Quantum mechanics and quantum Hall effect on Riemann surfaces
نویسندگان
چکیده
The quantum mechanics of a system of charged particles interacting with a magnetic field on Riemann surfaces is studied. We explicitly construct the wave functions of ground states in the case of a metric proportional to the Chern form of the θ-bundle, and the wave functions of the Landau levels in the case of the the Poincaré metric. The degeneracy of the the Landau levels is obtained by using the Riemann-Roch theorem. Then we construct the Laughlin wave function on Riemann surfaces and discuss the mathematical structure hidden in the Laughlin wave function. Moreover the degeneracy of the Laughlin states is also discussed.
منابع مشابه
Coulomb gas representation of quantum Hall effect on Riemann surfaces
Using the correlation function of chiral vertex operators of the Coulomb gas model, we find the Laughlin wavefunctions of quantum Hall effect, with filling factor ν = 1/m, on Riemann sufaces with Poincare metric. The same is done for quasihole wavefunctions. We also discuss their plasma analogy. e-mail:[email protected] e-mail:[email protected]
متن کاملCoulomb gas representation of qunatum Hall effect on Riemann surfaces
Using the correlation function of chiral vertex operators of the Coulomb gas model, we find the Laughlin wavefunctions of quantum Hall effect, with filling factor ν = 1/m, on Riemann sufaces with Poincare metric. The same is done for quasihole wavefunctions. We also discuss their plasma analogy. e-mail:[email protected] e-mail:[email protected]
متن کاملبررسی اثر صحیح کوانتومی هال در سیستمهای دارای ناخالصی به روش تبدیل پیمانه‌ای در حضور نقطه‌های کوانتومی
In this paper we study the integer quantum Hall effect (IQHE) on the systems with different types of impurities in delta and gaussian forms. The Landau energy levels in the presence of impurity split in two different levels,the extended and localized levels, emerging then the Hall step. Finally, we add a specified form of a quantum dot potential to a system with impurity, and observed that incr...
متن کاملhep-th/9706177 Strings and matrix models on genus g Riemann Surfaces
Comment: This is a summary of old work on connections between discrete area preserving diffeomorphisms, reduced SU(N) Yang-Mills, strings, and the quantum Hall effect on a Riemann surface of genus g. It is submitted to the archives due to the interest expressed by colleagues who are currently working on matrix models, and who could not have access to the proceedings in which the article was pub...
متن کاملSupersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces
Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators H(±) is chosen antilinear. Secondly, both these components of a super-Hamiltonian H are defined along certain topologically nontrivial complex curves r(±)(x) which spread over several Riemann sheets of the wave function. The non-uniqueness of our choice of the ma...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1993