75 research outputs found
Generalized Langevin Equation and non-Markovian fluctuation-dissipation theorem for particle-bath systems in external oscillating fields
The Generalized Langevin Equation (GLE) can be derived from a particle-bath
Hamiltonian, in both classical and quantum dynamics, and provides a route to
the (both Markovian and non-Markovian) fluctuation-dissipation theorem (FDT).
All previous studies have focused either on particle-bath systems with
time-independent external forces only, or on the simplified case where only the
tagged particle is subject to the external time-dependent oscillatory field.
Here we extend the GLE and the corresponding FDT for the more general case
where both the tagged particle and the bath oscillators respond to an external
oscillatory field. This is the example of a charged or polarisable particle
immersed in a bath of other particles that are also charged or polarizable,
under an external AC electric field. For this Hamiltonian, we find that the
ensemble average of the stochastic force is not zero, but proportional to the
AC field. The associated FDT reads as , where is
the random force, is the friction memory function, and is
a numerical prefactor
Collective response in light-matter interactions: The interplay between strong coupling and local dynamics
A model designed to mimic the implications of the collective optical response
of molecular ensembles in optical cavities on molecular vibronic dynamics is
investigated. Strong molecule-radiation field coupling is often reached when a
large number N of molecules respond collectively to the radiation field. In
electronic strong coupling, molecular nuclear dynamics following polariton
excitation reflects (a) the timescale separation between the fast electronic
and photonic dynamics and the slow nuclear motion on one hand, and (b) the
interplay between the collective nature of the molecule-field coupling and the
local nature of the molecules nuclear response on the other. The first implies
that the electronic excitation takes place, in the spirit of the Born
approximation, at an approximately fixed nuclear configuration. The second can
be rephrased as the intriguing question, can the collective nature of the
optical excitation lead to collective nuclear motion following polariton
formation, resulting in so-called polaron decoupled dynamics. We address this
issue by studying the dynamical properties of a simplified
Holstein-Tavis-Cummings type model, in which boson modes representing molecular
vibrations are replaced by two-level systems while the boson frequency and the
vibronic coupling are represented by the coupling between these levels (that
induces Rabi oscillations between them) and electronic state dependence of this
coupling. We investigate the short-time behavior of this model following
polariton excitation as well as its response to CW driving and its density of
states spectrum. We find that, while some aspects of the dynamical behavior
appear to adhere to the polaron decoupling picture, the observed dynamics
mostly reflect the local nature of the nuclear configuration of the electronic
polariton rather than this picture
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Microscopic Theory of Linear Response in Amorphous Materials
This thesis provides an analytical and systematic framework from first-principles to study dielectric and mechanical properties of disordered materials, as well as non-centrosymmetric crystals. The Caldeira-Leggett Hamiltonian opens a route to the (both Markovian and nonMarkovian) fluctuation-dissipation theorem (FDT) and gives rise to the generalised Langevin equation (GLE) in classical dynamics.
In the first place, I extend the GLE and the corresponding FDT for more general cases where both the tagged particle and bath oscillators respond to an external oscillatory field. This is the example of a charged or polarisable particle immersed in a bath of other particles that are also charged or polarisable, under an external AC electric field. Being linked to the vibrational density of states (VDOS), the dielectric function calculated based on the GLE is compared with experimental data for the paradigmatic case of molecular glasses: glycerol and Freons 112 & 113, around and above the glass transition temperature, Tg.
Moving to the mechanical aspect, the theory of nonaffine lattice dynamics is able to describe the various relaxation processes in the linear viscoelastic response of metallic glasses. In particular, to understand universal properties of relaxation, the VDOS obtained in simulations, or in experiments, is substituted into the model. The nonaffine contribution
to elasticity is also important for the pre-stressed/stretched harmonic networks. In order
to give an insight on nonaffinity, I compute static elastic constants of α-quartz, taking into
account the long-range Coulomb interaction. The nonaffine (softening) correction is found
very large, such that the overall elastic constants are at least 3-4 times smaller than the affine
Born-Huang estimate.
