Stochastic Schr\"odinger Equation for a Non-Markovian Dissipative Qubit-Qutrit System

We investigate the non-Markovian quantum dynamics of a hybrid open system consisting of one qubit and one qutrit by employing a stochastic Schr\"{o}dinger equation to generate diffusive quantum trajectories. We have established an exact quantum state diffusion (QSD) equation for the dissipative qubit-qutrit system coupled to a bosonic heat bath at zero temperature. As an important application, the non-Markovian QSD equation is employed to simulate the entanglement decay and generation measured by negativity. Finally, some steady state properties of the hybrid system are also discussed.Comment: EPL in pres

A Note on State Decomposition Independent Local Invariants

We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum state. They also give rise to necessary conditions for the equivalence of quantum states under local unitary transformations

Non-Markovian Relaxation of a Three-Level System: Quantum Trajectory Approach

The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schr\"{o}dinger equation called time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.Comment: 4 pages, 2 figure

Mathematical learning attributes impacting students' performance in Sarawak

The purpose of the study is to examine the mathematics learning attributes in mathematics classroom at the secondary school level in Malaysia. Students’ responses related to mathematics learning attributes were sought. A survey was conducted using a set of questionnaire (62 items) among rural secondary school students in the state of Sarawak, Malaysia. Four hundred and fifteen responses were collected. Self-reported students’ achievement in school based assessment was used as the measurement of mathematics performance which later was collapsed into categorical variables. Logistics Regressions was used to examine the significant predictors contributed to mathematics performance. The study indicates Learning Styles and Teaching Practices are predictors of students’ higher achievement in mathematics while other learning attributes are in place. This finding concurred with other studies which stressed the importance of teaching strategies and practices in mathematics learning class. Mathematics teacher must adapt their teaching technique according to their students’ learning style preferences and beliefs on mathematics to improve learning. This study will contribute to rural school educational research. The findings in this study would expand the current body of knowledge and data about the importance of learning attributes in pedagogical context. The study provides valuable information to teachers and school administrative to create effective learning program matching the needs of the students