arXiv subjects

Heiko Rieger

Publications and source records attributed to Heiko Rieger.

At least 91 records · Page 5Linked to original sources

arXiv2011

Quantum relaxation after a quench in systems with boundaries

We study the time-dependence of the magnetization profile, m_l(t), of a large finite open quantum Ising chain after a quench. We observe a cyclic variation, in which starting with an exponentially decreasing period the local magnetization arrives to a quasi-stationary regime, which is followed by an exponentially fast reconstruction period. The non-thermal behavior observed at near-surface sites turns over to thermal behavior for bulk sites. Besides the standard time- and length-scales a non-standard time-scale is identified in the reconstruction period.

cond-mat.stat-mech↗

arXiv2008

Broad edge of chaos in strongly heterogeneous Boolean networks

The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations. This turns out to behave in a universal way close to the phase boundary only for in-degree distributions with a finite second moment. In-degree distributions of the form $P_d(k)\sim k^{-γ}$ with $2<γ<3$, thus having a diverging second moment, lead to a slower increase of the Hamming distance when moving towards the unstable phase and to a broadening of the phase boundary for finite $N$ with decreasing $γ$. We conclude that the heterogeneous regulatory network connectivity facilitates the balancing between robustness and evolvability in living organisms.

cond-mat.stat-mech↗

arXiv2008

The quantum phase transition in the sub-ohmic spin-boson model: Quantum Monte-Carlo study with a continuous imaginary time cluster algorithm

A continuous time cluster algorithm for two-level systems coupled to a dissipative bosonic bath is presented and applied to the sub-ohmic spin-Boson model. When the power s of the spectral function J(w) \propto w^s is smaller than 1/2, the critical exponents are found to be classical, mean-field like. Potential sources for the discrepancy with recent renormalization group predictions are traced back to the effect of a dangerously irrelevant variable.

cond-mat.stat-mech↗

arXiv2008

Hot spot formation in tumor vasculature during tumor growth in an arterio-venous-network environment

Hot spots in tumors are regions of high vascular density in the center of the tumor and their analysis is an important diagnostic tool in cancer treatment. We present a model for vascular remodeling in tumors predicting that the formation of hot spots correlates with local inhomogeneities of the original arterio-venous vasculature of the healthy tissue. Probable locations for hot spots in the late stages of the tumor are locations of increased blood pressure gradients. The developing tumor vasculature is non-hierarchical but still complex displaying algebraically decaying density distributions.

q-bio.TO↗

arXiv2007

Finite temperature behavior of strongly disordered quantum magnets coupled to a dissipative bath

We study the effect of dissipation on the infinite randomness fixed point and the Griffiths-McCoy singularities of random transverse Ising systems in chains, ladders and in two-dimensions. A strong disorder renormalization group scheme is presented that allows the computation of the finite temperature behavior of the magnetic susceptibility and the spin specific heat. In the case of Ohmic dissipation the susceptibility displays a crossover from Griffiths-McCoy behavior (with a continuously varying dynamical exponent) to classical Curie behavior at some temperature $T^*$. The specific heat displays Griffiths-McCoy singularities over the whole temperature range. For super-Ohmic dissipation we find an infinite randomness fixed point within the same universality class as the transverse Ising system without dissipation. In this case the phase diagram and the parameter dependence of the dynamical exponent in the Griffiths-McCoy phase can be determined analytically.

cond-mat.dis-nn↗

arXiv2007

Entanglement entropy at infinite randomness fixed points in higher dimensions

The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and only at, the quantum phase transition that is governed by an infinite randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. This contrasts with the pure area law valid at the infinite randomness fixed point in the diluted transverse Ising model in higher dimensions.

cond-mat.dis-nn↗

arXiv2007

Finite-size scaling of pseudo-critical point distributions in the random transverse-field Ising chain

We study the distribution of finite size pseudo-critical points in a one-dimensional random quantum magnet with a quantum phase transition described by an infinite randomness fixed point. Pseudo-critical points are defined in three different ways: the position of the maximum of the average entanglement entropy, the scaling behavior of the surface magnetization, and the energy of a soft mode. All three lead to a log-normal distribution of the pseudo-critical transverse fields, where the width scales as $L^{-1/ν}$ with $ν=2$ and the shift of the average value scales as $L^{-1/ν_{typ}}$ with $ν_{typ}=1$, which we related to the scaling of average and typical quantities in the critical region.

