Dynamics of wavepacket tunneling in a periodic double-well potential

Temporal evolution of wavepacket tunneling in a periodic double-well torsional potential has been studied numerically. Peculiarities of wavepacket tunneling dynamics under conditions of asymmetric distortion of the periodic potential function have been analyzed. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 3, pp. 342–346, May–June, 2008.     

Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.     

Enhancing the Viscosity-Sensitive Range of a BODIPY Molecular Rotor by Two Orders of Magnitude

Molecular rotors are a class of fluorophores that enable convenient imaging of viscosity inside microscopic samples such as lipid vesicles or live cells. Currently, rotor compounds containing a boron-dipyrromethene (BODIPY) group are among the most promising viscosity probes. In this work, it is reported that by adding heavy-electron-withdrawing −NO₂ groups, the viscosity-sensitive range of a BODIPY probe is drastically expanded from 5–1500 cP to 0.5–50 000 cP. The improved range makes it, to our knowledge, the first hydrophobic molecular rotor applicable not only at moderate viscosities but also for viscosity measurements in highly viscous samples. Furthermore, the photophysical mechanism of the BODIPY molecular rotors under study has been determined by performing quantum chemical calculations and transient absorption experiments. This mechanism demonstrates how BODIPY molecular rotors work in general, why the −NO₂ group causes such an improvement, and why BODIPY molecular rotors suffer from undesirable sensitivity to temperature. Overall, besides reporting a viscosity probe with remarkable properties, the results obtained expand the general understanding of molecular rotors and show a way to use the knowledge of their molecular action mechanism for augmenting their viscosity-sensing properties.     

Accurate Calculation of Equilibrium Reduced Density Matrix for the System-Bath Model: a Multilayer Multiconfiguration Time-Dependent Hartree Approach and its Comparison to a Multi-Electronic-State Path Integral Molecular Dynamics Approach?

An efficient and accurate method for computing the equilibrium reduced density matrix is presented for treating open quantum systems characterized by the system-bath model. The method employs the multilayer multiconfiguration time-dependent Hartree theory for imaginary time propagation and an importance sampling procedure for calculating the quantum mechanical trace. The method is applied to the spin-boson Hamiltonian, which leads to accurate results in agreement with those produced by the multi-electronic-state path integral molecular dynamics method.     

The invalidity of intermolecular proton transfer triggered twisted intramolecular charge transfer in excited state for 2-(4′-diethylamino-2′-hydroxyphenyl)-1H-imidazo-[4,5-b]pyridine

The excited-state dynamics of the excited-state proton transfer and intramolecular twisted charge transfer (TICT) reactions of a molecular photoswitch 2-(4′-diethylamino-2′-hydroxyphenyl)-1H-imidazo-[4,5-b]pyridine (DHP) in aprotic and alcoholic solvents have been theoretically investigated by using time-dependent density functional theory. The excited-state intramolecular proton transfer (ESIPT) reaction of DHP proceeding upon excitation in all the solvents has been confirmed, and the dual emission has been assigned to the enol and keto forms of DHP. However, for methanol and ethanol solvents within strong hydrogen-bonded capacity, the intermolecular hydrogen bonds between DHP and methanol/ethanol would promote an excited-state double proton transfer (ESDPT) along the hydrogen-bonded bridge. Importantly, the previous proposed ESDPT-triggered TICT mechanism of DHP in methanol and ethanol was not supported by our calculations. The twist motion would increase the total energy of the system for both the products of ESIPT and ESDPT. According to the calculations of the transition states, the ESDPT reaction occurs much easier in keto form generated by ESIPT. Therefore, a sequential ESIPT and ESDPT mechanism of DHP in methanol and ethanol has been reasonably proposed.     

Time-dependent Calculations for Two-proton Decay Width with Schematic Density-dependent Contact Pairing Interaction

We calculate the two-proton decay width of the 6Be nucleus employing the schematic densitydependent contact potential for the proton-proton pairing interaction. The decay width is calculated with a time-dependent method, in which the two-proton emission is described as a time-evolution of a threebody meta-stable state. Model-dependence of the two-proton decay width has been shown by comparing the results obtained with the two different pairing models, schematic density-dependent contact and Minnesota interactions, which have zero and finite ranges, respectively.     

The Physical and Electronic Structure of M<Subscript>2</Subscript> Quadruply Bonded Complexes: A Density Functional Theory Study

The electronic structures and the physical properties (vertical excitation energies, vibrational stretching frequencies, and bond lengths) of a variety of M–M quadruply bonded (M = Mo, W) complexes are investigated using density functional theory (DFT). By utilizing a variety of pure and hybrid exchange-correlation (XC) functionals and a number basis sets, we are able to recommend a theoretical methodology for most efficiently probing the electronic structures of homoleptic M₂(O₂CR)₄ and bridged M₂(O₂C-X-CO₂)M₂ (R = organic group, typically H; X = conjugated organic group) complexes.

双曲方程外问题的完全无反射人工边界条件

研究了数值求解双曲方程外问题的人工边界方法.在圆形的人工边界上,得到了三类等价的完全无反射的人工边界条件.给出的数值例子验证了方法的有效性.     

Stability on finite time interval and time-dependent bifurcation analysis of Duffing's equations

The concept of stability on finite time interval is proposed and some stability theorems are established. The delayed bifurcation transition of Dufflng's equations with a time-dependent parameter is analyzed. Function is used to predict the bifurcation transition value. The sensitivity of the solutions to initial values and parameters is also studied.     

岩石裂纹演化及其力学特性的研究进展

综述评介了岩石裂纹（缺陷）演化及其力学特性研究的近期进展．其内容包括：微细观裂纹演化及其力学特性,时间相关性,裂纹扩展与岩石破坏,并结合某些工程问题进行了讨论．