Quantum Theory of Many-variable Systems and Fields


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An Introduction

Quantum field theory. Statistical mechanics.

Quantum Theory of Many Variable Systems and Fields (World Scientific Lecture Notes in Physics)

Quantum field theory Statistical mechanics Perturbation Quantum mechanics Quantum statistics Quantum theory. Related item. Bibliography Illustrated text. Related Internet Resources. Back to results.

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University of Birmingham Libraries. University of Bristol Libraries. We learned what we know today about the Universe by asking the right questions, which means by setting up physical systems and then performing the necessary measurements and observations to determine what the Universe is doing.

Despite what we might have intuited beforehand, the Universe showed us that the rules it obeys are bizarre, but consistent. The rules are just profoundly and fundamentally different from anything we'd ever seen before. It wasn't so surprising that the Universe was made of indivisible, fundamental units: quanta, like quarks, electrons or photons. What was surprising is that these individual quanta didn't behave like Newton's particles: with well-defined positions, momenta, and angular momenta. This has been borne out by a huge variety of experiments.

You cannot eliminate this intrinsic angular momentum; it is a property of this quantum of matter that cannot be extricated from this particle. However, you can pass this particle through a magnetic field. Now, what happens if you pass the electrons that deflected positively through another magnetic field? Well, if that field is:. Multiple successive Stern-Gerlach experiments, which split quantum particles along one axis according to their spins, will cause further magnetic splitting in directions perpendicular to the most recent one measured, but no additional splitting in the same direction.

This might sound counterintuitive, but it's not only a property inherent to the quantum Universe, but it's a property shared by any physical theory that obeys a specific mathematical structure: non-commutativity. The three directions of angular momentum don't commute with one another. Energy and time don't commute, leading to inherent uncertainties in the masses of short-lived particles.

And position and momentum don't commute either, meaning you cannot measure both where a particle is and how fast it's moving simultaneously to arbitrary accuracy. This diagram illustrates the inherent uncertainty relation between position and momentum. When one is known more accurately, the other is inherently less able to be known accurately. There is no fundamental position or momentum inherent to each particle; there is a mean expectation value with an uncertainty superimposed atop it. This uncertainty cannot be removed from quantum physics, as it represents an important aspect of our quantum reality.

These facts are weird, but they're not the only weird behavior of quantum mechanics. Place a cat into a sealed box with poisoned food and a radioactive atom. If the atom decays, the food is released and the cat will eat it and die.

If the atom doesn't decay, the cat cannot get the poisoned food, and remains alive. You open the box.

Just before you make the measurement or observation, is the cat dead or alive? According to the rules of quantum mechanics, you cannot know the outcome before making the observation. Inside the box, the cat will be either alive or dead, depending on whether a radioactive particle decayed or not. If the cat were a true quantum system, the cat would be neither alive nor dead, but in a superposition of both states until observed. For generations, this puzzle has stymied almost everyone who's tried to make sense of it.

Somehow, it seems like the outcome of a scientific experiment is fundamentally tied to whether we make a specific measurement or not. This has been called "the measurement problem" in quantum physics, and has been the subject of many essays, opinions, interpretations and declarations from physicists and laypersons alike.

Quantum Theory Of Many Variable Systems And Fields

This is a question many have asked over the past 90 years or so , attempting to obtain a deeper view of what's truly real. But despite many books and op-eds on the subject, from Lee Smolin to Sean Carroll to Adam Becker to Anil Ananthaswamy to many others , this might not even be a good question. Schematic of the third Aspect experiment testing quantum non-locality.

Entangled photons from the source are sent to two fast switches, that direct them to polarizing detectors. The switches change settings very rapidly, effectively changing the detector settings for the experiment while the photons are in flight. Different settings, puzzlingly enough, result in different experimental outcomes. The problem is that this is not possible in practice.

First of all, in the range from atoms and molecules to solids we are dealing with systems with an electron number and the same for nuclei ranging from 1 to 10 Which means that we are dealing with quantum mechanical wave functions of an enormous number of variables. Secondly, all these particles are interacting with Coulombic forces such that the motion of the particles are not independent and therefore equations can not be simplified.

We are therefore faced with the question how to theoretically predict properties of such systems. It is a central problem in theoretical physics and an enormous amount of work has been done to attack this problem. One key observation is that most experimental properties of many-particle systems involve one and two-body observables such as densities and currents, polarizabilities, spin quantum numbers, pair correlation functions etc. This suggests that it may be possible to describe the properties of many-body systems in terms of reduced quantities, i.

This idea has turned out to be very fruitful and has led to various theoretical approaches to attack the many-body problem.


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These approaches are nonequilibrium Green's function theory, density functional theory and density matrix theory. In our research group all these three approaches are developed and applied to the study of many-particle systems.

Quantum theory and determinism | SpringerLink

Nonequilibrium Green's functions is a general perturbative approach to calculate time-dependent observables of quantum many-body systems. The theory is based on expansion of these observables in powers of the two-body interactions, while external time-dependent fields are treated exactly.

Panel: Quantum Theory and Free Will - Chris Fields, Henry Stapp & Donald Hoffman

Often it turns out that order by order perturbation theory is insufficient. Therefore perturbative series are summed to infinite order. A key role in carrying out such resummations is played by the self-energy operator and the Dyson equation. In nonequilbrium theory the Dyson equation is translated into a set of integro-differential equations, known as the Kadanoff-Baym equations, that need to be solved by time-propagation. A pedagogical introduction to the whole theory for student with a background in standard quantum mechanics is given in.

Quantum Theory of Many-variable Systems and Fields Quantum Theory of Many-variable Systems and Fields
Quantum Theory of Many-variable Systems and Fields Quantum Theory of Many-variable Systems and Fields
Quantum Theory of Many-variable Systems and Fields Quantum Theory of Many-variable Systems and Fields
Quantum Theory of Many-variable Systems and Fields Quantum Theory of Many-variable Systems and Fields
Quantum Theory of Many-variable Systems and Fields Quantum Theory of Many-variable Systems and Fields
Quantum Theory of Many-variable Systems and Fields Quantum Theory of Many-variable Systems and Fields
Quantum Theory of Many-variable Systems and Fields Quantum Theory of Many-variable Systems and Fields

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