[en] In the present paper the low density limit of the nonchronological multitime correlation functions of boson number type operators is investigated. We prove that the limiting truncated nonchronological correlation functions can be computed using only a subclass of diagrams associated to noncrossing pair partitions and thus coincide with nontruncated correlation functions of suitable free number operators. The independent in the limit subalgebras are found and the limiting statistics is investigated. In particular, it is found that the cumulants of certain elements coincide in the limit with the cumulants of the Poisson distribution. An explicit representation of the limiting correlation functions and thus of the limiting algebra is constructed in a special case through suitably defined quantum white noise operators

[en] A new derivation of the quantum stochastic differential equation for the evolution operator in the low density limit is presented. We use the distribution approach and derive a new algebra for quadratic master fields in the low density limit by using the energy representation. We formulate the stochastic golden rule in the low density limit case for a system coupling with a Bose field via quadratic interaction. In particular, the vacuum expectation value of the evolution operator is computed and its exponential decay is shown. (author)

[en] We consider manipulation of the transmission coefficient for a quantum particle moving in one dimension where the shape of the potential is taken as the control. We show that the control landscape, the transmission as a functional of the potential, has no traps, i.e., any maxima correspond to full transmission. (author)

[en] Highlights: • Long distance mixed state transfer. • Unitary transformation of extended receiver as a tool for quantum state restoring. • Perfect transfer of 0-order coherence matrix. • Information encoded into higher-order coherence matrices. • Scale factors of state restoring. In this work, we study optimal transfer of quantum states via spin chains. We develop the protocol for structural restoring of multi-quantum coherence matrices of multi-qubit quantum states transferred from sender to receiver along a spin-1/2 chain. We also develop a protocol for constructing such 0-order coherence matrix that can be perfectly transferred in this process. The restoring protocol is based on the specially constructed unitary transformation applied to the state of the extended receiver. This transformation for a given length of the chain and Hamiltonian is universally optimal in the sense that ones constructed it can be applied to optimally restore any higher-order coherence matrices.