We have studied the AC response of a hopping model in the variable range hopping regime by dynamical Monte Carlo simulations. We find that the conductivity as function of frequency follows a universal scaling law. We also compare the numerical result
s to various theoretical predictions. Finally, we study the form of the conducting network as function of frequency.
In a recent paper [Vaikuntanathan and Jarzynski, Phys. Rev. E {bf 83}, 061120 (2011), arXiv:1105.1744] a model was introduced whereby work could be extracted from a thermal bath by measuring the energy of a particle that was thermalized by the bath a
nd manipulating the potential of the particle in the appropriate way, depending on the measurement outcome. If the extracted work is $W_1$ and the work $W_{text{er}}$ needed to be dissipated in order to erase the measured information in accordance with Landauers principle, it was shown that $W_1leq W_{text{er}}$ in accordance with the second law of thermodynamics. Here we extend this work in two directions: First, we discuss how accurately the energy should be measured. By increasing the accuracy one can extract more work, but at the same time one obtains more information that has to be deleted. We discuss what are the appropriate ways of optimizing the balance between the two and find optimal solutions. Second, whenever $W_1$ is strictly less than $W_{text{er}}$ it means that an irreversible step has been performed. We identify the irreversible step and propose a protocol that will achieve the same transition in a reversible way, increasing $W_1$ so that $W_1 = W_{text{er}}$.
We study the entropy and information flow in a Maxwell demon device based on a single-electron transistor with controlled gate potentials. We construct the protocols for measuring the charge states and manipulating the gate voltages which minimizes i
rreversibility for (i) constant input power from the environment or (ii) given energy gain. Charge measurement is modeled by a series of detector readouts for time-dependent gate potentials, and the amount of information obtained is determined. The protocols optimize irreversibility that arises due to (i) enlargement of the configuration space on opening the barriers, and (ii) finite rate of operation. These optimal protocols are general and apply to all systems where barriers between different regions can be manipulated.
Slow relaxation and aging of the conductance are experimental features of a range of materials, which are collectively known as electron glasses. We report dynamic Monte Carlo simulations of the standard electron glass lattice model. In a non-equilib
rium state, the electrons will often form a Fermi distribution with an effective electron temperature higher than the phonon bath temperature. We study the effective temperature as a function of time in three different situations: relaxation after a quench from an initial random state, during driving by an external electric field and during relaxation after such driving. We observe logarithmic relaxation of the effective temperature after a quench from a random initial state as well as after driving the system for some time $t_w$ with a strong electric field. For not too strong electric field and not too long $t_w$ we observe that data for the effective temperature at different waiting times collapse when plotted as functions of $t/t_w$ -- the so-called simple aging. During the driving period we study how the effective temperature is established, separating the contributions from the sites involved in jumps from those that were not involved. It is found that the heating mainly affects the sites involved in jumps, but at strong driving, also the remaining sites are heated.
A numerical study of the energy relaxation and conductivity of the Coulomb glass is presented. The role of many-electron transitions is studied by two complementary methods: a kinetic Monte Carlo algorithm and a master equation in configuration space
method. A calculation of the transition rate for two-electron transitions is presented, and the proper extension of this to multi-electron transitions is discussed. It is shown that two-electron transitions are important in bypassing energy barriers which effectively block sequential one-electron transitions. The effect of two-electron transitions is also discussed.
The efficiency of the future devices for quantum information processing is limited mostly by the finite decoherence rates of the qubits. Recently a substantial progress was achieved in enhancing the time, which a solid-state qubit demonstrates a cohe
rent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions the material-inherent sources of noise start to play a crucial role. In most cases the noise that quantum device demonstrate has 1/f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review we discuss the current state of the theory of the decoherence due to the qubit interaction with the fluctuators. We describe the effect of such an environment on different protocols of the qubit manipulations - free induction and echo signal. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function only. We describe the effect of the fluctuators using so-called spin-fluctuator model. Being quite realistic this model allows one to evaluate the qubit dynamics in the presence of one fluctuator exactly. This solution is found, and its features, including non-Gaussian effects are analyzed in details. We extend this consideration for the systems of large number of fluctuators, which interact with the qubit and lead to the 1/f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
We present experiments on slow shear flow in a split-bottom linear shear cell, filled with layered granular materials. Shearing through two different materials separated by a flat material boundary is shown to give narrow shear zones, which refract a
t the material boundary in accordance with Snells law in optics. The shear zone is the one that minimizes the dissipation rate upon shearing, i.e.a manifestation of the principle of least dissipation. We have prepared the materials as to form a granular lens. Shearing through the lens is shown to give a very broad shear zone, which corresponds to fulfilling Snells law for a continuous range of paths through the cell.
