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Register a new userThermal conductance of the coupled-rotator chain: Influence of temperature and size
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Added by
Constantino Tsallis
Publication date
2017
fields
Physics
and research's language is
English
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Thermal conductance of a homogeneous 1D nonlinear lattice system with neareast neighbor interactions has recently been computationally studied in detail by Li et al [Eur. Phys. J. B {bf 88}, 182 (2015)], where its power-law dependence on temperature $T$ for high temperatures is shown. Here, we address its entire temperature dependence, in addition to its dependence on the size $N$ of the system. We obtain a neat data collapse for arbitrary temperatures and system sizes, and numerically show that the thermal conductance curve is quite satisfactorily described by a fat-tailed $q$-Gaussian dependence on $TN^{1/3}$ with $q simeq 1.55$. Consequently, its $T toinfty$ asymptotic behavior is given by $T^{-alpha}$ with $alpha=2/(q-1) simeq 3.64$.
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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.
I study the universal finite-size scaling function for the lowest gap of the quantum Ising chain with a one-parameter family of ``defect boundary conditions, which includes periodic, open, and antiperiodic boundary conditions as special cases. The universal behavior can be described by the Majorana fermion field theory in $1+1$ dimensions, with the mass proportional to the deviation from the critical point. Although the field theory appears to be symmetric with respect to the inversion of the mass (Kramers-Wannier duality), the actual gap is asymmetric, reflecting the spontaneous symmetry breaking in the ordered phase which leads to the two-fold ground-state degeneracy in the thermodynamic limit. The asymptotic ground-state degeneracy in the ordered phase is realized by (i) formation of a bound state at the defect (except for the periodic/antiperiodic boundary condition) and (ii) effective reversal of the fermion number parity in one of the sectors (except for the open boundary condition), resulting in a rather nontrivial crossover ``phase diagram in the space of the boundary condition (defect strength) and mass.
The quest for non-Abelian quasiparticles has inspired decades of experimental and theoretical efforts, where the scarcity of direct probes poses a key challenge. Among their clearest signatures is a thermal Hall conductance with quantized half-integer value in natural units $ pi^2 k_B^2 T /3 h$ ($T$ is temperature, $h$ the Planck constant, $k_B$ the Boltzmann constant). Such a value was indeed recently observed in a quantum-Hall system and a magnetic insulator. We show that a non-topological thermal metal phase that forms due to quenched disorder may disguise as a non-Abelian phase by well approximating the trademark quantized thermal Hall response. Remarkably, the quantization here improves with temperature, in contrast to fully gapped systems. We provide numerical evidence for this effect and discuss its possible implications for the aforementioned experiments.
In this report, we develop a model for the resonant interaction between a pair of coupled quantum wires, under conditions where self-consistent effects lead to the formation of a local magnetic moment in one of the wires. Our analysis is motivated by the experimental results of Morimoto et al. [Appl. Phys. Lett. bf{82}, 3952 (2003)], who showed that the conductance of one of the quantum wires exhibits a resonant peak at low temperatures, whenever the other wire is swept into the regime where local-moment formation is expected. In order to account for these observations, we develop a theoretical model for the inter-wire interaction that calculated the transmission properties of one (the fixed) wire when the device potential is modified by the presence of an extra scattering term, arising from the presence of the local moment in the swept wire. To determine the transmission coefficients in this system, we derive equations describing the dynamics of electrons in the swept and fixed wires of the coupled-wire geometry. Our analysis clearly shows that the observation of a resonant peak in the conductance of the fixed wire is correlated to the appearance of additional structure (near $0.75cdot$ or $0.25cdot 2e^2/h$) in the conductance of the swept wire, in agreement with the experimental results of Morimoto et al.
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.
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