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In physics, thermalisation (in American English thermalization) is the process of physical bodies reaching thermal equilibrium through mutual interaction. In general the natural tendency of a system is towards a state of equipartition of energy or uniform temperature, maximising the system's entropy.
Examples of thermalisation include:
the achievement of equilibrium in a plasma
the process undergone by high-energy neutrons as they lose energy by collision with a moderator.
To investigate, the researchers devised an experiment using three quantum bits, the basic computational units of the quantum computer. Unlike classical computer bits, which utilize a binary system of two possible states (e.g., zero/one), a qubit can also use a superposition of both states (zero and one) as a single state. Additionally, multiple qubits can entangle, or link so closely that their measurements will automatically correlate. By manipulating these qubits with electronic pulses, Neill caused them to interact, rotate and evolve in the quantum analog of a highly sensitive classical system.
The result is a map of entanglement entropy of a qubit that, over time, comes to strongly resemble that of classical dynamics -- the regions of entanglement in the quantum map resemble the regions of chaos on the classical map. The islands of low entanglement in the quantum map are located in the places of low chaos on the classical map.
"There's a very clear connection between entanglement and chaos in these two pictures," said Neill. "And, it turns out that thermalisation is the thing that connects chaos and entanglement. It turns out that they are actually the driving forces behind thermalisation.
"What we realize is that in almost any quantum system, including on quantum computers, if you just let it evolve and you start to study what happens as a function of time, it's going to thermalize," added Neill, referring the quantum-level equilibration. "And this really ties together the intuition between classical thermalisation and chaos and how it occurs in quantum systems that entangle."
Chaos theory is the field of study in mathematics that studies the behavior of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect.
'Rosetta Stone' Of Bacterial Communication Discovered
July 13, 2009
Source: Duke University
Summary: The Rosetta Stone of bacterial communication may have been found. Although they have no sensory organs, bacteria can get a good idea about what's going on in their neighborhood and communicate with each other, mainly by secreting and taking in chemicals from their surrounding environment. Even though there are millions of different kinds of bacteria with their own ways of sensing the world around them, bioengineers believe they have found a principle common to all of them.
This thesis investigates thermalisation, correlations and entanglement in Bose-Einstein condensates. Bose-Einstein condensates are ultra-cold collections of identical bosonic atoms which accumulate in a single quantum state, forming a mesoscopic quantum object. They are clean and controllable quantum many-body systems that permit an unprecedented degree of experimental flexibility compared to other physical systems. Further, a tractable microscopic theory exists which allows a direct and powerful comparison between theory and experiment, propelling the field of quantum atom optics forward at an incredible pace. Here we explore some of the fundamental frontiers of the field, examining how non-classical correlations and entanglement can be created and measured, as well as how non-classical effects can lead to the rapid heating of atom clouds. We first investigate correlations between two weakly coupled condensates, a system analogous to a superconducting Josephson junction. The ground state of this system contains non-classical number correlation arising from the repulsion between the atoms. Such states are of interest because they may lead to more precise measurement devices such as atomic gyroscopes. Unfortunately thermal fluctuations can destroy these correlations, and great care is needed to experimentally observe non-classical effects. We show that adiabatic evolution can drive the isolated quantum system out of thermal equilibrium and decrease thermal noise, in agreement with a recent experiment [Esteve et al. Nature 455, 1216 (2008)]. This technique may be valuable for observing and using quantum correlated states in the future. Next, we analyze the rapid heating that occurs when a condensate is placed in a moving periodic potential. The dynamical instability responsible for the heating was the subject of much uncertainty, which we suggest was due to the inability of the mean-field approximation to account for important spontaneous scattering processes. We show that a model including non-classical spontaneous scattering can describe dynamical instabilities correctly in each of the regimes where they have been observed, and in particular we compare our simulations to an experiment performed at the University of Otago deep inside the spontaneous scattering regime. Finally, we proposed a method to create and detect entangled atomic wave-packets. Entangled atoms are interesting from a fundamental perspective, and may prove useful in future quantum information and precision measurement technologies. Entanglement is generated by interactions, such as atomic collisions in Bose-Einstein condensates. We analyze the type of entanglement generated via atomic collisions and introduce an abstract scheme for detecting entanglement and demonstrating the Einstein-Podolsky-Rosen paradox with ultra-cold atoms. We further this result by proposing an experiment where entangled wave-packets are created and detected. The entanglement is generated by the pairwise scattering that causes the instabilities in moving periodic potentials mentioned above. By careful arrangement, the instability process can be controlled to to produce two well-defined atomic wave-packets. The presence of entanglement can be proven by applying a series of laser pulses to interfere the wave-packets and then measuring the output populations. Realizing this experiment is feasible with current technology.
originally posted by: Reverbs
a reply to: Kashai
Could you give me a basic run down of chaos theory?
If I am reading correctly Chaos IS Entanglement ?
I have a lot of reading to do. This is a whole new avenue of thought I can go down.
Complexity theory is the study of how complicated patterns can result from simple behaviors of individuals within a system. Chaos is the study of how simple patterns can be generated from complicated underlying behavior. Chaos theory is really about finding the underlying patterns in apparently random data. It is unfortunate that science has chosen the word "chaos" to describe this form of order because the word "chaos" is at odds with common parlance, which suggests complete disorder. Nonetheless, science defines "chaos" as a form of order that lacks predictability.
Chaos theory helps us to understand patterns in nature. It has been used to model biological systems, which are some of the most chaotic systems imaginable. Chaotic patterns show up everywhere around the world, including cloud patterns, the currents of the ocean, the flow of blood through fractal blood vessels, the branches of trees, astronomy, epidemiology, and the effects of air turbulence.
Chaos theory states that, under certain conditions, ordered, regular patterns can be seen to arise out of seemingly random, erratic and turbulent processes. Chaos theory does not emphasize the inherent disorder and unpredictability of a system. Instead, chaos theory emphasizes the order inherent in the system and the universal behavior of similar systems.
Computer graphics makes it possible to study how these patterns appear and disappear with changes in the system parameters. Many patterns, such as the vortex of a tornado, stock market trends, and crowds of people can now be subjected to computer modeling.
Chaos can be simulated with simple computer graphics and a process called cellular automata (CA). With CAs, a fixed rule of pattern development is applied to a series of totally random initial conditions. With CAs, it possible to simulate how simple behaviors are generated from complex rules.