A soluble random-matrix model for relaxation in quantum systems

We study the relaxation of a degenerate two-level system interacting with a heat bath, assuming a random-matrix model for the system-bath interaction. For times larger than the duration of a collision and smaller than the Poincaré recurrence time, the survival probability of still finding the system at timet in the same state in which it was prepared att=0 is exactly calculated.

Memory-induced anomalous dynamics in a minimal random walk model

A discrete-time dynamics of a non-Markovian random walker is analyzed using a minimal model where memory of the past drives the present dynamics. In recent work N. Kumar et al., Phys. Rev. E 82, 021101 (2010)] we proposed a model that exhibits asymptotic superdiffusion, normal diffusion, and subdiffusion with the sweep of a single parameter. Here we propose an even simpler model, with minimal options for the walker: either move forward or stay at rest. We show that this model can also give rise to diffusive, subdiffusive, and superdiffusive dynamics at long times as a single parameter is varied. We show that in order to have subdiffusive dynamics, the memory of the rest states must be perfectly correlated with the present dynamics. We show explicitly that if this condition is not satisfied in a unidirectional walk, the dynamics is only either diffusive or superdiffusive (but not subdiffusive) at long times.

Molecular Dynamics Investigation of Structure and Transport in the K2O-2SiO2 System Using a Partial Charge Based Model Potential

Potassium disilicate glass and melt have been investigated by using a new partial charge based potential model in which nonbridging oxygens are differentiated from bridging oxygens by their charges. The model reproduces the structural data pertaining to the coordination polyhedra around potassium and the various bond angle distributions excellently. The dynamics of the glass has been studied by using space and time correlation functions. It is found that K ions migrate by a diffusive mechanism in the melt and by hops below the glass transition temperature. They are also found to migrate largely through nonbridging oxygenrich sites in the silicate matrix, thus providing support to the predictions of the modified random network model.

Molecular dynamics Investigation of structure and transport in the K2O-2SiO2 system using a partial charge based model potential

Potassium disilicate glass and melt have been investigated by using anew partial charge based potential model in which nonbridging oxygens are differentiated from bridging oxygens by their charges. The model reproduces the structural data pertaining to the coordination polyhedra around potassium and the various bond angle distributions excellently. The dynamics of the glass has been studied by using space and time correlation functions. It is found that K ions migrate by a diffusive mechanism in the melt and by hops below the glass transition temperature. They are also found to migrate largely through nonbridging oxygen-rich sites in the silicate matrix, thus providing support to the predictions of the modified random network model.

Self-organized criticality in dynamics without branching

We demonstrate the phenomenon of self-organized criticality (SOC) in a simple random walk model described by a random walk of a myopic ant, i.e., a walker who can see only nearest neighbors. The ant acts on the underlying lattice aiming at uniform digging, i.e., reduction of the height profile of the surface but is unaffected by the underlying lattice. In one, two, and three dimensions we have explored this model and have obtained power laws in the time intervals between consecutive events of "digging." Being a simple random walk, the power laws in space translate to power laws in time. We also study the finite size scaling of asymptotic scale invariant process as well as dynamic scaling in this system. This model differs qualitatively from the cascade models of SOC.

Effect of surface roughness on diffusion-limited charge transfer

A theory is developed for diffusion-limited charge transfer on a non-fractally rough electrode. The perturbation expressions are obtained for concentration, current density and measured diffusion-limited current for arbitrary one- and two-dimensional surface profiles. The random surface model is employed for a rough electrode\electrolyte interface. In this model the gross geometrical property of an electrochemically active rough surface - the surface structure factor-is related to the average electrode current, current density and concentration. Under short and long time regimes, various morphological features of the rough electrodes, i.e. excess area (related to roughness slope), curvature, correlation length, etc. are related to the (average) current transients. A two-point Pade approximant is used to develop an all time average current expression in terms of partial morphological features of the rough surface. The inverse problem of predicting the surface structure factor from the observed transients is also described. Finally, the effect of surface roughness is studied for specific surface statistics, namely a Gaussian correlation function. It is shown how the surface roughness enhances the overall diffusion-limited charge transfer current.

On the Limits of Spatial Reuse and Cooperative Communication for Dense Wireless Networks

We consider a dense ad hoc wireless network comprising n nodes confined to a given two dimensional region of fixed area. For the Gupta-Kumar random traffic model and a realistic interference and path loss model (i.e., the channel power gains are bounded above, and are bounded below by a strictly positive number), we study the scaling of the aggregate end-to-end throughput with respect to the network average power constraint, P macr, and the number of nodes, n. The network power constraint P macr is related to the per node power constraint, P macr, as P macr = np. For large P, we show that the throughput saturates as Theta(log(P macr)), irrespective of the number of nodes in the network. For moderate P, which can accommodate spatial reuse to improve end-to-end throughput, we observe that the amount of spatial reuse feasible in the network is limited by the diameter of the network. In fact, we observe that the end-to-end path loss in the network and the amount of spatial reuse feasible in the network are inversely proportional. This puts a restriction on the gains achievable using the cooperative communication techniques studied in and, as these rely on direct long distance communication over the network.

