Relativistic quantum chaos

Huang, Liang; Xu, Hongya; Grebogi, Celso; Lai, Ying Cheng

doi:10.1016/j.physrep.2018.06.006

Cited by 47 publications

(29 citation statements)

References 545 publications

(1,101 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the traditional field of quantum chaos that deals with nonrelativistic quantum systems described by scalar wave functions governed by the Schrödinger equation, the phenomenon of scarring has been extensively studied in the past four decades [4,36]. In the recently emergent field of relativistic quantum chaos [47,48] that treats systems described by spinor wave functions obeying the Dirac equation, there has also been a particular focus on scarring of massless Dirac fermions. In spite of the common feature between nonrelativistic and relativistic quantum scars, there are characteristic differences.…”

Section: Discussionmentioning

confidence: 99%

“…This in turn has stimulated interests in the relativistic quantum manifestations of classical chaos (see Refs. [47,48] and references therein). A seminal contribution was made by Sir Michael Berry and his collaborator, who studied the spectral properties of the eigenenergies of the massless Dirac equation for the chaotic neutrino billiard [49].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantization of massive Dirac billiards and unification of nonrelativistic and relativistic chiral quantum scars

Song

et al. 2019

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

Quantum scars constitute one of the fundamental pillars in the traditional field of nonrelativistic quantum chaos. In relativistic quantum systems, chiral scars have been discovered recently whose wave functions concentrate on odd periodic orbits and break the time-reversal symmetry. We develop a theoretical framework to unify the scarring phenomena in nonrelativistic and relativistic quantum systems, which were previously thought to be distinct. In particular, we exploit massive Dirac billiard systems and derive semiclassical quantization rules to bridge the two opposite limits: the massless Dirac case and the large mass regime where the system effectively degenerates into one governed by the Schrödinger equation. A nontrivial phase is uncovered, which depends on the mass, the wave number, and the angle of reflection, and we demonstrate that this phase plays a key role in transforming the chiral scars and in bridging the relativistic and nonrelativistic quantum scars. In the large-mass limit, time-reversal symmetry is restored, as evidenced by a spectral analysis.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantization of massive Dirac billiards and unification of nonrelativistic and relativistic chiral quantum scars

Song

et al. 2019

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…Relativistic quantum chaos. The study of the manifestations of classical chaos in relativistic quantum systems was pioneered by Sir Michael Berry and his collaborator [44] and recently emerged as an interdisciplinary field of research [45,46] with applications to Dirac material systems [47,48]. In contrast to the traditional field of (nonrelativistic) quantum chaos [49,50] where classical chaos often bears strong signatures in the corresponding quantum systems, such "fingerprints" tend to be weakened in the relativistic quantum counterparts [51,52].…”

Section: Introductionmentioning

confidence: 99%

Scattering of Dirac electrons from a skyrmion: Emergence of robust skew scattering

Wang

Lai

2020

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

We study electron scattering from a closed magnetic structure embedded in the top surface of a topological insulator (TI). Outside of the structure there is a uniform layer of ferromagnetic insulator (FMI), leading to a positive effective mass for the Dirac electrons. The mass inside the structure can be engineered to be negative, leading to a skyrmion structure. The geometric shape of the structure can be circular or deformed, leading to integrable or chaotic dynamics, respectively, in the classical limit. For a circular structure, the relativistic quantum scattering characteristics can be calculated analytically. For a deformed structure, we develop an efficient numerical method, the multiple multipole method, to solve the scattering wavefunctions. We find that, for scattering from a skyrmion, anomalous Hall effect as characterized by strong skew scattering can arise, which is robust against structural deformation due to the emergence of resonant modes. In the short (long) wavelength regime, the resonant modes manifest themselves as confined vortices (excited edge states). The origin of the resonant states is the spin phase factor of massive Dirac electrons at the skyrmion boundary. Further, in the short wavelength regime, for a circular skyrmion, a large number of angular momentum channels contribute to the resonant modes. In this regime, in principle, classical dynamics are relevant, but we find that geometric deformations, even those as severe as leading to fully developed chaos, have little effect on the resonant modes. The vortex structure of the resonant states makes it possible to electrically "charge" the skyrmion, rendering feasible to manipulate its motion electrically. In the long wavelength regime, only the lowest angular momentum channels contribute to the resonant modes, making the skew scattering sharply directional. These phenomena can be exploited for applications in generating dynamic skyrmions for information storage and in Hall devices.

show abstract

“…Most of the works on quantum chaos focus on systems described by the non-relativistic Schrödinger equation. Only recently a new field of interest emerged, namely relativistic quantum chaos [20,21]. These studies were triggered by the pioneering fabrication of graphene [22].…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, in that energy region the electronic properties of graphene are described by a Dirac equation so that graphene features relativistic phenomena [23,24]. Accordingly, the question arose whether the conclusions drawn on properties featured by generic non-relativistic quantum systems with a classically chaotic counterpart also apply to those of graphene dots, frequently referred to as graphene billiards; see [20,21,25] for an overview on numerical and experimental studies. With this focus on the spectral properties of graphene billiards in the relativistic energy region interest in those of a massless spin-1/2 paricle confined in a two-dimensional domain -named neutrino billiard in the seminal work [26] of 1987, where neutrinos still were considered to be massless -re-emerged.…”

Section: Introductionmentioning

confidence: 99%

Quantizing neutrino billiards: an expanded boundary integral method

Dietz

Huang

2019

New J. Phys.

View full text Add to dashboard Cite

With the pioneering fabrication of graphene the field of relativistic quantum chaos emerged. We will focus on the spectral properties of massless spin-1/2 particles confined in a bounded two-dimensional region, named neutrino billiards by Berry and Mondragon in 1987. A commonly used method for the determination of the eigenvalues is based on a boundary integral equation originating from Green's theorem. Yet, in the quantization one might face problems similar to those occurring for nonrelativistic quantum billiards. Especially in cases where the eigenvalue spectrum contains near degeneracies the identification of complete sequences of eigenvalues might be extremely elaborate, if not unfeasible. We propose an expanded boundary integral method, which yields complete eigenvalue sequences with a considerably lower numerical effort than the standard one. Actually, it corresponds to an extension of the method introduced in Veble et al (2007 New J. Phys. 9 15) to relativistic quantum billiards. To demonstrate its validity and its superior efficiency compared to the standard method, we apply both methods to a circular billiard of which the eigenvalues are known analytically and exhibit near degeneracies. Finally, we employ it for the quantization of a neutrino billiard with a hole, of which the spectrum contains many close lying levels and exhibits unusual fluctuation properties.

show abstract

Relativistic quantum chaos

Cited by 47 publications

References 545 publications

Quantization of massive Dirac billiards and unification of nonrelativistic and relativistic chiral quantum scars

Quantization of massive Dirac billiards and unification of nonrelativistic and relativistic chiral quantum scars

Scattering of Dirac electrons from a skyrmion: Emergence of robust skew scattering

Quantizing neutrino billiards: an expanded boundary integral method

Contact Info

Product

Resources

About