Goldilocks cooling: Demonstrating the quantum Mpemba effect in a two-level system
(2026) FYSK04 20261Department of Physics
Mathematical Physics
- Abstract
- This thesis investigates the quantum Mpemba effect, where an initially hotter system cools down faster than an initially colder one. This was demonstrated in a qubit system coupled to two environments. A thermal state is chosen as the initial state and then left to freely equilibrate. It was shown that the initial thermal state can be chosen in a way to accelerate the resulting relaxation process. The Liouvillian dynamics were analyzed and, by eliminating the contribution of the slowest decaying eigenmode (SDM) corresponding to accelerated relaxation dynamics, the effect was demonstrated. All states with vanishing SDM contributions were considered and found to belong to a plane in the Bloch sphere corresponding to a reduced state space. A... (More)
- This thesis investigates the quantum Mpemba effect, where an initially hotter system cools down faster than an initially colder one. This was demonstrated in a qubit system coupled to two environments. A thermal state is chosen as the initial state and then left to freely equilibrate. It was shown that the initial thermal state can be chosen in a way to accelerate the resulting relaxation process. The Liouvillian dynamics were analyzed and, by eliminating the contribution of the slowest decaying eigenmode (SDM) corresponding to accelerated relaxation dynamics, the effect was demonstrated. All states with vanishing SDM contributions were considered and found to belong to a plane in the Bloch sphere corresponding to a reduced state space. A thermal state could be shown to exist in this subspace, which is the Mpemba state that relaxes the fastest. The numerical relaxation dynamics were computed and the accelerated behavior of the Mpemba state verified. The fidelity of the Mpemba state also exhibits a steeper decay, consistent with the faster-decaying modes. The results were found to only strongly affect the solution in regions close to the steady state. (Less)
- Popular Abstract
- Cooling is a phenomenon we all know from everyday life. Whether it is in refrigeration or air-conditioning. It also plays a big role in computers, as well as many other appliances, where the different components need to be cooled to keep their performance up. Generally, when you cool something down it is expected to take longer if the initial thing is hotter to start with (assuming of course your fridge is at a constant temperature). If you put hot coffee in the fridge it should take longer to cool than a can of store bought soda.
The Mpemba effect however states that this is not always the case. It says that under certain circumstances a liquid at a higher initial temperature can freeze faster than a colder one, which is quite... (More) - Cooling is a phenomenon we all know from everyday life. Whether it is in refrigeration or air-conditioning. It also plays a big role in computers, as well as many other appliances, where the different components need to be cooled to keep their performance up. Generally, when you cool something down it is expected to take longer if the initial thing is hotter to start with (assuming of course your fridge is at a constant temperature). If you put hot coffee in the fridge it should take longer to cool than a can of store bought soda.
The Mpemba effect however states that this is not always the case. It says that under certain circumstances a liquid at a higher initial temperature can freeze faster than a colder one, which is quite surprising, counterintuitive behavior. It is named after Erasto Mpemba, who discovered the effect while being a middle schooler trying to make ice cream during a lunch break. However, even after publishing his findings together with the physicist D. G. Osbourne the validity of their findings remains controversial.
In this thesis, a similar effect is examined, the quantum Mpemba effect, which in its idea is derived from the Mpema effect. Here, the concept is applied to a quantum mechanical system on a very small scale, which leads to different physical phenomena and a different mathematical description. These differences make the quantum Mpemba effect possible. We tried to demonstrate this effect in a two level quantum system and investigate the reasons for it.
In this system, there is only a hot state, and a cold one, and the temperature is defined via the probability of the state being hot or cold. This system, the drink in the classical analogy, is a mixture of hot and cold which then can be left to reach the same state as environment baths, which are analogous to a fridge in the classical system. Doing this, the time it takes for the system to reach equilibrium (i.e. drink and fridge have the same temperature) can be found. It was found that by changing the initial state in a certain way, it always reaches the final state faster if you wait long enough and zoom in on the differences.
Geometrically this can be visualized very nicely. The quantum two level system can be described by positions in a sphere, with temperature being one axis in this sphere. In this thesis I showed that the quantum Mpemba effect can be represented by a plane in this sphere. Here the point where the axis with the temperature intersects the plane the effect occurs.
While this effect cannot be used to explain the original Mpemba effect and, admittedly, has very little to do with his work it can still be useful. Quantum computers, which use the special properties of quantum mechanics, can use this speedup to do computations faster. As well as that, the world of nano and quantum technologies is growing very fast right now with many more promising applications of this effect. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/student-papers/record/9234304
- author
- Ulbricht, Lasse LU
- supervisor
-
- Peter Samuelsson LU
- Daniel Holst LU
- organization
- course
- FYSK04 20261
- year
- 2026
- type
- M2 - Bachelor Degree
- subject
- keywords
- Mpemba effect, Cooling, Open quantum systems, Lindblad dynamics, Relaxation, Quantum thermodynamics, Bloch sphere, Qubit, Gibbs state, Temperature
- language
- English
- id
- 9234304
- date added to LUP
- 2026-06-10 08:48:43
- date last changed
- 2026-06-10 08:48:43
@misc{9234304,
abstract = {{This thesis investigates the quantum Mpemba effect, where an initially hotter system cools down faster than an initially colder one. This was demonstrated in a qubit system coupled to two environments. A thermal state is chosen as the initial state and then left to freely equilibrate. It was shown that the initial thermal state can be chosen in a way to accelerate the resulting relaxation process. The Liouvillian dynamics were analyzed and, by eliminating the contribution of the slowest decaying eigenmode (SDM) corresponding to accelerated relaxation dynamics, the effect was demonstrated. All states with vanishing SDM contributions were considered and found to belong to a plane in the Bloch sphere corresponding to a reduced state space. A thermal state could be shown to exist in this subspace, which is the Mpemba state that relaxes the fastest. The numerical relaxation dynamics were computed and the accelerated behavior of the Mpemba state verified. The fidelity of the Mpemba state also exhibits a steeper decay, consistent with the faster-decaying modes. The results were found to only strongly affect the solution in regions close to the steady state.}},
author = {{Ulbricht, Lasse}},
language = {{eng}},
note = {{Student Paper}},
title = {{Goldilocks cooling: Demonstrating the quantum Mpemba effect in a two-level system}},
year = {{2026}},
}