Open quantum dots: Physics of the non‐Hermitian Hamiltonian

Ferry, D. K.; Akis, R.; Burke, Anthony M.; Knežević, I.; Brunner, Roland; Bird, J. P.; Meisels, R.; Kuchar, F.

doi:10.1002/prop.201200065

Cited by 8 publications

(4 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They can also be applied to other models, such as the Su-Schrieffer-Heeger (SSH) type model that has nonreciprocal hopping for every two nearestneighbor bonds, as we have verified in the Supplemental Material [84]. Our theory may be implemented, for instance, in open quantum dot [102][103][104][105], cold-atom [28,[48][49][50][106][107][108], and monitored quantum circuit systems [109,110].…”

mentioning

confidence: 93%

Symmetry breaking and spectral structure of the interacting Hatano-Nelson model

et al. 2022

View full text Add to dashboard Cite

We study the Hatano-Nelson model, i.e., a one-dimensional non-Hermitian chain of spinless fermions with nearest-neighbor nonreciprocal hopping, in the presence of repulsive nearest-neighbor interactions. At half filling, we find two PT transitions, as the interaction strength increases. The first transition is marked by an exceptional point between the first and the second excited state in a finite-size system and is a first-order symmetry-breaking transition into a charge-density wave regime. Persistent currents characteristic of the Hatano-Nelson model abruptly vanish at the transition. The second transition happens at a critical interaction strength that scales with the system size and can thus only be observed in finite-size systems. It is characterized by a collapse of all energy eigenvalues onto the real axis. We further show that in a strong interaction regime, but away from half filling, the many-body spectrum shows point gaps with nontrivial winding numbers, akin to the topological properties of the single-particle spectrum of the Hatano-Nelson chain, which indicates the skin effect of extensive many-body eigenstates under open boundary conditions. Our results can be applied to other models such as the non-Hermitian Su-Schrieffer-Heeger-type model and contribute to an understanding of fermionic many-body systems with non-Hermitian Hamiltonians.

show abstract

mentioning

confidence: 93%

Symmetry breaking and spectral structure of the interacting Hatano-Nelson model

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Here we may mention especially inelastic quantum scattering and transport by complex potentials V [20][21][22][23][24][25][26] and optical waveguides [27][28][29] that are all examples of applied NHQM. Eigenvalues of a non-Hermitian Hamiltonian are generally complex.…”

Section: Introductionmentioning

confidence: 99%

Wave transport and statistical properties of an open non-Hermitian quantum dot with parity-time symmetry

2014

View full text Add to dashboard Cite

A basic quantum-mechanical model for wave functions and current flow in open quantum dots or billiards is investigated. The model involves non-Hertmitian quantum mechanics, parity-time (PT ) symmetry, and PT -symmetry breaking. Attached leads are represented by positive and negative imaginary potentials. Thus probability densities, currents flows, etc., for open quantum dots or billiards may be simulated in this way by solving the Schrödinger equation with a complex potential. Here we consider a nominally open ballistic quantum dot emulated by a planar microwave billiard. Results for probability distributions for densities, currents (Poynting vector), and stress tensor components are presented and compared with predictions based on Gaussian random wave theory. The results are also discussed in view of the corresponding measurements for the analogous microwave cavity. The model is of conceptual as well as of practical and educational interest.

show abstract

“…The second is to perform a trace over the environmental states which yields just the reduced set of pointer states. This procedure has been known for a considerable time [ 9 , 10 , 11 ], and the derivations of the following form have been discussed extensively [ 3 , 12 , 13 ]. The result is the transport equation for the projected/desired part of the device

where

and P and Q = 1 − P are the projection super-operators that project the desired dynamics of the device onto a reduced density matrix, or to its conjugate parts, respectively.…”

Section: The Nature Of Complex Quantum Systemsmentioning

confidence: 99%

“…The second is to perform a trace over the environmental states which yields just the reduced set of pointer states. This procedure has been known for a considerable time [9][10][11], and the derivations of the following form have been discussed extensively [3,12,13]. The result is the transport equation for the projected/desired part of the device…”

Section: The Nature Of Complex Quantum Systemsmentioning

confidence: 99%

Complex Systems in Phase Space

Ferry

Nedjalkov

Weinbub

et al. 2020

Entropy

View full text Add to dashboard Cite

The continued reduction of semiconductor device feature sizes towards the single-digit nanometer regime involves a variety of quantum effects. Modeling quantum effects in phase space in terms of the Wigner transport equation has evolved to be a very effective approach to describe such scaled down complex systems, accounting from full quantum processes to dissipation dominated transport regimes including transients. Here, we discuss the challanges, myths, and opportunities that arise in the study of these complex systems, and particularly the advantages of using phase space notions. The development of particle-based techniques for solving the transport equation and obtaining the Wigner function has led to efficient simulation approaches that couple well to the corresponding classical dynamics. One particular advantage is the ability to clearly illuminate the entanglement that can arise in the quantum system, thus allowing the direct observation of many quantum phenomena.

show abstract

Open quantum dots: Physics of the non‐Hermitian Hamiltonian

Cited by 8 publications

References 60 publications

Symmetry breaking and spectral structure of the interacting Hatano-Nelson model

Symmetry breaking and spectral structure of the interacting Hatano-Nelson model

Wave transport and statistical properties of an open non-Hermitian quantum dot with parity-time symmetry

Complex Systems in Phase Space

Contact Info

Product

Resources

About