scholarly journals Iterative solutions to the steady-state density matrix for optomechanical systems

2015 ◽  
Vol 91 (1) ◽  
Author(s):  
P. D. Nation ◽  
J. R. Johansson ◽  
M. P. Blencowe ◽  
A. J. Rimberg
Keyword(s):  
Steady State ◽  
Density Matrix ◽  
State Density ◽  
Optomechanical Systems ◽  
Iterative Solutions

scholarly journals Modules or Mean-Fields?

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 552 ◽  
Author(s):  
Thomas Parr ◽  
Noor Sajid ◽  
Karl J. Friston
Keyword(s):  
Steady State ◽  
Message Passing ◽  
Mean Field Theory ◽  
Functional Anatomy ◽  
Mean Field ◽  
State Density ◽  
Stochastic Dynamical Systems ◽  
Conditional Independency ◽  
The Brain ◽  
Non Equilibrium

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

scholarly journals Classical Chaos Described by a Density Matrix

Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 739-746
Author(s):  
Andres Mauricio Kowalski ◽  
Angelo Plastino ◽  
Gaspar Gonzalez
Keyword(s):  
Density Matrix ◽  
Pure State ◽  
Classical Limit ◽  
Degrees Of Freedom ◽  
Temporal Evolution ◽  
Entropy Density ◽  
State Density ◽  
Unexpected Result ◽  
Semiclassical Model ◽  
Classical Chaos

In this paper, a reference to the semiclassical model, in which quantum degrees of freedom interact with classical ones, is considered. The classical limit of a maximum-entropy density matrix that describes the temporal evolution of such a system is analyzed. Here, it is analytically shown that, in the classical limit, it is possible to reproduce classical results. An example is classical chaos. This is done by means a pure-state density matrix, a rather unexpected result. It is shown that this is possible only if the quantum part of the system is in a special class of states.

Steady-state quantum correlation measurement in hybrid optomechanical systems

2020 ◽  
pp. 2050046
Author(s):  
Tesfay Gebremariam Tesfahannes ◽  
Merkebu Dereje Getahune
Keyword(s):  
Correlation Function ◽  
Steady State ◽  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Optical Cavity ◽  
Quantum Correlations ◽  
Correlation Measurement ◽  
Atomic Ensemble ◽  
Optomechanical System ◽  
Optomechanical Systems

In this paper, we investigate the steady-state of quantum correlation measurement of hybrid optomechanical systems. The first system consists of a single optomechanical system simultaneously coupled to a mechanical oscillator. While the second system is a hybrid optomechanical system consisting of an atomic ensemble placed in between the optical cavity and mirror. For both optomechanical systems, we formulate the Hamiltonian and the explicit expression of the covariance matrix leading to the dynamic of the system. Under the linearization approximation, we investigate the steady-state quantum correlations which are quantified through the correlation function of non-Hermitian operators, while the logarithmic negativity is used to quantify the amount of quantum entanglement between the subsystems. Furthermore, our proposed quantum correlation function can be used to quantify the entangled bipartite states that are correlative and transfer information. It is found that the transfer of quantum correlations between the subsystem is related to the detuning and coupling strength. Our results provide a realistic route toward remote quantum entanglement detection and a framework of future realistic fiber-optic quantum network operating applications.

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