3,821 research outputs found
Interacting quantum walkers: Two-body bosonic and fermionic bound states
We investigate the dynamics of bound states of two interacting particles,
either bosons or fermions, performing a continuous-time quantum walk on a
one-dimensional lattice. We consider the situation where the distance between
both particles has a hard bound, and the richer situation where the particles
are bound by a smooth confining potential. The main emphasis is on the velocity
characterizing the ballistic spreading of these bound states, and on the
structure of the asymptotic distribution profile of their center-of-mass
coordinate. The latter profile generically exhibits many internal fronts.Comment: 31 pages, 14 figure
Survival of classical and quantum particles in the presence of traps
We present a detailed comparison of the motion of a classical and of a
quantum particle in the presence of trapping sites, within the framework of
continuous-time classical and quantum random walk. The main emphasis is on the
qualitative differences in the temporal behavior of the survival probabilities
of both kinds of particles. As a general rule, static traps are far less
efficient to absorb quantum particles than classical ones. Several lattice
geometries are successively considered: an infinite chain with a single trap, a
finite ring with a single trap, a finite ring with several traps, and an
infinite chain and a higher-dimensional lattice with a random distribution of
traps with a given density. For the latter disordered systems, the classical
and the quantum survival probabilities obey a stretched exponential asymptotic
decay, albeit with different exponents. These results confirm earlier
predictions, and the corresponding amplitudes are evaluated. In the
one-dimensional geometry of the infinite chain, we obtain a full analytical
prediction for the amplitude of the quantum problem, including its dependence
on the trap density and strength.Comment: 35 pages, 10 figures, 2 tables. Minor update
Return probability of fermions released from a 1D confining potential
We consider non-interacting fermions prepared in the ground state of a 1D
confining potential and submitted to an instantaneous quench consisting in
releasing the trapping potential. We show that the quantum return probability
of finding the fermions in their initial state at a later time falls off as a
power law in the long-time regime, with a universal exponent depending only on
and on whether the free fermions expand over the full line or over a
half-line. In both geometries the amplitudes of this power-law decay are
expressed in terms of finite determinants of moments of the one-body
bound-state wavefunctions in the potential. These amplitudes are worked out
explicitly for the harmonic and square-well potentials. At large fermion
numbers they obey scaling laws involving the Fermi energy of the initial state.
The use of the Selberg-Mehta integrals stemming from random matrix theory has
been instrumental in the derivation of these results.Comment: 24 pages, 1 tabl
Bayesian Semiparametric Multivariate Density Deconvolution
We consider the problem of multivariate density deconvolution when the
interest lies in estimating the distribution of a vector-valued random variable
but precise measurements of the variable of interest are not available,
observations being contaminated with additive measurement errors. The existing
sparse literature on the problem assumes the density of the measurement errors
to be completely known. We propose robust Bayesian semiparametric multivariate
deconvolution approaches when the measurement error density is not known but
replicated proxies are available for each unobserved value of the random
vector. Additionally, we allow the variability of the measurement errors to
depend on the associated unobserved value of the vector of interest through
unknown relationships which also automatically includes the case of
multivariate multiplicative measurement errors. Basic properties of finite
mixture models, multivariate normal kernels and exchangeable priors are
exploited in many novel ways to meet the modeling and computational challenges.
Theoretical results that show the flexibility of the proposed methods are
provided. We illustrate the efficiency of the proposed methods in recovering
the true density of interest through simulation experiments. The methodology is
applied to estimate the joint consumption pattern of different dietary
components from contaminated 24 hour recalls
Non-equilibrium fluctuations and mechanochemical couplings of a molecular motor
We investigate theoretically the violations of Einstein and Onsager
relations, and the efficiency for a single processive motor operating far from
equilibrium using an extension of the two-state model introduced by Kafri {\em
et al.} [Biophys. J. {\bf 86}, 3373 (2004)]. With the aid of the Fluctuation
Theorem, we analyze the general features of these violations and this
efficiency and link them to mechanochemical couplings of motors. In particular,
an analysis of the experimental data of kinesin using our framework leads to
interesting predictions that may serve as a guide for future experiments.Comment: 4 pages, 4 figures, accepted to Phys. Rev. Let
Ameliorating effect of microdoses of a potentized homeopathic drug, Arsenicum Album, on arsenic-induced toxicity in mice
BACKGROUND: Arsenic in groundwater and its accumulation in plants and animals have assumed a menacing proportion in a large part of West Bengal, India and adjoining areas of Bangladesh. Because of the tremendous magnitude of the problem, there seems to be no way to tackle the problem overnight. Efforts to provide arsenic free water to the millions of people living in these dreaded zones are being made, but are awfully inadequate. In our quest for finding out an easy, safe and affordable means to combat this problem, a homeopathic drug, Arsenicum Album-30, appears to yield promising results in mice. The relative efficacies of two micro doses of this drug, namely, Arsenicum Album-30 and Arsenicum Album-200, in combating arsenic toxicity have been determined in the present study on the basis of some accepted biochemical protocols. METHODS: Mice were divided into different sets of control (both positive and negative) and treated series (As-intoxicated, As-intoxicated plus drug-fed). Alanine amino transferase (ALT) and aspartate amino transferase (AST) activities and reduced glutathione (GSH) level in liver and blood were analyzed in the different series of mice at six different fixation intervals. RESULTS: Both Arsenicum Album-30 and Arsenicum Album-200 ameliorated arsenic-induced toxicity to a considerable extent as compared to various controls. CONCLUSIONS: The results lend further support to our earlier views that microdoses of potentized Arsenicum Album are capable of combating arsenic intoxication in mice, and thus are strong candidates for possible use in human subjects in arsenic contaminated areas under medical supervision
- …