Quantum Corrections to Fidelity Decay in Chaotic Systems

By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt echo. Our semiclassical results for the fidelity amplitude agree with random matrix theory (RMT) and supersymmetry predictions in the universal Fermi golden rule regime. The calculated quantum corrections can be viewed as arising from a static random perturbation acting on nearly self-retracing interfering paths, and hence will be suppressed for time-varying perturbations. Moreover, using trajectory-based methods we show a relation, recently obtained in RMT, between the fidelity amplitude and the cross-form factor for parametric level correlations. Beyond RMT, we compute Ehrenfest-time effects on the fidelity amplitude. Furthermore our semiclassical approach allows for a unified treatment of the fidelity, both in the Fermi golden rule and Lyapunov regimes, demonstrating that quantum corrections are suppressed in the latter.Comment: 14 pages, 4 figure

Edge effects in graphene nanostructures: II. Semiclassical theory of spectral fluctuations and quantum transport

We investigate the effect of different edge types on the statistical properties of both the energy spectrum of closed graphene billiards and the conductance of open graphene cavities in the semiclassical limit. To this end, we use the semiclassical Green's function for ballistic graphene flakes that we have derived in Reference 1. First we study the spectral two point correlation function, or more precisely its Fourier transform the spectral form factor, starting from the graphene version of Gutzwiller's trace formula for the oscillating part of the density of states. We calculate the two leading order contributions to the spectral form factor, paying particular attention to the influence of the edge characteristics of the system. Then we consider transport properties of open graphene cavities. We derive generic analytical expressions for the classical conductance, the weak localization correction, the size of the universal conductance fluctuations and the shot noise power of a ballistic graphene cavity. Again we focus on the effects of the edge structure. For both, the conductance and the spectral form factor, we find that edge induced pseudospin interference affects the results significantly. In particular intervalley coupling mediated through scattering from armchair edges is the key mechanism that governs the coherent quantum interference effects in ballistic graphene cavities

Semiclassical approach to the ac-conductance of chaotic cavities

We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accounting for Ehrenfest time effects. We consider the case of a cavity connected through many leads to a macroscopic circuit which contains ac-sources. In addition to the reservoir the cavity itself is capacitively coupled to a gate. By incorporating tunnel barriers between cavity and leads we obtain results for arbitrary tunnel rates. Finally, based on our findings we investigate the effect of dephasing on the charge relaxation resistance of a mesoscopic capacitor in the linear low-frequency regime

Unpacking A Moment: Decolonization in the Performing Arts?

“The Moment” occurred during an intercultural and interdisciplinary artistic workshop, inspiring a long-term artistic collaboration and many conversations about decolonization in the performing arts. What can we learn about decolonization from the collaboration of Indigenous and non-Indigenous artists and scholars? Our collective analysis and reflection will demonstrate two things: the benefits of and challenges to a careful consideration of respectful collaboration among musicians from different traditions in a post-Truth and Reconciliation Commission context, and new ways of engaging in music research which are collaborative and possibly decolonial.Le « moment » s’est produit au cours d’un atelier artistique interculturel et interdisciplinaire, inspirant une collaboration artistique à long terme et de nombreuses conversations au sujet de la décolonisation des arts vivants. Que pouvons-nous apprendre de la décolonisation à partir de la collaboration d’artistes et d’universitaires autochtones et non autochtones? Notre analyse collective et notre réflexion démontreront deux choses : les bénéfices et les difficultés d’un examen consciencieux de la collaboration respectueuse entre musiciens provenant de traditions différentes dans le contexte de l’après-Commission de vérité et de réconciliation, et de nouvelles façons d’aborder la recherche musicale qui soient collaboratives et si possible décoloniales

The semiclassical origin of curvature effects in universal spectral statistics

We consider the energy averaged two-point correlator of spectral determinants and calculate contributions beyond the diagonal approximation using semiclassical methods. Evaluating the contributions originating from pseudo-orbit correlations in the same way as in [S. Heusler {\textit {et al.}}\ 2007 Phys. Rev. Lett. {\textbf{98}}, 044103] we find a discrepancy between the semiclassical and the random matrix theory result. A complementary analysis based on a field-theoretical approach shows that the additional terms occurring in semiclassics are cancelled in field theory by so-called curvature effects. We give the semiclassical interpretation of the curvature effects in terms of contributions from multiple transversals of periodic orbits around shorter periodic orbits and discuss the consistency of our results with previous approaches

Loschmidt echo for local perturbations: non-monotonous cross-over from the Fermi-golden-rule to the escape-rate regime

We address the sensitivity of quantum mechanical time evolution by considering the time decay of the Loschmidt echo (LE) (or fidelity) for local perturbations of the Hamiltonian. Within a semiclassical approach we derive analytical expressions for the LE decay for chaotic systems for the whole range from weak to strong local perturbations and identify different decay regimes which complement those known for the case of global perturbations. For weak perturbations a Fermi-golden-rule (FGR) type behavior is recovered. For strong perturbations the escape-rate regime is reached, where the LE decays exponentially with a rate independent of the perturbation strength. The transition between the FGR regime and the escape-rate regime is non-monotonic, i.e. the rate of the exponential time-decay of the LE oscillates as a function of the perturbation strength. We further perform extensive quantum mechanical calculations of the LE based on numerical wave packet evolution which strongly support our semiclassical theory. Finally, we discuss in some detail possible experimental realizations for observing the predicted behavior of the LE.Comment: 27 pages, 7 figures; important changes throughout the pape

Periodic-orbit theory of universal level correlations in quantum chaos

Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in establishing the full correlator such that its Fourier transform, the spectral form factor, is determined for all times, below and above the Heisenberg time. We cover dynamics with and without time reversal invariance (from the orthogonal and unitary symmetry classes). A key step in our reasoning is to sum the periodic-orbit expansion in terms of a matrix integral, like the one known from the sigma model of random-matrix theory.Comment: 44 pages, 11 figures, changed title; final version published in New J. Phys. + additional appendices B-F not included in the journal versio