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Register a new userHatano-Nelson model with a periodic potential
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We study a generalisation of the Hatano-Nelson Hamiltonian in which a periodic modulation of the site energies is present in addition to the usual random distribution. The system can then become localized by disorder or develop a band gap, and the eigenspectrum shows a wide variety of topologies. We determine the phase diagram, and perform a finite size scaling analysis of the localization transition.
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In this paper, we investigate the ground-state properties of a bosonic Tonks-Girardeau gas confined in a one-dimensional periodic potential. The single-particle reduced density matrix is computed numerically for systems up to $N=265$ bosons. Scaling analysis of the occupation number of the lowest orbital shows that there are no Bose-Einstein Condensation(BEC) for the periodically trapped TG gas in both commensurate and incommensurate cases. We find that, in the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, -0.5 and 1, respectively, while in the incommensurate case, they are 0.5, -0.5 and 1.5, respectively. These exponents are related to each other in a universal relation.
We analyze the classical problem of the stochastic dynamics of a particle confined in a periodic potential, through the so called Ilin and Khasminskii model, with a novel semi-analytical approach. Our approach gives access to the transient and the asymptotic dynamics in all damping regimes, which are difficult to investigate in the usual Brownian model. We show that the crossover from the overdamped to the underdamped regime is associated with the loss of a typical time scale and of a typical length scale, as signaled by the divergence of the probability distribution of a certain dynamical event. In the underdamped regime, normal diffusion coexists with a non Gaussian displacement probability distribution for a long transient, as recently observed in a variety of different systems. We rationalize the microscopic physical processes leading to the non-Gaussian behavior, as well as the timescale to recover the Gaussian statistics. The theoretical results are supported by numerical calculations and are compared to those obtained for the Brownian model.
We consider a particle in a one-dimensional box of length $L$ with a Maxwell bath at one end and a reflecting wall at the other end. Using a renewal approach, as well as directly solving the master equation, we show that the system exhibits a slow power law relaxation with a logarithmic correction towards the final equilibrium state. We extend the renewal approach to a class of confining potentials of the form $U(x) propto x^alpha$, $x>0$, where we find that the relaxation is $sim t^{-(alpha+2)/(alpha-2)}$ for $alpha >2$, with a logarithmic correction when $(alpha+2)/(alpha-2)$ is an integer. For $alpha <2$ the relaxation is exponential. Interestingly for $alpha=2$ (harmonic potential) the localised bath can not equilibrate the particle.
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The collective effect on the viscosity is essential for warm dense metals. The statistics of random-walk ions and the Debye shielding effect describing the collective properties are introduced in the random-walk shielding-potential viscosity model (RWSP-VM). As a test, the viscosities of several metals (Be, Al, Fe and U) are obtained, which cover from low-Z to high-Z elements. The results indicate that RWSP-VM is a universal accurate and highly efficient model for calculating the viscosity of metals in warm dense state.
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