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The two-dimensional CGHS model provides an interesting toy-model for the study of black hole evaporation. For this model, a quantum effective action, which incorporates Hawking radiation and backreaction, can be explicitly constructed. In…
The two dimensional substructure of general relativity and gravity, and the two dimensional geometry of quantum effect by black hole are disclosed. Then the canonical quantization of the two dimensional theory of gravity is performed. It is…
In preceding papers a Landauer-Buttiker type representation of bulk current transport has been successfully used for the numerical simulation of the magneto transport of 2-dimensional electron systems in the high magnetic field regime. In…
In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed…
The Quantum Hall Effect for free electrons in external periodic field is discussed without using the linear response approximation. We find that the Hall conductivity is related in a simple way to Floquet energies (associated to the…
We study first order fluctuations of a relativistic membrane in the curved background of a black hole. The zeroth-order solution corresponds to a spherical membrane tightly covering the event horizon. We obtain a massive Klein-Gordon…
We study Faraday rotation in the quantum relativistic limit. Starting from the photon self-energy in the presence of a constant magnetic field the rotation of the polarization vector of a plane electromagnetic wave which travel along the…
We measured the magnetoresistance of bilayer quantum Hall (QH) effects at the fractional filling factor $\nu =2/3$ by changing the total electron density and the density difference between two layers. Three different QH states were…
We investigate the gravitational impulse by using the generalized formulation of the quantum Boltzmann equation (QBE), wherein the initial states are taken as wave packets rather than plane waves. The QBE operates within an open quantum…
Generalized $1+0$-dimensional Liouvillean dynamics describing deformations of the Sachdev-Ye-Kitaev (SYK) model, as well as the various $1+1$-dimensional dilaton and Horava-Lifshitz gravity theories, can all be mapped onto single-particle…
We show a new property of sonic black holes. After deriving the metric of a sonic black hole from the Schrodinger equation and quantizing the perturbation fields near the sonic event horizon, we show particles of Hawking radiation can act…
In this thesis, I will present studies on the collective modes of the fractional quantum Hall states, which are bulk neutral excitations reflecting the incompressibility that defines the topological nature of these states. It was first…
We theoretically consider disorder and temperature effects on the integer quantum Hall effect (IQHE) using a variety of distinct and complementary analytical and numerical techniques. In particular, we address simple, physical, and…
Quantum Hall effect wavefunctions corresponding to the filling factors 1/2p+1, 2/2p+1,..., 2p/2p+1, 1, are shown to form a basis of irreducible cyclic representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus, the wavefunctions…
A fractional quantum Hall liquid with multiple edges is considered. The computation of transport quantities such as current, noise and noise cross correlations in such multiple edge samples requires the implementation of so called Klein…
We present in this paper experimental results on the transport hysteresis in electron double quantum well structures. Exploring the measurement technique of fixing the magnetic field and sweeping a front gate voltage (Vg), we are able to…
We determine the wave functions for arbitrarily polarized quantum Hall states by employing the doublet model which has been proposed recently to describe arbitrarily polarized quantum Hall states. Our findings recover the well known fully…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
We numerically study the interplay of band structure, topological invariant and disorder effect in two-dimensional electron system of graphene in a magnetic field. Two \emph{distinct} quantum Hall effect (QHE) regimes exist in the energy…
We show the inconsistency of the argument linking the integral quantum Hall effect to gauge invariance. The inconsistency mainly consists of equating gauge and real vector potential transformations for a particular system geometry. Correct…