Bumped by Community user
    Bumped by Community user
4 reformulated the question
source | link

Introduction

The Keldysh path integralKeldysh path integral can be thought of as a reformulation of the quantum optical master equationmaster equation, which describes the markovian time evolution of the density operator of an open quantum system in the Schrödinger-pictureSchrödinger-picture. 

It is also well known that theThe Keldysh-formalism allows one to calculate Green's functionsGreen's functions. But fundamentally the Green's functions should be defined in the Heisenberg-pictureHeisenberg-picture, because they contain operators evaluated at different times. 

It is also well known thatBut the formulation of the Heisenberg-picture for open quantum systems requires the introduction of noise termsnoise terms into the equations of motion. Without the noise terms, the product rule does not hold for the time derivative.

Question

My question is, that does anyone know any good references for linking these Heisenberg picture calculations based on quantum stochastic calculus to the Green's functions in the Keldysh-formalism?

Note

Note

I know that ifIf the environmentalenviromental variables are explicitly taken into account then the original system + the environment can be regarded as a larger closed system. Of course oneOne can then use the unitary time evolution operator to switch between the Schrödinger and the Heisenberg picture. My question was about linking these different formalisms at the level of the smaller system, where the environmentalenviromental degrees of freedom are not present. For example, it is known that the Keldysh path integral can be derived from the Markovianmarkovian master equation directly, without going back to the system + environment formulation.

The Keldysh path integral can be thought of as a reformulation of the quantum optical master equation, which describes the markovian time evolution of the density operator of an open quantum system in the Schrödinger-picture.

It is also well known that the Keldysh-formalism allows one to calculate Green's functions. But fundamentally the Green's functions should be defined in the Heisenberg-picture, because they contain operators evaluated at different times.

It is also well known that the formulation of the Heisenberg-picture for open quantum systems requires the introduction of noise terms into the equations of motion.

Question

My question is that does anyone know any good references for linking these Heisenberg picture calculations based on quantum stochastic calculus to the Green's functions in the Keldysh-formalism?

Note

I know that if the environmental variables are explicitly taken into account then the original system + the environment can be regarded as a larger closed system. Of course one can then use the unitary time evolution operator to switch between the Schrödinger and the Heisenberg picture. My question was about linking these different formalisms at the level of the smaller system, where the environmental degrees of freedom are not present. For example, it is known that the Keldysh path integral can be derived from the Markovian master equation directly, without going back to the system + environment formulation.

Introduction

The Keldysh path integral can be thought of as a reformulation of the quantum optical master equation, which describes the markovian time evolution of the density operator of an open quantum system in the Schrödinger-picture. 

The Keldysh-formalism allows one to calculate Green's functions. But fundamentally the Green's functions should be defined in the Heisenberg-picture, because they contain operators evaluated at different times. 

But the formulation of the Heisenberg-picture for open quantum systems requires the introduction of noise terms into the equations of motion. Without the noise terms, the product rule does not hold for the time derivative.

Question

My question is, that does anyone know any good references for linking these Heisenberg picture calculations based on quantum stochastic calculus to the Green's functions in the Keldysh-formalism?

Note

If the enviromental variables are explicitly taken into account then the original system + the environment can be regarded as a larger closed system. One can then use the unitary time evolution operator to switch between the Schrödinger and the Heisenberg picture. My question was about linking these different formalisms at the level of the smaller system, where the enviromental degrees of freedom are not present. For example, the Keldysh path integral can be derived from the markovian master equation directly, without going back to the system + environment formulation.

    Notice added Book Recommendation by Qmechanic
    Post Made Community Wiki by Qmechanic
3 too long comment added as a note
source | link

The Keldysh path integral can be thought of as a reformulation of the quantum optical master equation, which describes the markovian time evolution of the density operator of an open quantum system in the Schrödinger-picture.

It is also well known that the Keldysh-formalism allows one to calculate Green's functions. But fundamentally the Green's functions should be defined in the Heisenberg-picture, because they contain operators evaluated at different times.

It is also well known that the formulation of the Heisenberg-picture for open quantum systems requires the introduction of noise terms into the equations of motion.

Question

My question is that does anyone know any good references for linking these Heisenberg picture calculations based on quantum stochastic calculus to the Green's functions in the Keldysh-formalism?

Note

I know that if the environmental variables are explicitly taken into account then the original system + the environment can be regarded as a larger closed system. Of course one can then use the unitary time evolution operator to switch between the Schrödinger and the Heisenberg picture. My question was about linking these different formalisms at the level of the smaller system, where the environmental degrees of freedom are not present. For example, it is known that the Keldysh path integral can be derived from the Markovian master equation directly, without going back to the system + environment formulation.

The Keldysh path integral can be thought of as a reformulation of the quantum optical master equation, which describes the markovian time evolution of the density operator of an open quantum system in the Schrödinger-picture.

It is also well known that the Keldysh-formalism allows one to calculate Green's functions. But fundamentally the Green's functions should be defined in the Heisenberg-picture, because they contain operators evaluated at different times.

It is also well known that the formulation of the Heisenberg-picture for open quantum systems requires the introduction of noise terms into the equations of motion.

Question

My question is that does anyone know any good references for linking these Heisenberg picture calculations based on quantum stochastic calculus to the Green's functions in the Keldysh-formalism?

The Keldysh path integral can be thought of as a reformulation of the quantum optical master equation, which describes the markovian time evolution of the density operator of an open quantum system in the Schrödinger-picture.

It is also well known that the Keldysh-formalism allows one to calculate Green's functions. But fundamentally the Green's functions should be defined in the Heisenberg-picture, because they contain operators evaluated at different times.

It is also well known that the formulation of the Heisenberg-picture for open quantum systems requires the introduction of noise terms into the equations of motion.

Question

My question is that does anyone know any good references for linking these Heisenberg picture calculations based on quantum stochastic calculus to the Green's functions in the Keldysh-formalism?

Note

I know that if the environmental variables are explicitly taken into account then the original system + the environment can be regarded as a larger closed system. Of course one can then use the unitary time evolution operator to switch between the Schrödinger and the Heisenberg picture. My question was about linking these different formalisms at the level of the smaller system, where the environmental degrees of freedom are not present. For example, it is known that the Keldysh path integral can be derived from the Markovian master equation directly, without going back to the system + environment formulation.

    Tweeted twitter.com/StackPhysics/status/971286922785116162
2 edited tags
| link
1
source | link