The gapless surface states of topological insulators could enable quantitatively different types of electronic device. A study of the topological insulating Bi2Se3 thin films finds that a gap in these states opens up in films below a certain thickness. This in turn suggests that in thicker films, gapless states exist on both upper and lower surfaces.
In this paper, we construct a generalized Darboux transformation for the nonlinear Schrödinger equation. The associated N-fold Darboux transformation is given in terms of both a summation formula and determinants. As applications, we obtain compact representations for the Nth-order rogue wave solutions of the focusing nonlinear Schrödinger equation and Hirota equation. In particular, the dynamics of the general third-order rogue wave is discussed and shown to exhibit interesting structures.
We describe a new effect in semiconductor spintronics that leads to dissipationless spin currents in paramagnetic spin-orbit coupled systems. We argue that in a high-mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin current that flows perpendicular to the charge current is intrinsic. In the usual case where both spin-orbit split bands are occupied, the intrinsic spin-Hall conductivity has a universal value for zero quasiparticle spectral broadening.
Linear spin wave theory provides the leading term in the calculation of the excitation spectra of long-range ordered magnetic systems as a function of . This term is acquired using the Holstein–Primakoff approximation of the spin operator and valid for small δS fluctuations of the ordered moment. We propose an algorithm that allows magnetic ground states with general moment directions and single-Q incommensurate ordering wave vector using a local coordinate transformation for every spin and a rotating coordinate transformation for the incommensurability. Finally we show, how our model can determine the spin wave spectrum of the magnetic C-site langasites with incommensurate order.
The rise of the new generation of cyber threats demands more sophisticated and intelligent cyber defense solutions equipped with autonomous agents capable of learning to make decisions without the knowledge of human experts. Several reinforcement learning methods (e.g., Markov) for automated network intrusion tasks have been proposed in recent years. In this paper, we introduce a new generation of the network intrusion detection method, which combines a Q-learning based reinforcement learning with a deep feed forward neural network method for network intrusion detection. Our proposed Deep Q-Learning (DQL) model provides an ongoing auto-learning capability for a network environment that can detect different types of network intrusions using an automated trial-error approach and continuously enhance its detection capabilities. We provide the details of fine-tuning different hyperparameters involved in the DQL model for more effective self-learning. According to our extensive experimental results based on the NSL-KDD dataset, we confirm that the lower discount factor, which is set as 0.001 under 250 episodes of training, yields the best performance results. Our experimental results also show that our proposed DQL is highly effective in detecting different intrusion classes and outperforms other similar machine learning approaches.
Subwavelength confinement of light with plasmonics is promising for nanophotonics and optoelectronics. However, it is nontrivial to obtain narrow plasmonic resonances due to the intrinsically high optical losses and radiative damping in metallic structures. In this review, a thorough summary of the recent research progress on achieving high‐quality (high‐Q) factor plasmonic resonances is provided, emphasizing the fundamentals and six resonant mode types, including surface lattice resonances, multipolar resonances, plasmonic Fano resonances, plasmon‐induced transparency, guided‐mode resonances, and Tamm plasmon resonances. The applications of high‐Q plasmonic resonances in spectrally selective thermal emission, sensing, single‐photon emission, filtering, and band‐edge lasing are also discussed.
Iordanis Kerenidis, Jonas Landman, Alessandro Luongo
et al.
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over the corresponding classical algorithms. In this paper, we introduce q-means, a new quantum algorithm for clustering which is a canonical problem in unsupervised machine learning. The $q$-means algorithm has convergence and precision guarantees similar to $k$-means, and it outputs with high probability a good approximation of the $k$ cluster centroids like the classical algorithm. Given a dataset of $N$ $d$-dimensional vectors $v_i$ (seen as a matrix $V \in \mathbb{R}^{N \times d})$ stored in QRAM, the running time of q-means is $\widetilde{O}\left( k d \frac{\eta}{\delta^2}\kappa(V)(\mu(V) + k \frac{\eta}{\delta}) + k^2 \frac{\eta^{1.5}}{\delta^2} \kappa(V)\mu(V) \right)$ per iteration, where $\kappa(V)$ is the condition number, $\mu(V)$ is a parameter that appears in quantum linear algebra procedures and $\eta = \max_{i} ||v_{i}||^{2}$. For a natural notion of well-clusterable datasets, the running time becomes $\widetilde{O}\left( k^2 d \frac{\eta^{2.5}}{\delta^3} + k^{2.5} \frac{\eta^2}{\delta^3} \right)$ per iteration, which is linear in the number of features $d$, and polynomial in the rank $k$, the maximum square norm $\eta$ and the error parameter $\delta$. Both running times are only polylogarithmic in the number of datapoints $N$. Our algorithm provides substantial savings compared to the classical $k$-means algorithm that runs in time $O(kdN)$ per iteration, particularly for the case of large datasets.
Takuya Hiraoka, Takahisa Imagawa, Taisei Hashimoto
et al.
Randomized ensembled double Q-learning (REDQ) (Chen et al., 2021b) has recently achieved state-of-the-art sample efficiency on continuous-action reinforcement learning benchmarks. This superior sample efficiency is made possible by using a large Q-function ensemble. However, REDQ is much less computationally efficient than non-ensemble counterparts such as Soft Actor-Critic (SAC) (Haarnoja et al., 2018a). To make REDQ more computationally efficient, we propose a method of improving computational efficiency called DroQ, which is a variant of REDQ that uses a small ensemble of dropout Q-functions. Our dropout Q-functions are simple Q-functions equipped with dropout connection and layer normalization. Despite its simplicity of implementation, our experimental results indicate that DroQ is doubly (sample and computationally) efficient. It achieved comparable sample efficiency with REDQ, much better computational efficiency than REDQ, and comparable computational efficiency with that of SAC.
Abstract By examining asymptotic behavior of certain infinite basic (q-) hypergeometric sums at roots of unity (that is, at a ‘q-microscopic’ level) we prove polynomial congruences for their truncations. The latter reduce to non-trivial (super)congruences for truncated ordinary hypergeometric sums, which have been observed numerically and proven rarely. A typical example includes derivation, from a q-analogue of Ramanujan's formula ∑ n = 0 ∞ ( 4 n 2 n ) ( 2 n n ) 2 2 8 n 3 2 n ( 8 n + 1 ) = 2 3 π , of the two supercongruences S ( p − 1 ) ≡ p ( − 3 p ) ( mod p 3 ) and S ( p − 1 2 ) ≡ p ( − 3 p ) ( mod p 3 ) , valid for all primes p > 3 , where S ( N ) denotes the truncation of the infinite sum at the N-th place and ( − 3 ⋅ ) stands for the quadratic character modulo 3.