Search results for "Landau quantization"
showing 10 items of 23 documents
Electronic and acoustic-phonon inter-Landau-level Raman scattering in GaAs/AlxGa1−xAs multiple quantum wells
1995
We present an experimental study of inter-Landau-level excitations in undoped GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple quantum wells in high magnetic fields by means of Raman scattering. The experiments were performed in Faraday backscattering geometry with the field along the growth axis, using circularly polarized light for resonant excitation of low-index magneto-optical transitions between Landau levels. We observe two types of peaks. One of them, present in both Stokes and anti-Stokes regions at a constant Raman shift, corresponds to the electron cyclotron energy. We attribute it to electronic Raman scattering from a quasistationa…
Landau Fermi Liquid Theory and Beyond
2014
In this chapter we consider the Landau theory of the Fermi liquid that has a long history and remarkable results in describing a numerous properties of the electron liquid in ordinary metals and Fermi liquids of the \(^3\)He type. The theory is based on the assumption that elementary excitations determine the physics at low temperatures, resembling that of weakly interacting Fermi gas. These excitations behave as quasiparticles with a certain effective mass. The effective mass \(M^*\) exhibits a simple universal behavior, for it is independent of the temperature, pressure, and magnetic field strength and is a parameter of the theory. Microscopically deriving the equation determining the eff…
Multi-Resolution Analysis and Fractional Quantum Hall Effect: More Results
2009
In a previous paper we have proven that any multi-resolution analysis of $L^2(\R)$ produces, for even values of the inverse filling factor and for a square lattice, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives rise to an orthonormal set in the LLL. We have also discussed the inverse construction. In this paper we simplify the procedure, clarifying the role of the kq-representation. Moreover, we extend our previous results to the more physically relevant case of a triangular lattice and to odd values of the inverse filling factor. We also comment on other possible shapes of the lattice as well as on the extension to ot…
Multi-Resolution Analysis and Fractional Quantum Hall Effect: an Equivalence Result
2001
In this paper we prove that any multi-resolution analysis of $\Lc^2(\R)$ produces, for some values of the filling factor, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives rise to an orthonormal set in the LLL. We also give the inverse construction. Moreover, we extend this procedure to the higher Landau levels and we discuss the analogies and the differences between this procedure and the one previously proposed by J.-P. Antoine and the author.
Wavelet-like orthonormal bases for the lowest Landau level
1994
As a first step in the description of a two-dimensional electron gas in a magnetic field, such as encountered in the fractional quantum Hall effect, we discuss a general procedure for constructing an orthonormal basis for the lowest Landau level, starting from an arbitrary orthonormal basis in L2(R). We discuss in detail two relevant examples coming from wavelet analysis, the Haar and the Littlewood-Paley bases.
Direct URCA process in neutron stars with strong magnetic fields
1997
We calculate the emissivity for the direct URCA process in strongly magnetized, degenerate matter in neutron stars, under $\beta $-equilibrium. We show that, if the magnetic field is large enough for protons and electrons to be confined to the ground Landau levels, the field-free threshold condition on proton concentration no longer holds, and direct URCA reactions are open for an arbitrary proton concentration. Direct URCA process leads to an early phase of fast neutron star cooling. This circumstance allows us to constrain the initial magnetic field inside observed pulsars.
Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces
2015
In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we will find new interesting feature…
Supersymmetric associated vector coherent states and generalized Landau levels arising from two-dimensional supersymmetry
2008
We describe a method for constructing vector coherent states for quantum supersymmetric partner Hamiltonians. The method is then applied to such partner Hamiltonians arising from a generalization of the fractional quantum Hall effect. Explicit examples are worked out.
Pseudo-Bosons from Landau Levels
2010
We construct examples of pseudo-bosons in two dimensions arising from the Hamiltonian for the Landau levels. We also prove a no-go result showing that non-linear combinations of bosonic creation and annihilation operators cannot give rise to pseudo-bosons.
Tuning the Pseudospin Polarization of Graphene by a Pseudomagnetic Field.
2016
One of the intriguing characteristics of honeycomb lattices is the appearance of a pseudo-magnetic field as a result of mechanical deformation. In the case of graphene, the Landau quantization resulting from this pseudo-magnetic field has been measured using scanning tunneling microscopy. Here we show that a signature of the pseudo-magnetic field is a local sublattice symmetry breaking observable as a redistribution of the local density of states. This can be interpreted as a polarization of graphene's pseudospin due to a strain induced pseudo-magnetic field, in analogy to the alignment of a real spin in a magnetic field. We reveal this sublattice symmetry breaking by tunably straining grap…