Quantum mechanics & the big world
04 Apr 2007-
TL;DR: In this paper, it is shown that quantum superposition states can be subtly influenced by the physics associated with spontaneous symmetry breaking, which destroys the quantum nature of the qubit and renders it useless for quantum computation.
Abstract: Quantum Mechanics is one of the most successful
physical theories of the last century. It explains physical
phenomena from the smallest to the largest lengthscales.
Despite this triumph, quantum mechanics is often perceived
as a mysterious theory, involving superposition states that are
alien to our everyday Big World.
The construction of a future quantum computer relies on
our ability to manipulate quantum superposition states in
qubits. In this thesis it is shown that these qubits can be subtly
influenced by the physics associated with spontaneous symmetry
breaking. This process destroys the quantum nature of
the qubit and renders it useless for quantum computation.
An even more fundamental problem with quantum superpositions
is that they cannot be reconciled with the theory of
general relativity. In the end of this thesis a model is proposed
which describes the effective, deteriorating, influence of
gravity on quantum states, thus suggesting a path toward the
demise of quantum mechanics in the big world.
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01 Jan 2009
TL;DR: In this paper, the authors studied the effect of time-dependent symmetry breaking in the Lieb-Mattis model of an antiferromagnet with the path integral mechanism.
Abstract: Symmetry breaking is studied in many systems by introducing a static symmetry breaking field. By taking the right limits, one can prove that certain symmetries in a system will be broken spontaneously. One might wonder what the results are when the symmetry breaking field depends on time, and if it differs from a static case. It turns out that it does. The study focuses on the Lieb-Mattis model for an antiferromagnet. It is an infinite range model in the sense that all the spins on one sublattice interact with all spins on the other sublattice. This model has a wide range of applications as it effectively contains the thin spectrum for the familiar class of Heisenberg models. In order to study time-dependent symmetry breaking of the Lieb-Mattis model, one needs the path integral mechanism. It turns out that for solving a general quadratic Hamiltonian, only two solutions of the classical Euler-Lagrange equation of motion need to be known. Furthermore, the introduction of a boundary condition to the system is investigated, where the problem is limited to half-space. The effects of the boundary condition can be implemented at the very end when a set of wave functions and the propagator of the time-dependent system is known. The Lieb-Mattis model of an antiferromagnet is studied with the developed path integral mechanism. A linear symmetry breaking field is introduced and its consequences are computed. An instantaneous state can be defined, which represents the results that a static treatment would have given us by simply implementing the time-dependence at the end. This is compared with the true dynamical state that is calculated by means of the path integral mechanism. A density of defects is defined, which is a measure of the difference between the dynamical symmetry-broken ground state and the instantaneous one. The behaviour of the density of defects can be summarised in a phase diagram, which is controlled by two system parameters: the initial time that the field is switched on, and the final time. The phase diagram consists of three regions. First of all, it contains a defect creation regime in which the defect density increases but does not saturate before the final time is reached. Secondly, there exists a defect saturation regime where the defects are present and are saturated at the final time. Finally, there exists a defect free region, in which no defects can be found. The results of the linear field case can be generalised to other shapes of the time-dependent symmetry-breaking field. The same phases can be identified in the phase diagram and only the quantitative behaviour of the phase diagram changes. Therefore one concludes that in general the way in which a symmetry is broken matters for the resulting symmetry broken ground state.
Cites methods from "Quantum mechanics & the big world"
...This master’s research project is a continuation of part of the work done in this group before in the context of Jasper van Wezel’s PhD [1]....
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...breaking and motivation This master’s research project is a continuation of part of the work done in this group before in the context of Jasper van Wezel’s PhD [1]....
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