123 research outputs found
A scaling theory of quantum breakdown in solids
We propose a new scaling theory for general quantum breakdown phenomena. We
show, taking Landau-Zener type breakdown as a particular example, that the
breakdown phenomena can be viewed as a quantum phase transition for which the
scaling theory is developed. The application of this new scaling theory to
Zener type breakdown in Anderson insulators, and quantum quenching has been
discussed.Comment: 3 page
Continuous transition of social efficiencies in the stochastic strategy Minority Game
We show that in a variant of the Minority Game problem, the agents can reach
a state of maximum social efficiency, where the fluctuation between the two
choices is minimum, by following a simple stochastic strategy. By imagining a
social scenario where the agents can only guess about the number of excess
people in the majority, we show that as long as the guess value is sufficiently
close to the reality, the system can reach a state of full efficiency or
minimum fluctuation. A continuous transition to less efficient condition is
observed when the guess value becomes worse. Hence, people can optimize their
guess value for excess population to optimize the period of being in the
majority state. We also consider the situation where a finite fraction of
agents always decide completely randomly (random trader) as opposed to the rest
of the population that follow a certain strategy (chartist). For a single
random trader the system becomes fully efficient with majority-minority
crossover occurring every two-days interval on average. For just two random
traders, all the agents have equal gain with arbitrarily small fluctuations.Comment: 8 pages, 6 fig
Statistics of the Kolkata Paise Restaurant Problem
We study the dynamics of a few stochastic learning strategies for the
'Kolkata Paise Restaurant' problem, where N agents choose among N equally
priced but differently ranked restaurants every evening such that each agent
tries get to dinner in the best restaurant (each serving only one customer and
the rest arriving there going without dinner that evening). We consider the
learning strategies to be similar for all the agents and assume that each
follow the same probabilistic or stochastic strategy dependent on the
information of the past successes in the game. We show that some 'naive'
strategies lead to much better utilization of the services than some relatively
'smarter' strategies. We also show that the service utilization fraction as
high as 0.80 can result for a stochastic strategy, where each agent sticks to
his past choice (independent of success achieved or not; with probability
decreasing inversely in the past crowd size). The numerical results for
utilization fraction of the services in some limiting cases are analytically
examined.Comment: 10 pages, 3 figs; accepted in New J Phy
Phase transitions in crowd dynamics of resource allocation
We define and study a class of resources allocation processes where
agents, by repeatedly visiting resources, try to converge to optimal
configuration where each resource is occupied by at most one agent. The process
exhibits a phase transition, as the density of agents grows, from an
absorbing to an active phase. In the latter, even if the number of resources is
in principle enough for all agents (), the system never settles to a
frozen configuration. We recast these processes in terms of zero-range
interacting particles, studying analytically the mean field dynamics and
investigating numerically the phase transition in finite dimensions. We find a
good agreement with the critical exponents of the stochastic fixed-energy
sandpile. The lack of coordination in the active phase also leads to a
non-trivial faster-is-slower effect.Comment: 7 pages, 7 fig
Precursors of catastrophe in the BTW, Manna and random fiber bundle models of failure
We have studied precursors of the global failure in some self-organised
critical models of sand-pile (in BTW and Manna models) and in the random fiber
bundle model (RFB). In both BTW and Manna model, as one adds a small but fixed
number of sand grains (heights) to any central site of the stable pile, the
local dynamics starts and continues for an average relaxation time (\tau) and
an average number of topplings (\Delta) spread over a radial distance (\xi). We
find that these quantities all depend on the average height (h_{av}) of the
pile and they all diverge as (h_{av}) approaches the critical height (h_{c})
from below: (\Delta) (\sim (h_{c}-h_{av}))(^{-\delta}), (\tau \sim
(h_{c}-h_{av})^{-\gamma}) and (\xi) (\sim) ((h_{c}-h_{av})^{-\nu}). Numerically
we find (\delta \simeq 2.0), (\gamma \simeq 1.2) and (\nu \simeq 1.0) for both
BTW and Manna model in two dimensions. In the strained RFB model we find that
the breakdown susceptibility (\chi) (giving the differential increment of the
number of broken fibers due to increase in external load) and the relaxation
time (\tau), both diverge as the applied load or stress (\sigma) approaches the
network failure threshold (\sigma_{c}) from below: (\chi) (\sim) ((\sigma_{c})
(-)(\sigma)^{-1/2}) and (\tau) (\sim) ((\sigma_{c}) (-)(\sigma)^{-1/2}). These
self-organised dynamical models of failure therefore show some definite
precursors with robust power laws long before the failure point. Such
well-characterised precursors should help predicting the global failure point
of the systems in advance.Comment: 13 pages, 9 figures (eps
Mean field and Monte Carlo studies of the magnetization-reversal transition in the Ising model
Detailed mean field and Monte Carlo studies of the dynamic
magnetization-reversal transition in the Ising model in its ordered phase under
a competing external magnetic field of finite duration have been presented
here. Approximate analytical treatment of the mean field equations of motion
shows the existence of diverging length and time scales across this dynamic
transition phase boundary. These are also supported by numerical solutions of
the complete mean field equations of motion and the Monte Carlo study of the
system evolving under Glauber dynamics in both two and three dimensions.
