Defect-induced condensation and central peak at elastic phase transitions

Static and dynamical properties of elastic phase transitions under the influence of short--range defects, which locally increase the transition temperature, are investigated. Our approach is based on a Ginzburg--Landau theory for three--dimensional crystals with one--, two-- or three--dimensional soft sectors, respectively. Systems with a finite concentration $n_{\rm D}$ of quenched, randomly placed defects display a phase transition at a temperature $T_c(n_{\rm D})$, which can be considerably above the transition temperature $T_c^0$ of the pure system. The phonon correlation function is calculated in single--site approximation. For $T>T_c(n_{\rm D})$ a dynamical central peak appears; upon approaching $T_c(n_{\rm D})$, its height diverges and its width vanishes. Using an appropriate self--consistent method, we calculate the spatially inhomogeneous order parameter, the free energy and the specific heat, as well as the dynamical correlation function in the ordered phase. The dynamical central peak disappears again as the temperatur is lowered below $T_c(n_{\rm D})$. The inhomogeneous order parameter causes a static central peak in the scattering cross section, with a finite $k$ width depending on the orientation of the external wave vector ${\bf k}$ relative to the soft sector. The jump in the specific heat at the transition temperatur of the pure system is smeared out by the influence of the defects, leading to a distinct maximum instead. In addition, there emerges a tiny discontinuity of the specific heat at $T_c(n_{\rm D})$. We also discuss the range of validity of the mean--field approach, and provide a more realistic estimate for the transition temperature.Comment: 11 pages, 11 ps-figures, to appear in PR

Quantum Charge Transport and Conformational Dynamics of Macromolecules

We study the dynamics of quantum excitations inside macromolecules which can undergo conformational transitions. In the first part of the paper, we use the path integral formalism to rigorously derive a set of coupled equations of motion which simultaneously describe the molecular and quantum transport dynamics, and obey the fluctuation/dissipation relationship. We also introduce an algorithm which yields the most probable molecular and quantum transport pathways in rare, thermally-activated reactions. In the second part of the paper, we apply this formalism to simulate the propagation of a charge during the collapse of a polymer from an initial stretched conformation to a final globular state. We find that the charge dynamics is quenched when the chain reaches a molten globule state. Using random matrix theory we show that this transition is due to an increase of quantum localization driven by dynamical disorder.Comment: 11 pages, 2 figure

Unexpected systematic degeneracy in a system of two coupled Gaudin models with homogeneous couplings

We report an unexpected systematic degeneracy between different multiplets in an inversion symmetric system of two coupled Gaudin models with homogeneous couplings, as occurring for example in the context of solid state quantum information processing. We construct the full degenerate subspace (being of macroscopic dimension), which turns out to lie in the kernel of the commutator between the two Gaudin models and the coupling term. Finally we investigate to what extend the degeneracy is related to the inversion symmetry of the system and find that indeed there is a large class of systems showing the same type of degeneracy.Comment: 13 pages, 4 figure

Conservation law of operator current in open quantum systems

We derive a fundamental conservation law of operator current for master equations describing reduced quantum systems. If this law is broken, the temporal integral of the current operator of an arbitrary system observable does not yield in general the change of that observable in the evolution. We study Lindblad-type master equations as examples and prove that the application of the secular approximation during their derivation results in a violation of the conservation law. We show that generally any violation of the law leads to artificial corrections to the complete quantum dynamics, thus questioning the accuracy of the particular master equation.Comment: 5 pages, final versio

Bell-state preparation for electron spins in a semiconductor double quantum dot

A robust scheme for state preparation and state trapping for the spins of two electrons in a semiconductor double quantum dot is presented. The system is modeled by two spins coupled to two independent bosonic reservoirs. Decoherence effects due to this environment are minimized by application of optimized control fields which make the target state to the ground state of the isolated driven spin system. We show that stable spin entanglement with respect to pure dephasing is possible. Specifically, we demonstrate state trapping in a maximally entangled state (Bell state) in the presence of decoherence.Comment: 9 pages, 4 figure

Critical sound attenuation in a diluted Ising system

The field-theoretic description of dynamical critical effects of the influence of disorder on acoustic anomalies near the temperature of the second-order phase transition is considered for three-dimensional Ising-like systems. Calculations of the sound attenuation in pure and dilute Ising-like systems near the critical point are presented. The dynamical scaling function for the critical attenuation coefficient is calculated. The influence of quenched disorder on the asymptotic behaviour of the critical ultrasonic anomalies is discussed.Comment: 12 RevTeX pages, 4 figure

Quantum features derived from the classical model of a bouncer-walker coupled to a zero-point field

In our bouncer-walker model a quantum is a nonequilibrium steady-state maintained by a permanent throughput of energy. Specifically, we consider a "particle" as a bouncer whose oscillations are phase-locked with those of the energy-momentum reservoir of the zero-point field (ZPF), and we combine this with the random-walk model of the walker, again driven by the ZPF. Starting with this classical toy model of the bouncer-walker we were able to derive fundamental elements of quantum theory. Here this toy model is revisited with special emphasis on the mechanism of emergence. Especially the derivation of the total energy hbar.omega and the coupling to the ZPF are clarified. For this we make use of a sub-quantum equipartition theorem. It can further be shown that the couplings of both bouncer and walker to the ZPF are identical. Then we follow this path in accordance with previous work, expanding the view from the particle in its rest frame to a particle in motion. The basic features of ballistic diffusion are derived, especially the diffusion constant D, thus providing a missing link between the different approaches of our previous works.Comment: 14 pages, based on a talk given at "Emergent Quantum Mechanics (Heinz von Foerster Conference 2011)", see http://www.univie.ac.at/hvf11/congress/EmerQuM.htm

Non-Markovian dynamics for bipartite systems

We analyze the appearance of non-Markovian effects in the dynamics of a bipartite system coupled to a reservoir, which can be described within a class of non-Markovian equations given by a generalized Lindblad structure. A novel master equation, which we term quantum Bloch-Boltzmann equation, is derived, describing both motional and internal states of a test particle in a quantum framework. When due to the preparation of the system or to decoherence effects one of the two degrees of freedom is amenable to a classical treatment and not resolved in the final measurement, though relevant for the interaction with the reservoir, non-Markovian behaviors such as stretched exponential or power law decay of coherences can be put into evidence.Comment: published version, 15 pages, revtex, no figure

Exact Results for the One-Dimensional Self-Organized Critical Forest-Fire Model

We present the analytic solution of the self-organized critical (SOC) forest-fire model in one dimension proving SOC in systems without conservation laws by analytic means. Under the condition that the system is in the steady state and very close to the critical point, we calculate the probability that a string of $n$ neighboring sites is occupied by a given configuration of trees. The critical exponent describing the size distribution of forest clusters is exactly $\tau = 2$ and does not change under certain changes of the model rules. Computer simulations confirm the analytic results.Comment: 12 pages REVTEX, 2 figures upon request, dro/93/