On Blockwise Symmetric Matchgate Signatures and Higher Domain \#CSP

For any $n\geq 3$ and $q\geq 3$, we prove that the {\sc Equality} function $(=_n)$ on $n$ variables over a domain of size $q$ cannot be realized by matchgates under holographic transformations. This is a consequence of our theorem on the structure of blockwise symmetric matchgate signatures. %due to the rank of the matrix form of the blockwise symmetric standard signatures, %where $(=_n)$ is an equality signature on domain $\{0, 1, \cdots, q-1\}$. This has the implication that the standard holographic algorithms based on matchgates, a methodology known to be universal for \#CSP over the Boolean domain, cannot produce P-time algorithms for planar \#CSP over any higher domain $q\geq 3$

The Critical Properties of a Modulated Quantum Sine-Gordon Model

A new procedure of trial variational wave functional is proposed for investigating the mass renormailzation and the local structure of the ground state of a one-dimensional quantum sine-Gordon model with linear spatial modulation, whose ground state differs from that without modulation. The phase diagram obtained in parameters $(\alpha \Lambda ^{-2},\beta ^{2})$ plane shows that the vertical part of the boundary between soliton lattice phase and incommensurate (IC) phase with vanishing gap sticks at $\beta ^{2}$ $=4\pi$, the IC phase can only appear for $\beta ^{2}$ $\geq 4\pi$ and the IC phase regime is enlarged with increasing spatial modulation in the case of definite parameter $\alpha \Lambda ^{-2}$. The transition is of the continuous type on the vertical part of the boundary, while it is of the first order on the boundary for $\beta ^{2}>4\pi$.Comment: 12 pages in tex, 7 PS figure

FAQ-based Question Answering via Word Alignment

In this paper, we propose a novel word-alignment-based method to solve the FAQ-based question answering task. First, we employ a neural network model to calculate question similarity, where the word alignment between two questions is used for extracting features. Second, we design a bootstrap-based feature extraction method to extract a small set of effective lexical features. Third, we propose a learning-to-rank algorithm to train parameters more suitable for the ranking tasks. Experimental results, conducted on three languages (English, Spanish and Japanese), demonstrate that the question similarity model is more effective than baseline systems, the sparse features bring 5% improvements on top-1 accuracy, and the learning-to-rank algorithm works significantly better than the traditional method. We further evaluate our method on the answer sentence selection task. Our method outperforms all the previous systems on the standard TREC data set

Does temperature favor quantum coherence of a dissipative two-level system?

The quantum dynamics of a two-level system coupled to an Ohmic spin- bath is studied by means of the perturbation approach based on a unitary transformation. A scattering function $\xi_k$ is introduced in the transformation to take into account quantum fluctuations. By the master equation within the Born approximation, nonequilibrium dynamics quantities are calculated. The method works well for the coupling constant $0 < \alpha < \alpha_c$ and a finite bare tunneling $\Delta$. It is found that (i) only at zero temperature with small coupling or moderate one does the spin-spin-bath model display identical behavior as the well known spin-boson-bath model; (ii) in comparison with the known results of spin-boson-bath model, the coherence-incoherence transition point, which occurs at $\alpha_c={1/2}[1+\eta\Delta/\omega_c]$, is temperature independent; (iii) the nonequilibrium correlation function $P(t)=$, evolves without temperature dependence while depends on temperature. Both $P(t)$ and not only satisfy their initial conditions, respectively, and also have correct long time limits. Besides, the Shiba's relation and sum rule are exactly satisfied in the coherent regime for this method. Our results show that increasing temperature does not help the system suppress decoherence in the coherent regime, i.e., finite temperature does not favor the coherent dynamics in this regime. Thus, the finite-temperature dynamics induced by two kinds of baths spin-bath and boson-bath exhibit distinctly different physics.Comment: 21 pages 4 figure

Quantum critical point of spin-boson model and infrared catastrophe in bosonic bath

An analytic ground state is proposed for the unbiased spin-boson Hamiltonian, which is non-Gaussian and beyond the Silbey-Harris ground state with lower ground state energy. The infrared catastrophe in Ohmic and sub-Ohmic bosonic bath plays an important role in determining the degeneracy of the ground state. We show that the infrared divergence associated with the displacement of the nonadiabatic modes in bath may be removed from the proposed ground state for the coupling $\alpha<\alpha_c$. Then $\alpha_c$ is the quantum critical point of a transition from non-degenerate to degenerate ground state and our calculated $\alpha_c$ agrees with previous numerical results.Comment: 11 pages, 2 figure

Deformable Deep Convolutional Generative Adversarial Network in Microwave Based Hand Gesture Recognition System

