How the transport properties of an extended system is affected by coupling to active reservoirs is a significant, yet virtually unexplored question. Here we address this issue in the context of energy transport between two active reservoirs connected by a chain of harmonic oscillators. The couplings to the reservoirs, which exert correlated stochastic forces on the boundary oscillators, lead to fascinating behavior of the energy current and kinetic temperature profile, which we compute exactly in the thermodynamic limit. We show that the stationary active current (i) changes non-monotonically as the activity of the reservoirs are changed, leading to a negative differential conductivity (NDC), and (ii) exhibits an unexpected direction reversal at some finite value of the activity drive. For the example of a dichotomous active force, we find the physical origin of the NDC using nonequilibrium response formalism. It turns out that the kinetic temperature profile remains uniform at the bulk, and can be expressed in a form similar to the thermally driven case. We show that despite this apparent similarity, no effective thermal picture can be consistently built in general. However, such a picture emerges in the small activity limit, where many of the well-known results are recovered.
We study the motion of active patchy colloids in an optical trap using experiments, theory and numerical simulations. To achieve isotropic and harmonic confinement, we prototype microparticles with a nearly uniform refractive index and verify that, in the absence of activity, the confined motion is identical to that of optically homogeneous Brownian particles. If the activity is turned on by means of vertical AC fields, the density distributions are described by Boltzmann-like statistics (Gaussian with effective temperature) only for strongly confining traps, whereas weaker potentials give ris…
We study the stationary state of a chain of harmonic oscillators driven by two active reservoirs at the two ends. These reservoirs exert correlated stochastic forces on the boundary oscillators which eventually leads to a nonequilibrium stationary state of the system. We consider three most well-known dynamics for the active force, namely, active Ornstein-Uhlenbeck process, run-and-tumble process and active Brownian process, all of which have exponentially decaying two-point temporal correlations but very different higher order fluctuations. We show that irrespective of the specific dynamics o…
We present an exact solution for the heat conductance along a harmonic chain connecting two reservoirs at different temperatures. In this model, the end points correspond to Brownian particles with different damping coefficients. Such analytical expression for the heat conductance covers its behavior from mesoscopic to very long one-dimensional quantum chains, and validates the ballistic nature of the heat transport in the latter example. This implies the absence of the Fourier law for classical and quantum harmonic chains. We also provide a thorough analysis of the normal modes of system whic…
One of the major challenges in stochastic thermodynamics is to compute the distributions of stochastic observables for small-scale systems for which fluctuations play a significant role. Hitherto much theoretical and experimental research has focused on systems composed of passive Brownian particles. In this paper, we study the heat fluctuations in a system of interacting active particles. Specifically we consider a one-dimensional harmonic chain of $N$ active Ornstein-Uhlenbeck particles, with the chain ends connected to heat baths of different temperatures. We compute the moment-generating f…
We study conformations of the Gaussian polymer chains in d-dimensional space in the presence of an external field with the harmonic potential. We apply a path integral approach to derive an explicit expression for the probability distribution function of the gyration radius. We calculate this function using Monte Carlo simulations and show that our numerical and theoretical results are in a good agreement for different values of the external field.
Fourier's law from a chain of coupled planar harmonic oscillators under energy conserving noise
我们研究了热沿着一个链的粒子相互作用，通过一个谐波势，并在其两端的热库。每个粒子都有两个自由度，并且受到随机噪声的影响，该噪声在保持动能不变的同时产生速度的无穷小变化。这是通过一个朗之万方程与乘性噪声建模。我们表明，这种能量守恒随机噪声的引入导致傅立叶定律。通过一个近似的解决方案，成为精确的热力学极限，我们还表明，热导率$κ$的行为作为$κ= a L/(b+λL)$为大值的强度$λ$的能量守恒噪声和大链尺寸$L$。因此，我们得出结论，在热力学极限的导热系数是有限的，并由$κ=a/λ$。
We consider one-dimensional systems of all-to-all harmonically coupled particles with arbitrary masses, subject to two Langevin thermal baths. The couplings correspond to the mean-field limit of long-range interactions. Additionally, the particles can be subject to a harmonic on-site potential to break momentum conservation. Using the non-equilibrium Green operator formalism, we calculate the transmittance, the heat flow and local temperatures, for arbitrary configurations of masses. For identical masses, we show analytically that, the heat flux decays with the system size $N$, as $1/N$, regar…
Harmonic oscillator chains connecting two harmonic reservoirs at different constant temperatures cannot act as thermal diodes, irrespective of structural asymmetry. However, here we prove that perfectly harmonic junctions can rectify heat once the reservoirs (described by white Langevin noise) are placed under temperature gradients, which are asymmetric at the two sides, an effect that we term "temperature-gradient harmonic oscillator diodes". This nonlinear diode effect results from the additional constraint -- the imposed thermal gradient at the boundaries. We demonstrate the rectification b…
The nonzero ground-state energy of the quantum mechanical harmonic oscillator implies quantum fluctuations around the minimum of the potential with the mean square value proportional to Planck's constant. In classical mechanics thermal fluctuations occur when the oscillator is coupled to a heat bath of temperature $T$. At finite temperature quantum statistical mechanics allows the description of the transition from pure quantum fluctuations at $T=0$ to classical thermal fluctuations in the high temperature limit. It was early pointed out by Peierls that the mean square thermal fluctuations in …
In this paper, thermal transport in bond-disordered harmonic chains is revisited in detail using a nonequilibrium Green's function formalism. For strong bond disorder, thermal conductivity is independent of the system size. However, kinetic temperatures described by the local number of states coupling to external heat reservoirs are anomalous since they form a nonlinear profile in the interior of the system. Both results are accounted for in a unified manner in terms of the frequency-dependent localization length. From this argument, we derive a generic formula describing the asymptotic profil…
We consider heat transport in one-dimensional harmonic chains with isotopic disorder, focussing our attention mainly on how disorder correlations affect heat conduction. Our approach reveals that long-range correlations can change the number of low-frequency extended states. As a result, with a proper choice of correlations one can control how the conductivity $κ$ scales with the chain length $N$. We present a detailed analysis of the role of specific long-range correlations for which a size-independent conductivity is exactly recovered in the case of fixed boundary conditions. As for free bou…
We discuss the driven harmonic chain with fixed boundary conditions subject to weak coupling strength disorder. We discuss the evaluation of the Liapunov exponent in some detail expanding on the dynamical system theory approach by Levi et al. We show that including mass disorder the mass and coupling strength disorder can be combined in a renormalised mass disorder. We review the method of Dhar regarding the disorder-averaged heat current, apply the approach to the disorder-averaged large deviation function and finally comment on the validity of the Gallavotti-Cohen fluctuation theorem. The pa…
Motivated by recent discussion about the possibility of non-Clausius (from cold to hot) heat flow, we revisit the familiar model of an impurity atom of mass $M$ embedded in an otherwise uniform one-dimensional harmonic lattice of host atoms of mass $m$. Assuming that the initial distributions for the impurity and the rest of the lattice have canonical forms with given temperatures, we show that the average kinetic energy of the impurity may increase with time even if its initial temperature is higher than or equal to that of the lattice. Such an increase is only temporary in uniform lattices a…
