Motivated by thermal conductivity experiments in spin chain compounds, we propose a phenomenological model to account for a ballistic magnetic transport coupled to a diffusive phononic one, along the line of the seminal two-temperature diffusive transport Sanders-Walton model. Although the expression for the effective thermal conductivity is identical to that of Sanders-Walton, the interpretation is entirely different, as the "magnetic conductivity" is replaced by an "effective transfer conductivity" between the magnetic and phononic component. This model also reveals the fascinating possibility of visualizing the ballistic character of magnetic transport, for appropriately chosen material parameters, as a two peak counter-propagating feature in the phononic temperature. It is also appropriate for the analysis of any thermal transport experiment involving a diffusive component coupled to a ballistic one.
We study ballistic thermal transport in Heisenberg spin chain with nearest-neighbor ferromagnetic interactions at low temperatures. Explicit expressions for transmission coefficients are derived for thermal transport in a periodic spin chain of arbitrary junction length by a spin-wave model. Our analytical results agree very well with the ones from nonequilibrium Green's function method. Our study shows that the transmission coefficient oscillates with the frequency of thermal wave. Moreover, the thermal transmission shows strong dependence on the intrachain coupling, the length of the spin ch…
Thermal rectification is of importance not only for fundamental physics, but also for potential applications in thermal manipulations and thermal management. However, thermal rectification effect usually decays rapidly with system size. Here, we show that a mass-graded system, with two diffusive leads separated by a ballistic spacer, can exhibit large thermal rectification effect, with the rectification factor independent of system size. The underlying mechanism is explained in terms of the effective size-independent thermal gradient and the match/mismatch of the phonon bands. We also show the…
In this thesis we showed that Non-equilibrium Green's Function Perturbation Theory (NEGF) is really the overarching perturbative transport theory. This is shown in great detail by using NEGF as a starting point and developing in 3 directions to obtain the usual transport-related expressions. The 3 directions are: Landauer-like theory, kinetic theory and Green-Kubo linear response theory. This thesis is concerned with using NEGF to generalize the 2 directions of Landauer-like theory and the kinetic theory. Firstly, NEGF is used to derive phonon-phonon Hedin-like functional derivative equations …
We derive expressions for energy flow in terms of lattice normal mode coordinates and energy transmission involving reduced group velocities. With a version of Landauer formula appropriate for lattice dynamic approach, the phonon transmission coefficients and thermal conductance are calculated for two kinds of acoustically mismatched junctions: different chirality nanotubes (11,0) to (8,0), and Si-Ge superlattice structure. Our calculation shows a mode-dependent transmission in nanotube junction and a resonantly modulated ballistic thermal conductance in superlattice. The superlattice result s…
Flexural oscillations of free-standing films, nano-membranes and nano-wires are attracting growing attention for their importance to the thermal, electrical and mechanical properties of 2D materials. Here we report on the observation of short-timescale ballistic motion in the flexural mode of a nano-membrane cantilever, driven by thermal fluctuation of flexural phonons, including measurements of ballistic velocities and displacements performed with sub-atomic resolution, using a new free electron edge-scattering technique. Within intervals <10 μs, the membrane moves ballistically at a constant…
Through an exact analysis using quantum Langevin dynamics, we demonstrate the crossover from ballistic to diffusive thermal transport in a harmonic chain with each site connected to Ohmic heat reservoirs. The temperatures of the two heat baths at the boundaries are specified from before whereas the temperatures of the interior heat reservoirs are determined self-consistently by demanding that in the steady state, on average, there is no heat current between any such (self-consistent) reservoir and the harmonic chain. Essence of our study is that the effective mean free path separating the ball…
Using a generalized Langevin equation of motion, quantum ballistic thermal transport is obtained from classical molecular dynamics. This is possible because the heat baths are represented by random noises obeying quantum Bose-Einstein statistics. The numerical method gives asymptotically exact results in both the low-temperature ballistic transport regime and high-temperature strongly nonlinear classical regime. The method can be thought of as a semi-classical approximation to the quantum transport problem. A one-dimensional quartic on-site model is used to demonstrate the crossover from balli…
We study conversion of thermal energy to mechanical energy and vice versa in $α$-Fermi-Pasta-Ulam-Tsingou~(FPUT) chain with spatially sinusoidal profile of initial temperature. We show analytically that coupling between macroscopic dynamics and quasiballistic heat transport gives rise to mechanical vibrations with growing amplitude. This new phenomenon is referred to as "ballistic resonance". At large times, these mechanical vibrations decay monotonically, and therefore the well-known FPUT recurrence paradox occurring at zero temperature is eliminated at finite temperatures.