cond-mat.dis-nn↗

arXiv2007

Path integral Monte Carlo study of the interacting quantum double-well model: Quantum phase transition and phase diagram

The discrete time path integral Monte Carlo (PIMC) with a one-particle density matrix approximation is applied to study the quantum phase transition in the coupled double-well chain. To improve the convergence properties, the exact action for a single particle in a double well potential is used to construct the many-particle action. The algorithm is applied to the interacting quantum double-well chain for which the zero-temperature phase diagram is determined. The quantum phase transition is studied via finite-size scaling and the critical exponents are shown to be compatible with the classical two-dimensional (2D) Ising universality class -- not only in the order-disorder limit (deep potential wells) but also in the displacive regime (shallow potential wells).

cond-mat.stat-mech↗

arXiv2006

Super-Aging in two-dimensional random ferromagnets

We study the aging properties, in particular the two-time autocorrelations, of the two-dimensional randomly diluted Ising ferromagnet below the critical temperature via Monte-Carlo simulations. We find that the autocorrelation function displays additive aging $C(t,t_w)=C_{st}(t)+C_{ag}(t,t_w)$, where the stationary part $C_{st}$ decays algebraically. The aging part shows anomalous scaling $C_{ag}(t,t_w)={\cal C}(h(t)/h(t_w))$, where $h(u)$ is a non-homogeneous function excluding a $t/t_w$ scaling.

cond-mat.dis-nn↗

arXiv2006

Comparative study of the transcriptional regulatory networks of E. coli and yeast: Structural characteristics leading to marginal dynamic stability

Dynamical properties of the transcriptional regulatory network of {\it Escherichia coli} and {\it Saccharomyces cerevisiae} are studied within the framework of random Boolean functions. The dynamical response of these networks to a single point mutation is characterized by the number of mutated elements as a function of time and the distribution of the relaxation time to a new stationary state, which turn out to be different in both networks. Comparison with the behavior of randomized networks reveals relevant structural characteristics other than the mean connectivity, namely the organization of circuits and the functional form of the in-degree distribution. The abundance of single-element circuits in {\it E. coli} and the power-law in-degree distribution of {\it S. cerevisiae} shift their dynamics towards marginal stability overcoming the restrictions imposed by their mean connectivities, which is argued to be related to the simultaneous presence of robustness and adaptivity in living organisms.

q-bio.MN↗

arXiv2006

Strong Randomness Fixed Point in the Dissipative Random Transverse Field Ising Model

The interplay between disorder, quantum fluctuations and dissipation is studied in the random transverse Ising chain coupled to a dissipative Ohmic bath with a real space renormalization group. A typically very large length scale, L*, is identified above which the physics of frozen clusters dominates. Below L* a strong disorder fixed point determines scaling at a pseudo-critical point. In a Griffiths-McCoy region frozen clusters produce already a finite magnetization resulting in a classical low temperature behavior of the susceptibility and specific heat. These override the confluent singularities that are characterized by a continuously varying exponent z and are visible above a temperature T* ~ L*^{-z}.

cond-mat.dis-nn↗

arXiv2006

Strong disorder renormalization group study of S=1/2 Heisenberg antiferromagnet layers/bilayers with bond randomness, site dilution and dimer dilution

Using a numerical implementation of strong disorder renormalization group, we study the low-energy, long-distance properties of layers and bilayers of $S = 1/2$ Heisenberg antiferromagnets with different type of disorder: bond randomness, site and dimer dilution. Generally the systems exhibit an ordered and a disordered phase separated by a phase boundary on which the static critical exponents appear to be independent of bond randomness in the strong disorder regime, while the dynamical exponent is a continuous function of the bond disorder strength. The low-energy fixed points of the off-critical phases are affected by the actual form of the disorder, and the disorder induced dynamical exponent depends on the disorder strength. As the strength of bond disorder is increased, there is a set of crossovers in the properties of the low-energy singularities. For weak disorder quantum fluctuations play the dominant role. For intermediate disorder non-localized disorder fluctuations are relevant, which become localized for even stronger bond disorder. We also present some quantum Monte Carlo simulations results to support the strong disorder renormalization approach.

