Transport and spectral features in non-Hermitian open systems

Tzortzakakis, A. F.; Makris, Konstantinos G.; Szameit, Alexander; Economou, E. N.

doi:10.1103/physrevresearch.3.013208

Cited by 40 publications

(30 citation statements)

References 63 publications

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“…Here, we address these connections for the general, nonreciprocal and non-Hermitian case. Aiming at a de-scription that is physical and flexible, we adopt the unifying perspective of transport, which has been instrumental to identify the specific signatures of individual physical effects in Hermitian [46,47] and non-Hermitian settings [44,45,[48][49][50][51][52][53][54][55][56][57][58][59][60][61][62]. This perspective allows us to analytically formulate the spectral conditions for a range of distinct physical phenomena, such as reflectionless scattering [49,52], transparency [56], coherent perfect absorption [44,45,50], and lasing [50,51,63,64], and contrast these with the quantisation conditions of finite systems with open or periodic boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Compatibility of transport effects in non-Hermitian nonreciprocal systems

Ghaemi-Dizicheh

Schomerus

2021

Phys. Rev. A

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Section: Introductionmentioning

confidence: 99%

Compatibility of transport effects in non-Hermitian nonreciprocal systems

Ghaemi-Dizicheh

Schomerus

2021

Phys. Rev. A

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“…In this work, we have considered dispersionless media with uniform loss or gain in which the TM is fully determined. When fluctuations of the absorption rate are on a scale smaller than the spatial extent of a mode, the effect may be expected to be small, but nonuniformity in dissipation on a larger scale can lead to hopping of energy between modes [127][128][129][130]. Dispersion may alter the frequency of modes, but the modal description given here does not depend on dispersion in the dielectric constant and should not change.…”

Section: Discussionmentioning

confidence: 97%

Wave excitation and dynamics in non-Hermitian disordered systems

Huang

Kang

Genack

2022

Phys. Rev. Research

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Dynamic and steady state aspects of wave propagation are deeply connected in lossless open systems in which the scattering matrix is unitary. There is then an equivalence among the energy excited within the medium through all channels, the Wigner time delay, which is the sum of dwell times in all channels coupled to the medium, and the density of states. But these equivalences fall away in the presence of material loss or gain. In this paper, we use microwave measurements, numerical simulations, and theoretical analysis to discover the changing relationships among the internal field, transmission, transmission time, dwell time, total excited energy, and the density of states in with loss and gain, and their dependence upon dimensionality and spectral overlap. The field, including the contribution of the still coherent incident wave, is a sum over modal partial fractions with amplitudes that are independent of loss and gain. The total energy excited is equal to the dwell time. When modes are spectrally isolated, the energy is proportional to the sum of products of the modal contribution to the density of states and the ratio of the linewidth without and with absorption. When modes overlap, however, the total energy is further reduced by loss and enhanced by gain. In 1D, the average transmission time is independent of loss, gain, and scattering strength. In higher dimensions, however, the average transmission time falls with loss, scattering strength and channel number, and increases with gain. It is the sum over Lorentzian functions associated with the zeros as well as the poles of the transmission matrix. This endows transmission zeros with robust topological characteristics: in unitary media, zeros occur either singly on the real axis or as conjugate pairs in the complex frequency plane. The transmission zeros are moved down or up in the complex plane by an amount equal to the internal rate of decay or growth of the field. In weakly absorbing media, the spectrum of the transmission time of the lowest transmission eigenchannel is the sum of Lorentzians due to transmission zeros plus a background due to far-off-resonance poles. As the scattering strength increases, conjugate pairs of zeros are brought to the real axis and converted to two single zeros which are constrained to move on the real axis until they combine and leave the real axis as a conjugate pair. The average density of transmission zeros in the complex plane is found from the fall of the average transmission time with absorption as zeros are swept into the lower half of the complex frequency plane. As a sample is deformed, two single zeros and a conjugate pair of zeros may interconvert on the real axis with a square root singularity in the sensitivity of the spacing between transmission zeros to structural change. Thus, the disposition of poles and zeros in the complex frequency plane provides a framework for understanding and controlling wave propagation in non-Hermitian systems.

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“…A noticeable exception is provided by the Hatano-Nelson model in the limiting case of unidirectional hopping [1], which is amenable for some analytical treatment. The realization of synthetic lattices with asymmetric hopping and controlled disorder, demonstrated in recent experiments [14,87,88], have stimulated a renewed interest in the understanding of the interplay among non-Hermiticity, topology and disorder [89][90][91][92] with potential impact to applications, such as in the design of non-Hermitian topological classical or quantum sensors [93].…”

Section: Introductionmentioning

confidence: 99%

Spectral deformations in non-Hermitian lattices with disorder and skin effect: A solvable model

Longhi

2021

Phys. Rev. B

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We derive analytical results on energy spectral phase transitions and deformations in the simplest model of one-dimensional lattice displaying the non-Hermitian skin effect, namely the Hatano-Nelson model with unidirectional hopping, under on-site potential uncorrelated disorder in complex energy plane. While the energy spectrum under open boundary conditions (OBC) exactly reproduces the distribution of on-site potential disorder, the energy spectrum under periodic boundary conditions (PBC) undergoes spectral deformations, from one or more closed loops in the fully delocalized phase, with no overlap with the OBC spectrum, to a mixed spectrum (closed loops and some OBC energies) in the mobility edge phase, to a complete collapse toward the OBC spectrum in the bulk localized phase. Such transitions are observed as the strength of disorder is increased. Depending on the kind of disorder, different interesting behaviors are found. In particular, for continuous disorder with a radial distribution in complex energy plane it is shown that in the delocalized phase the energy spectrum under PBC is locked and fully insensitive to disorder, while transition to the bulk localized phase is signaled by the change of a topological winding number. When the disorder is described by a discrete distribution, the bulk localization transition never occurs, while topological phase transitions associated to PBC energy spectral splittings can be observed.

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Transport and spectral features in non-Hermitian open systems

Cited by 40 publications

References 63 publications

Compatibility of transport effects in non-Hermitian nonreciprocal systems

Compatibility of transport effects in non-Hermitian nonreciprocal systems

Wave excitation and dynamics in non-Hermitian disordered systems

Spectral deformations in non-Hermitian lattices with disorder and skin effect: A solvable model

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