In this work we study the asymmetric heat flow, i.e., thermal rectification, of a one-dimensional, mass-graded system consisting of acoupled harmonic oscillator lattice (ballistic spacer) and two diffusive leads attached to the boundaries of the former with both nearest-neighbor and next-nearest-neighbor (NNN) interactions. The latter enhance the rectification properties of the system and specially its independence on system size. The system presents a maximum rectification efficiency for a very precise value of the parameter that controls the coupling strength of the NNN interactions that dep…
There has been much interest in semiconductor superlattices because of showing very low thermal conductivities. This makes them especially suitable for applications in a variety of devices for thermoelectric generation of energy, heat control at the nanometric length scale, etc. Recent experiments have confirmed that the effective thermal conductivity of superlattices at room temperature have a minimum for very short periods (in the order of nanometers) as some kinetic calculations had anticipated previously. This work will show advances on a thermodynamic theory of heat transport in nanometri…
The behavior of a spin undergoing Larmor precession in the presence of fluctuating fields is of interest to workers in many fields. The fluctuating fields cause frequency shifts and relaxation which are related to their power spectrum, which can be determined by taking the Fourier transform of the auto-correlation functions of the field fluctuations. Recently we have shown how to calculate these correlation functions for all values of mean free path (ballistic to diffusive motion) in finite bounded regions, using the model of persistent continuous time random walks (CTRW) for particles subject…
Quantum mechanics and Coulomb interaction dictate the behavior of small circuits. The thermal implications cover fundamental topics from quantum control of heat to quantum thermodynamics, with prospects of novel thermal machines and an ineluctably growing influence on nanocircuit engineering. Experimentally, the rare observations thus far include the universal thermal conductance quantum and heat interferometry. However, evidences for many-body thermal effects paving the way to markedly different heat and electrical behaviors in quantum circuits remain wanting. Here we report on the observatio…
Microscopic current fluctuations are inseparable from conductance. We give an integral account of both quantized conductance and nonequilibrium thermal noise in one-dimensional ballistic wires. Our high-current noise theory opens a very different window on such systems. Central to the role of nonequilibrium ballistic noise is its direct and robust dependence on the statistics of carriers. For, with increasing density, they undergo a marked crossover from classical to strongly degenerate behavior. This is singularly evident where the two-probe conductance shows quantized steps: namely, at the d…
We first propose fundamental solutions of wave propagation in one-dimensional dispersive chain subject to a localized initial perturbation in the displacement. Analytical solutions are obtained for both second order nonlinear dispersive chain and homogenous harmonic chain. Solution was also compared with numerical results from molecular dynamics (MD) simulations. Locally dominant phonon modes (k-space) are introduced based on these solutions. These locally defined phonon modes k(x,t) spatially and temporally varying with x and t are critical to the establishment of the local thermodynamic equi…
The thermal transport across metal-insulator interface can be characterized by electron-phonon interaction through which an electron lead is coupled to a phonon lead if phonon-phonon coupling at the interface is very weak. We investigate the thermal conductance and rectification flowing between the electron part and the phonon part using nonequilibrium Green's function method. It is found that the thermal conductance has a nonmonotonic behavior as a function of average temperature or the coupling strength between the phonon leads in the metal part and the insulator one. The metal-insulator int…
Motivated by recent experimental findings, we study the contribution of a quantum critical optical phonon branch to the thermal conductivity of a paraelectric system. We consider the proximity of the optical phonon branch to transverse acoustic phonon branch and calculate its contribution to the thermal conductivity within the Kubo formalism. We find a low temperature power law dependence of the thermal conductivity as $T^α$, with $1 < α< 2$, (lower than $T^3$ behavior) due to optical phonons near the quantum critical point. This result is in accord with the experimental findings and indicates…
We study thermal processes in infinite harmonic crystals having a unit cell with arbitrary number of particles. Initially particles have zero displacements and random velocities, corresponding to some initial temperature profile. Our main goal is to calculate spatial distribution of kinetic temperatures, corresponding to degrees of freedom of the unit cell, at any moment in time. An approximate expression for the temperatures is derived from solution of lattice dynamics equations. It is shown that the temperatures are represented as a sum of two terms. The first term describes high-frequency o…
