The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow. §1. IntroductionIn the framework of the theory of quantum stochastic calculus developed by pioneering work of Hudson and Parthasarathy [6], quantum stochastic differential equations (qsde) of the form

Evans-Hudson flows are constructed for a class of quantum dynamical semigroups with unbounded generator on UHF algebras, which appeared in [Rev. Math. Phys. 5 (3) (1993) 587-600]. It is shown that these flows are unital and covariant. Ergodicity of the flows for the semigroups associated with partial states is also discussed.

Using coordinate-free basic operators on toy Fock spaces, quantum random walks are defined following the ideas of Attal and Pautrat. Extending the result for one dimensional noise, strong convergence of quantum random walks associated with bounded structure maps to Evans-Hudson flow is proved under suitable assumptions. Starting from the bounded generator of a given uniformly continuous quantum dynamical semigroup on a von Neumann algebra, we have constructed quantum random walks which converges strongly and the strong limit gives an Evans-Hudson dilation for the semigroup.

This is a continuation of the earlier work [13] to characterize stationary unitary increment Gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with a technical assumption on the domain of the generator, unitary equivalence of the processes to the solution of Hudson-Parthasarathy equation is proved.

Background Femoral nerve block (FNB) provides effective analgesia and is a widely used technique for postoperative pain relief for orthopedic procedures on lower limbs. This study aims to compare the efficacy of ultrasonography (USG) versus peripheral nerve stimulator (PNS)-guided FNB in knee arthroscopic procedures. Methodology This randomized comparative study included two study groups with 30 participants in each group who were given FNB with either PNS or USG for knee arthroscopic procedures following spinal anesthesia. The study evaluated the number of needle repositioning, the time taken for performing the block, the efficacy of postoperative analgesia based on the duration of the block, and patient satisfaction. Results The number of needle repositioning and time taken to finish the procedure using USG was lower compared to the group using PNS (p < 0.001). The duration of the block was comparable in both groups (p = 0.584). Patients were satisfied with both techniques and responded as either very good or outstanding and chose neither as inferior (p = 0.310). Conclusions Both techniques have equal efficacy concerning the duration of the effect of the block and patient satisfaction. However, the procedural time and number of needle repositioning were significantly less in the group where USG was used for the block.