Quantum walk on a comb with infinite teeth

We study continuous time quantum random walk on a comb with infinite teeth and show that the return probability to the starting point decays with time t as t−1. We analyse the diffusion along the spine and into the teeth and show that the walk can escape into the teeth with a finite probability and goes to infinity along the spine with a finite probability. The walk along the spine and into the teeth behaves qualitatively as a quantum random walk on a line. This behaviour is quite different from that of classical random walk on the comb.

Random-Gate-Voltage Induced Al’tshuler–Aronov–Spivak Effect in Topological Edge States

Helical edge states are the hallmark of the quantum spin Hall insulator. Recently, several experiments have observed transport signatures contributed by trivial edge states, making it difficult to distinguish between the topologically trivial and nontrivial phases. Here, we show that helical edge states can be identified by the random-gate-voltage induced Φ 0/2-period oscillation of the averaged electron return probability in the interferometer constructed by the edge states. The random gate voltage can highlight the Φ 0/2-period Al’tshuler–Aronov–Spivak oscillation proportional to sin2(2πΦ/Φ 0) by quenching theΦ 0-period Aharonov–Bohm oscillation. It is found that the helical spin texture induced π Berry phase is key to such weak antilocalization behavior with zero return probability at Φ = 0. In contrast, the oscillation for the trivial edge states may exhibit either weak localization or antilocalization depending on the strength of the spin-orbit coupling, which has finite return probability at Φ = 0. Our results provide an effective way for the identification of the helical edge states. The predicted signature is stabilized by the time-reversal symmetry so that it is robust against disorder and does not require any fine adjustment of system.

Return probability and self-similarity of the Riesz walk

The quantum walk is a counterpart of the random walk. The 2-state quantum walk in one dimension can be determined by a measure on the unit circle in the complex plane. As for the singular continuous measure, results on the corresponding quantum walk are limited. In this situation, we focus on a quantum walk, called the Riesz walk, given by the Riesz measure which is one of the famous singular continuous measures. The present paper is devoted to the return probability of the Riesz walk. Furthermore, we present some conjectures on the self-similarity of the walk.

Conformal Floquet dynamics with a continuous drive protocol

We study the properties of a conformal field theory (CFT) driven periodically with a continuous protocol characterized by a frequency ωD. Such a drive, in contrast to its discrete counterparts (such as square pulses or periodic kicks), does not admit exact analytical solution for the evolution operator U. In this work, we develop a Floquet perturbation theory which provides an analytic, albeit perturbative, result for U that matches exact numerics in the large drive amplitude limit. We find that the drive yields the well-known heating (hyperbolic) and non-heating (elliptic) phases separated by transition lines (parabolic phase boundary). Using this and starting from a primary state of the CFT, we compute the return probability (Pn), equal (Cn) and unequal (Gn) time two-point primary correlators, energy density(En), and the mth Renyi entropy ($$ {S}_n^m $$ S n m ) after n drive cycles. Our results show that below a crossover stroboscopic time scale nc, Pn, En and Gn exhibits universal power law behavior as the transition is approached either from the heating or the non-heating phase; this crossover scale diverges at the transition. We also study the emergent spatial structure of Cn, Gn and En for the continuous protocol and find emergence of spatial divergences of Cn and Gn in both the heating and non-heating phases. We express our results for $$ {S}_n^m $$ S n m and Cn in terms of conformal blocks and provide analytic expressions for these quantities in several limiting cases. Finally we relate our results to those obtained from exact numerics of a driven lattice model.

