93,698 research outputs found
Zeno Dynamics and High-Temperature Master Equations Beyond Secular Approximation
Complete positivity of a class of maps generated by master equations derived
beyond the secular approximation is discussed. The connection between such
class of evolutions and physical properties of the system is analyzed in depth.
It is also shown that under suitable hypotheses a Zeno dynamics can be induced
because of the high temperature of the bath.Comment: 9 pages, 2 figure
On the Debate Concerning the Proper Characterisation of Quantum Dynamical Evolution
There has been a long-standing and sometimes passionate debate between
physicists over whether a dynamical framework for quantum systems should
incorporate not completely positive (NCP) maps in addition to completely
positive (CP) maps. Despite the reasonableness of the arguments for complete
positivity, we argue that NCP maps should be allowed, with a qualification:
these should be understood, not as reflecting 'not completely positive'
evolution, but as linear extensions, to a system's entire state space, of CP
maps that are only partially defined. Beyond the domain of definition of a
partial-CP map, we argue, much may be permitted.Comment: To be presented at the 2012 biennial meeting of the Philosophy of
Science Association (PSA), San Diego, Californi
Recovering complete positivity of non-Markovian quantum dynamics with Choi-proximity regularization
A relevant problem in the theory of open quantum systems is the lack of
complete positivity of dynamical maps obtained after weak-coupling
approximations, a famous example being the Redfield master equation. A number
of approaches exist to recover well-defined evolutions under additional
Markovian assumptions, but much less is known beyond this regime. Here we
propose a numerical method to cure the complete-positivity violation issue
while preserving the non-Markovian features of an arbitrary original dynamical
map. The idea is to replace its unphysical Choi operator with its closest
physical one, mimicking recent work on quantum process tomography. We also show
that the regularized dynamics is more accurate in terms of reproducing the
exact dynamics: this allows to heuristically push the utilization of these
master equations in moderate coupling regimes, where the loss of positivity can
have relevant impact.Comment: 12 pages, 5 figure
Canonically consistent quantum master equation
We put forth a new class of quantum master equations that correctly reproduce
the asymptotic state of an open quantum system beyond the infinitesimally weak
system-bath coupling limit. Our method is based on incorporating the knowledge
of the reduced steady state into its dynamics. The correction not only steers
the reduced system towards a correct steady state but also improves the
accuracy of the dynamics, thereby refining the archetypal Born-Markov
weak-coupling second-order master equations. In case of equilibrium, since a
closed form for the steady state exists in terms of a mean force Gibbs state,
we utilize this form to correct the Redfield quantum master equation. Using an
exactly solvable harmonic oscillator system we benchmark our approach with the
exact solution showing that our method also helps correcting the long-standing
issue of positivity violation, albeit without complete positivity. Our method
of a canonically consistent quantum master equation, opens a new perspective in
the theory of open quantum systems leading to a reduced density matrix accurate
beyond the commonly used Redfield and Lindblad equations, while retaining the
same conceptual and numerical complexity
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