Related papers: Holonomy in the Schwarzschild-Droste Geometry
We introduce a notion of retraction between continuous maps of topological spaces and study the behavior of several numerical invariants under such retractions. These include (co)homological dimensions, the Lusternik-Schnirelmann category,…
The late-time dynamics of quantum many-body systems is organized in distinct dynamical universality classes, characterized by their conservation laws and thus by their emergent hydrodynamic transport. Here, we study transport in the…
A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…
We study charge transport of quantum critical points described by conformal field theories in 2+1 spacetime dimensions. The transport is described by an effective field theory on an asymptotically anti-de Sitter spacetime, expanded to…
Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems…
For the ``Hopf bundle'' $S^1\to S^{2n,1} \to {\mathbb H}^n$, horizontal lifts of simple closed curves are studied. Let $\gamma$ be a piecewise smooth, simple closed curve on a complete totally geodesic surface $S$ in the base space. Then…
We study magnetization transport at high temperatures in several spin ladder systems as well as in next-nearest-neighbor coupled spin chains. In the integrable ladder considered we analytically show that the transport is ballistic in…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…
This paper investigates the motion of a rotating test body in the Schwarzschild space-time. After reduction, this problem reduces to an analysis of a three-degree-of-freedom. Hamiltonian system whose desired trajectories lie on the…
Modular parallel transport is a generalization of Berry phases, applied to modular (entanglement) Hamiltonians. Here we initiate the study of modular parallel transport for disjoint field theory regions. We study modular parallel transport…
A general form of the Hamiltonian for electrons confined to a curved one-dimensional (1D) channel with spin-orbit coupling (SOC) linear in momentum is rederived and is applied to a U-shaped channel. Discretizing the derived continuous 1D…
The Hall viscosity, a non-dissipative transport coefficient analogous to Hall conductivity, is considered for quantum fluids in gapped or topological phases. The relation to mean orbital spin per particle discovered in previous work by one…
The Berry curvature and quantum metric are the imaginary part and real part, respectively, of the quantum geometric tensor which characterizes the topology of quantum states. The former is known to generate a zoo of important discoveries…
The quantum geometry plays a crucial role in the nonlinear transport of quantum materials. Here, we use the Boltzmann transport formalism to study the magnetic control of nonlinear transport induced by the quantum metric in two-dimensional…
In this paper we establish a one-to-one correspondence between $S^1$-gerbes with connections, on the one hand, and their holonomies, for simply connected manifolds, or their parallel transports, in the general case, on the other hand. This…
We study the electron transport in three terminal junctions and quantum rings looking for the classical deflection of electron trajectories in presence of intersubband scattering. We indicate that although the Aharonov-Bohm oscillations and…
We study the coherent transport in multi-terminal mesoscopic Aharonov-Bohm ring with a quantum dot embedded in an arm. Employing the Friedel sum rule for the effective single-particle levels in the quantum dot, we explain some anomalous…
The dc conductance and the Hall voltage of planar arrays of interconnected quantum wires are calculated numerically. Our systems are derived from finite patches of aperiodic graphs, with completely symmetric scatterers placed on their…
We study the dynamics of electrons in crystalline solids in the presence of inhomogeneous external electric and magnetic fields. We present a manifestly gauge-invariant operator-based approach without relying on a semiclassical wavepacket…
A class of curves with special conformal properties (conformal curves) is studied on the Reissner-Nordstr\"om spacetime. It is shown that initial data for the conformal curves can be prescribed so that the resulting congruence of curves…