Damped motion in a two-dimensional double well I. Proton tunneling in a hydrogen bond

A model is presented to decribe proton transfer between two sites of a hydrogen bond forming part of a larger molecular complex in a thermal environment. The tunneling motion of the proton is assumed to couple strongly to the end atom vibration of the hydrogen bond via an interaction of the small polaron type. The end atom vibration interacts with the remaining vibrations of the molecular complex and the surrounding medium. These degrees of freedom are treated as an ensemble of harmonic oscillators forming a heat bath and therefore giving rise to a random force acting on, and a damping of, the end atom vibration. Via this vibration the tunneling motion of the proton is damped, too, thus describing an effective transfer from one site to another. The rate coefficient for the transfer reaction is calculated according to Kubo's theor, as an integral over the time correlation function of the reactive flux. Both the end atom vibration and the heat both have an influence on the reaction rate, which therefore depends on both types of coupling constants. The rate constant for systems like a hydrogen bond between two oxygen atoms is not directly related to the tunneling frequency, but may show resonance features when the oscillator frequency is comparable to the level splitting of the two lowest lying proton states.     

Relaxation in a double potential well

Kinetic equations are deduced for the density matrix describing the relaxation in a two-level system interacting with a heat reservoir. It is assumed that the frequency of transition between the levels is small relative to the characteristic frequency of fluctuation in the reservoir; the interaction may be of any strength. The equations are used to discuss the relaxation in such a system.     

Decoherence in an anharmonic oscillator coupled to a thermal environment: a semiclassical forward-backward approach

The decoherence of an anharmonic oscillator in a thermal harmonic bath is examined via a semiclassical approach. A computational strategy is presented and exploited to calculate the time dependence of the purity and the decay of individual matrix elements in the energy representation for a variety of initial states. The time dependence of the decoherence is found to depend on the temperature of the bath, the coupling strength, the initial state of the oscillator, and the choice of quantity measuring the decoherence. Recurrences in the purity and in the off-diagonal matrix elements are observed, as well as the collapse of these matrix elements to the diagonal, providing evidence for the retention of quantum coherence for time scales longer than that indicated by the purity. The results are used to analyze the utility of the Caldeira-Leggett and Redfield models of decoherence and to assess the dependence of dephasing rates on the degree of structure in phase space. In several cases we find that the dephasing dynamics can be described as an initial Zeno-effect regime, followed by a Caldeira-Leggett region, followed by recurrences.     

Time evolution of a single spin inhomogeneously coupled to an interacting spin environment

We study the time evolution of a single spin coupled by exchange interaction to an environment of interacting spin bath modeled by the XY Hamiltonian. By evaluating the spin correlator of the single spin, we observed that the decay rate of the spin oscillations strongly depends on the relative magnitude of the exchange coupling between the single spin and its nearest neighbor J(') and coupling among the spins in the environment J. The decoherence time varies significantly based on the relative coupling magnitudes of J and J('). The decay rate law has a Gaussian profile when the two exchange couplings are of the same order J(') approximately J but converts to exponential and then a power law as we move to the regimes of J(')>J and J(')相似文献   

Exact solutions of an asymmetric double well potential

Journal of Mathematical Chemistry - The analytical solutions of an asymmetric double well potential $$V(x)=a, x^2-b, x^3+c, x^4$$ are found to be a triconfluent Heun function $$H_{T}(alpha ,...     

Vibrational molecular quantum computing: basis set independence and theoretical realization of the Deutsch-Jozsa algorithm

The phase of quantum gates is one key issue for the implementation of quantum algorithms. In this paper we first investigate the phase evolution of global molecular quantum gates, which are realized by optimally shaped femtosecond laser pulses. The specific laser fields are calculated using the multitarget optimal control algorithm, our modification of the optimal control theory relevant for application in quantum computing. As qubit system we use vibrational modes of polyatomic molecules, here the two IR-active modes of acetylene. Exemplarily, we present our results for a Pi gate, which shows a strong dependence on the phase, leading to a significant decrease in quantum yield. To correct for this unwanted behavior we include pressure on the quantum phase in our multitarget approach. In addition the accuracy of these phase corrected global quantum gates is enhanced. Furthermore we could show that in our molecular approach phase corrected quantum gates and basis set independence are directly linked. Basis set independence is also another property highly required for the performance of quantum algorithms. By realizing the Deutsch-Jozsa algorithm in our two qubit molecular model system, we demonstrate the good performance of our phase corrected and basis set independent quantum gates.     

Computerized simulation of aerosol-droplet desolvation in an inductively coupled plasma

A mathematical model for the desolvation of solvent droplets has been used in conjunction with an existing code for simulation of ICP fundamental parameters. The combination has been used for the calculation of droplet histories and desolvation behavior along the central channel of an ICP. Calculations have been performed for droplets of various sizes and under a variety of ICP operating conditions. As central-channel gas flow rate increases, the point of complete desolvation of the droplet shifts upward in the plasma, away from the load coil. This relationship is fairly linear. As forward power increases, the point of complete desolvation moves down in the discharge, closer to the load coil. This is approximately an inverse relationship. Finally, simulation of behavior for a log-normal size distribution of a large number of droplets (10⁸) shows that the number of surviving droplets falls sigmoidally with height above the load coil. For most nebulizer/spray chamber systems, the desolvation process is complete at a well-defined height in the plasma.     

