Struct RegularizedBoseKernel 

pub struct RegularizedBoseKernel {
    pub lambda: f64,
}

Regularized bosonic analytical continuation kernel

In dimensionless variables x = 2τ/β - 1, y = βω/Λ, the integral kernel is:

K(x, y) = y * exp(-Λ y (x + 1) / 2) / (1 - exp(-Λ y))

This kernel is used for bosonic Green’s functions. The factor y regularizes the singularity at ω = 0, making the kernel well-behaved for numerical work.

The dimensionalized kernel is related by:

K(τ, ω) = ωmax * K(2τ/β - 1, ω/ωmax)

where ωmax = Λ/β.

Properties

• Centrosymmetric: K(x, y) = K(-x, -y)
• ypower = 1: Spectral function transforms as ρ’(y) = y * ρ(y)
• Bosonic only: Does not support fermionic statistics
• Weight function: w(β, ω) = 1/ω for bosonic statistics

Numerical Stability

The expression v / (exp(v) - 1) is evaluated using expm1 for small |v|.

Fields

lambda: f64

Kernel cutoff parameter Λ = β × ωmax

Implementations

impl RegularizedBoseKernel

pub fn new(lambda: f64) -> Self

Create a new RegularizedBoseKernel

Arguments

• lambda - Kernel cutoff Λ (must be non-negative)

Panics

Panics if lambda < 0

Trait Implementations

impl AbstractKernel for RegularizedBoseKernel

fn compute<T: CustomNumeric + Copy + Debug>(&self, x: T, y: T) -> T

Compute the kernel value K(x, y) with high precision

fn is_centrosymmetric(&self) -> bool

Check if the kernel is centrosymmetric

impl CentrosymmKernel for RegularizedBoseKernel

fn compute_reduced<T: CustomNumeric + Copy + Debug>( &self, x: T, y: T, symmetry: SymmetryType, ) -> T

Compute the reduced kernel value

fn lambda(&self) -> f64

Get the cutoff parameter Λ (lambda)

impl Clone for RegularizedBoseKernel

fn clone(&self) -> RegularizedBoseKernel

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for RegularizedBoseKernel

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl KernelProperties for RegularizedBoseKernel

type SVEHintsType<T> = RegularizedBoseSVEHints<T> where T: Copy + Debug + Send + Sync + CustomNumeric + 'static

Associated type for SVE hints

fn ypower(&self) -> i32

Power with which the y coordinate scales.

fn conv_radius(&self) -> f64

Convergence radius of the Matsubara basis asymptotic model

fn xmax(&self) -> f64

Get the upper bound of the x domain

fn ymax(&self) -> f64

Get the upper bound of the y domain

fn regularizer<S: StatisticsType + 'static>( &self, _beta: f64, omega: f64, ) -> f64

A regularizer for a bosonic kernel for avoiding a divergence at omega = 0.

fn sve_hints<T>(&self, epsilon: f64) -> Self::SVEHintsType<T>

where T: Copy + Debug + Send + Sync + CustomNumeric + 'static,

Create SVE hints for this kernel type.

impl PartialEq for RegularizedBoseKernel

fn eq(&self, other: &RegularizedBoseKernel) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Copy for RegularizedBoseKernel

impl StructuralPartialEq for RegularizedBoseKernel