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Register a new userCoexistence of ballistic and Fourier regimes in the $beta$-FPUT lattice
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Commonly, thermal transport properties of one-dimensional systems are found to be anomalous. Here, we perform a numerical and theoretical study of the $beta$-FPUT chain, considered a prototypical model for one-dimensional anharmonic crystals, in contact with thermostats at different temperatures. We give evidence that, in steady state conditions, the {it local} wave energy spectrum can be naturally split into modes that are essentially ballistic (non-interacting or scarcely interacting) and kinetic modes (interacting enough to relax to local thermodynamic equilibrium). We show numerically that the well-known divergence of the energy conductivity is related to how the transition region between these two sets of modes shifts in $k$-space with the system size $L$, due to properties of the collision integral of the system. Moreover, we show that the kinetic modes are responsible for a macroscopic behavior compatible with Fouriers law. Our work sheds light on the long-standing problem of the applicability of standard thermodynamics in one-dimensional nonlinear chains, testbed for understanding the thermal properties of nanotubes and nanowires.
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We show that the one dimensional discrete nonlinear Schrodinger chain (DNLS) at finite temperature has three different dynamical regimes (ultra-low, low and high temperature regimes). This has been established via (i) one point macroscopic thermodynamic observables (temperature $T$ , energy density $epsilon$ and the relationship between them), (ii) emergence and disappearance of an additional almost conserved quantity (total phase difference) and (iii) classical out-of-time-ordered correlators (OTOC) and related quantities (butterfly speed and Lyapunov exponents). The crossover temperatures $T_{textit{l-ul}}$ (between low and ultra-low temperature regimes) and $T_{textit{h-l}}$ (between high and low temperature regimes) extracted from these three different approaches are consistent with each other. The analysis presented here is an important step forward towards the understanding of DNLS which is ubiquitous in many fields and has a non-separable Hamiltonian form. Our work also shows that the different methods used here can serve as important tools to identify dynamical regimes in other interacting many body systems.
We characterize a transition from normal to ballistic diffusion in a bouncing ball dynamics. The system is composed of a particle, or an ensemble of non-interacting particles, experiencing elastic collisions with a heavy and periodically moving wall under the influence of a constant gravitational field. The dynamics lead to a mixed phase space where chaotic orbits have a free path to move along the velocity axis, presenting a normal diffusion behavior. Depending on the control parameter, one can observe the presence of featured resonances, known as accelerator modes, that lead to a ballistic growth of velocity. Through statistical and numerical analysis of the velocity of the particle, we are able to characterize a transition between the two regimes, where transport properties were used to characterize the scenario of the ballistic regime. Also, in an analysis of the probability of an orbit to reach an accelerator mode as a function of the velocity, we observe a competition between the normal and ballistic transport in the mid range velocity.
We introduce and analyze a quantum spin/Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the scaling limit, but manifests itself on the lattice. Namely, we find explicit lattice expressions for the supersymmetry generators and currents. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. These confirm the coexistence between two (topologically) ordered ground states and a disordered one in the gapped phase. Deforming the model by including explicit chiral symmetry breaking, we find the phases persist up to an unusual chiral phase transition where the supersymmetry becomes exact even on the lattice.
In contrary to other 1D momentum-conserving lattices such as the Fermi-Pasta-Ulam $beta$ (FPU-$beta$) lattice, the 1D coupled rotator lattice is a notable exception which conserves total momentum while exhibits normal heat conduction behavior. The temperature behavior of the thermal conductivities of 1D coupled rotator lattice had been studied in previous works trying to reveal the underlying physical mechanism for normal heat conduction. However, two different temperature behaviors of thermal conductivities have been claimed for the same coupled rotator lattice. These different temperature behaviors also intrigue the debate whether there is a phase transition of thermal conductivities as the function of temperature. In this work, we will revisit the temperature dependent thermal conductivities for the 1D coupled rotator lattice. We find that the temperature dependence follows a power law behavior which is different with the previously found temperature behaviors. Our results also support the claim that there is no phase transition for 1D coupled rotator lattice. We also give some discussion about the similarity of diffusion behaviors between the 1D coupled rotator lattice and the single kicked rotator also called the Chirikov standard map.
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 to scattering by fixed (frozen) scattering centers so that the speed of the moving particles is not changed by the collisions. In this work we show how scattering with energy exchange from an ensemble of scatterers in thermal equilibrium can be incorporated into the CTRW. We present results for 1,2 and 3 dimensions. The results agree for all these cases contrary to the previously studied frozen models. Our results for the velocity autocorrelation function show a long time tail $left( sim t^{-1/2}right) $, which we also obtain from conventional diffusion theory, with the same power, independent of dimensionality. Our results are valid for any Markovian scattering kernel as well as any kernel based on a scattering cross section $sim1/v.$
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