An analysis of the rate of isomerization in molecules with an asymmetric double well potential

The classical theory of the rate of unimolecular isomerization developed by Gray andRice as extended by Zhao and Rice is applied to the calculation of the rate of isomerization in modelsystems which have linear asymmetric double well potentials. We are interested in this system fortwo reasons. First, we are interested in the detailed dynamical processes for the mentioned systembecause it is widely related to practical chemical reactions. Second, the present model systemhas an asymmetric double well potential, which provides a different test of the accuracy of theapproximations used in the Gray-Zhao-Rice theory than posed by previous applications. We havecalculated relaxation rates and relaxation times for the model systems on different time scales.We find that for the systems under studies the Gray-Zhao-Rice version of the classical theory ofisomerization rate yields values in good agreement with those generated from trajectory calculationsand from the Reactive Island theory of De Leon et al.     

Development of an algorithm for peak detection in comprehensive two-dimensional chromatography

A method for peak detection in two-dimensional chromatography is presented. The algorithm applies first the methods developed for peak detection in one-dimensional chromatography to detect peaks in one dimension. In a second step, a decision tree is applied to decide which one-dimensional peaks are originated from the same compound and have to be 'merged' into one two-dimensional peak. To this end, different features of the peaks (second-dimension peak regions and second-dimension retention times) are compared and different criteria (common peak regions, retention time differences, unimodality in the first dimension) are applied. Different options can be used, depending on the nature of the data. The user controls this decision tree by establishing several options and "switches". The algorithm was tested with GCxGC chromatograms obtained for a commercial air-freshener sample, detecting and merging the modulated peaks belonging to the same compound. Recommendations for the set of options and switches are given. A utility that calculates and sums peak areas from merged peaks is added to facilitate automated quantification. Although the algorithm was developed for GCxGC, its application to comprehensive two-dimensional liquid chromatography (LCxLC) data should at most require minor modifications.     

Extended diffusion in a double well potential: Transition from classical to quantum regime

The transition between the classical and quantum regimes in the diffusion of a particle in a 2-4 double-well potential is treated via the strong collision model in the high-temperature limit. Both the classical and semiclassical position correlation functions, their spectra, and correlation times are evaluated using the memory function formalism. It is shown that even in the high temperature limit, marked classical-quantum transition effects appear in the observables when collisions are rare.     

A simple and effective technique to locate quasi-degeneracy in a symmetric double well potential

Perturbation theory based model can be used to locate the quasi-degeneracy in an arbitrary double well potential. This method, extensively explain the effect of the coupling term on pair of states called quasi-degenerate. This model helps us to calculate the energy of the pair of quasi-degenerate states using appreciably small basis. Dispersion equation corresponding to the split energy levels are presented in a very explicit form. Numerical calculation shows that the proposed method can give extremely accurate results for symmetric double-well potentials.     

A hybrid hydrodynamic-Liouvillian approach to mixed quantum-classical dynamics: application to tunneling in a double well

The hybrid quantum-classical approach of Burghardt and Parlant [Burghardt, I.; Parlant, G. J. Chem. Phys. 2004, 120, 3055], referred to here as the quantum-classical moment (QCM) approach, is demonstrated for the dynamics of a quantum double well coupled to a classical harmonic coordinate. The approach combines the quantum hydrodynamic and classical Liouvillian representations by the construction of a particular type of moments (that is, partial hydrodynamic moments) whose evolution is determined by a hierarchy of coupled equations. For pure states, which are at the center of the present study, this hierarchy terminates at the first order. In the Lagrangian picture, the deterministic trajectories result in dynamics which is Hamiltonian in the classical subspace, while the projection onto the quantum subspace evolves under a generalized hydrodynamic force. Importantly, this force also depends upon the classical (Q, P) variables. The present application demonstrates the tunneling dynamics in both the Eulerian and Lagrangian representations. The method is exact if the classical subspace is harmonic, as is the case for the systems studied here.     

Quantum dynamical simulation of electron-transfer reactions in an anharmonic environment

The multilayer multiconfiguration time-dependent Hartree theory is applied to study the quantum dynamics of ultrafast electron-transfer reactions in a condensed-phase environment with anharmonic potential functions. Effects of anharmonicity for both the nuclear degrees of freedom of the environment and the intramolecular vibrational degrees of freedom are investigated. Whereas the former can in principle be mapped to a fictitious harmonic bath, the latter cannot be represented in this way and, thus, go beyond the commonly employed linear response approximation. Numerical examples are presented to illustrate these findings.     

