Related papers: Laughlin wave function, Berry Phase and Quantizati…
We consider the semiclassical equations of motion of a particle when both an external electromagnetic field and the Berry gauge field in the momentum space are present. It is shown that these equations are Hamiltonian and relations between…
We consider the Anomalous Hall (AH) state induced by interactions in a three-orbital per unit-cell model. To be specific we consider a model appropriate for the Copper-Oxide lattice to highlight the necessary conditions for time-reversal…
The Lie group adiabatic evolution determined by a Lie algebra parameter dependent Hamiltonian is considered. It is demonstrated that in the case when the parameter space of the Hamiltonian is a homogeneous K\"ahler manifold its fundamental…
Within this article one finds the statement of the Klein-Gordon problem within the real Hilbert space formalism ($\mathbbm R$HS) in terms of complex wave functions, and in terms of quaternionic wave functions as well. The complex…
We show that the Fractional Quantum Hall Effect can be phenomenologically described as a special flow of a quantum incompressible Euler liquid. This flow consists of a large number of vortices of the same chirality. In this approach each…
We analize the Berry-Keating model and the Sierra and Rodr\'iguez-Laguna Hamiltonian within the polymeric quantization formalism. By using the polymer representation, we obtain for both models, the associated polymeric quantum Hamiltonians…
In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a non-relativistic spinless system. This Lagrangian is written as a difference between a function $T$, which represents the…
The edge states of a sample displaying the quantum Hall effect (QHE) can be described by a 1+1 dimensional (conformal) field theory of $d$ massless scalar fields taking values on a $d$-dimensional torus. It is known from the work of…
The evolution of a two level system with a slowly varying Hamiltonian, modeled as s spin 1/2 in a slowly varying magnetic field, and interacting with a quantum environment, modeled as a bath of harmonic oscillators is analyzed using a…
We study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed (d+2)-form on the parameter space which generalizes the…
We consider two-dimensional Hamiltonians on a torus with finite range, finite strength interactions and a unique ground state with a non-vanishing spectral gap, and a conserved local charge, as defined precisely in the text. Using the local…
We show that the introduction of a more general closed-shell operator allows one to extend Laughlin's wave function to account for the richer hierarchies (1/3, 2/5, 3/7 ...; 1/5, 2/9, 3/13, ..., etc.) found experimentally. The construction…
We investigate Laughlin's fractional quantum Hall effect wave function in the cylinder geometry of Laughlin's integer quantum Hall effect argument, at filling factor 1/3. We show that the plasma analogy leads to a periodic density, and that…
Chern-Simons-Matter Lagrangian with noncompact gauge symmetry group is considered. The theory is quantized in the holomorphic gauge with a complex gauge fixing condition. The model is discussed, in which the the gauge and matter fields are…
We consider fractional quantum Hall states built on Laughlin's original N-body wave-functions, i.e., they are of the form holomorphic times gaussian and vanish when two particles come close, with a given polynomial rate. Such states appear…
It is remarkably difficult to reconcile unitary and Vilenkin's wave function. For example, the natural conserved inner product found in quantum unimodular gravity applies to the Hartle-Hawking wave function, but fails for its Vilenkin…
A microscopic theory of current partition in fractional quantum Hall liquids, described by chiral Luttinger liquids, is developed to compute the noise correlations, using the Keldysh technique. In this Hanbury-Brown and Twiss geometry, at…
A gauge invariant reformulation of nonrelativistic fermions in background magnetic fields is used to obtain the Laughlin and Jain wave functions as exact results in Mean Field Theory (MFT). The gauge invariant framework trades the U(1)…
We show that braiding transformation is a natural approach to describe quantum entanglement, by using the unitary braiding operators to realize entanglement swapping and generate the GHZ states as well as the linear cluster states. A…
The spontaneous baryogenesis scenario explains how a baryon asymmetry can develop while baryon violating interactions are still in thermal equilibrium. However, generation of the chemical potential from the derivative coupling is dubious…