A Nontrivial Scaling Limit for Multiscale Markov Chains

We consider Markov chains with fast and slow variables and show that in a suitable scaling limit, the dynamics becomes deterministic, yet is far away from the standard mean field approximation. This new limit is an instance of self-induced stochastic resonance which arises due to matching between a rare event timescale on the one hand and the natural timescale separation in the underlying problem on the other. Here it is illustrated on a model of a molecular motor, where it is shown to explain the regularity of the motor gait observed in some experiments.     

Special Features of Nuclear Reactions Involving Loosely Bound Cluster Nuclei

Physics of Atomic Nuclei - Reactions involving loosely bound nuclei have many special features. An enhancement of interaction cross sections in the subbarrier energy region is one of them. This...     

Robustness of Quantum Markov Chains

If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum relative entropy) of the distribution to the nearest Markov chain distribution is precisely the conditional information. We prove here that this simple situation does not obtain for quantum conditional information. We show that for tri-partite quantum states the quantum conditional information is always a lower bound for the minimum relative entropy distance to a quantum Markov chain state, but the distance can be much greater; indeed the two quantities can be of different asymptotic order and may even differ by a dimensional factor.     

Multifractal Nonrigidity of Topological Markov Chains

Given a multifractal spectrum, we consider the problem of whether it is possible to recover the potential that originates the spectrum. The affirmative solution of this problem would correspond to a “multifractal” classification of dynamical systems, i.e., a classification solely based on the information given by multifractal spectra. For the entropy spectrum on topological Markov chains we show that it is possible to have both multifractal rigidity and multifractal “nonrigidity”, by appropriately varying the Markov chain and the potential defining the spectrum. The “nonrigidity” even occurs in some generic sense. This strongly contrasts to the usual opinion among some experts that it should be possible to recover the potential up to some equivalence relation, at least in some generic sense. Supported by the Center for Mathematical Analysis, Geometry, and Dynamical Systems, through FCT by Program POCTI/FEDER and the grant SFRH/BD/10154/2002.     

Metastable Distributions of Markov Chains with Rare Transitions

In this paper we consider Markov chains \(X^\varepsilon _t\) with transition rates that depend on a small parameter \(\varepsilon \). We are interested in the long time behavior of \(X^\varepsilon _t\) at various \(\varepsilon \)-dependent time scales \(t = t(\varepsilon )\). The asymptotic behavior depends on how the point \((1/\varepsilon , t(\varepsilon ))\) approaches infinity. We introduce a general notion of complete asymptotic regularity (a certain asymptotic relation between the ratios of transition rates), which ensures the existence of the metastable distribution for each initial point and a given time scale \(t(\varepsilon )\). The technique of i-graphs allows one to describe the metastable distribution explicitly. The result may be viewed as a generalization of the ergodic theorem to the case of parameter-dependent Markov chains.     

Hitting Times of Rare Events in Markov Chains

A general condition for a Markov process with finite states is given for the convergence of the normalized hitting time of a rare event to a mean one exponential law. It is then applied to the boundary driven symmetric simple exclusion process for an open set of density profiles which does not contain the stationary density profile.     

Tunneling and Metastability of Continuous Time Markov Chains

We propose a definition of tunneling and of metastability for a continuous time Markov process on countable state spaces. We obtain sufficient conditions for a irreducible positive recurrent Markov process to exhibit a tunneling behaviour. In the reversible case these conditions can be expressed in terms of the capacities and of the stationary measure of the Markov process.     

A Simple Discrete Model of Brownian Motors: Time-periodic Markov Chains

In this paper, we consider periodically inhomogeneous Markov chains, which can be regarded as a simple version of physical model—Brownian motors. We introduce for them the concepts of periodical reversibility, detailed balance, entropy production rate and circulation distribution. We prove the equivalence of the following statements: The time-periodic Markov chain is periodically reversible; It is in detailed balance; Kolmogorov's cycle condition is satisfied; Its entropy production rate vanishes; Every circuit and its reversed circuit have the same circulation weight. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors, i.e. the existence of net circulation, can occur only in nonequilibrium and irreversible systems. Moreover, we verify the large deviation property and the Gallavotti-Cohen fluctuation theorem of sample entropy production rates of the Markov chain.     

Markov Chains theory in the detection of research activities in physics

Conclusions The Markov Chains model was applied on a sample of citation data to predict the shifting trends of scientific inquiry from science and technology to social science subjects [7]. The validity of the findings awaits verification by future data. The same technique has recently been utilized to predict the movements of authors among nine subtopics in ethnomusicology [11]. Although a validation was attempted, unfortunately, inadequate data rendered the comparison inconclusive. In the present study, publications from the 1961–1970 Index were used to model the process of subfield shifts in a physics journal. It was assumed that authors movements among subfields of physics as shown in the subject headings assigned would reflect the subject shifts of the journal. The rate of change between the initial probability distribution and the limiting probability distribution were used to predict developmental trends. Finally, the subject distribution of publications appearing in the next ten-year Index validated the prediction. It is reasonable to conclude that the Markov Chains model appears to predict the shifts of research trends in a specialty journal.This publication was supported in part by NIH Grants RO 1-LM-04177 and KO 4-LM-00078 from the National Library of Medicine.     

