Related papers: Discrete Quantum Geometry and Intrinsic Spin Hall …
Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads…
In this paper we present an experiment where we measured the quantum coherence of a quasiparticle injected at a well-defined energy above the Fermi sea into the edge states of the integer quantum Hall regime. Electrons are introduced in an…
Recent reports of spin-orbit coupling enhancement in chemically modified graphene have opened doors to studies of the spin Hall effect with massless chiral fermions. Here, we theoretically investigate the interaction and impurity density…
Using the density matrix renormalization group (DMRG) method, we study the quantum coherence in one-dimensional disordered Fermi systems. We consider in detail spinless fermions on a ring, and compare the influence of several kinds of…
A semiclassical theory for magnetotrasport in a quantum Hall system near filling factor $\nu = 1/2 $ based on the Composite Fermions physical picture is used to analyze the effect of local flattening of the Composite Fermion Fermi surface…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
The quantum Hall effect in the three-dimensional anisotropic tight-binding electrons is investigated in the field-induced spin density wave phases with a magnetic field tilted to any direction. The Hall conductivity, $\sigma_{xy}$ and…
In loop quantum gravity the discrete nature of quantum geometry acts as a natural regulator for matter theories. Studies of quantum field theory in quantum space-times in spherical symmetry in the canonical approach have shown that the main…
We outline a strategy to compute deeply inelastic scattering structure functions using a hybrid quantum computer. Our approach takes advantage of the representation of the fermion determinant in the QCD path integral as a quantum mechanical…
We study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We…
A solvable 2-dimensional conformally invariant midi-superspace model for black holes is obtained by imposing spherical symmetry in 4-dimensional conformally invariant Einstein gravity. The Wheeler-DeWitt equation for the theory is solved…
The subtle interplay between quantum statistics and interactions is at the origin of many intriguing quantum phenomena connected to superfluidity and quantum magnetism. The controlled setting of ultracold quantum gases is well suited to…
The quantum Hall effect is investigated in a high-mobility two-dimensional electron gas on the surface of a cylinder. The novel topology leads to a spatially varying filling factor along the current path. The resulting inhomogeneous…
In this paper we study theoretically how the local geometry of the Fermi surface (FS) of a layered conductor can affect quantum oscillations in the thermodynamic observables. We introduce a concrete model of the FS of a layered conductor.…
The quantum Hall ferromagnet at filling fraction $\nu = 1$ has some unusual properties due to the remarkable identity between the topological density of a spin distortion and the associated electrical charge density. We investigate the…
We apply the method of conical singularities to calculate the tree-level entropy and its one-loop quantum corrections for a charged Kerr black hole. The Euclidean geometry for the Kerr-Newman metric is considered. We show that for an…
This thesis explores the application of differential geometric and general relativistic techniques to deepen our understanding of quantum mechanical systems. We focus on three systems, employing these mathematical frameworks to uncover…
We investigate the intrinsic anomalous thermal Hall effect as an effective probe of the order parameters of non-unitary pairing states of the putative spin-triplet superconductor UTe$_2$. We consider all symmetry-allowed non-unitary states…
Layered singlet paired superconductors with disorder and broken time reversal symmetry are studied. The phase diagram demonstrates charge-spin separation in transport. In terms of the average intergrain transmission and the interlayer…
In a previous paper, we showed how certain orientations of the edges of a graph G embedded in a closed oriented surface S can be understood as discrete spin structures on S. We then used this correspondence to give a geometric proof of the…