Finally, I formulate the analytical expression of the dynamical structure factor by averaging over all quenched disorder along the acoustic branch, which stores the information
of phonon transport in disordered materials. The Rayleigh scattering may be enhanced by
a logarithmic factor in an intermediate range of wavenumber. I present a tensorial replica
field-theoretic derivation based on heterogeneous or fluctuating elasticity, which suggests that
long-range spatial correlations (in power-law decay) of elastic constants (or stress tensors)
might be responsible for the logarithmic enhancement to Rayleigh scattering of phonons in amorphous solids.CSC-Cambridge scholarshi
Hyperballistic transport in dense ionized matter under external AC electric fields
The Langevin equation is ubiquitously employed to numerically simulate
plasmas and dusty plasmas. However, the usual assumption of white noise becomes
untenable when the system is subject to an external AC electric field. This is
because the charged particles in the plasma, which provide the thermal bath for
the particle transport, become themselves responsive to the AC field and the
thermal noise is field-dependent and non-Markovian. We theoretically study the
particle diffusivity in a Langevin transport model for a tagged charged
particle immersed in a dense plasma of charged particles that act as the
thermal bath, under an external AC electric field, by properly accounting for
the effects of the AC field on the thermal bath statistics. We analytically
derive the time-dependent generalized diffusivity for different initial
conditions. The generalized diffusivity exhibits damped oscillatory-like
behaviour with initial very large peaks, where the generalized diffusion
coefficient is enhanced by orders of magnitude with respect to the
infinite-time steady-state value. The latter coincides with the Stokes-Einstein
diffusivity in the absence of external field. For initial conditions where the
external field is already on at and the system is thermalized under DC
conditions for , the short-time behaviour is hyperballistic, (where MSD is the mean-squared displacement), leading to giant
enhancement of the particle transport. Finally, the theory elucidates the role
of medium polarization on the local Lorentz field, and allows for estimates of
the effective electric charge due to polarization by the surrounding charges
Possible origin of -relaxation in amorphous metal alloys from atomic-mass differences of the constituents
We employ an atomic-scale theory within the framework of nonaffine lattice
dynamics to uncover the origin of the Johari-Goldstein (JG) -relaxation
in metallic glasses (MGs). Combining simulation and experimental data with our
theoretical approach, we reveal that the large mass asymmetry between the
elements in a LaNiAl MG leads to a clear separation in the
respective relaxation time scales, giving strong evidence that JG relaxation is
controlled by the lightest atomic species present. Moreover, we show that only
qualitative features of the vibrational density of states determine the overall
observed mechanical response of the glass, paving the way for a possible
unified theory of secondary relaxations in glasses
Vibrational density of states of amorphous solids with long-ranged power-law-correlated disorder in elasticity.
A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states D([Formula: see text]) of disordered solids. The results provide the first prediction of a boson peak in amorphous materials where spatial correlations in the internal stresses (or elastic constants) are of power-law form, as is often the case in experimental systems, leading to a logarithmic enhancement of (Rayleigh) phonon attenuation. A logarithmic correction of the form [Formula: see text] is predicted to occur in the plot of the reduced excess DOS for frequencies around the boson peak in 3D. Moreover, the theory provides scaling laws of the density of states in the low-frequency region, including a [Formula: see text] regime in 3D, and provides information about how the boson peak intensity depends on the strength of power-law decay of fluctuations in elastic constants or internal stress. Analytical expressions are also derived for the dynamic structure factor for longitudinal excitations, which include a logarithmic correction factor, and numerical calculations are presented supporting the assumptions used in the theory
Disentangling α and β relaxation in orientationally disordered crystals with theory and experiments.
We use a microscopically motivated generalized Langevin equation (GLE) approach to link the vibrational density of states (VDOS) to the dielectric response of orientational glasses (OGs). The dielectric function calculated based on the GLE is compared with experimental data for the paradigmatic case of two OGs: freon-112 and freon-113, around and just above T_{g}. The memory function is related to the integral of the VDOS times a spectral coupling function γ(ω_{p}), which tells the degree of dynamical coupling between molecular degrees of freedom at different eigenfrequencies. The comparative analysis of the two freons reveals that the appearance of a secondary β relaxation in freon-112 is due to cooperative dynamical coupling in the regime of mesoscopic motions caused by stronger anharmonicity (absent in freon-113) and is associated with the comparatively lower boson peak in the VDOS. The proposed framework brings together all the key aspects of glassy physics (VDOS with the boson peak, dynamical heterogeneity, dissipation, and anharmonicity) into a single model
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