# Two level system in a thermal noise electric field

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• kelly0303
In summary, the conversation discusses using SE to numerically simulate the evolution of a 2 level system under an external sinusoidal electric field. There is also another electric field present, created by the coupling of the 2 level system to a resonant circuit, and the individual is interested in the case when the system is in thermal equilibrium with the circuit. They are unsure how to model the thermal noise-like electric field in their Hamiltonian and are seeking advice. This topic is considered niche and they plan to do a literature review on it.
kelly0303
Hello! I have a 2 level system with a dipole moment d. I want to simulate numerically the evolution of the system under an external sinusoidal electric field (far off resonant). This is straightforward using SE. However I also have on top of that another electric field, created by a coupling of the 2 level system (ion) to a resonant circuit (not necessarily relevant but in this case I have an ion inside a Penning trap inducing image charges to a resonant RLC circuit). I'm interested in the case when the ion is in thermal equilibrium with the rlc circuit. I assume that the noise from the circuit will induce further population transfer between the 2 levels of the system. However I'm not sure how to model this thermal noise-like electric field, as an extra off diagonal term in my Hamiltonian. Can someone advice me about it? Thank you!

This is niche research stuff. Time to do a literature review

## 1. What is a two level system in a thermal noise electric field?

A two level system in a thermal noise electric field is a simplified model used to study the behavior of a system with only two energy levels in the presence of thermal noise and an applied electric field. It is commonly used in fields such as quantum mechanics and statistical physics to understand the behavior of atoms, molecules, and other systems.

## 2. How does a two level system behave in a thermal noise electric field?

In a thermal noise electric field, a two level system can undergo transitions between its two energy levels due to the presence of thermal fluctuations. The applied electric field can also affect the energy levels and the probability of transitions between them. The behavior of the system is described by the Boltzmann distribution, which determines the probability of the system being in a certain energy level at a given temperature.

## 3. What is the significance of studying two level systems in a thermal noise electric field?

Studying two level systems in a thermal noise electric field allows us to gain a better understanding of the behavior of more complex systems that can be modeled as a collection of two level systems. It also has practical applications in fields such as quantum computing, where understanding the behavior of two level systems is crucial for developing efficient algorithms.

## 4. How is the behavior of a two level system affected by temperature and electric field strength?

The behavior of a two level system is highly dependent on temperature and electric field strength. At higher temperatures, the system is more likely to undergo transitions between its energy levels due to increased thermal fluctuations. Similarly, a stronger electric field can increase the probability of transitions between energy levels and can also shift the energy levels themselves.

## 5. Are there any real-world examples of two level systems in a thermal noise electric field?

Yes, there are many real-world examples of two level systems in a thermal noise electric field. One common example is the behavior of atoms or molecules in a gas, where the energy levels of the particles can be affected by an applied electric field and thermal noise. Another example is the behavior of qubits in quantum computing, which can be modeled as two level systems in the presence of thermal noise and an applied electric field.

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