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Daniel Kaplan

Publications and source records attributed to Daniel Kaplan.

45 records · Page 3Linked to original sources
arXiv2022

Multiplicative preprojective algebras are 2-Calabi-Yau

We prove that multiplicative preprojective algebras, defined by Crawley-Boevey and Shaw, are 2-Calabi-Yau algebras, in the case of quivers containing unoriented cycles. If the quiver is not itself a cycle, we show that the center is trivial, and hence the Calabi-Yau structure is unique. If the quiver is a cycle, we show that the algebra is a non-commutative crepant resolution of its center, the ring of functions on the corresponding multiplicative quiver variety with a type A surface singularity. We also prove that the dg versions of these algebras (arising as certain Fukaya categories) are formal. We conjecture that the same properties hold for all non-Dynkin quivers, with respect to any extended Dynkin subquiver (note that the cycle is the type A case). Finally, we prove that multiplicative quiver varieties-for all quivers-are formally locally isomorphic to ordinary quiver varieties. In particular, they are all symplectic singularities (which implies they are normal and have rational Gorenstein singularities). This includes character varieties of Riemann surfaces with punctures and monodromy conditions. We deduce this from a more general statement about 2-Calabi--Yau algebras (following Bocklandt, Galluzzi, and Vaccarino).

math.RA↗
arXiv2021

Mixed axial-gravitational anomaly from emergent curved spacetime in nonlinear charge transport

In 3+1 dimensional spacetime, two vector gauge anomalies are known: The chiral anomaly and the mixed axial-gravitational anomaly. While the former is well documented and tied to the presence of a magnetic field, the latter instead requires a nonzero spacetime curvature, which has made it rather difficult to study. In this work, we show that a quantum anomaly arises in the second-order electrical response for zero magnetic field, which creates a dc-current that can be either longitudinal or transverse to electric field. Consequently, the continuity equation for the chiral current is not conserved at order $τ^{-1}$, where $τ$ is the quasiparticle relaxation time. We can identify the anomaly as a mixed axial-gravitational one, and predict a material in which the anomaly-induced current can be isolated in a purely electrical measurement. Our findings indicate that charge transport generically derives from quasiparticle motion in an emergent curved spacetime, with potentially far-reaching consequences for all types of response functions.

cond-mat.mes-hall↗
arXiv2020

Nonvanishing sub-gap photocurrent as a probe of lifetime effects

For semiconductors and insulators, it is commonly believed that in-gap transitions into non-localized states are smoothly suppressed in the clean limit, i.e. at zero temperature their contribution vanishes due to the unavailability of states. We present a novel type of sub-gap response which shows that this intuition does not generalize beyond linear response. Namely, we find that the dc current due to the bulk photovoltaic effect can be finite and mostly temperature independent in an allowed window of sub-gap transitions. We expect that a moderate range of excitation energies lies between the bulk energy gap and the mobility edge where this effect is observable. Using a simplified relaxation time model for the band broadening, we find the sub-gap dc-current to be temperature-independent for non-interacting systems but temperature-dependent for strongly interacting systems. Thus, the sub-gap response may be used to distinguish whether a state is single-particle localized or many-body localized.

cond-mat.mes-hall↗
arXiv2020

Consequences of Time-reversal-symmetry Breaking in the Light-Matter Interaction: Berry Curvature, Quantum Metric and Diabatic Motion

Nonlinear optical response is well studied in the context of semiconductors and has gained a renaissance in studies of topological materials in the recent decade. So far it mainly deals with non-magnetic materials and it is believed to root in the Berry curvature of the material band structure. In this work, we revisit the general formalism for the second-order optical response and focus on the consequences of the time-reversal-symmetry ($\mathcal{T}$) breaking, by a diagrammatic approach. We have identified three physical mechanisms to generate a dc photocurrent, i.e. the Berry curvature, the quantum metric, and the diabatic motion. All three effects can be understood intuitively from the anomalous acceleration. The first two terms are respectively the antisymmetric and symmetric parts of the quantum geometric tensor. The last term is due to the dynamical antilocalization that appears from the phase accumulation between time-reversed fermion loops. Additionally, we derive the semiclassical conductivity that includes both intra- and interband effects. We find that $\mathcal{T}$-breaking can lead to a greatly enhanced non-linear anomalous Hall effect that is beyond the contribution by the Berry curvature dipole.

cond-mat.mes-hall↗
arXiv2020

Frobenius Degenerations of Preprojective Algebras

In this paper, we study a preprojective algebra for quivers decorated with $k$-algebras and bimodules, which generalizes work of Gabriel for ordinary quivers, work of Dlab and Ringel for $k$-species, and recent work of de Thanhoffer de Völcsey and Presotto, which has recently appeared from a different perspective in work of Külshammer. As for undecorated quivers, we show that its moduli space of representations recovers the Hamiltonian reduction of the cotangent bundle over the space of representations of the decorated quiver. These algebras yield degenerations of ordinary preprojective algebras, by folding the quiver and then degenerating the decorations. We prove that these degenerations are flat in the Dynkin case, and conjecture, based on computer results, that this extends to arbitrary decorated quivers.

math.RA↗
arXiv2018

Spectrum of the Laplacian on Regular Polyhedra

We study eigenvalues and eigenfunctions of the Laplacian on the surfaces of four of the regular polyhedrons: tetrahedron, octahedron, icosahedron and cube. We show two types of eigenfunctions: nonsingular ones that are smooth at vertices, lift to periodic functions on the plane and are expressible in terms of trigonometric polynomials; and singular ones that have none of these properties. We give numerical evidence for conjectured asymptotic estimates of the eigenvalue counting function. We describe an enlargement phenomenon for certain eigenfunctions on the octahedron that scales down eigenvalues by a factor of $\frac{1}{3}$.

math.AP↗
arXiv2018

Rapid-scan acousto-optical delay line with 34 kHz scan rate and 15 attosecond precision

An optical fast-scan delay exploiting the near-collinear interaction between a train of ultrashort optical pulses and an acoustic wave propagating in a birefringent crystal is introduced. In combination with a femtosecond Er:fiber laser, the scheme is shown to delay few-fs pulses by up to 6 ps with a precision of 15 as. A resolution of 5 fs is obtained for a single sweep at a repetition rate of 34 kHz. This value can be improved to 39 as for multiple scans at a total rate of 0.3 kHz.

physics.ins-det↗
arXiv2018

High Temperature Superconductivity: A Simple Model Exploiting Hydrogen Bonds

Lately, there has been much interest in high temperature superconductors, and more recently hydrogen-based superconductors. This work offers a simple model which explains the behavior of the superconducting gap based on BCS theory, and reproduces most effects seen in experiments, including the isotope effect and T_c enhancement as a function of pressure. We show that this is due to a combination of the factors appearing in the gap equation: the matrix element between the proton states, and the level splitting of the proton.

cond-mat.supr-con↗