Improving query focused summarization using look-ahead strategy

Query focused summarization is the task of producing a compressed text of original set of documents based on a query. Documents can be viewed as graph with sentences as nodes and edges can be added based on sentence similarity. Graph based ranking algorithms which use 'Biased random surfer model' like topic-sensitive LexRank have been successfully applied to query focused summarization. In these algorithms, random walk will be biased towards the sentences which contain query relevant words. Specifically, it is assumed that random surfer knows the query relevance score of the sentence to where he jumps. However, neighbourhood information of the sentence to where he jumps is completely ignored. In this paper, we propose look-ahead version of topic-sensitive LexRank. We assume that random surfer not only knows the query relevance of the sentence to where he jumps but he can also look N-step ahead from that sentence to find query relevance scores of future set of sentences. Using this look ahead information, we figure out the sentences which are indirectly related to the query by looking at number of hops to reach a sentence which has query relevant words. Then we make the random walk biased towards even to the indirect query relevant sentences along with the sentences which have query relevant words. Experimental results show 20.2% increase in ROUGE-2 score compared to topic-sensitive LexRank on DUC 2007 data set. Further, our system outperforms best systems in DUC 2006 and results are comparable to state of the art systems.

Baryon squishing in synthetic dimensions by effective SU(M) gauge fields

The ``synthetic dimension'' proposal A. Celi et al., Phys. Rev. Lett. 112, 043001 (2014)] uses atoms with M internal states (''flavors'') in a one-dimensional (1D) optical lattice, to realize a hopping Hamiltonian equivalent to the Hofstadter model (tight-binding model with a given magnetic flux per plaquette) on an M-sites-wide square lattice strip. We investigate the physics of SU(M) symmetric interactions in the synthetic dimension system. We show that this system is equivalent to particles with SU(M) symmetric interactions] experiencing an SU(M) Zeeman field at each lattice site and a non-Abelian SU(M) gauge potential that affects their hopping. This equivalence brings out the possibility of generating nonlocal interactions between particles at different sites of the optical lattice. In addition, the gauge field induces a flavor-orbital coupling, which mitigates the ``baryon breaking'' effect of the Zeeman field. For M particles, concomitantly, the SU(M) singlet baryon which is site localized in the usual 1D optical lattice, is deformed to a nonlocal object (''squished baryon''). We conclusively demonstrate this effect by analytical arguments and exact (numerical) diagonalization studies. Our study promises a rich many-body phase diagram for this system. It also uncovers the possibility of using the synthetic dimension system to laboratory realize condensed-matter models such as the SU(M) random flux model, inconceivable in conventional experimental systems.

Multi-state-choice automata model for expedient learning in random environment

A new automata model Mr,k, with a conceptually significant innovation in the form of multi-state alternatives at each instance, is proposed in this study. Computer simulations of the Mr,k, model in the context of feature selection in an unsupervised environment has demonstrated the superiority of the model over similar models without this multi-state-choice innovation.

Fixed points in a Hopfield model with random asymmetric interactions

We calculate analytically the average number of fixed points in the Hopfield model of associative memory when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. Addition of the antisymmetric part causes an exponential decrease in the total number of fixed points. If the relative strength of the antisymmetric component is small, then its presence does not cause any substantial degradation of the quality of retrieval when the memory loading level is low. We also present results of numerical simulations which provide qualitative (as well as quantitative for some aspects) confirmation of the predictions of the analytic study. Our numerical results suggest that the analytic calculation of the average number of fixed points yields the correct value for the typical number of fixed points.

Ising model on a random network with annealed or quenched disorder

We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of fourfold coordinated sites connected via variable length one-dimensional chains. Our emphasis is on nonuniversal properties and we consider the transition temperature and other equilibrium thermodynamic properties, including those associated with one-dimensional fluctuations arising from the chains. We use analytic methods in the annealed case, and a Monte Carlo simulation for the quenched disorder. Our objective is to study the difference between quenched and annealed results with a broad random distribution of interaction parameters. The former represents a situation where the time scale associated with the randomness is very long and the corresponding degrees of freedom can be viewed as frozen, while the annealed case models the situation where this is not so. We find that the transition temperature and the entropy associated with one-dimensional fluctuations are always higher for quenched disorder than in the annealed case. These differences increase with the strength of the disorder up to a saturating value. We discuss our results in connection to physical systems where a broad distribution of interaction strengths is present.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Coalescence of drops in stirred dispersion. A white noise model for coalescence

Coalescence between two droplets in a turbulent liquid-liquid dispersion is generally viewed as a consequence of forces exerted on the drop-pair squeezing out the intervening continuous phase to a critical thickness. A new synthesis is proposed herein which models the film drainage as a stochastic process driven by a suitably idealized random process for the fluctuating force. While the true test of the model lies in detailed parameter estimations with measurement of drop-size distributions in coalescing dispersions, experimental measurements on average coalescence frequencies lend preliminary support to the model.

Optimal maintenance policy for equipment subject to random deterioration and random failure A modern control theory approach.

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example