Traditional vision-based hand gesture recognition systems is limited under dark circumstances. In this paper, we build a hand gesture recognition system based on microwave transceiver and deep learning algorithm. A Doppler radar sensor with dual receiving channels at 5.8GHz is used to acquire a big database of hand gestures signals. The received hand gesture signals are then processed with time-frequency analysis. Based on these big databases of hand gesture, we propose a new machine learning architecture called deformable deep convolutional generative adversarial network. Experimental results show the new architecture can upgrade the recognition rate by 10% and the deformable kernel can reduce the testing time cost by 30%.Comment: Accepted by International Conference on Wireless Communications and Signal Processing 201

1d Quantum Harmonic Oscillator Perturbed by a Potential with Logarithmic Decay

In this paper we prove an infinite dimensional KAM theorem, in which the assumptions on the derivatives of perturbation in \cite{GT} are weakened from polynomial decay to logarithmic decay. As a consequence, we apply it to 1d quantum harmonic oscillators and prove the reducibility of a linear harmonic oscillator, $T=- \frac{d^2}{dx^2}+x^2$, on $L^2(\R)$ perturbed by a quasi-periodic in time potential $V(x,\omega t; \omega)$ with logarithmic decay. This entails the pure-point nature of the spectrum of the Floquet operator $K$, where K:=-{\rm i}\sum_{k=1}^n\omega_k\frac{\partial}{\partial \theta_k}- \frac{d^2}{dx^2}+x^2+\varepsilon V(x,\theta;\omega), is defined on L^2(\R) \otimes L^2(\T^n) and the potential $V(x,\theta;\omega)$ has logarithmic decay as well as its gradient in $\omega$.Comment: arXiv admin note: substantial text overlap with arXiv:1003.2793 by other author

Reducibility of quantum harmonic oscillator on Rd R^d with differential and quasi-periodic in time potential

We improve the results by Gr\'ebert and Paturel in \cite{GP} and prove that a linear Schr\"odinger equation on $R^d$ with harmonic potential $|x|^2$ and small $t$-quasiperiodic potential as $${\rm i}u_t - \Delta u+|x|^2u+\varepsilon V(\omega t,x)u=0, \ (t,x)\in R\times R^d$$ reduces to an autonomous system for most values of the frequency vector $\omega\in R^n$. The new point is that the potential $V(\theta,\cdot )$ is only in ${\mathcal{C}^{\beta}}(T^n, \mathcal{H}^{s}(R^d))$ with $\beta$ large enough. As a consequence any solution of such a linear PDE is almost periodic in time and remains bounded in some suitable Sobolev norms

Holographaic Alogorithms on Bases of Rank 2

An essential problem in the design of holographic algorithms is to decide whether the required signatures can be realized by matchgates under a suitable basis transformation (SRP). For holographic algorithms on domain size 2, [1, 2, 4, 5] have built a systematical theory. In this paper, we reduce SRP on domain size k>2 to SRP on domain size 2 for holographic algorithms on bases of rank 2. Furthermore, we generalize the collapse theorem of [3] to domain size k>2.Comment: 7 page

Effects of counterrotating interaction on driven tunneling dynamics: coherent destruction of tunneling and Bloch-Siegert shift

We investigate the dynamics of a driven two-level system (classical Rabi model) using the counter-rotating-hybridized rotating wave method (CHRW), which is a simple method based on a unitary transformation with a parameter $\xi$. This approach is beyond the traditional rotating-wave approximation (Rabi-RWA) and more importantly, remains the RWA form with a renormalized tunneling strength and a modified driving strength. The reformulated rotating wave method not only possesses the same mathematical simplicity as the Rabi-RWA but also allows us to explore the effects of counter-rotating (CR) components. We focus on the properties of off-resonance cases for which the Rabi-RWA method breaks down. After comparing the results of different RWA schemes and those of the numerically exact method in a wide range of parameter regime, we show that the CHRW method gives the accurate driven dynamics which is in good agreement with the numerical method. Moreover, the other RWA methods appear as various limiting cases of the CHRW method. The CHRW method reveals the effects of the CR terms clearly by means of coherent destruction of tunneling and Bloch-Siegert shift. Our main results are as follows: (i) the dynamics of the coherent destruction of tunneling is explicitly given and its dependence on $\Delta$ is clarified, which is quantitatively in good agreement with the exact results; (ii) the CR modulated Rabi frequency and the Bloch-Siegert shift are analytically calculated, which is the same as the exact results up to fourth order; (iii) the validity of parameter regions of different RWA methods are given and the comparison of dynamics of these methods are shown. Since the CHRW approach is mathematically simple as well as tractable and physically clear, it may be extended to some complicated problems where it is difficult to do a numerical study.Comment: 28pages,6 figures. arXiv admin note: text overlap with arXiv:1602.0441