Mining Maximal Dynamic Spatial Co-Location Patterns

A spatial co-location pattern represents a subset of spatial features whose instances are prevalently located together in a geographic space. Although many algorithms of mining spatial co-location pattern have been proposed, there are still some problems: 1) they miss some meaningful patterns (e.g., {Ganoderma_lucidumnew, maple_treedead} and {water_hyacinthnew(increase), algaedead(decrease)}), and get the wrong conclusion that the instances of two or more features increase/decrease (i.e., new/dead) in the same/approximate proportion, which has no effect on prevalent patterns. 2) Since the number of prevalent spatial co-location patterns is very large, the efficiency of existing methods is very low to mine prevalent spatial co-location patterns. Therefore, first, we propose the concept of dynamic spatial co-location pattern that can reflect the dynamic relationships among spatial features. Second, we mine small number of prevalent maximal dynamic spatial co-location patterns which can derive all prevalent dynamic spatial co-location patterns, which can improve the efficiency of obtaining all prevalent dynamic spatial co-location patterns. Third, we propose an algorithm for mining prevalent maximal dynamic spatial co-location patterns and two pruning strategies. Finally, the effectiveness and efficiency of the method proposed as well as the pruning strategies are verified by extensive experiments over real/synthetic datasets.Comment: 10 pages,7 figure

Quantum interface between a transmon qubit and spins of nitrogen-vacancy centers

Hybrid quantum circuits combining advantages of each individual system have provided a promising platform for quantum information processing. Here we propose an experimental scheme to directly couple a transmon qubit to an individual spin in the nitrogen-vacancy (NV) center, with a coupling strength three orders of magnitude larger than that for a single spin coupled to a microwave cavity. This direct coupling between the transmon and the NV center could be utilized to make a transmon bus, leading to a coherently virtual exchange among different single spins. Furthermore, we demonstrate that, by coupling a transmon to a low-density NV ensemble, a SWAP operation between the transmon and NV ensemble is feasible and a quantum non-demolition measurement on the state of NV ensemble can be realized on the cavity-transmon-NV-ensemble hybrid system. Moreover, on this system, a virtual coupling can be achieved between the cavity and NV ensemble, which is much larger in magnitude than the direct coupling between the cavity and the NV ensemble. The photon state in cavity can be thus stored into NV spins more efficiently through this virtual coupling.Comment: 24 pages, 5 figure

Improved Silbey-Harris polaron ansatz for the spin-boson model

In this paper, the well-known Silbey-Harris (SH) polaron ansatz for the spin-boson model is improved by adding orthogonal displaced Fock states. The obtained results for the ground state in all baths converge very quickly within finite displaced Fock states and corresponding SH results are corrected considerably. Especially for the sub-Ohmic spin-boson model, the converging results are obtained for 0 < s < 1/2 in the fourth-order correction and very accurate critical coupling strengths of the quantum phase transition are achieved. Converging magnetization in the biased spin-boson model is also arrived at. Since the present improved SH ansatz can yield very accurate, even almost exact results, it should have wide applications and extensions in various spin-boson model and related fields.Comment: 9 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1410.099

Quantum criticality of the sub-Ohmic spin-boson model within displaced Fock states

The spin-boson model is analytically studied using displaced Fock states (DFS) without discretization of the continuum bath. In the orthogonal displaced Fock basis, the ground-state wavefunction can be systematically improved in a controllable way. Interestingly, the zeroth-order DFS reproduces exactly the well known Silbey-Harris results. In the framework of the second-order DFS, the magnetization and the entanglement entropy are exactly calculated. It is found that the magnetic critical exponent $\beta$ is converged to $0.5$ in the whole sub-Ohmic bath regime $0<s<1$, compared with that by the exactly solvable generalized Silbey-Harris ansatz. It is strongly suggested that the system with sub-Ohmic bath is always above its upper critical dimension, in sharp contrast with the previous findings. This is the first evidence of the violation of the quantum-classical Mapping for .Comment: 8 pages, 4 figure

Concise analytic solutions to the quantum Rabi model with two arbitrary qubits

Using extended coherent states, an analytical exact study has been carried out for the quantum Rabi model (QRM) with two arbitrary qubits in a very concise way. The $G$-functions with $2 \times 2$ determinants are generally derived. For the same coupling constants, the simplest $G$-function, resembling that in the one-qubit QRM, can be obtained. Zeros of the $G$-function yield the whole regular spectrum. The exceptional eigenvalues, which do not belong to the zeros of the $G$ function, are obtained in the closed form. The Dark states in the case of the same coupling can be detected clearly in a continued-fraction technique. The present concise solution is conceptually clear and practically feasible to the general two-qubit QRM and therefore has many applications.Comment: 13 pages, 3 figure

Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model

In this paper, the finite size Dicke model of arbitrary number of qubits is solved analytically in an unified way within extended coherent states. For the $N=2k$ or $2k-1$ Dicke models ($k$ is an integer), the $G$-function, which is only an energy dependent $k \times k$ determinant, is derived in a transparent manner. The regular spectrum is completely and uniquely given by stable zeros of the $G$-function. The closed-form exceptional eigenvalues are also derived. The level distribution controlled by the pole structure of the $G$-functions suggests non-integrability for $N>1$ model at any finite coupling in the sense of recent criterion in literature. A preliminary application to the exact dynamics of genuine multipartite entanglement in the finite $N$ Dicke model is presented using the obtained exact solutions.Comment: 18 pages, 5 figure

Quantum Rabi-Stark model: Solutions and exotic energy spectra

The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling are present on an equal footing, are studied within the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived in a compact way, much simpler than previous ones obtained in the Bargmann representation. The zeros of transcendental functions reproduce completely the regular spectra. In terms of the explicit pole structure of these functions, two kinds of exceptional eigenvalues are obtained and distinguished in a transparent manner. Very interestingly, a first-order quantum phase transition indicated by level crossing of the ground state and the first excited state is induced by the positive nonlinear Stark-like coupling, which is however absent in any previous isotropic quantum Rabi models. When the absolute value of the nonlinear coupling strength is equal to twice the cavity frequency, this model can be reduced to an effective quantum harmonic oscillator, and solutions are then obtained analytically. The spectra collapse phenomenon is observed at a critical coupling, while below this critical coupling, infinite discrete spectra accumulate into a finite energy from below.Comment: 16 pages, 4 figure

Slow manifolds for stochastic systems with non-Gaussian stable L\'evy noise

This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable L\'evy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the fast variables to reduce the dimension of these coupled dynamical systems. It is shown that as the scale parameter tends to zero, the slow manifolds converge to critical manifolds in distribution, which helps understand long time dynamics. The approximation of slow manifolds with error estimate in distribution are also considered.Comment: 35 pages, 6 figures. The authors are grateful to Bj\"orn Schmalfu{\ss}, Ren\'e Schilling, Georg Gottwald, Jicheng Liu and Jinlong Wei for helpful discussions on stochastic differenial equations driven by L\'evy motion

The mixed quantum Rabi model

The analytical exact solutions to the mixed quantum Rabi model (QRM) including both one- and two-photon terms are found by using Bogoliubov operators. Transcendental functions in terms of $4 \times 4$ determinants responsible for the exact solutions are derived. These so-called $G$-functions with pole structures can be reduced to the previous ones in the unmixed QRMs. The zeros of $G$-functions reproduce completely the regular spectra. The exceptional eigenvalues can also be obtained by another transcendental function. From the pole structure, we can derive two energy limits when the two-photon coupling strength tends to the collapse point. All energy levels only collapse to the lower one, which diverges negatively. The level crossings in the unmixed QRMs are relaxed to avoided crossings in the present mixed QRM due to absence of parity symmetry. In the weak two-photon coupling regime, the mixed QRM is equivalent to an one-photon QRM with an effective positive bias, suppressed photon frequency and enhanced one-photon coupling, which may pave a highly efficient and economic way to access the deep-strong one-photon coupling regime.Comment: 11 pages, 8 figure

Quantum phase transitions in the spin-boson model without the counterrotating terms

We study the spin-boson model without the counterrotating terms by a numerically exact method based on variational matrix product states. Surprisingly, the second-order quantum phase transition (QPT) is observed for the sub-Ohmic bath in the rotating-wave approximations. Moreover, first-order QPTs can also appear before the critical points. With the decrease of the bath exponents, these first-order QPTs disappear successively, while the second-order QPT remains robust. The second-order QPT is further confirmed by multi-coherent-states variational studies, while the first-order QPT is corroborated with the exact diagonalization in the truncated Hilbert space. Extension to the Ohmic bath is also performed, and many first-order QPTs appear successively in a wide coupling regime, in contrast to previous findings. The previous pictures for many physical phenomena for the spin-boson model in the rotating-wave approximation have to be modified at least at the strong coupling.Comment: 10 pages, 10 figure