cond-mat.dis-nn↗

arXiv2006

Elastic lines on splayed columnar defects studied numerically

We investigate by exact optimization method properties of two- and three-dimensional systems of elastic lines in presence of splayed columnar disorder. The ground state of many lines is separable both in 2d and 3d leading to a random walk -like roughening in 2d and ballistic behavior in 3d. Furthermore, we find that in the case of pure splayed columnar disorder in contrast to point disorder there is no entanglement transition in 3d. Entanglement can be triggered by perturbing the pure splay system with point defects.

cond-mat.supr-con↗

arXiv2006

Random-exchange quantum Heisenberg antiferromagnets on the square lattice

The ground state properties of random-exchange spin-1/2 Heisenberg antiferromagnets on the square lattice are investigated using a combination of quantum Monte Carlo simulations, exact numerical diagonalizations, and spin wave calculations. Whereas arbirarily weak disorder has a drastic effect on 1d Heisenberg AFM, we find that in two dimensions the characteristics of the ground state like long-range order is robust even against strong disorder. While the antiferromagnetic order parameter and the spin stiffness are exponentially reduced for singular exchange distributions, they vanish only in the limit of infinite randomness.

cond-mat.str-el↗

arXiv2006

Maximum flow and topological structure of complex networks

The problem of sending the maximum amount of flow $q$ between two arbitrary nodes $s$ and $t$ of complex networks along links with unit capacity is studied, which is equivalent to determining the number of link-disjoint paths between $s$ and $t$. The average of $q$ over all node pairs with smaller degree $k_{\rm min}$ is $ _{k_{\rm min}} \simeq c k_{\rm min}$ for large $k_{\rm min}$ with $c$ a constant implying that the statistics of $q$ is related to the degree distribution of the network. The disjoint paths between hub nodes are found to be distributed among the links belonging to the same edge-biconnected component, and $q$ can be estimated by the number of pairs of edge-biconnected links incident to the start and terminal node. The relative size of the giant edge-biconnected component of a network approximates to the coefficient $c$. The applicability of our results to real world networks is tested for the Internet at the autonomous system level.

cond-mat.stat-mech↗

arXiv2005

Disorder-induced phases in the S=1 antiferromagnetic Heisenberg chain

We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random S=1 antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function, and the string order parameter. For this distribution at weak disorder, the systems is in the gapless Haldane phase with a disorder dependent dynamical exponent, z, and z=1 signals, the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-to-end correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.

cond-mat.stat-mech↗

arXiv2005

Domain Growth in Ising Systems with Quenched Disorder

We present results from extensive Monte Carlo (MC) simulations of domain growth in ferromagnets and binary mixtures with quenched disorder. These are modeled by the "random-bond Ising model" and the "dilute Ising model" with either nonconserved (Glauber) spin-flip kinetics or conserved (Kawasaki) spin-exchange kinetics. In all cases, our MC results are consistent with power-law growth with an exponent $θ(T,ε)$ which depends on the quench temperature $T$ and the disorder amplitude $ε$. Such exponents arise naturally when the coarsening domains are trapped by energy barriers which grow logarithmically with the domain size. Our MC results show excellent agreement with the predicted dependence of $θ(T,ε)$.

cond-mat.dis-nn↗

arXiv2004

Condensation Phenomena in Nano-Pores - a Monte Carlo Study

The non-equilibrium dynamics of condensation phenomena in nano-pores is studied via Monte Carlo simulation of a lattice gas model. Hysteretic behavior of the particle density as a function of the density of a reservoir is obtained for various pore geometries in two and three dimensions. The shape of the hysteresis loops depend on the characteristics of the pore geometry. The evaporation of particles from a pore can be fitted to a stretched exponential decay of the particle density $ρ_f(t) \sim exp [ -(t/τ)^β]$. Phase separation dynamics inside the pore is effectively described by a random walk of the non-wetting phases. Domain evolution is significantly slowed down in presence of random wall-particle potential and gives rise to a temperature dependent growth exponent. On the other hand roughness of the pore wall only delays the onset of a pure domain growth.

cond-mat.soft↗