# Kubo formula

The Kubo formula, named for Ryogo Kubo, is an equation which expresses the linear response of an observable quantity due to a time-dependent perturbation.wikipedia
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### Linear response function

linear response theorylinear responsesusceptibility
The Kubo formula, named for Ryogo Kubo, is an equation which expresses the linear response of an observable quantity due to a time-dependent perturbation.
This defines particularly the Kubo formula, which considers the general case that the "force" h(t) is a perturbation of the basic operator of the system, the Hamiltonian, where \hat B corresponds to a measurable quantity as input, while the output x(t) is the perturbation of the thermal expectation of another measurable quantity \hat A(t).

### Ryogo Kubo

Kubo
The Kubo formula, named for Ryogo Kubo, is an equation which expresses the linear response of an observable quantity due to a time-dependent perturbation.

### Perturbation theory (quantum mechanics)

perturbation theoryperturbativeperturbation
The Kubo formula, named for Ryogo Kubo, is an equation which expresses the linear response of an observable quantity due to a time-dependent perturbation.

### Partition function (statistical mechanics)

partition functionpartition functionsgrand partition function
::where is the partition function.

### Heaviside step function

Heaviside functionunit step functionHeaviside unit step function
The perturbation is described by an additional time dependence in the Hamiltonian: where \theta (t) is the Heaviside function ( = 1 for positive times, =0 otherwise) and \hat V(t) is hermitian and defined for all t, so that \hat H(t) has for positive t-t_0 again a complete set of real eigenvalues E_n(t).

### Density matrix

density operatordensity matricesvon Neumann equation
However, one can again find the time evolution of the density matrix rsp.

### Schrödinger equation

Schrödinger's equationwave mechanicsSchrödinger wave equation
The time dependence of the states is governed by the Schrödinger equation which thus determines everything, corresponding of course to the Schrödinger picture.

### Schrödinger picture

Schrödinger representationSchrödinger operatorswave-mechanical
The time dependence of the states is governed by the Schrödinger equation which thus determines everything, corresponding of course to the Schrödinger picture.

### Interaction picture

Dirac pictureinteraction HamiltonianSchwinger–Tomonaga equation
But since \hat{V}(t) is to be regarded as a small perturbation, it is convenient to now use instead the interaction picture representation, in lowest nontrivial order.

### Second quantization

second-quantization formalismcanonically quantizedCovariant formulation