Dynamics of a multimode system coupled to multiple heat baths probed by two-dimensional infrared spectroscopy

Reduced equation of motion for a multimode system coupled to multiple heat baths is constructed by extending the quantum Fokker-Planck equation with low-temperature correction terms (J. Phys. Soc. Jpn. 2005, 74, 3131). Unlike such common approaches used to describe intramolecular multimode vibration as a Bloch-Redfield theory and a stochastic theory, the present formalism is defined by the molecular coordinates. To explore the correlation among different modes through baths, we consider two cases of system-bath couplings. One is a correlated case in which two modes are coupled to a single bath, and the other is an uncorrelated case in which each mode is coupled to a different bath. We further classify the correlated case into two cases, the plus- and minus-correlated cases, according to distinct correlation manners. For these, one-dimensional and two-dimensional infrared (2D-IR) spectra are calculated numerically by solving the equation of motion. It is demonstrated that 2D-IR spectroscopy has the ability to analyze the correlation of fluctuation-dissipation processes among different modes.     

Melting in two-dimensional Yukawa systems: a Brownian dynamics simulation

We studied the melting behavior of two-dimensional colloidal crystals with a Yukawa pair potential by Brownian dynamics simulations. The melting follows the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario with two continuous phase transitions and a middle hexatic phase. The two phase-transition points were accurately identified from the divergence of the translational and orientational susceptibilities. Configurational temperatures were employed to monitor the equilibrium of the overdamped system and the strongest temperature fluctuation was observed in the hexatic phase. The inherent structure obtained by rapid quenching exhibits three different behaviors in the solid, hexatic, and liquid phases. The measured core energy of the free dislocations, E(c) = 7.81 ± 0.91 k(B)T, is larger than the critical value of 2.84 k(B)T, which consistently supports the KTHNY melting scenario.     

Comprehensive two-dimensional gas chromatography coupled to a rapid-scanning quadrupole mass spectrometer: principles and applications

The principles, practicability and potential of comprehensive two-dimensional (2D) gas chromatography coupled to a rapid-scanning quadrupole mass spectrometer (GC x GC-qMS) for the analysis of complex flavour mixtures in food, allergens in fragrances and polychlorinated biphenyls (PCBs) were studied. With a scan speed of 10,000 amu/s, monitoring over a mass range of up to 200 atomic mass unit (amu) can be achieved at an acquisition frequency of 33 Hz. Extending this mass range and/or increasing the data acquisition frequency results in a loss of spectral quality. Optimal parameter settings allow, next to unambiguous identification/confirmation of target compounds on the basis of high-quality mass spectra, fully satisfactory quantification (three to four modulations per peak) with linear calibration plots and detection limits in the low-pg level. The potential of time-scheduled data acquisition to increase the effective mass range within one GC x GC run was also explored. The analyses, with baseline separation of the flavours, allergens and PCB target compounds, took less than 30 min.     

Controllable photoluminescence properties of an anion-dye-intercalated layered double hydroxide by adjusting the confined environment

This article reports a novel method to tune the photoluminance properties of ammonium 1-anilinonaphthalene-8-sulfonate (ANS) in a 2D matrix of layered double hydroxide (LDH) by changing the interlayer microenvironment. ANS and a series of surfactants with different alkyl chain lengths (pentanesulphonate (PES), hexanesulphonate (HES), heptanesulphonate (HPS), decanesulphonate (DES), and dodecylsulphonate (DDS)) were respectively cointercalated into the galleries of ZnAl-LDH by the anion exchange method. Thin films of ANS/surfactant-LDHs obtained by the solvent evaporation method possess good c orientation as revealed by XRD and SEM. It was found that the ANS/HPS-LDH film showed the maximum fluorescence efficiency and the longest intensity-average lifetime among these ANS/surfactant-LDH composites owing to the "size-matching" rule between the organic dye and surfactant. Moreover, the fluorescence properties can be tuned by changing the relative molar ratio of ANS/HPS, and the film containing 20% ANS (molar percentage, expressed as ANS(20%)/HPS-LDH) exhibits the maximum fluorescence efficiency, the longest average lifetime, and significantly enhanced photo and thermal stability. In addition, the composite films show fluorescence anisotropy, attributed to the preferential orientation of ANS in the LDH gallery. Therefore, this work demonstrates a feasible approach to tuning the photoluminescence properties of a dye confined in an inorganic 2D matrix via changing the interlayer microenvironment, which may be considered to be a good candidate for solid photoluminescence materials, nonlinear optics, and polarized luminescence materials.     

Bichromatically driven double well: parametric perspective of the strong field control landscape reveals the influence of chaotic states

The aim of this work is to understand the influence of chaotic states in control problems involving strong fields. Towards this end, we numerically construct and study the strong field control landscape of a bichromatically driven double well. A novel measure based on correlating the overlap intensities between Floquet states and an initial phase space coherent state with the parametric motion of the quasienergies is used to construct and interpret the landscape features. "Walls" of no control, which are robust under variations of the relative phase between the fields, are seen on the control landscape and associated with multilevel interactions involving chaotic Floquet states.