Time Evolution Of Correlations Research Articles

Bloch oscillations and the lack of the decay of the false vacuum in a one-dimensional quantum spin chain

We consider the decay of the false vacuum, realised within a quantum quench into an anti-confining regime of the Ising spin chain with a magnetic field opposite to the initial magnetisation. Although the effective linear potential between the domain walls is repulsive, the time evolution of correlations still shows a suppression of the light cone and a reduction of vacuum decay {via suppression of the growth of nucleated bubbles. The suppression of the bubble growth is a lattice effect, and can be assigned to emergent Bloch oscillations.

Definition and Time Evolution of Correlations in Classical Statistical Mechanics.

The study of dense gases and liquids requires consideration of the interactions between the particles and the correlations created by these interactions. In this article, the N-variable distribution function which maximizes the Uncertainty (Shannon’s information entropy) and admits as marginals a set of (N−1)-variable distribution functions, is, by definition, free of N-order correlations. This way to define correlations is valid for stochastic systems described by discrete variables or continuous variables, for equilibrium or non-equilibrium states and correlations of the different orders can be defined and measured. This allows building the grand-canonical expressions of the uncertainty valid for either a dilute gas system or a dense gas system. At equilibrium, for both kinds of systems, the uncertainty becomes identical to the expression of the thermodynamic entropy. Two interesting by-products are also provided by the method: (i) The Kirkwood superposition approximation (ii) A series of generalized superposition approximations. A theorem on the temporal evolution of the relevant uncertainty for molecular systems governed by two-body forces is proved and a conjecture closely related to this theorem sheds new light on the origin of the irreversibility of molecular systems. In this respect, the irreplaceable role played by the three-body interactions is highlighted.

Spatial distribution and time evolution of correlation in ultracold neutral plasmas

The correlation of ultracold neutral plasmas extracted from the pair correlation function is presented in detail. To get its spatial distribution and time evolution, a large scale simulation using a full molecular-dynamics method with open boundary condition is performed, and the expansion of an ultracold plasma is simulated. We demonstrate that the coupling strength extracted from pair correlation is a good measure for the correlation in ultracold plasma except at the very early stage. The ion–ion pair correlation arises at the timescale of . And results imply that there is a strong coupling area at the outer plasma during the expansion.

Density nonlinearities in field theories for a toy model of fluctuating nonlinear hydrodynamics of supercooled liquids

We study a zero-dimensional version of the fluctuating nonlinear hydrodynamics (FNH) of supercooled liquids originally investigated by Das and Mazenko (DM) [Shankar P. Das and Gene F. Mazenko Phys. Rev. A 34, 2265 (1986)]. The time-dependent density-like and momentum-like variables are introduced with no spatial degrees of freedom in this toy model. The structure of nonlinearities takes the similar form to the original FNH, which allows one to study in a simpler setting the issues raised recently regarding the field theoretical approaches to glass forming liquids. We study the effects of density nonlinearities on the time evolution of correlation and response functions by developing field theoretic formulations in two different ways: first by following the original prescription of DM and then by constructing a dynamical action which possesses a linear time-reversal symmetry as proposed recently. We show explicitly that, at the one-loop order of the perturbation theory, the DM-type field theory does not support a sharp ergodic-nonergodic transition, while the other admits one. The simple nature of the toy model in the DM formulation allows us to develop numerical solutions to a complete set of coupled dynamical equations for the correlation and response functions at the one-loop order.

Time evolution of correlations in strongly interacting fermions after a quantum quench

Using the adaptive time-dependent density-matrix renormalization group, we study the time evolution of density correlations of interacting spinless fermions on a one-dimensional lattice after a sudden change in the interaction strength. Over a broad range of model parameters, the correlation function exhibits a characteristic light-cone-like time evolution representative of a ballistic transport of information. Such behavior is observed both when quenching an insulator into the metallic region and also when quenching within the insulating region. However, when a metallic state beyond the quantum critical point is quenched deep into the insulating regime, no indication for ballistic transport is observed. Instead, stable domain walls in the density correlations emerge during the time evolution, consistent with the predictions of the Kibble-Zurek mechanism.

Reaction-Diffusion Processes with Multi-Species of Particles

We study reaction-diffusion processes with multi-species of particles on a hypercubic lattice. We define the particle density operators for multi-species case and express the time evolution equation of correlation functions in quantum Hamiltonian formalism. We consider the conditions that the time evolution of correlation functions does not generate higher-order correlation functions. These conditions are called the closed conditions. Moreover we generalize the dual processes which are known in the symmetric exclusion processes and find that the Hamiltonian of the dual processes fixes the time evolution of correlation functions of processes with multi-species of particles.

Time evolution of correlations in a random sequential adsorption process

The pair correlation function C(r,t) for random sequential adsorption of particles with nearest-neighbor exclusion on a one-dimensional lattice evolves in time as C(r,t) = −1/2e−2(1−e−t)∑∞n=0{ [−2(1−e−t)]2n+r+1/(2n+r+1)!}. The distribution of the number of adsorbed particles on a lattice with N sites is shown to have a variance N(1 − e−t)e−4(1−e−t) for large N.