2,891 research outputs found
Thermal inclusions: how one spin can destroy a many-body localized phase
Many-body localized (MBL) systems lie outside the framework of statistical
mechanics, as they fail to equilibrate under their own quantum dynamics. Even
basic features of MBL systems such as their stability to thermal inclusions and
the nature of the dynamical transition to thermalizing behavior remain poorly
understood. We study a simple model to address these questions: a two level
system interacting with strength with localized bits subject to
random fields. On increasing , the system transitions from a MBL to a
delocalized phase on the \emph{vanishing} scale , up to
logarithmic corrections. In the transition region, the single-site eigenstate
entanglement entropies exhibit bi-modal distributions, so that localized bits
are either "on" (strongly entangled) or "off" (weakly entangled) in
eigenstates. The clusters of "on" bits vary significantly between eigenstates
of the \emph{same} sample, which provides evidence for a heterogenous
discontinuous transition out of the localized phase in single-site observables.
We obtain these results by perturbative mapping to bond percolation on the
hypercube at small and by numerical exact diagonalization of the full
many-body system. Our results imply the MBL phase is unstable in systems with
short-range interactions and quenched randomness in dimensions that are
high but finite.Comment: 17 pages, 12 figure
The double Caldeira-Leggett model: Derivation and solutions of the master equations, reservoir-induced interactions and decoherence
In this paper we analyze the double Caldeira-Leggett model: the path integral
approach to two interacting dissipative harmonic oscillators. Assuming a
general form of the interaction between the oscillators, we consider two
different situations: i) when each oscillator is coupled to its own reservoir,
and ii) when both oscillators are coupled to a common reservoir. After deriving
and solving the master equation for each case, we analyze the decoherence
process of particular entanglements in the positional space of both
oscillators. To analyze the decoherence mechanism we have derived a general
decay function for the off-diagonal peaks of the density matrix, which applies
both to a common and separate reservoirs. We have also identified the expected
interaction between the two dissipative oscillators induced by their common
reservoir. Such reservoir-induced interaction, which gives rise to interesting
collective damping effects, such as the emergence of relaxation- and
decoherence-free subspaces, is shown to be blurred by the high-temperature
regime considered in this study. However, we find that different interactions
between the dissipative oscillators, described by rotating or counter-rotating
terms, result in different decay rates for the interference terms of the
density matrix.Comment: 42 pages, 7 figures, new discussion added, typos adde
An exact master equation for the system-reservoir dynamics under the strong coupling regime and non-Markovian dynamics
In this paper we present a method to derive an exact master equation for a
bosonic system coupled to a set of other bosonic systems, which plays the role
of the reservoir, under the strong coupling regime, i.e., without resorting to
either the rotating-wave or secular approximations. Working with phase-space
distribution functions, we verify that the dynamics are separated in the
evolution of its center, which follows classical mechanics, and its shape,
which becomes distorted. This is the generalization of a result by Glauber, who
stated that coherent states remain coherent under certain circumstances,
specifically when the rotating-wave approximation and a zero-temperature
reservoir are used. We show that the counter-rotating terms generate
fluctuations that distort the vacuum state, much the same as thermal
fluctuations.Finally, we discuss conditions for non-Markovian dynamics
MASS TRANSFER CORRELATION FOR THE REMOVAL OF COPPER IONS FROM WASTEWATER
One of the biggest problems with ore processing in extractive metallurgical industries is the high toxicity of the heavy metals waste content (e.g., copper, lead, nickel and chrome). This work investigates the copper (II) Ãons removal from aqueous solutions in concentrations up to 1000 ppm. Therefore, a fluidized bed electrolytic reactor was used with flow-by configuration considered as a hopeful method due to the large specific surface area and the high mass transfer rate. The performance of the electrochemical reactor was investigated by using different porosities. Dimensionless Sherwood and Reynolds numbers were correlated to characterize the mass transport properties of the reactor, and they were fitted to the equation Sh = a.Reb.Sc1/3
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