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International Journal of Modern Physics C

One-electron propagation in Fermi, Pasta, Ulam disordered chains with Gaussian acoustic pulse pumping

L. D. da Silva, J. L. L. dos Santos, Adhemar Ranciaro Neto, M.O. Sales, F. A. B. F. de Moura

Published Jul 17, 2017• 4 citations
Publisher

Abstract

In this work, we consider a one-electron moving on a Fermi, Pasta, Ulam disordered chain under effect of electron–phonon interaction and a Gaussian acoustic pulse pumping. We describe electronic dynamics using quantum mechanics formalism and the nonlinear atomic vibrations using standard classical physics. Solving numerical equations related to coupled quantum/classical behavior of this system, we study electronic propagation properties. Our calculations suggest that the acoustic pumping associated with the electron–lattice interaction promote a sub-diffusive electronic dynamics.

DOI
10.1142/s0129183117501005

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We study the statistics and short-time dynamics of the classical and the quantum Fermi-Pasta-Ulam chain in the thermal equilibrium. We analyze the distributions of single-particle configurations by integrating out the rest of the system. At low temperatures, we observe a systematic increase in the mobility of the chain when transitioning from classical to quantum mechanics due to zero-point energy effects. We analyze the consequences of quantum dispersion on the dynamics at short times of configurational correlation functions.
We investigate the mechanism of heat conduction in one-dimensional (1D) quantum FPU chain with quantum fluctuation in the framework of semiquantal molecular dynamics. In the semiquantal many-body simulations, a Hartree-type many-body wave function is adopted for a whole chain and a single-particle state of a particle is represented by a trial wave function with Jackiw–Kerman (JK) form. With the help of the Dirac's time-dependent variational principle (TDVP), a set of equations of the variational parameters contained in the JK wave packet is obtained, and it describes the quantum dynamics of the nonlinear lattices approximately. These equations not only prove highly efficient in recovering dynamics of classical heat conduction, but also allow exploring the case with quantum mechanical characteristics. As a consequence, we find the thermal conductivity diverges with system size as well as in the classical version when considering quantum fluctuation. Furthermore, in three different temperature regions it is observed that the enhancement of the quantum fluctuation increases the heat flux through the 1D quantum FPU chain.
We study the effect of increasing the range of interactions on phonon relaxation in a chain of atoms with quartic anharmonicity. The study is motivated by recent numerical studies, showing that the value of the exponent alpha characterizing the divergence of conductivity with system size apparently depends on the presence of second neighbor couplings. We perform a quantum calculation of the wave-vector (q) dependent relaxation rate gamma(q) in the second order perturbation theory. The nonanalytic dependence of gamma(q) arises due to small-q singularity of the collision integral. We find that gamma(q) proportional to Aq(5/3) + Bq2. This gives rise to an asymptotic value alpha = 0.4, but the q2 terms lead to a higher apparent value of alpha at small sizes of the chain.
We study the equilibrium time correlations for the conserved fields of classical anharmonic chains and argue that their dynamic correlator can be predicted on the basis of nonlinear fluctuating hydrodynamics. In fact, our scheme is more general and would also cover other one-dimensional Hamiltonian systems, for example, classical and quantum fluids. Fluctuating hydrodynamics is a nonlinear system of conservation laws with noise. For a single mode, it is equivalent to the noisy Burgers equation, for which explicit solutions are available. Our focus is the case of several modes. No exact solution has been found so far, and we rely on a one-loop approximation. The resulting mode-coupling equations have a quadratic memory kernel and describe the time evolving 3×3 correlator matrix of the locally conserved fields. Long time asymptotics is computed analytically, and finite time properties are obtained through a numerical simulation of the mode-coupling equations.
We present two quantum-classical hybrid methods for simulating the time-dependence of electron-phonon systems that treat electronic correlations numerically exactly and optical-phonon degrees of freedom classically. These are a time-dependent Lanczos and a matrix-product state method, each combined with the multi-trajectory Ehrenfest approach. Due to the approximations, reliable results are expected for the adiabatic regime of small phonon frequencies. We discuss the convergence properties of both methods for a system of interacting spinless fermions in one dimension and provide a benchmark for the Holstein chain. As a first application, we study the decay of charge density wave order in a system of interacting spinless fermions coupled to Einstein oscillators and in the presence of quenched disorder. We investigate the dependence of the relaxation dynamics on the electron-phonon coupling strength and provide numerical evidence that the coupling of strongly disordered systems to classical oscillators leads to delocalization, thus destabilizing the (finite-size) many-body localization in this system.
We investigate the influence of the on-site Hubbard interaction UUU on the eigenstates and dynamics of two electrons restricted to move in a linear chain with long-range correlated disorder. We solve the time-dependent Schr\"odinger equation to follow the time evolution of an initially localized Gaussian two-electron wave packet. In the regime of strongly correlated disorder, for which one-electron extended eigenstates emerge near the band center, the electron-electron coupling promotes the trapping of a finite portion of the wave packet. In the presence of a uniform electric field, the wave packet develops complex Bloch oscillations. The power spectrum of the centroid's velocity trace shows a splitting near the typical semiclassical Bloch frequency, as well as a frequency doubling phenomenon for intermediate couplings which is related to the bounded states components that are present in the wave packet. Finally, we show that localized and extended two-electron eigenstates coexist near the band center with the level spacing distribution showing a universal Poissonian form irrespective to the Hubbard coupling.