Dissipative quantum dynamics

Equation for the Dissipative Quantum Dynamics of Multilevel Systems. 

To account for the radiative decay of CC excited states we consider the density operator p, Eq. (35), reduced to the CC solvent states. It is a standard task of dissipative quantum dynamics to derive an equation of motion for p with a second order account for the CC-photon coupling, Eq. (24) (see, for example, [40]). Focusing on the excited CC-state contribution, in the most simple case (Markov and secular approximation) we expect the following equation of motion... 

A dissipative quantum dynamics approach including spontaneous photon emission is based on a separation of the total Hamiltonian into a system part, here the CC Hamiltonian Eq. (1), the reservoir part given by the photon Hamiltonian and a system reservoir coupling Hs-r represented by the CC-photon coupling, Eq. (24). In most applications the latter Hamiltonian can be written as follows... 

P. Saalfrank and R. Kosloff. Quantum dynamics of bond breaking in a dissipative environment Indirect and direct photodesorption of neutrals from metals. J. Chem. Phys., 105 2441, 1996. 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

In conclusion, we present herein a rather compelling model for the short-time dynamics of the excited states in DNA chains that incorporates both charge-transfer and excitonic transfer. It is certainly not a complete model and parametric refinements are warranted before quantitative predictions can be established. For certain, there are various potentially important contributions we have left out disorder in the system, the fluctuations and vibrations of the lattice, polarization of the media, dissipation, quantum decoherence. We hope that this work serves as a starting point for including these physical interactions into a more comprehensive description of this system. 

A. Mauger and N. Pother, Aging effects in the quantum dynamics of a dissipative free particle Non-Ohmic case. Phys. Rev. E 65, 056107 (2002). 

S. Zhang and E. Poliak (2003) Quantum dynamics for dissipative systems A numerical study of the Wigner-Fokker-Planck equation. J. Chem. Phys. 118, p. 4357... 

In past studies, we applied classical molecular dynamics simulation to explore macroscopic heme cooling and predicted a timescale of 6ps [55,57,62], in good agreement with experimental measurements [33]. On the other hand, the mode-specific quantum dynamical studies indicate a faster timescale ( 2ps for the V4 and modes) [35,88-90], One possible reason for this difference in timescales is that the initially excited V4 and V7 modes do not dissipate their excess energy directly to the environment. 

ABSTRACT We present a dynamical scheme for biological systems. We use methods and techniques of quantum field theory since our analysis is at a microscopic molecular level. Davydov solitons on biomolecular chains and coherent electric dipole waves are described as collective dynamical modes. Electric polarization waves predicted by Frohlich are identified with the Goldstone massless modes of the theory with spontaneous breakdown of the dipole-rotational symmetry. Self-organization, dissipativity, and stability of biological systems appear as observable manifestations of the microscopic quantum dynamics. 

The atomistic methods usually employ atoms, molecules or their group and can be classified into three main categories, namely the quantum mechanics (QM), molecular dynamics (MD) and Monte Carlo (MC). Other atomistic modeling techniques such as tight bonding molecular dynamics (TBMD), local density (LD), dissipative particle dynamics (DPD), lattice Boltzmann (LB), Brownian dynamics (BD), time-dependent Ginzbuig-Lanau method, Morse potential function model, and modified Morse potential fimction model were also applied afterwards. 

This article will focus on the reduced dynamics formulations for a general quantum system (ifg) embedded in a dissipative quantum bath (/ib) in the presence of time-dependent external classical field e t). Denote the system-... 

This is one of the simple and most commonly used method to perform multiscale simulation. By definition calculation of parameters for classical MD simulation from quantum chemical calculation is also a multiscale simulation. Therefore, most of the force filed e.g., OPLS," AMBER, GROMOS available for simulations of liquid, polymers, biomolecules are derived from quantum chemical calculations can be termed as multiscale simulation. To bridge scales from classical MD to mesoscale, different parameter can be calculated and transferred to the mesoscale simulation. One of the key examples will be calculation of solubiUty parameter from all atomistic MD simulations and transferring it to mesoscale methods such dissipative particle dynamics (DPD) or Brownian dynamics (BD) simulation. Here, in this context of multiscale simulation only DPD simulation along with the procedure of calculation of solubility parameter from all atomistic MD simulation will be discussed. 

To this date, no stable simulation methods are known which are successful at obtaining quantum dynamical properties of arbitrary many-particle systems over long times. However, significant progress has been made recently in the special case where a low-dimensional nonlinear system is coupled to a dissipative bath of harmonic oscillators. The system-bath model can often provide a realistic description of the effects of common condensed phase environments on the observable dynamics of the microscopic system of interest. A typical example is that of an impurity in a crystalline solid, where the harmonic bath arises naturally from the small-amplitude lattice vibrations. The harmonic picture is often relevant even in situations where the motion of individual solvent atoms is very anhaimonic in such cases validity of the linear response approximation can lead to Gaussian behavior of appropriate effective modes by virtue of the central limit theorem. ... 

We can also turn the question around. In chemical kinetics, we need a model to fit the data. This model can be simple, as in first-order reactions where the decay is exponential, or more complicated depending on a complex mechanism. If we do not have a model, our data are just that, data. We could try to fit to a variety of functions, but as there is an infinite number of different functions, that is a pointless exercise. As we have seen in the classical part of this chapter, even for a simple reaction a variety of models are possible, based on dissipative classical dynamics, and we can use these models to try to understand our data. This often involves varying the external parameters, temperature, pH, viscosity, and polarizabihty, but our model should tell us what to expect for such variations for instance, how the rate constant for a reaction depends on those parameters. If our models are quantum mechanical in nature, it is mandatory that we also provide a mechanism for decay, and show how the decay constant or constants depend on external parameters. 

Baer R and Kosloff R 1997 Quantum dissipative dynamics of adsorbates near metal surfaces a surrogate Hamiltonian theory applied to hydrogen on nickel J. Chem. Rhys. 106 8862... 

Dissipation via Quantum Chemical Hysteresis during High-Pressure Compression A First-Principles Molecular Dynamics Study of Phosphates. 

A relaxation process will occur when a compound state of the system with large amplitude of a sparse subsystem component evolves so that the continuum component grows with time. We then say that the dynamic component of this state s wave function decays with time. Familiar examples of such relaxation processes are the a decay of nuclei, the radiative decay of atoms, atomic and molecular autoionization processes, and molecular predissociation. In all these cases a compound state of the physical system decays into a true continuum or into a quasicontinuum, the choice of the description of the dissipative subsystem depending solely on what boundary conditions are applied at large distances from the atom or molecule. The general theory of quantum mechanics leads to the conclusion that there is a set of features common to all compound states of a wide class of systems. For example, the shapes of many resonances are nearly the same, and the rates of decay of many different kinds of metastable states are of the same functional form. 

In this tribute and memorial to Per-Olov Lowdin we discuss and review the extension of Quantum Mechanics to so-called open dissipative systems via complex deformation techniques of both Hamiltonian and Liouvillian dynamics. The review also covers briefly the emergence of time scales, the definition of the quasibosonic pair entropy as well as the precise quantization relation between the temperature and the phenomenological relaxation time. The issue of microscopic selforganization is approached through the formation of certain units identified as classical Jordan blocks appearing naturally in the generalised dynamical picture. 

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