Formation of a quasi-equilibrium domain structure of crystals of the TGS group near TC

In the temperature range ΔT ≈ 321 K ÷ 322 K, the kinetics of the nonequilibrium domain structure of triglycine sulphate crystals, both pure and with specially introduced defects, has been studied by means of piezoresponse force microscopy technique. The temporal change in the domain structure as a set of regions with a scalar order parameter of P (r, t) = +1 and −1 for oppositely polarized domains was analysed by the behaviour of the space-time correlation function C(r,t) = ·Р(r,t)Р(0,t)Ò. At different distances from the Curie point Tc, the characteristic length Lc, as a scale measure of the average domain size, increases with time according to the power law Lc(t)~(t−t0)a. A decrease of the exponent a with distance from Tc can be a consequence of the transition of the domain structure of TGS crystals from a non-conservative state to aconservative one.

Path-integral approximations to quantum dynamics

Imaginary-time path-integral or ‘ring-polymer’ methods have been used to simulate quantum (Boltzmann) statistical properties since the 1980s. This article reviews the more recent extension of such methods to simulate quantum dynamics, summarising the chain of approximations that links practical path-integral methods, such as centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), to the exact quantum Kubo time-correlation function. We focus on single-surface Born–Oppenheimer dynamics, using the infrared spectrum of water as an illustrative example, but also survey other recent applications and practical techniques, as well as the limitations of current methods and their scope for future development. Graphic abstract

Non-adiabatic Matsubara Dynamics and Non-adiabatic Ring Polymer Molecular Dynamics

We present the non-adiabatic Matsubara dynamics, a general framework for computing the time-correlation function (TCF) of electronically non-adiabatic systems. This new formalism is derived based on the generalized Kubo-transformed time-correlation function, using the Wigner representation for both the nuclear degrees of freedom (DOF) and the electronic mapping variables. By dropping the non-Matsubara nuclear normal modes in the quantum Liouvillian and explicitly integrate these modes out of the TCF, we derived the non-adiabatic Matsubara dynamics approach. Further making the approximation to drop the imaginary part of the Matsubara Liouvillian and enforce the nuclear momentum integral to be real, we arrived at the non-adiabatic ring-polymer molecular dynamics (NRPMD) approach. We have further justified the capability of NRPMD for simulating the non-equilibrium time-correlation function. This work provides the rigorous theoretical foundation for several recently proposed state-dependent RPMD approaches and offers a general framework for developing new non-adiabatic quantum dynamics approaches in the future.

Non-adiabatic Matsubara Dynamics and Non-adiabatic Ring Polymer Molecular Dynamics

We present the non-adiabatic Matsubara dynamics, a general framework for computing the time-correlation function (TCF) of electronically non-adiabatic systems. This new formalism is derived based on the generalized Kubo-transformed time-correlation function, using the Wigner representation for both the nuclear degrees of freedom (DOF) and the electronic mapping variables. By dropping the non-Matsubara nuclear normal modes in the quantum Liouvillian and explicitly integrate these modes out of the TCF, we derived the non-adiabatic Matsubara dynamics approach. Further making the approximation to drop the imaginary part of the Matsubara Liouvillian and enforce the nuclear momentum integral to be real, we arrived at the non-adiabatic ring-polymer molecular dynamics (NRPMD) approach. We have further justified the capability of NRPMD for simulating the non-equilibrium time-correlation function. This work provides the rigorous theoretical foundation for several recently proposed state-dependent RPMD approaches and offers a general framework for developing new non-adiabatic quantum dynamics approaches in the future.

Shear viscosity of massless classical fields in scalar theory

We investigate the shear viscosity of massless classical scalar fields in the $\phi^4$ theory on a lattice by using the Green–Kubo formula. Based on the scaling property of the classical field, the shear viscosity is represented using a scaling function. The equilibrium expectation value of the time-correlation function of the energy–momentum tensor is evaluated as the ensemble average of the classical field configurations, whose time evolution is obtained by solving the classical equation of motion starting from the initial condition in thermal equilibrium. It is found that there are two distinct damping time scales in the time-correlation function, which is found to show damped oscillation behavior in the early stage around a slow monotonic decay with an exponential form, and the slow decay part is found to dominate the shear viscosity in the massless classical field theory. This kind of slow decay is also known to exist in molecular dynamics simulations, so it may be a generic feature of dense matter.

Vibrational Relaxation of Functional Groups in dAMP Molecules Probed with UV Resonance Raman Spectroscopy

Dynamical properties of functional groups in 2�-deoxyadenosine-5�-monophosphate (dAMP) compound, were identified by UV resonance Raman spectroscopy (UVRR), upon varying nucleotide concentration in aqueous solution (200-600 μM). The studied full-widths at half-maximum (fwhm�s) were found between 13 - 21 cm-1 and the corresponding global relaxation times were faster than 0.817 ps and slower than 0.506 ps. Also, the band around 1430 cm-1 (C4N9-δC8H) in the UV resonance Raman spectrum of dAMP molecule at 400 μM concentration in aqueous solution, was selected for vibrational band shape analysis through time correlation function (CF) concept. Current theories developed for vibrational dephasing (Kubo-Rothschild and Oxtoby) have been applied to this profile and relevant relaxation parameters have been obtained and discussed. The best fit parameters for this dissipation channel of the vibrational excitation energy were established. To our knowledge this is the first UVRR study on nucleotide vibrational band shape analysis through time correlation function concept.

Rate Constants, Reactive Flux

This chapter discusses a direct approach to the calculation of the rate constant k(T) that bypasses the detailed state-to-state reaction cross-sections. The method is based on the calculation of the reactive flux across a dividing surface on the potential energy surface. Versions based on classical as well as quantum mechanics are described. The classical version and its relation to Wigner’s variational theorem and recrossings of the dividing surface is discussed. Neglecting recrossings, an approximate result based on the calculation of the classical one-way flux from reactants to products is considered. Recrossings can subsequently be included via a transmission coefficient. An alternative exact expression is formulated based on a canonical average of the flux time-correlation function. It concludes with the quantum mechanical definition of the flux operator and the derivation of a relation between the rate constant and a flux correlation function.

Statistical Characterization of Novel 3D Cluster-Based MIMO Vehicle-to-Vehicle Models for Urban Street Scattering Environments

We develop a novel three-dimensional (3D) cluster-based channel model for vehicle-to-vehicle (V2V) communications under the scenarios of urban street scattering environments. The proposed model combines the flexibility of geometrical channel models with the existing state-of-the-art 3D V2V models. To provide an accurate representation of specific locations and realistic V2V fading environments in a computationally manageable fashion, all clusters are divided into three groups of use cases including “ahead,” “between,” and “behind” clusters according to the relative locations of clusters. Using the proposed V2V model, we first derive the closed-form expressions of the channel impulse response (CIR), including the line-of-sight (LoS) components and cluster components. Subsequently, for three categories of clusters, the corresponding statistical properties of the reference model are studied. We additionally derive the expressions of the 3D space-time correlation function (STCF), the autocorrelation function (ACF), and 2D STCF. Finally, comparisons with on-road measurement data and numerical experiments demonstrate the validity and effectiveness of the proposed 3D cluster-based V2V model.