arXiv subjects

Jiao Wang

Publications and source records attributed to Jiao Wang.

At least 55 records · Page 3Linked to original sources

arXiv2014

Non-integrability and the Fourier heat conduction law

We study in momentum-conserving systems, how nonintegrable dynamics may affect thermal transport properties. As illustrating examples, two one-dimensional (1D) diatomic chains, representing 1D fluids and lattices, respectively, are numerically investigated. In both models, the two species of atoms are assigned two different masses and are arranged alternatively. The systems are nonintegrable unless the mass ratio is one. We find that when the mass ratio is slightly different from one, the heat conductivity may keep significantly unchanged over a certain range of the system size and as the mass ratio tends to one, this range may expand rapidly. These results establish a new connection between the macroscopic thermal transport properties and the underlying dynamics.

cond-mat.stat-mech↗

arXiv2014

Finite-size effects on current correlation functions

We study why the calculation of current correlation functions (CCFs) still suffers from finite size effects even when the periodic boundary condition is taken. Two important one dimensional, momentum conserving systems are investigated as examples. Intriguingly, it is found that the state of a system recurs in the sense of microcanonical ensemble average, and such recurrence may result in oscillations in CCFs. Meanwhile, we find that the sound mode collisions induce an extra time decay in a current so that its correlation function decays faster (slower) in a smaller (larger) system. Based on these two unveiled mechanisms, a procedure for correctly evaluating the decay rate of a CCF is proposed, with which our analysis suggests that the global energy CCF decays as $\sim t^{-\frac{2}{3}}$ in the diatomic hard-core gas model and in a manner close to $\sim t^{-\frac{1}{2}}$ in the Fermi-Pasta-Ulam-$β$ model.

cond-mat.stat-mech↗

arXiv2014

Unconventional quantum criticality in the kicked rotor

The quantum kicked rotor (QKR) driven by $d$ incommensurate frequencies realizes the universality class of $d$-dimensional disordered metals. For $d>3$, the system exhibits an Anderson metal-insulator transition which has been observed within the framework of an atom optics realization. However, the absence of genuine randomness in the QKR reflects in critical phenomena beyond those of the Anderson universality class. Specifically, the system shows strong sensitivity to the algebraic properties of its effective Planck constant $\tilde h \equiv 4π/q$. For integer $q$, the system may be in a globally integrable state, in a `super-metallic' configuration characterized by diverging response coefficients, Anderson localized, metallic, or exhibit transitions between these phases. We present numerical data for different $q$-values and effective dimensionalities, with the focus being on parameter configurations which may be accessible to experimental investigations.

cond-mat.stat-mech↗

arXiv2013

Kicked-Harper model vs On-Resonance Double Kicked Rotor Model: From Spectral Difference to Topological Equivalence

Recent studies have established that, in addition to the well-known kicked Harper model (KHM), an on-resonance double kicked rotor model (ORDKR) also has Hofstadter's butterfly Floquet spectrum, with strong resemblance to the standard Hofstadter's spectrum that is a paradigm in studies of the integer quantum Hall effect. Earlier it was shown that the quasi-energy spectra of these two dynamical models (i) can exactly overlap with each other if an effective Planck constant takes irrational multiples of 2*pi and (ii) will be different if the same parameter takes rational multiples of 2*pi. This work makes some detailed comparisons between these two models, with an effective Planck constant given by 2*pi M/N, where M and N are coprime and odd integers. It is found that the ORDKR spectrum (with two periodic kicking sequences having the same kick strength) has one flat band and $N-1$ non-flat bands whose largest width decays in power law as K to the power of N+2, where K is a kicking strength parameter. The existence of a flat band is strictly proven and the power law scaling, numerically checked for a number of cases, is also analytically proven for a three-band case. By contrast, the KHM does not have any flat band and its band width scales linearly with K. This is shown to result in dramatic differences in dynamical behavior, such as transient (but extremely long) dynamical localization in ORDKR, which is absent in KHM. Finally, we show that despite these differences, there exist simple extensions of KHM and ORDKR (upon introducing an additional periodic phase parameter) such that the resulting extended KHM and ORDKR are actually topologically equivalent, i.e., they yield exactly the same Floquet-band Chern numbers and display topological phase transitions at the same kick strengths. A theoretical derivation of this topological equivalence is provided.

nlin.CD↗

arXiv2013

Non-ergodicity and localization of invariant measure for two colliding masses

We show evidence, based on extensive and carefully performed numerical experiments, that the system of two elastic hard-point masses in one-dimension is not ergodic for a generic mass ratio and consequently does not follow the principle of energy equipartition. This system is equivalent to a right triangular billiard. Remarkably, following the time-dependent probability distribution in a suitably chosen velocity direction space, we find evidence of exponential localization of invariant measure. For non-generic mass ratios which correspond to billiard angles which are rational, or weak irrational multiples of pi, the system is ergodic, in consistence with existing rigorous results.

