Relaxation process in a regime of quantum chaos

We show that the quantum relaxation process in a classically chaotic open dynamical system is characterized by a quantum relaxation time scale t_q. This scale is much shorter than the Heisenberg time and much larger than the Ehrenfest time: t_q ~ g^alpha where g is the conductance of the system and the exponent alpha is close to 1/2. As a result, quantum and classical decay probabilities remain close up to values P ~ exp(-sqrt(g)) similarly to the case of open disordered systems.Comment: revtex, 5 pages, 4 figures discussion of the relations between time scale t_q and weak localization correction and between dynamical and disordered systems is adde

Low energy transition in spectral statistics of 2D interactingfermions

We study the level spacing statistics $P(s)$ and eigenstate properties of spinless fermions with Coulomb interaction on a two dimensional lattice at constant filling factor and various disorder strength. In the limit of large lattice size, $P(s)$ undergoes a transition from the Poisson to the Wigner-Dyson distribution at a critical total energy independent of the number of fermions. This implies the emergence of quantum ergodicity induced by interaction and delocalization in the Hilbert space at zero temperature.Comment: revtex, 5 pages, 4 figures; new data for eigenfunctions are adde

Ground state properties of the 2D disordered Hubbard model

We study the ground state of the two-dimensional (2D) disordered Hubbard model by means of the projector quantum Monte Carlo (PQMC) method. This approach allows us to investigate the ground state properties of this model for lattice sizes up to $10 \times 10$, at quarter filling, for a broad range of interaction and disorder strengths. Our results show that the ground state of this system of spin-1/2 fermions remains localised in the presence of the short-ranged Hubbard interaction.Comment: 7 pages, 9 figure

How backscattering off a point impurity can enhance the current and make the conductance greater than e^2/h per channel

It is well known that while forward scattering has no effect on the conductance of one-dimensional systems, backscattering off a static impurity suppresses the current. We study the effect of a time-dependent point impurity on the conductance of a one-channel quantum wire. At strong repulsive interaction (Luttinger liquid parameter g<1/2), backscattering renders the linear conductance greater than its value e^2/h in the absence of the impurity. A possible experimental realization of our model is a constricted quantum wire or a constricted Hall bar at fractional filling factors nu=1/(2n+1) with a time-dependent voltage at the constriction.Comment: 7 pages, 2 figure

Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement

Coherent propagation of two interacting particles in $1d$ weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This mapping allows to clarify the mechanism of enhancement of the localization length which turns out to be rather different from the one considered in the literature. Although the existence of enhancement is transparent, an analytical solution of the matrix model was found only for very short samples. For a more realistic situation numerical simulations were performed. The result of these simulations is consistent with l_{2}/l_1 \sim l_1^{\gamma} , where $l_1$ and $l_2$ are the single and two particle localization lengths and the exponent $\gamma$ depends on the strength of the interaction. In particular, in the limit of strong particle-particle interaction there is no enhancement of the coherent propagation at all ($l_{2} \approx l_1$).Comment: 23 pages, REVTEX, 3 eps figures, improved version accepted for publication in Phys. Rev.

Unconventional decay law for excited states in closed many-body systems

We study the time evolution of an initially excited many-body state in a finite system of interacting Fermi-particles in the situation when the interaction gives rise to the ``chaotic'' structure of compound states. This situation is generic for highly excited many-particle states in quantum systems, such as heavy nuclei, complex atoms, quantum dots, spin systems, and quantum computers. For a strong interaction the leading term for the return probability $W(t)$ has the form $W(t)\simeq \exp (-\Delta_E^2t^2)$ with $\Delta_E^2$ as the variance of the strength function. The conventional exponential linear dependence $W(t)=C\exp (-\Gamma t)$ formally arises for a very large time. However, the prefactor $C$ turns out to be exponentially large, thus resulting in a strong difference from the conventional estimate for $W(t)$.Comment: RevTex, 4 pages including 1 eps-figur

Non-Fermi-liquid behavior in the Kondo lattices induced by peculiarities of magnetic ordering and spin dynamics

A scaling consideration of the Kondo lattices is performed with account of singularities in the spin excitation spectral function. It is shown that a non-Fermi-liquid (NFL) behavior between two critical values of the bare $s-f$ coupling constant occurs naturally for complicated magnetic structures with several magnon branches. This may explain the fact that a NFL behavior takes place often in the heavy-fermion systems with peculiar spin dynamics. Another kind of a NFL-like state (with different critical exponents) can occur for simple antiferromagnets with account of magnon damping, and for paramagnets, especially with two-dimensional character of spin fluctuations. The mechanisms proposed lead to some predictions about behavior of specific heat, resistivity, magnetic susceptibility, and anisotropy parameter, which can be verified experimentally.Comment: 16 pages, RevTeX, 4 Postscript figures. Extended versio

The Parallel Magnetoconductance of Interacting Electrons in a Two Dimensional Disordered System

The transport properties of interacting electrons for which the spin degree of freedom is taken into account are numerically studied for small two dimensional diffusive clusters. On-site electron-electron interactions tend to delocalize the electrons, while long-range interactions enhance localization. On careful examination of the transport properties, we reach the conclusion that it does not show a two dimensional metal insulator transition driven by interactions. A parallel magnetic field leads to enhanced resistivity, which saturates once the electrons become fully spin polarized. The strength of the magnetic field for which the resistivity saturates decreases as electron density goes down. Thus, the numerical calculations capture some of the features seen in recent experimental measurements of parallel magnetoconductance.Comment: 10 pages, 6 figure

25 Years of Self-organized Criticality: Concepts and Controversies

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers

Evaluating the contribution of rare variants to type 2 diabetes and related traits using pedigrees

A major challenge in evaluating the contribution of rare variants to complex disease is identifying enough copies of the rare alleles to permit informative statistical analysis. To investigate the contribution of rare variants to the risk of type 2 diabetes (T2D) and related traits, we performed deep whole-genome analysis of 1,034 members of 20 large Mexican-American families with high prevalence of T2D. If rare variants of large effect accounted for much of the diabetes risk in these families, our experiment was powered to detect association. Using gene expression data on 21,677 transcripts for 643 pedigree members, we identified evidence for large-effect rare-variant cis-expression quantitative trait loci that could not be detected in population studies, validating our approach. However, we did not identify any rare variants of large effect associated with T2D, or the related traits of fasting glucose and insulin, suggesting that large-effect rare variants account for only a modest fraction of the genetic risk of these traits in this sample of families. Reliable identification of large-effect rare variants will require larger samples of extended pedigrees or different study designs that further enrich for such variants