Related papers: Non-Hermitian Landau Levels
Building on the development of momentum state lattices (MSLs) over the past decade, we introduce a simple extension of this technique to higher dimensions. Based on the selective addressing of unique Bragg resonances in matter-wave systems,…
In 1998, Carl Bender challenged the perceived wisdom of quantum mechanics that the Hamiltonian operator describing any quantum mechanical system has to be Hermitian. He showed that Hamiltonians that are invariant under combined parity-time…
Configurations of pure SU(2) gauge field theory on the lattice are transformed to Landau gauge. After Fourier transformation, large momentum amplitudes are suppressed (filtered) by a variable amount, and the configurations are transformed…
We use an algebraic approach to the calculation of Landau levels for a uniform magnetic field in the symmetric gauge with a vector potential A = (1/2) (B x r), where B is assumed to be constant. The magnetron quantum number constitutes the…
Tensor-network methods enable probing dynamics of strongly interacting quantum many-body systems, including gauge theories, via Hamiltonian simulation, hence bypassing sign problems. They also have the potential to inform efficient…
Symplectic ensemble of disordered non-Hermitian Hamiltonians is studied. Starting from a model with an imaginary magnetic field, we derive a proper supermatrix $\sigma $-model. The zero-dimensional version of this model corresponds to a…
We consider 2D fermions on a plane with a perpendicular magnetic field, described by Landau levels. It is wellknown that, semiclassically, restriction to the lowest Landau levels (LLL) implies two constraints on a 4D phase space, that…
Two Non-Hermitian fermion models are proposed and analyzed by using Foldy-Wouthuysen transformations. One model has Lorentz symmetry breaking and the other has a non-Hermitian mass term. It is shown that each model has real energies in a…
Dirac fermions in graphene may experiment dispersive pseudo-Landau levels due to a homogeneous pseudomagnetic field and a position-dependent Fermi velocity induced by strain. In this paper, we study the (semi-classical) dynamics of these…
The Hamiltonian formulation for a non-Abelian gauge theory in two spatial dimensions is carried out in terms of a gauge-invariant matrix parametrization of the fields. The Jacobian for the relevant transformation of variables is given in…
Analytical calculations based on a Landau Level (LL) picture are reported for an interface (with a finite-width Quantum Well (QW)) and for a fully three-dimensional charged quantum electronic system in an external magnetic field. They lead…
In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians…
In half-filled high Landau levels, two-dimensional electron systems possess collective phases which exhibit a strongly anisotropic resistivity tensor. A weak, but as yet unknown, rotational symmetry-breaking potential native to the host…
In this article we study two-dimensional Dirac Hamiltonians with non-commutativity both in coordinates and momenta from an algebraic perspective. In order to do so, we consider the graded Lie algebra $\mathfrak{sl}(2|1)$ generated by…
We investigate the quantum-mechanical interpretation of models with non-Hermitian Hamiltonians and real spectra. After describing a general framework to reformulate such models in terms of Hermitian Hamiltonians defined on the Hilbert space…
Alternating current RLC electric circuits form an accessible and highly tunable platform simulating Hermitian as well as non-Hermitian (nH) quantum systems. We propose here a circuit realization of nH Dirac and Weyl Hamiltonians subject to…
The purpose of this paper is to formulate a kinetic theory describing transport properties of electrons in a uniform magnetic field of arbitrary magnitude. Exposing an electronic system to a constant magnetic field quenches its energy bands…
In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…
In this paper we extend the standard differential geometric theory of Hamiltonian dynamics to noncommutative spaces, beginning with symplectic forms. Derivations on the algebra are used instead of vector fields, and interior products and…
Non-Hermitian systems exhibit a fundamental spectral dichotomy absent in Hermitian physics: the eigenvalue spectrum and the eigenstate spectrum can deviate significantly in the thermodynamic limit. We explain how non-Hermitian Hamiltonians…