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Register a new userDynamic critical phenomena in disordered systems with finite geometry
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We study the critical dynamics of hyper-cubic finite size system in the presence of quenched short-range correlated disorder. By using the random $T_c$ model A for the critical dynamics and the renormalization group method in the vicinity of the upper critical dimension $d=4$, we derive in first order of $epsilon$ the expression for the relaxation time. Its finite-size scaling behavior is discussed both analytically and numerically in details. This was made possible by analyzing carefully the finite--size effects on the Onsager kinetic coefficient. The obtained results are compared to those reported in the literature.
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Barkhausen noise as found in magnets is studied both with and without the presence of long-range (LR) demagnetizing fields using the non-equilibrium, zero-temperature random-field Ising model. Two distinct subloop behaviors arise and are shown to be in qualitative agreement with experiments on thin film magnets and soft ferromagnets. With LR fields present subloops resemble a self-organized critical system, while their absence results in subloops that reflect the critical point seen in the saturation loop as the system disorder is changed. In the former case, power law distributions of noise are found in subloops, while in the latter case history-induced critical scaling is studied in avalanche size distributions, spin-flip correlation functions, and finite-size scaling of the second moments of the size distributions. Results are presented for simulations of over 10^8 spins.
We study the problem of wave transport in a one-dimensional disordered system, where the scatterers of the chain are $n$ barriers and wells with statistically independent intensities and with a spatial extension $l_c$ which may contain an arbitrary number $delta/2pi$ of wavelengths, where $delta = k l_c$. We analyze the average Landauer resistance and transmission coefficient of the chain as a function of $n$ and the phase parameter $delta$. For weak scatterers, we find: i) a regime, to be called I, associated with an exponential behavior of the resistance with $n$, ii) a regime, to be called II, for $delta$ in the vicinity of $pi$, where the system is almost transparent and less localized, and iii) right in the middle of regime II, for $delta$ very close to $pi$, the formation of a band gap, which becomes ever more conspicuous as $n$ increases. In regime II, both the average Landauer resistance and the transmission coefficient show an oscillatory behavior with $n$ and $delta$. These characteristics of the system are found analytically, some of them exactly and some others approximately. The agreement between theory and simulations is excellent, which suggests a strong motivation for the experimental study of these systems. We also present a qualitative discussion of the results.
It is well known that for ordinary one-dimensional (1D) disordered systems, the Anderson localization length $xi$ diverges as $lambda^m$ in the long wavelength limit ($lambdarightarrow infty$ ) with a universal exponent $m=2$, independent of the type of disorder. Here, we show rigorously that pseudospin-1 systems exhibit non-universal critical behaviors when they are subjected to 1D random potentials. In such systems, we find that $xipropto lambda^m$ with $m$ depending on the type of disorder. For binary disorder, $m=6$ and the fast divergence is due to a super-Klein-tunneling effect (SKTE). When we add additional potential fluctuations to the binary disorder, the critical exponent $m$ crosses over from 6 to 4 as the wavelength increases. Moreover, for disordered superlattices, in which the random potential layers are separated by layers of background medium, the exponent $m$ is further reduced to 2 due to the multiple reflections inside the background layer. To obtain the above results, we developed a new analytic method based on a stack recursion equation. Our analytical results are in excellent agreements with the numerical results obtained by the transfer-matrix method (TMM). For pseudospin-1/2 systems, we find both numerically and analytically that $xiproptolambda^2$ for all types of disorder, same as ordinary 1D disordered systems. Our new analytical method provides a convenient way to obtain easily the critical exponent $m$ for general 1D Anderson localization problems.
We study phase transitions in a two dimensional weakly interacting Bose gas in a random potential at finite temperatures. We identify superfluid, normal fluid, and insulator phases and construct the phase diagram. At T=0 one has a tricritical point where the three phases coexist. The truncation of the energy distribution at the trap barrier, which is a generic phenomenon in cold atom systems, limits the growth of the localization length and in contrast to the thermodynamic limit the insulator phase is present at any temperature.
We study the spreading of single-site excitations in one-dimensional disordered Klein-Gordon chains with tunable nonlinearity $|u_{l}|^{sigma} u_{l}$ for different values of $sigma$. We perform extensive numerical simulations where wave packets are evolved a) without and, b) with dephasing in normal mode space. Subdiffusive spreading is observed with the second moment of wave packets growing as $t^{alpha}$. The dependence of the numerically computed exponent $alpha$ on $sigma$ is in very good agreement with our theoretical predictions both for the evolution of the wave packet with and without dephasing (for $sigma geq 2$ in the latter case). We discuss evidence of the existence of a regime of strong chaos, and observe destruction of Anderson localization in the packet tails for small values of $sigma$.
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