Time-dependent decoherence-free subspace

Wu, Shunan; Wang, L C

doi:10.1088/1751-8113/45/40/405305

Cited by 33 publications

(23 citation statements)

References 29 publications

(52 reference statements)

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“…Previous papers have used classical physics to calculate and compare the molecular p and large-scale q A components of Π, demonstrating that indeed they of comparable magnitudes (Ingber, 2011(Ingber, , 2012Ingber et al, 2014;Nunez et al, 2013). Also, in the context of quantum mechanics, the wave function of the Π system was calculated, and it was demonstrated that overlap with multiple collisions during the observed long durations of typical Ca 2+ waves (Ingber, 2015;Ingber et al, 2014) support a Zeno effect (Facchi et al, 2004;Facchi and Pascazio, 2008;Giacosa and Pagliara, 2014;Kozlowski et al, 2015;Patil et al, 2015;Wu et al, 2012;Zhang et al, 2014) promoting long coherence times. This approach also suggests some nanosystem-pharmaceutical applications (Ingber, 2015).…”

Section: Introduction To Top-down Premise (Tdp)mentioning

confidence: 89%

Statistical mechanics of neocortical interactions: Large-scale EEG influences on molecular processes

Ingber

2016

Journal of Theoretical Biology

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Calculations further support the premise that large-scale synchronous firings of neurons may affect molecular processes. The context is scalp electroencephalography (EEG) during short-term memory (STM) tasks. The mechanism considered is Π=p+qA (SI units) coupling, where p is the momenta of free Ca(2+) waves, q the charge of Ca(2+) in units of the electron charge, and A the magnetic vector potential of current I from neuronal minicolumnar firings considered as wires, giving rise to EEG. Data has processed using multiple graphs to identify sections of data to which spline-Laplacian transformations are applied, to fit the statistical mechanics of neocortical interactions (SMNI) model to EEG data, sensitive to synaptic interactions subject to modification by Ca(2+) waves.

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Section: Introduction To Top-down Premise (Tdp)mentioning

confidence: 89%

Statistical mechanics of neocortical interactions: Large-scale EEG influences on molecular processes

Ingber

2016

Journal of Theoretical Biology

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“…which is the very condition for t-DFSs discussed in Ref. [15]. In other words, when the open quantum system is engineered by an coherent control according to Eq.…”

Section: T) With This Notation the Off-diagonal Block Of The Hamiltmentioning

confidence: 85%

Adiabatic evolution of decoherence-free subspaces and its shortcuts

Huang

2017

Phys. Rev. A

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The adiabatic theorem and shortcuts-to-adiabaticity for time-dependent open quantum systems are explored in this paper. Starting from the definition of dynamical stable decoherence-free subspace, we show that, under a compact adiabatic condition, the quantum state remains in the timedependent decoherence-free subspace with an extremely high purity, even though the dynamics of the open quantum system may be not adiabatic. The adiabatic condition mentioned here in the adiabatic theorem for open systems is very similar with that for closed quantum systems, except that the operators required to change slowly are the Lindblad operators. We also show that the adiabatic evolution of decoherence-free subspaces (will be refereed to as adiabatic decoherencefree subspaces(ADFSs) later ) depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems has to be engineered according to the incoherent control protocol. Besides, the shortcuts-to-adiabaticity for the adiabatic decoherence-free subspaces is also presented based on the transitionless quantum driving method. Finally, we provide an example that consists of a two-level system coupled to a broad band squeezed vacuum field to show our theory. Our approach employs Markovian master equations and the theory can apply to finite-dimensional quantum open systems.

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“…Secondly, the evolution of the dynamical invariants I C is governed by Eq. (19). The dynamics of I C is similar to the Markovian-Lindblad master equation with the Lindblad operators B α and the Hamilto-…”

Section: B Decoherence Free Subspace and Dynamical Invariantsmentioning

confidence: 85%

Dynamical invariants of open quantum systems

Zhang

2015

Phys. Rev. A

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For a closed quantum system, a dynamical invariant is defined as an operator whose expectation value is a constant. In this paper, we extend the concept of dynamical invariants from closed systems to open systems. A dynamical equation for invariants (the dynamical invariant condition) is derived for Markovian dynamics. Different from dynamical invariants of closed quantum systems, the time evolution of dynamical invariants of open quantum systems is no longer unitary, and eigenvalues of any invariant are time-dependent in general. Since any hermitian operator which can fulfill the dynamical invariant condition is a dynamical invariant, we construct a type of special dynamical invariants of which a part of the eigenvalues is still constant. The dynamical invariants in the subspace spanned by these eigenstates thus evolve unitarily.

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Time-dependent decoherence-free subspace

Cited by 33 publications

References 29 publications

Statistical mechanics of neocortical interactions: Large-scale EEG influences on molecular processes

Statistical mechanics of neocortical interactions: Large-scale EEG influences on molecular processes

Adiabatic evolution of decoherence-free subspaces and its shortcuts

Dynamical invariants of open quantum systems

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