# Quantum linear response theory?

• baranas
In summary, linear response theory in quantum mechanics is a practical method for predicting experimental measurements on quantum systems. It allows researchers to calculate impedance and other properties of driven systems and is useful in determining the feasibility of experiments. One can learn more about this theory through lecture notes by Andrei Tokmakof at MIT and books by Mazenko and Kubo.
baranas
Can anyone introduce, what is linear response theory in quantum mechanics? Or suggest, where i could read about it, to get acquaintance with it?

I don't know much about quantum linear response theory but I am also trying to learn. I found a series of lecture notes by Andrei Tokmakof at MIT. This one seems to be the most relevant.
http://www.mit.edu/~tokmakof/TDQMS/Notes/8._Linear_Response_2-09.pdf.

There are two books referenced on page 20 of the notes linked to in post #2. In the book by Mazenko, section 2.1 is useful. You may also want to check the 4th chapter of Kubo's et al. book <Statistical Physics II>.

It is worth noting that this theory is very "practical", in that it allows you to figure out what you would actually MEASURE in an experiment on a quantum system.
Years ago I e.g. used it to calculate the impedance(in ohms) of a driven system (described by a JC hamiltonian) as a function of applied magnetic field, which in turn allowed me to model a particular experiment to see if it was feasible.
Very useful.

## 1. What is quantum linear response theory?

Quantum linear response theory is a mathematical framework used to study the response of quantum mechanical systems to external perturbations. It allows us to understand how the system's properties change in response to small changes in its environment or external fields.

## 2. How is quantum linear response theory different from classical linear response theory?

Unlike classical linear response theory, which is based on the assumption of small perturbations and a linear response of the system, quantum linear response theory takes into account the fundamental principles of quantum mechanics, such as superposition and uncertainty. This allows for a more accurate description of the response of quantum systems.

## 3. What are some applications of quantum linear response theory?

Quantum linear response theory has various applications in fields such as condensed matter physics, quantum chemistry, and quantum information science. It is used to study the behavior of materials under different conditions, model the behavior of molecules and chemical reactions, and design quantum devices for information processing.

## 4. How is quantum linear response theory used in experiments?

In experiments, quantum linear response theory is used to analyze and interpret data obtained from measurements of quantum systems. It can also be used to design experiments that can probe the response of a system to different perturbations and gain a deeper understanding of its properties.

## 5. What are some current challenges in quantum linear response theory?

One of the main challenges in quantum linear response theory is extending it to more complex systems, such as those with many interacting particles. Another challenge is developing efficient numerical methods for calculating response functions in large systems, as the calculations can become computationally intensive.

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