Transient dynamics of a one-dimensional Holstein polaron under the influence of an external electric field

Following the Dirac-Frenkel time-dependent variational principle, transient dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal exciton-phonon coupling in an external electric field is studied by employing the multi-D$_2$ {\it Ansatz}, also known as a superposition of the usual Davydov D$_2$ trial states. Resultant polaron dynamics has significantly enhanced accuracy, and is in perfect agreement with that derived from the hierarchy equations of motion method. Starting from an initial broad wave packet, the exciton undergoes typical Bloch oscillations. Adding weak exciton-phonon coupling leads to a broadened exciton wave packet and a reduced current amplitude. Using a narrow wave packet as the initial state, the bare exciton oscillates in a symmetric breathing mode, but the symmetry is easily broken by weak coupling to phonons, resulting in a non-zero exciton current. For both scenarios, temporal periodicity is unchanged by exciton-phonon coupling. In particular, at variance with the case of an infinite linear chain, no steady state is found in a finite-sized ring within the anti-adiabatic regime. For strong diagonal coupling, the multi-$\rm D_2$ {\it Anstaz} is found to be highly accurate, and the phonon confinement gives rise to exciton localization and decay of the Bloch oscillations

Variational approach to time-dependent fluorescence of a driven qubit

We employ the Dirac-Frenkel variational principle and multiple Davydov ansatz to study time-dependent fluorescence spectra of a driven qubit in the weak- to strong qubit-reservoir coupling regimes, where both the Rabi frequency and spontaneous decay rate are comparable to the transition frequency of the qubit. Our method agrees well with the time-local master-equation approach in the weak-coupling regime, and offers a flexible way to compute the spectra from the bosonic dynamics instead of two-time correlation functions. While the perturbative master equation breaks down in the strong-coupling regime, our method actually becomes more accurate due to the use of bosonic coherent states under certain conditions. We show that the counter-rotating coupling between the qubit and the reservoir has considerable contributions to the photon number dynamics and the spectra under strong driving conditions even though the coupling is moderately weak. The time-dependent spectra are found to be generally asymmetric, a feature that is derived from photon number dynamics. In addition, it is shown that the spectral profiles can be dramatically different from the Mollow triplet due to strong dissipation and/or multiphoton processes associated with the strong driving. Our formalism provides a unique perspective to interpret time-dependent spectra.Comment: 19 pages, 8 figure

Ground state properties of sub-Ohmic spin-boson model with simultaneous diagonal and off-diagonal coupling

By employing the variational approach, density matrix renormalization group (DMRG), exact diagonalization as well as symmetry and mean-field analyses, the ground state properties of the two-bath spin boson model with simultaneous diagonal and off-diagonal coupling are systematically studied in the sub-Ohmic regime. A novel quantum phase transition from a doubly degenerate "localized phase" to the other doubly degenerate "delocalized phase" is uncovered. Via the multi-D1 ansatz as the variational wave function, transition points are determined accurately, consistent with the results from DMRG and exact diagonalization. An effective spatial dimension $d_{eff} = 2.37(6)$ is then estimated, which is found to be compatible with the mean-field prediction. Furthermore, the quantum phase transition is inferred to be of first order for the baths described by a continuous spectral density function. In the case of single mode, however, the transition is softened.Comment: revised version after the paper is publishe

Finite-temperature time-dependent variation with multiple Davydov states

The Dirac-Frenkel time-dependent variational approach with Davydov Ans\"atze is a sophisticated, yet efficient technique to obtain an acuurate solution to many-body Schr\"odinger equations for energy and charge transfer dy- namics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperatures dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In or- der to demonstrate the applicability of this approach, we compare real-time quantum dynamics of the spin-boson model calculated with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ans\"atze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.Comment: 8 pages, 3 figure

Research on Energy Response Characteristics of Rock under Harmonic Vibro-Impacting Drilling

Open access via Springer Compact Agreement The support of National Natural Science Foundation of China (No. 51704074) and Youth Science Foundation of Heilongjiang Province (No. QC2018049) are gratefully acknowledged. The work is also supported by Talent Cultivation Foundation (No. SCXHB201703; No. ts26180119; No. td26180141) and Youth Science Foundation (No. 2019QNL-07) of Northeast Petroleum University.Peer reviewedPublisher PD

Empirical Assessment and Comparison of Educational Efficiency between Major Countries across the World

Education is a fundamental factor to enhance a country’s comprehensive national strength and international competitiveness. Recently, several governments have been attracting investments in educational sectors in contemplation of meliorating a country’s overall strength. This study empirically assesses and compares the educational efficiency of 29 major countries across the world using panel data for 2010–2016 by employing data envelopment analysis (DEA) and the super-slacks-based measure (super-SBM) model at the static level combined with the Malmquist index (MI) to investigate educational efficiency at the dynamic level. The results indicate, inter alia, huge average education efficiency differences existed among the studied countries, the highest being Japan (3.2845) and lowest Norway (0.4137), there are differences in the bias of technological progress among the studied countries during the sample period and technological progress directly affects the sustainability of educational efficiency, the growth rate of total factor productivity (TFP) index has been reduced in 2010–2013 but increased in 2014–2016 and techno-logical progress has been the dominant factor influencing the rise of the education TFP index. Based on the results, this study identifies the merits and drawbacks of education efficiency across the sample countries and presents relevant recommendations to promote investment in the education sector and human capital