arXiv subjects

Benjamin Schwager

Publications and source records attributed to Benjamin Schwager.

5 recordsLinked to original sources

arXiv2026

Curvature-induced bound states in quantum wires

A classical particle under spatial constraints is strictly confined to live on a specific space manifold or path, but this assumption is incompatible with the zero-point fluctuations of a quantum particle. One way to describe quantum mechanics under constraints is the confinement potential approach (CPA). For a non-relativistic particle, the CPA maps the problem onto the solution of a Schr\"odinger-type equation in an isometrically embedded Riemannian submanifold of Euclidean space while the motion along orthogonal directions are decoupled and spatially confined. This approach respects quantum uncertainty, and one of its key results is the appearance of geometry- and metric-induced potentials that affect the stationary states and the dynamics of the particle. For particles constrained to different spaces, such as structures hosting sharp bents, vertices, wedges, conical apices, tips, or self-intersections, a formalism beyond the CPA is needed. Here, a step towards a CPA extension for irregular spaces is presented. After classifying the possible geometric irregularities concerning the CPA formalism, the presentation is focused on a sharply bent quantum wire modeled as an embedded curve with singular (but absolute integrable) curvature. For a subclass fulfilling the additional requirement that the geometric potential is a distribution of first order, a solution scheme for the confined Schr\"odinger equation is presented based on singular Sturm-Liouville theory and operator theoretic methods. The analytical considerations and numerical simulations evidence the existence of curvature-induced bound states with non-differentiable wave functions localized around the singular point, with an extension well beyond the singularity. Furthermore, a multitude of scattering states appear that may affect the transport and optical properties of the system.

quant-ph↗

arXiv2025

Signatures of real-space geometry, topology, and metric tensor in quantum transport in periodically corrugated spaces

The motion of a quantum particle constrained to a two-dimensional non-compact Riemannian manifold with non-trivial metric can be described by a flat-space Schroedinger-type equation at the cost of introducing local mass and metric and geometry-induced effective potential with no classical counterpart. For a metric tensor periodically modulated along one dimension, the formation of bands is demonstrated and transport-related quantities are derived. Using S-matrix approach, the quantum conductance along the manifold is calculated and contrasted with conventional quantum transport methods in flat spaces. The topology, e.g. whether the manifold is simply connected, compact or non-compact shows up in global, non-local properties such as the Aharonov-Bohm phase. The results vividly demonstrate emergent phenomena due to the interplay of reduced-dimensionality, particles quantum nature, geometry, and topology.

cond-mat.mes-hall↗

arXiv2024

Laser-Dressed States on Riemannian Manifolds: A Generalization of the Kramers-Henneberger Transformation

Quantum particles under geometric constraints are sensitive to the geometry and topology of the underlying space. We analytically study the laser-driven nonlinear dynamics of a quantum particle whose motion is constrained to a two-dimensional Riemannian manifold embedded in a three-dimensional hyperspace. The geometry of space results in a potential-like term that supports bound states on the manifold. In the presence of a laser field, we derive expressions for a generalized Kramers-Henneberger-type unitary transformation which is shown to be generally space- and time-dependent, and deduce a Schr\"odinger-like equation in the Kramers-Henneberger frame. Compared to a flat (geometrically trivial) space, new time-averaged coefficients of differential operators and operator-valued perturbation terms appear which determine the geometry-dependent laser-dressed states on Riemannian manifolds.

quant-ph↗

arXiv2024

Quantum Scattering of Spinless Particles in Riemannian Manifolds

Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized curvature modulations, scattering occurs from an emergent geometric potential and the metric tensor field. Analytical and full numerical simulations identify the geometric potential as the primary source for low-energy scattering, while the metric tensor field of the curved space governs high-energy diffraction. Compared to flat spaces, important differences in the validity range of perturbation approaches are found and demonstrated by full numerical simulations using combined finite element and boundary element methods. As an illustration, we consider a Gaussian-shaped dent leading to effects known as gravitational lensing. Experimentally, the considered setup is realizable based on geometrically engineered 2D materials.

quant-ph↗

arXiv2024

Wigner time delay and Hartman effect in quantum motion along deformed Riemannian manifolds

Elastic scattering of a wave can be quantified by a shift in the phase with respect to the incoming wave phase. A qualitative measure of the time during which the effect occurs is given by the Wigner time delay. The tunneling time in turn is known to saturate with increasing tunneling barrier width (Hartman effect). Here, we analyze the elastic quantum mechanical scattering in a deformed one-dimensional Riemannian manifold, particularly with respect to the Wigner time delay and conclude on the Hartman effect. It is shown that scattering due to local curvature variations imply imperfect conduction behavior indicating resonance states and leads to a Wigner time delay which, at low energies, is in variance with the classical time delay that is inferred from the arc length. At moderate and high energies, however, classical and quantum time delays coincide.

quant-ph↗