Classical nucleation theory predicts different mechanisms of domain growth in
two regimes marked by the strength of the external field, and the nature of the
Monte Carlo phase boundary can be comprehended satisfactorily using the theory.
The order of the transition changes from a continuous to a discontinuous one as
one crosses over from coalescence regime (stronger field) to nucleation regime
(weaker field). Finite size scaling theory can be applied in the coalescence
regime, where the best fit estimates of the critical exponents are obtained for
two and three dimensions.Comment: 16 pages latex, 13 ps figures, typos corrected, references adde
Use of rating systems in the process towards sustainable construction
Since the large scale industrialization occurred, the profit oriented human activity has led to a
constantly growing environmental degradation. Nowadays, that the actual severity of the problem
in hand is impossible to ignore and the spectrum of the future consequences emerges in its
full extent, several actions towards the adaptation of sustainability principles in the most problematic
sectors of human activity are undertaken. One of these sectors is building sector, incorporating
the production, transport, use and replacement of building materials, the use of the
building itself (energy consumption for lighting, ventilation, heating and cooling, water consumption
etc), the reuse of the building or its materials, the demolition of the building and the
disposal of the demolition products. The energy consumed in operating buildings serves as indication
of the building sector’s contribution to the total environmental aggravation induced by
human activity. According to (OECD, 2003), in the European OECD countries, the building
sector consumes the highest amount of energy (40%) in comparison to the transport (22%) and
industry sectors (38%). Given the fact that the afore-mentioned quantities include the energy
amounts consumed only for the operation of the building, while other processes – unbreakably
bonded to construction – such as manufacture and transport of building materials, are not cocalculated,
an estimation regarding the impact of the building sector on the environment can be
drawn.COST, European Science Foundatio
Griffiths-McCoy singularities in the transverse field Ising model on the randomly diluted square lattice
The site-diluted transverse field Ising model in two dimensions is studied
with Quantum-Monte-Carlo simulations. Its phase diagram is determined in the
transverse field (Gamma) and temperature (T) plane for various (fixed)
concentrations (p). The nature of the quantum Griffiths phase at zero
temperature is investigated by calculating the distribution of the local
zero-frequency susceptibility. It is pointed out that the nature of the
Griffiths phase is different for small and large Gamma.Comment: 21 LaTeX (JPSJ macros included), 12 eps-figures include
Quantum Annealing and Analog Quantum Computation
We review here the recent success in quantum annealing, i.e., optimization of
the cost or energy functions of complex systems utilizing quantum fluctuations.
The concept is introduced in successive steps through the studies of mapping of
such computationally hard problems to the classical spin glass problems. The
quantum spin glass problems arise with the introduction of quantum
fluctuations, and the annealing behavior of the systems as these fluctuations
are reduced slowly to zero. This provides a general framework for realizing
analog quantum computation.Comment: 22 pages, 7 figs (color online); new References Added. Reviews of
Modern Physics (in press
A Novel Quantum Transition in a Fully Frustrated Transverse Ising Antiferromagnet
We consider a long-range Ising antiferromagnet (LRIAF) put in a transverse
field. Applying quantum Monte Carlo method, we study the variation of order
parameter (spin correlation in Trotter time direction), susceptibility and
average energy of the system for various values of the transverse field at
different temperatures. The antiferromagnetic order is seen to get immediately
broken as soon as the thermal or quantum fluctuations are added. We also
discuss the phase diagram for the Sherrington-Kirkpatrick (SK) model with the
same LRIAF bias, also in presence of a transverse field. We find that while the
antiferromagnetic order is immediately broken as one adds an infinitesimal
transverse field or thermal fluctuation to the system, an infinitesimal SK spin
glass disorder is enough to induce a stable glass order in the antiferromagnet.
This glass order eventually gets destroyed as the thermal or quantum
fluctuations increased beyond their threshold values and the transition to para
phase occurs. Indications of this novel phase transition are discussed. Because
of the presence of full frustration, this surrogate property of the LRIAF for
incubation of stable spin glass phase in it (induced by addition of a small
disorder) should enable eventually the study of classical and quantum spin
glass phases by using some perturbation theory with respect to the disorder.Comment: 9 pages, 5 figure
- …