Transport Properties Of A Non-hermitian Aharonov-Bohm Ring

In this thesis,we study the transport properties of non-Hermitian AharonovBhom(AB)ring systems.By introducing imaginary potentials in the quantum dots embedded in the arms of the AB ring,we discuss the effects of non-Hermitian terms on the transport properties of the systems.Adjusting parameters in the quantum dots,we construct AB ring systems with either PT symmetry or anti-PT symmetry.The conductance and coherence phenomena of such systems are studied.In chapter one,we briefly introduce the development history of non-Hermitian quantum mechanics and its application in the field of open systems.We discuss PT symmetry,PT symmetric non-Hermitian quantum mechanics and some related experiments.We also introduce the concept of quantum transport,which is an important method for probing physical properties of quantum systems.We focus on systems of quantum dots and describe their transport properties.In chapter two,we study the system of an AB ring with a quantum dot embedded in each arm.Applying the method of scattering matrix,we derive the expressions of the transmission amplitude and the reflection amplitude.We notice that the transmission of the system is independent of the distribution of phase factors in the arms.Using Landauer formula,we calculate the conductance of the system and discuss how it is affected by the non-Hermitian terms and the magnetic flux threading through the ring.We notice that the asymmetric Fano profile will show up in the conductance spectrum with certain parameters.In the third chapter,we introduce anti-PT symmetry and discuss the conditions under which the AB ring system will be anti-PT symmetric.We calculate the transmission amplitude,the reflection amplitude and the conductance of the anti-PT non-Hermitian AB ring system.In the last chapter,we summarize the main content of the thesis and discuss future research directions.