nlin.CD↗

arXiv2013

Why asymmetric interparticle interaction can result in convergent heat conductivity

We show that the asymmetric inter-particle interactions may induce rapid decay of heat current autocorrelation in one-dimensional momentum conserving lattices. When the asymmetry degree and the temperature are appropriate, the decay is sufficient rapid for resulting a convergence conductivity practically. To understand the underlying mechanism, we further studied the relaxation behavior of the hydrodynamic modes. It is shown that for lattice with symmetric potential, the heat mode relaxs in the superdiffusive manner, while in the case of asymmetric potential, the heat mode may relax in the normal manner.

cond-mat.stat-mech↗

arXiv2013

Exponential Quantum Spreading in a Class of Kicked Rotor Systems near High-Order Resonances

Long-lasting quantum exponential spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104 (2011)]. The underlying mechanism, unrelated to the chaotic motion in the classical limit but resting on quasi-integrable motion in a pseudoclassical limit, is identified for one special case. By presenting a detailed study of the same model, this work offers a framework to explain long-lasting quantum exponential spreading under much more general conditions. In particular, we adopt the so-called "spinor" representation to treat the kicked-rotor dynamics under high-order resonance conditions and then exploit the Born-Oppenheimer approximation to understand the dynamical evolution. It is found that the existence of a flat-band (or an effectively flat-band) is one important feature behind why and how the exponential dynamics emerges. It is also found that a quantitative prediction of the exponential spreading rate based on an interesting and simple pseudoclassical map may be inaccurate. In addition to general interests regarding the question of how exponential behavior in quantum systems may persist for a long time scale, our results should motivate further studies towards a better understanding of high-order resonance behavior in delta-kicked quantum systems.

nlin.CD↗

arXiv2013

Diffusion of heat, energy, momentum, and mass in one-dimensional systems

We study diffusion processes of local fluctuations of heat, energy, momentum, and mass in three paradigmatic one-dimensional systems. For each system, diffusion processes of four physical quantities are simulated and the cross correlations between them are investigated. We find that, in all three systems, diffusion processes of energy and mass can be perfectly expressed as a linear combination of those of heat and momentum, suggesting that diffusion processes of heat and momentum may represent the heat mode and the sound mode in the hydrodynamic theory. In addition, the dynamic structure factor, which describes the diffusion behavior of local mass density fluctuations, is in general insufficient for probing diffusion processes of other quantities because in some cases there is no correlation between them. We also find that the diffusion behavior of heat can be qualitatively different from that of energy, and, as a result, previous studies trying to relate heat conduction to energy diffusion should be revisited.

cond-mat.stat-mech↗

arXiv2013

Conservation Laws and Thermodynamic Efficiencies

We show that generic systems with a single relevant conserved quantity reach the Carnot efficiency in the thermodynamic limit. Such a general result is illustrated by means of a diatomic chain of hard-point elastically colliding particles where the total momentum is the only relevant conserved quantity.

cond-mat.stat-mech↗

arXiv2013

Breakdown of effective phonon theory in one-dimensional chains with asymmetric interactions

Phonons are universal language for solid state theory. Effective phonon theory (self-consistent harmonic approximation) have been extensively used to access the weakly nonlinear effect in solid materials, which are standard content in textbook. In this manuscript, we test the effective phonon theory in one-dimensional chains with asymmetric interactions. It is found that simulation results agree well with theoretical predictions for symmetric cases, while significantly deviate from theoretical predictions for asymmetric cases. Our results imply the asymmetric interaction can provide stronger phonon-phonon interaction, which lead to break down of the effective phonon theory.

cond-mat.stat-mech↗

arXiv2012

Breakdown of the power-law decay prediction of the heat current correlation in one-dimensional momentum conserving lattices

We show that the asymmetric inter-particle interactions can induce rapid decay of the heat current correlation in one-dimensional momentum conserving lattices. When the asymmetry degree is appropriate, even exponential decay may arise. This fact suggests that the power-law decay predicted by the hydrodynamics may not be applied to the lattices with asymmetric inter-particle interactions, and as a result, the Green-Kubo formula may instead lead to a convergent heat conductivity in the thermodynamic limit. The mechanism of the rapid decay is traced back to the fact that the heat current has to drive a mass current additionally in the presence of the asymmetric inter-particle interactions.

