^*$-algebra are shown to yield a $m+1$-dimensional Choquet simplex, which collapses to a segment in the full case. Finally, the spectrum of the position operators on the $m$-truncated $t$-free Fock space is also determined.Comment: 15 page

Freedman's theorem for unitarily invariant states on the CCR algebra

The set of states on ${\rm CCR}(\ch)$, the CCR algebra of a separable Hilbert space $\ch$, is here looked at as a natural object to obtain a non-commutative version of Freedman's theorem for unitarily invariant stochastic processes. In this regard, we provide a complete description of the compact convex set of states of ${\rm CCR}(\ch)$ that are invariant under the action of all automorphisms induced in second quantization by unitaries of $\ch$. We prove that this set is a Bauer simplex, whose extreme states are either the canonical trace of the CCR algebra or Gaussian states with variance at least $1$.Comment: 22 page