Analysing flood history and simulating the nature of future floods using Gumbel method and Log-Pearson Type III: the case of the Mayurakshi River Basin, India

Floods of the Mayurakshi River Basin (MRB) have been historically documented since 1860. The high magnitude, low-frequency flood events have drastically changed to low magnitude, high-frequency flood events in the post-dam period, especially after the 1950s, when the major civil structures (Massanjore dam, Tilpara barrage, Brahmani barrage, Deucha barrage, and Bakreshwar weir) were constructed in the MRB. The present study intends to find out the nature of flood frequency using the extreme value method of Gumbel and Log-Pearson type III (LP-III). The results show that the highest flood magnitude (11,327 m3 s−1) was observed during 1957–2009 for the Tilpara barrage with a return probability of 1.85% and the lowest (708 m3 s−1) recorded by the Bakreshwar weir during 1956–77 with a return probability of 4.55%. In the present endeavour, we have computed the predicted discharge for the different return periods, like 2, 5, 10, 25, 50,100, and 200 years. The quantile-quantile plot shows that the expected discharge calculated using LP-III is more normally distributed than that of Gumbel. Moreover, Kolmogorov–Smirnov (KS) test, Anderson–Darling (AD), and x2 distribution show that LP-III distribution is more normally distributed than the Gumbel at 0.01 significance level, implying its greater reliability and acceptance in the flood simulation of the MRB.

Black bear translocations in response to nuisance behaviour indicate increased effectiveness by translocation distance and landscape context

ContextTranslocation is a widely used non-lethal tool to mitigate human–wildlife conflicts, particularly for carnivores. Multiple intrinsic and extrinsic factors may influence translocation success, yet the influence of release-site landscape context on the success of translocations of wildlife involved in nuisance behaviour is poorly understood. Moreover, few studies of translocated wildlife involved in nuisance behaviour have provided estimates of translocation success under different scenarios. AimsWe evaluated the role of intrinsic (age, sex) and extrinsic (translocation distance, landscape composition) features on translocation success of American black bears (Ursus americanus) involved in nuisance behaviour and provide spatially explicit predictions of success under different scenarios. MethodsWe analysed data from 1462 translocations of 1293 bears in Wisconsin, USA, from 1979 to 2016 and evaluated two measures of translocation success: repeated nuisance behaviour and probability of returning to a previous capture location. Key resultsTranslocation distances ranged from 2 to 235km (mean=57km). Repeated nuisance behaviour was recorded following 13.2% of translocation events (192 of 1457) and was not significantly affected by translocation distance. Bears repeated nuisance behaviour and were recaptured at their previous captures site (i.e. returned) after 64% of translocation events (114 of 178). Return probability decreased with an increasing translocation distance, and yearling bears were less likely to return than were adults. The proportions of agriculture and forest within 75km and 100km respectively, of the release site had positive and negative effects on return probability. ConclusionsMangers can use bear characteristics and landscape context to improve translocation success. For example, achieving a 10% predicted probability of return would require translocation distances of 49–60km for yearlings in low-agriculture and high-forest landscapes. In contrast, estimated return probability for adults was ≥38% across all translocation distances (0–124km) and almost all landscape contexts. ImplicationsOur results emphasise the importance of considering the effects of landscape conditions for developing spatially explicit guidelines for maximising translocation success.

No Percolation at Criticality on Certain Groups of Intermediate Growth

We prove that critical percolation has no infinite clusters almost surely on any unimodular quasi-transitive graph satisfying a return probability upper bound of the form $p_n(v,v) \leq \exp \left [-\Omega (n^\gamma )\right ]$ for some $\gamma>1/2$. The result is new in the case that the graph is of intermediate volume growth.

How to probe the microscopic onset of irreversibility with ultracold atoms

The microscopic onset of irreversibility is finally becoming an experimental subject. Recent experiments on microscopic open and even isolated systems have measured statistical properties associated with entropy production, and hysteresis-like phenomena have been seen in cold atom systems with dissipation (i.e. effectively open systems coupled to macroscopic reservoirs). Here we show how experiments on isolated systems of ultracold atoms can show dramatic irreversibility like cooking an egg. In our proposed experiments, a slow forward-and-back parameter sweep will sometimes fail to return the system close to its initial state. This probabilistic hysteresis is due to the same non-adiabatic spreading and ergodic mixing in phase space that explains macroscopic irreversibility, but realized without dynamical chaos; moreover this fundamental mechanism quantitatively determines the probability of return to the initial state as a function of tunable parameters in the proposed experiments. Matching the predicted curve of return probability will be a conclusive experimental demonstration of the microscopic onset of irreversibility.