Special Features of Impulse Electronophotoluminescence

We consider special features of luminescence and its excitation on exposure of condensed substances to nanosecond beams of electrons with an energy of 100–300 keV at a peak power density exceeding 3·10⁶ W/cm². This kind of luminescence (iephluminescence) is excited in the absence of dynamic equilibrium between the electrons injected into the substance and leaving it. The depth of a brightly luminescing layer is an order of magnitude larger than the depth of penetration of electrons into the substance. The basic mechanism underlying the excitation of the impurity centers of luminescence in this layer of the substance is the radiative recombination of electron–hole pairs on impurity ions without a change of the ion charge. We show that the iefluminescence encompasses the positive qualities of electro, xray, photo, and cathodoluminescence. The high brightness and informativeness of the spectrum of iephluminescence allows the use of the latter for a fast nondestructive analysis of a substance.     

Scaling Properties of Energy Gap in Dimerized Spinless Fermion Chains with Quasiperiodic Modulation

By employing the exact diagonalization method, we investigate the low-energy benavlour ot the almenzed spinless fermion chains with quasiperiodic modulation. It is found that for off-diagonal modulation, the energy gap with length N scales as exp（-cN^ω） with nonuniversal exponent ω if the dimerization is nonzero. However, for diagonal modulation, there may exist a critical dimerization δc beyond which the system exhibits a metal-insulator transition.     

Acceleration of Convergence to Equilibrium in Markov Chains by Breaking Detailed Balance

We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review existing results showing that irreversible processes converge faster to their steady state than reversible ones. We show how this behaviour appears in the hydrodynamic limit of such processes, as described by macroscopic fluctuation theory, and we provide a quantitative expression for the acceleration of convergence in this setting. We give a geometrical interpretation of this acceleration, in terms of currents that are antisymmetric under time-reversal and orthogonal to the free energy gradient, which act to drive the system away from states where (reversible) gradient-descent dynamics result in slow convergence to equilibrium.     

Dynamical Entropy of Generalized Quantum Markov Chains on Gauge-invariant C *-algebras

We prove that the mean entropy and the dynamical entropy are equal for generalized quantum Markov chains on gauge-invariant C ^*-algebras.     

Characteristics of Entanglement Wave in Two Parallel Spin Chains

Based on the solvable spin-1/2 Heisenberg chain we demonstrate how two many-body systems are entangled due to their partial entanglement. The entanglement wave in the two spin chains displays a damped oscillation if the spin number is N 〉 3, and only propagates with a certain velocity depending on the coupling constant J. Moreover, the entanglement wave will be reflected on the other ends of the two spin chains. A simple scheme for transferring some special two-qubit states to other two distant qubits is also proposed.     

Tunneling and Metastability of Continuous Time Markov Chains II, the Nonreversible Case

We proposed in Beltrán and Landim (J.?Stat. Phys. 140:1065?C1114, 2010) a new approach to prove the metastable behavior of reversible dynamics based on potential theory and local ergodicity. In this article we extend this theory to nonreversible dynamics based on the Dirichlet principle proved in Gaudillière and Landim (arXiv:1111.2445, 2011). We?also include in this article the proof of the metastability of a class of birth and death chains.     

The Special Features of Superluminal Evanescent Mode Propagation

The formal analogy between classical evanescentmodes and particle tunneling in wave mechanics hasrecently initiated microwave experiments. Studies withmicrowaves and later with single photons have revealed superluminal group and energy velocities ofevanescent modes (the classical analogy to tunnelingsolutions). Microwave experiments have even demonstratedsuperluminal propagation of frequency bandwidth limited signals. This result does allow achange of chronological order of events in an inertialsystem or between different inertial systems. Evanescentmodes do exist in a space free of time. The measured and the calculated dwell time of evanescentmodes are zero inside a barrier.     

Yangian and Topological Basis Expressions of Two Types of XXZ Spin Chains

We construct a set of orthogonal topological basis states, based on which Temperley-Lieb algebra (TLA) generators U_ij can be reduced into four subspaces. According to the relations between the XXZ model and TLA generators U_ij, two types of eigenstates of the XXZ model can be expressed by a topological basis. We also analyze the Yangian realizations of XXZ model systems and illustrate them with figures.

     

Critical Behavior of Two Interacting Linear Polymer Chains in a Good Solvent

A model of two interacting (chemically different) linear polymer chains is solved exactly using the real-space renormalization group transformation on a family of Sierpinski gasket type fractals and on a truncated 4-simplex lattice. The members of the family of the Sierpinski gasket-type fractals are characterized by an integer scale factorb which runs from 2 to ∞. The Hausdorff dimensiond _F of these fractals tends to 2 from below asb → ∞. We calculate the contact exponenty for the transition from the State of segregation to a State in which the two chains are entangled forb = 2-5. Using arguments based on the finite-size scaling theory, we show that forb→∞, y = 2 - v(b) d _F, wherev is the end-toend distance exponent of a chain. For a truncated 4-simplex lattice it is shown that the system of two chains either remains in a State in which these chains are intermingled in such a way that they cannot be told apart, in the sense that the chemical difference between the polymer chains completely drop out of the thermodynamics of the system, or in a State in which they are either zipped or entangled. We show the region of existence of these different phases separated by tricritical lines. The value of the contact exponenty is calculated at the tricritical points.