cond-mat.stat-mech↗

arXiv2012

Thermal Rectification in Graded Materials

In order to identify the basic conditions for thermal rectification we investigate a simple model with non-uniform, graded mass distribution. The existence of thermal rectification is theoretically predicted and numerically confirmed, suggesting that thermal rectification is a typical occurrence in graded systems, which are likely to be natural candidates for the actual fabrication of thermal diodes. In view of practical implications, the dependence of rectification on the asymmetry and system's size is studied.

cond-mat.stat-mech↗

arXiv2012

Normal heat conduction in one dimensional momentum conserving lattices with asymmetric interactions

The heat conduction behavior of one dimensional momentum conserving lattice systems with asymmetric interparticle interactions is numerically investigated. It is found that with certain degree of interaction asymmetry, the heat conductivity measured in nonequilibrium stationary states converges in the thermodynamical limit, in clear contrast to the well accepted viewpoint that Fourier's law is generally violated in low dimensional momentum conserving systems. It suggests in nonequilibrium stationary states the mass gradient resulted from the asymmetric interactions may provide an additional phonon scattering mechanism other than that due to the nonlinear interactions.

cond-mat.stat-mech↗

arXiv2012

Long-lasting Exponential Spreading in Periodically Driven Quantum Systems

Using a dynamical model relevant to cold-atom experiments, we show that long-lasting exponential spreading of wave packets in momentum space is possible. Numerical results are explained via a pseudo-classical map, both qualitatively and quantitatively. Possible applications of our findings are also briefly discussed.

nlin.CD↗

arXiv2011

The effect of discrete breathers on heat conduction in nonlinear chains

Intensive studies in the past decades have suggested that the heat conductivity $κ$ diverges with the system size $L$ as $κ\sim L^α$ in one dimensional momentum conserving nonlinear lattices and the value of $α$ is universal. But in the Fermi-Pasta-Ulam-$β$ lattices with next-nearest-neighbor interactions we find that $α$ strongly depends on $γ$, the ratio of the next-nearest-neighbor coupling to the nearest-neighbor coupling. We relate the $γ$-dependent heat conduction to the interactions between the long-wavelength phonons and the randomly distributed discrete breathers. Our results provide an evidence to show that the nonlinear excitations affect the heat transport.

cond-mat.stat-mech↗

arXiv2011

Energy transfer process in gas models of Lennard-Jones interactions

We perform simulations to investigate how the energy carried by a molecule transfers to others in an equilibrium gas model. For this purpose we consider a microcanonical ensemble of equilibrium gas systems, each of them contains a tagged molecule located at the same position initially. The ensuing transfer process of the energy initially carried by the tagged molecule is then exposed in terms of the ensemble-averaged energy density distribution. In both a 2D and a 3D gas model with Lennard-Jones interactions at room temperature, it is found that the energy carried by a molecule propagates in the gas ballistically, in clear contrast with the Gaussian diffusion widely assumed in previous studies. A possible scheme of experimental study of this issue is also proposed

physics.class-ph↗

arXiv2010

Generating a Fractal Butterfly Floquet Spectrum in a Class of Driven SU(2) Systems: Eigenstate Statistics

The Floquet spectra of a class of driven SU(2) systems have been shown to display butterfly patterns with multifractal properties. The implication of such critical spectral behavior for the Floquet eigenstate statistics is studied in this work. Following the methodologies for understanding the fractal behavior of energy eigenstates of time-independent systems on the Anderson transition point, we analyze the distribution profile, the mean value, and the variance of the logarithm of the inverse participation ratio of the Floquet eigenstates associated with multifractal Floquet spectra. The results show that the Floquet eigenstates also display fractal behavior, but with features markedly different from those in time-independent Anderson-transition models. This motivated us to propose a new type of random unitary matrix ensemble, called "power-law random banded unitary matrix" ensemble, to illuminate the Floquet eigenstate statistics of critical driven systems. The results based on the proposed random matrix model are consistent with those obtained from our dynamical examples with or without time-reversal symmetry.

nlin.CD↗

arXiv2009

Energy Diffusion in Gases

In the air surrounding us, how does a particle diffuse? Thanks to Einstein and other pioneers,it has been well known that generally the particle will undergo the Brownian motion, and in the last century this insight has been corroborated by numerous experiments and applications. Another fundamental question is how the energy carried by a particle diffuses. The conventional transport theories assumed the Brownian motion as the underlying energy transporting mechanism, but however, it should be noticed that in fact this assumption has never been tested and verified directly in experiments. Here we show that in clear contrast to the prediction based on the Brownian motion, in equilibrium gases the energy diffuses ballistically instead, spreading in a way analogous to a tsunami wave. This finding suggests a conceptually new perspective for revisiting the existing energy transport theories of gases, and provides a chance to solve some important application problems having challenged these theories for decades.

cond-mat.stat-mech↗