Application In Quantum Informatics Of The Dynamics Of Ising Model In Transverse Field

In the 1980s,the theory of quantum mechanics was introduced into information sci-ence and computational science,forming an new-developed interdisciplinary subject:quantum information science.In quantum informatics,we use the quantum state of the microscopic system as the carrier of information,and use the principles of quantum me-chanics to manipulate the microscopic system to realize the information transmission and process.In recent years,the further development of quantum information science has brought new perspectives and opportunities to information science.The unique characteristics of quantum systems,such as quantum coherence and entanglement,also makes quantum computational science show attractive prospects.On the other side,the birth and development of quantum information science,in turn,provides a new per-spective for quantum theory,enriches the content of quantum theory itself,deepens the understanding of the basic principles of quantum mechanics,offers more possibilities for verify the quantum science.The flourishing development of quantum informatics al-so opens up new possibilities for the study of complex and difficult quantum many body systems.In recent years,quantum informatics has begun to be applied to open systems,thermodynamics of quantum systems,quantum-classical transitions,etc.,to explore the correspondence and extension of the basic principles of classical physics in quantum mechanics.With the development of quantum many body system theory,the dynamical characteristics of quantum many body systems have attracted people's interest.Non-equilibrium quantum many body systems often exhibit interesting behaviors that differ from those obtained by statistical theory and thermodynamic theory using equilibrium states.Be-cause the dynamic behavior of many body quantum systems involves exponential number of quantum excited states and is in a non-thermodynamic equilibrium state,the non-equilibrium quantum statistical theory provides the main method for the dynamics of quantum many body systems.In the past few decades,such researches mainly include Quantum Quench and Quantum Thermalization,which are important topics in modern quantum physics research.The dynamics of quantum phase transition systems also provide many interesting topics.These types of research fall into two categories:dynamical quantum phase transition and dynamics of a quantum phase transition.In this paper,we use the concepts in quantum information to study the dynamic characteristics of quantum phase transitions.The role of dynamical quantum phase transitions in memory effect of the open system is studied.And how the thermodynamic properties and dimensions of the environment influence the memory of an open system are explored.Moreover,we explored the application of the dynamics of a quantum phase transitions in the extraction of random numbers.At first,we studied the role of the environment's dynamical quantum phase transi-tion in the memory effect of an open systems.The dynamics of an open quantum system is non-Markovian when memory effect is non-negligible.However,it is currently difficult to find a universal method to define and measure the memory effect of quantum open systems.By examining the memory kernel of the Nakajima-Zwanzig master e-quation,we study the memory effect in a theoretical model consisting of a spin coupled to an environment of an Ising spin chain subject to a transverse field.We find that it can be dictated by either the time correlation in the environment,or the system-environment correlation,depending on the strength of the transverse field and the state of the environment.We analyze the information loss to the environment and backflow from it,and discover that the back ofinformation flow is not always a reliable indicator for the nature of the dynamics.Following the previous part of the work,we obtained the Nakajima-Zwanzig mas-ter equation of the central spin system at finite temperature,and analyzed the effects of environment's size,temperature and magnetic field strength on memory effect of the open system.We discover that the thermal fluctuation enhances system-environment correlation in our model,leading to increased memory effect that is more prominent in larger environment and becomes dominant at higher temperatures to give rise to non-Markovian dynamics.Near the critical point of the environment,we find Fisher zeroes in the Loschmidt echo exist for finite environment sizes satisfying certain conditions,which results in exotic memory effects that can have a major impact on the system dynamics.In the last part,we discuss the application of the dynamics of quantum phase transitions in extracting random numbers.If you change the parameters of a quantum phase transition system that was originally in equilibrium,from the disordered phase to the ordered phase,different regions are randomly formed.The boundary of the regions is called Kink.We analyze the randomness of Kink formed in the transverse field Ising model,and propose a scheme for extracting random numbers.In general,the randomness of a random number extracted by measuring a quantum system contains two parts:classical randomness and quantum randomness.We define the Quantum coherence under the degenerate measurement basis and use it to evaluate the quantum randomness of random numbers in our proposal.