Random Matrix Theory Distributions (quanguru.QuantumToolbox.rmtDistributions)#

Contains probability density functions (PDF) from Random Matrix Theory (RMT).

Functions#

EigenVectorDist(x, dim[, beta])

Computes PDF \(P(x)\) of eigenvector statistics at x for three universality classes (COE (beta=1), CUE (beta=2), and CSE (beta=4)) of dimension \(dim\).

WignerDyson(x[, beta])

Calculate Wigner Surmise (Wigner-Dyson) PDF at x for three universality classes (COE (beta=1), CUE (beta=2), and CSE (beta=4)).

WignerSurmise(x[, beta])

Calculate Wigner Surmise (Wigner-Dyson) PDF at x for three universality classes (COE (beta=1), CUE (beta=2), and CSE (beta=4)).

Poissonian(x, lam)

Poisson PDF at x.

Function Name

Docstrings

Examples

Unit Tests

Tutorials

EigenVectorDist

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WignerDyson

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WignerSurmise

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Poissonian

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EigenVectorDist(x: float, dim: int, beta: int = 1) → float[source]#

Computes PDF \(P(x)\) of eigenvector statistics at x for three universality classes (COE (beta=1), CUE (beta=2), and CSE (beta=4)) of dimension \(dim\).

Read here more details and derivations.

Parameters:

  • x (float) – component amplitude

  • dim (int) – dimension of the matrix

  • beta (int) – Dyson parameter of universality class

Returns:

Eigenvector statistics PDF at x

Return type:

float

Examples

# TODO

WignerDyson(x: float, beta: int = 1) → float[source]#

Calculate Wigner Surmise (Wigner-Dyson) PDF at x for three universality classes (COE (beta=1), CUE (beta=2), and CSE (beta=4)). Used in nearest-neighbour eigen-value/phase spacing statistics.

For these definitions and more details.

Parameters:

  • x (float) – a float greater or equal to zero

  • beta (int, optional) – Dyson parameter of universality class, by default 1

Returns:

Wigner Surmise (Wigner-Dyson) PDF at x

Return type:

float

Examples

# TODO

Poissonian(x: float, lam: float) → float[source]#

Poisson PDF at x.

Parameters:

  • x (float) – a float larger than zero

  • lam (float) – Poisson parameter \(\lambda\)

Returns:

Poisson PDF at x.

Return type:

float

Examples

# TODO