On the single‐particle‐reduced entropy of a gated nanowire system in the Coulomb blockade regime

Castelo, José María; Indlekofer, K. M.; Malindretos, J.

doi:10.1002/pssr.201307235

Cited by 1 publication

(3 citation statements)

References 20 publications

(28 reference statements)

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“…Once the statistical operator

{\overset{ρ}{true}}_{rel}

of the system is known, the von Neumann entropy (in bit) can be obtained as follows:

S = - normalTr false({\overset{ρ}{true}}_{rel} {log}_{2} {\overset{ρ}{true}}_{rel} false) = - \sum_{J = 0}^{normaldim false(F_{rel} false) - 1} w_{J} {log}_{2} false(w_{J} false),

which is a measure of the mixture degree of the system's preparation. For pure states (

S = 0

), a measure of correlation is obtained by the single‐particle‐reduced entropy (in bit)

S_{1} = - normalTr false(ρ_{1} {log}_{2} ρ_{1} false) = - \sum_{j = 0}^{N_{\max} - 1} ξ_{j} {log}_{2} false(ξ_{j} false),

which has the disadvantage of depending also on the degree of mixture . (Note that

S_{1}

as defined above includes non‐relevant states as well.…”

Section: Modified Correlation Entropymentioning

confidence: 99%

“…which has the disadvantage of depending also on the degree of mixture [6,7]. (Note that S 1 as defined above includes non-relevant states as well.)…”

Section: Papermentioning

confidence: 99%

“…It has been shown that the single‐particle‐reduced entropy

S_{1}

as calculated from the single‐particle density matrix ()

ρ_{1}

can be interpreted as a measure of correlation for such pure states. If the preparation of the system is given by a mixture of states,

S_{1}

also depends on the degree of mixture and so this quantity is no longer suitable as a measure of correlation alone.…”

Section: Introductionmentioning

confidence: 99%

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Modified correlation entropy of a gated nanowire system described by a numerically determined non‐equilibrium many‐body statistical operator

Castelo

Indlekofer

2015

Physica Status Solidi (b)

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A numerical correlation measure of the interacting electrons in a semiconductor nanowire‐based field‐effect transistor (NWFET) is presented, which solely quantifies correlation whether the preparation of the system is pure or mixed, in contrast to the single‐particle‐reduced entropy, which depends on the degree of correlation and mixture as well. This numerical measure, which is termed modified correlation entropy ΔS, is based on the concept of von Neumann entropy, whose calculation is dependent on the non‐equilibrium many‐body statistical operator of the system. Therefore, we present a numerical approach to construct such a non‐equilibrium many‐body statistical operator trueρˆrel for relevant quasi‐bound electronic states in a NWFET. As a constraint for trueρˆrel, we assume that the single‐particle density matrix ρ1 is a given quantity, resulting from a non‐equilibrium Green's function (NEGF) calculation for the NWFET for a given set of applied voltages. The eigenbasis of trueρˆrel is assumed to be identical to the eigenbasis of the projected many‐body Hamiltonian trueHˆrel within a relevant Fock subspace of the quasi‐bound subsystem. As for the eigenvalues wN of trueρˆrel, we furthermore assume that wN have a generalized Boltzmann form, parameterized by effective electrochemical potentials of natural orbitals and a given temperature. Once trueρˆrel is obtained, we calculate and compare the modified entropy ΔS, the single‐particle‐reduced entropy S1 and the von Neumann entropy S for two different transport regimes of the NWFET.

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“…Once the statistical operator

{\overset{ρ}{true}}_{rel}

of the system is known, the von Neumann entropy (in bit) can be obtained as follows:

S = - normalTr false({\overset{ρ}{true}}_{rel} {log}_{2} {\overset{ρ}{true}}_{rel} false) = - \sum_{J = 0}^{normaldim false(F_{rel} false) - 1} w_{J} {log}_{2} false(w_{J} false),

which is a measure of the mixture degree of the system's preparation. For pure states (

S = 0

), a measure of correlation is obtained by the single‐particle‐reduced entropy (in bit)

S_{1} = - normalTr false(ρ_{1} {log}_{2} ρ_{1} false) = - \sum_{j = 0}^{N_{\max} - 1} ξ_{j} {log}_{2} false(ξ_{j} false),

which has the disadvantage of depending also on the degree of mixture . (Note that

S_{1}

as defined above includes non‐relevant states as well.…”

Section: Modified Correlation Entropymentioning

confidence: 99%

“…which has the disadvantage of depending also on the degree of mixture [6,7]. (Note that S 1 as defined above includes non-relevant states as well.)…”

Section: Papermentioning

confidence: 99%

“…It has been shown that the single‐particle‐reduced entropy

S_{1}

as calculated from the single‐particle density matrix ()

ρ_{1}

can be interpreted as a measure of correlation for such pure states. If the preparation of the system is given by a mixture of states,

S_{1}

also depends on the degree of mixture and so this quantity is no longer suitable as a measure of correlation alone.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modified correlation entropy of a gated nanowire system described by a numerically determined non‐equilibrium many‐body statistical operator

Castelo

Indlekofer

2015

Physica Status Solidi (b)

Self Cite

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show abstract

On the single‐particle‐reduced entropy of a gated nanowire system in the Coulomb blockade regime

Abstract: J. M. Castelo et al.: Single-particle-reduced entropy of a gated nanowire system www.pss-rapid.com status solidi physica rrl J. M. Castelo et al.: Single-particle-reduced entropy of a gated nanowire system

Cited by 1 publication

References 20 publications

Modified correlation entropy of a gated nanowire system described by a numerically determined non‐equilibrium many‐body statistical operator

Modified correlation entropy of a gated nanowire system described by a numerically determined non‐equilibrium many‐body statistical operator

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