Discrete and Weyl density of states for photonic dispersion relation

Aydin, Alhun; Oikonomou, Thomas; Bagci, G. Baris; Şişman, Altuğ

doi:10.1088/1402-4896/ab0bc5

Cited by 6 publications

(4 citation statements)

References 23 publications

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“…Close to the LEBE, the photonic spectrum can be computed from the hyperbolic Laplacian ∆ g for any L < 1 using Dirichlet boundary conditions. The DOS of eigenvalues ε of the Laplacian follows Weyl's law ρ W (ε) [66][67][68][69], with area = πL 2 /(1 − L 2 ) and circ = 2πL/(1−L 2 ) the area and circumference of the finite hyberbolic disk, respectively. Using ε = M (ω−E 0 ), we arrive at…”

mentioning

confidence: 99%

Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models

et al. 2022

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Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum simulation and computation. In recent groundbreaking experiments, the immense flexibility of superconducting microwave resonators was utilized to realize hyperbolic lattices that emulate quantum physics in negatively curved space. Here we investigate experimentally feasible settings in which a few superconducting qubits are coupled to a bath of photons evolving on the hyperbolic lattice. We compare our numerical results for finite lattices with analytical results for continuous hyperbolic space on the Poincaré disk. We find good agreement between the two descriptions in the long-wavelength regime. We show that photon-qubit bound states have a curvature-limited size. We propose to use a qubit as a local probe of the hyperbolic bath, for example by measuring the relaxation dynamics of the qubit. We find that, although the boundary effects strongly impact the photonic density of states, the spectral density is well described by the continuum theory. We show that interactions between qubits are mediated by photons propagating along geodesics. We demonstrate that the photonic bath can give rise to geometrically-frustrated hyperbolic quantum spin models with finite-range or exponentially-decaying interaction.

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confidence: 99%

Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models

et al. 2022

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“…It is also appropriate to mention here that, the fact that Weyl law can successfully produce all the lower dimensional quantum size effect corrections [47,48] relies on its remarkable success in predicting the behaviors of eigenvalues. This makes it a reliable tool to analytically study quantum size effects in confined systems, via for example Weyl density of states [34,40,47,48].…”

Section: Ground State Reduction Due To Sphericitymentioning

confidence: 99%

Spectral properties of size-invariant shape transformation

Aydin¹

2023

Preprint

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Size-invariant shape transformation is a technique of changing the shape of a domain while preserving its sizes under the Lebesgue measure. In quantum confined systems, this transformation leads to so-called quantum shape effects in the physical properties of confined particles associated with the Dirichlet spectrum of the confining medium. Here we show that the geometric couplings between levels generated by the size-invariant shape transformations cause nonuniform scaling in the eigenspectra. In particular, the nonuniform level scaling is characterized by two distinct spectral features: lowering of the first eigenvalue (ground state reduction) and changing of the spectral gaps (energy level splitting or degeneracy formation depending on the symmetries). We explain the ground state reduction by the increase in local breadth (i.e. parts of the domain becoming less confined) that is associated with the sphericity of these local portions of the domain. We accurately quantify the sphericity using two different measures: the radius of the inscribed n-sphere and the Hausdorff distance. Due to Rayleigh-Faber-Krahn inequality, the greater the sphericity, the lower the first eigenvalue. Then, level splitting or degeneracy, depending on the symmetries of the initial configuration, becomes a direct consequence of size-invariance dictating the eigenvalues to have the same asymptotic behavior due to Weyl law. Furthermore, we find that the ground state reduction causes a quantum thermal avalanche which is the underlying reason for the peculiar effect of spontaneous transitions to lower entropy states in systems exhibiting the quantum shape effect. Unusual spectral characteristics of size-preserving transformations can assist in designing confinement geometries that could lead to classically inconceivable quantum thermal machines.

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“…For weakly confined systems, bounded continuum approximation gives more accurate results than the usual continuum approximation, because the former takes the non-zero value of the ground state into account, whereas the latter considers a continuous spectrum starting from zero energy values [1,[58][59][60][61]. Although both approximations are sufficient for the chosen length of longitudinal direction in this work, we choose to use bounded continuum approximation to get more precise results.…”

Section: Non-interacting Electrons In a Core-shell Nanostructurementioning

confidence: 99%

Quantum shape oscillations in the thermodynamic properties of confined electrons in core–shell nanostructures

Aydin¹,

Fransson²,

Şişman³

2021

J. Phys.: Condens. Matter

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Quantum shape effect appears under the size-invariant shape transformations of strongly confined structures. Such a transformation distinctively influences the thermodynamic properties of confined particles. Due to their characteristic geometry, core–shell nanostructures are good candidates for quantum shape effects to be observed. Here we investigate the thermodynamic properties of non-interacting degenerate electrons confined in core–shell nanowires consisting of an insulating core and a GaAs semiconducting shell. We derive the expressions of shape-dependent thermodynamic quantities and show the existence of a new type of quantum oscillations due to shape dependence, in chemical potential, internal energy, entropy and specific heat of confined electrons. We provide physical understanding of our results by invoking the quantum boundary layer concept and evaluating the distributions of quantized energy levels on Fermi function and in state space. Besides the density, temperature and size, the shape per se also becomes a control parameter on the Fermi energy of confined electrons, which provides a new mechanism for fine tuning the Fermi level and changing the polarity of semiconductors.

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Discrete and Weyl density of states for photonic dispersion relation

Cited by 6 publications

References 23 publications

Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models

Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models

Spectral properties of size-invariant shape transformation

Quantum shape oscillations in the thermodynamic properties of confined electrons in core–shell nanostructures

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