Figure 1

Temperature profiles for (a) system with even number of sites $N=32,64$ and with ${\gamma }_L={\gamma }_R=1.0$ and (b) system with odd number of sites $N=33,65$ and with ${\gamma }_L=1.5,{\gamma }_R=0.5$. Other parameters were set to $m_a=0.75,m_b=0.25,k=1,T_L=1.5,T_R=0.5$. The mass of the first particle is always taken to be $m_a$. Note that in (a), the heavier particles are hotter, while in (b), the lighter particles are hotter. The horizontal dashed lines indicate the analytic predictions for $N\to \infty$, from Eqs. (11), (12).Reuse & Permissions

Figure 2

Temperatures at odd and even sites for a chain with even number of particles, plotted as a function of $\gamma ={\gamma }_L={\gamma }_R$, $m_a=0.75,m_b=0.25,k=1,T_L=1.5,T_R=0.5$. We also plot separately the contributions of the acoustic and optical modes to the temperature at any site. The inset shows $J$ and also the contributions of the acoustic and optical modes.Reuse & Permissions

Figure 3

Temperatures at odd and even sites for a chain with odd number of particles, plotted as a function of ${\gamma }_R$ with ${\gamma }_L=1$, $m_a=0.75,m_b=0.25,k=1,T_L=1.5,T_R=0.5$. We also plot separately the contributions of the acoustic and optical modes to the temperature at any site. The inset shows the variation of heat current with ${\gamma }_R$ and also the contributions of the acoustic and optical modes.Reuse & Permissions

Figure 4

Temperature profiles with energy- and momentum-conserving noisy dynamics for a harmonic chain with even number of particles. Other parameters were taken to be $m_a=0.5$, $m_b=1.5$, ${\gamma }_L={\gamma }_R=1.0$ and $T_L=2.0,T_R=1.0$.Reuse & Permissions

Figure 5

Temperature profiles with energy- and momentum-conserving noisy dynamics for a harmonic chain with an odd number of particles. Other parameters were taken to be $m_a=0.5$, $m_b=1.5$, ${\gamma }_L={\gamma }_R=1.0$ and $T_L=2.0,T_R=1.0$.Reuse & Permissions

Figure 6

Temperature profiles with only energy-conserving noisy dynamics for a harmonic chain with even number of particles. Other parameters were taken to be $m_a=0.5$, $m_b=1.5$, ${\gamma }_L={\gamma }_R=1.0$ and $T_L=2.0,T_R=1.0$.Reuse & Permissions

Figure 7

Temperature profiles with only energy-conserving noisy dynamics for a harmonic chain with an odd number of particles. Other parameters were taken to be $m_a=0.5$, $m_b=1.5$, ${\gamma }_L={\gamma }_R=1.0$ and $T_L=2.0,T_R=1.0$.Reuse & Permissions

Figure 8

Simulation results for temperature profile for a two-dimensional $N\times W$ strip of harmonically coupled particles with a periodic arrangement of masses. The sites on the strip are labeled $(i,j)$ with $i=1,\cdots ,N$ and $j=1,...,W$. Particles at sites with even $i+j$ have mass $m_a$ and others have masses $m_b$. Heat baths are attached to all sites on the layers $i=1$ (temperature $T_L$) and $i=N$ (temperature $T_R$). Periodic boundary conditions are imposed in the transverse ($j$) direction. Upper plot shows the average temperature on successive layers for chains of lengths $N=32$ and $N=64$. There are oscillations in the transverse direction also and this is shown in the lower plot which shows the temperatures $T_{i,j}$ on all sites of a section of the $N=64$ chain. Note that from symmetry we have $T_{i,j}=T_{i,j+2}$, and this can be observed here. The width of the strips was taken to be $W=4$. The other parameters were taken to be $m_a=0.6$, $m_b=1.4$, ${\gamma }_L={\gamma }_R=1.0$ and $T_L=2.0,T_R=1.0$.Reuse & Permissions