Topological Quantum Computing
... states requires that π = π † . So π is a real matrix. Furthermore, we get that the eigenvalues of π must all be 1 or -1. In our one dimensional case, this means that the matrix of π must just be 1 or -1, as we expect for bosons and fermions respectively. This is not the case in two dimensions. With ...
... states requires that π = π † . So π is a real matrix. Furthermore, we get that the eigenvalues of π must all be 1 or -1. In our one dimensional case, this means that the matrix of π must just be 1 or -1, as we expect for bosons and fermions respectively. This is not the case in two dimensions. With ...
On the energy of homogeneous cosmologies
... homogeneous cosmologies are naturally described in terms of a preferred homogeneous tetrad, then an energy-momentum expression based on the Hamiltonian for this preferred tetrad is clearly appropriate. There have been several other studies aimed at finding the total energy of the expanding universe. ...
... homogeneous cosmologies are naturally described in terms of a preferred homogeneous tetrad, then an energy-momentum expression based on the Hamiltonian for this preferred tetrad is clearly appropriate. There have been several other studies aimed at finding the total energy of the expanding universe. ...
Feeling the Future again
... branch up into separate worlds each of them representing one potential quantum state. The collapse postulate is replaced by a change in perspective during the measurement process. During superposition all quantum states are treated as a whole leading to wave-like outcome of the quantum system. This ...
... branch up into separate worlds each of them representing one potential quantum state. The collapse postulate is replaced by a change in perspective during the measurement process. During superposition all quantum states are treated as a whole leading to wave-like outcome of the quantum system. This ...
Quantum state majorization at the output of bosonic Gaussian
... the channel, the output suffers certain amount of noise. For a long time it has been conjectured, but never proved, that output states of Gaussian channels corresponding to coherent input signals are the less noisy ones (in the sense of a majorization criterion). In this work we prove this conjectur ...
... the channel, the output suffers certain amount of noise. For a long time it has been conjectured, but never proved, that output states of Gaussian channels corresponding to coherent input signals are the less noisy ones (in the sense of a majorization criterion). In this work we prove this conjectur ...
Chapter 6 Euclidean Path Integral
... where as before w0 = q ′ is the initial position and wn = q the final position. The right hand side is identical to the partition function for a one-dimensional lattice system with sites labeled by the index j and with fixed boundary conditions. The action in the exponent couples nearest-neighbor va ...
... where as before w0 = q ′ is the initial position and wn = q the final position. The right hand side is identical to the partition function for a one-dimensional lattice system with sites labeled by the index j and with fixed boundary conditions. The action in the exponent couples nearest-neighbor va ...
APPENDIX A
... in a given interaction. In different terms, as one furnishes the necessary amount of energy to the entity, to get it off the bond, it is engaged in, it is essentially, the rest relativistic energy which would pile it up. Then the rest relativistic energy, due to the relativistic law of energy conser ...
... in a given interaction. In different terms, as one furnishes the necessary amount of energy to the entity, to get it off the bond, it is engaged in, it is essentially, the rest relativistic energy which would pile it up. Then the rest relativistic energy, due to the relativistic law of energy conser ...
Quantum Phase Transitions
... As we approach the phase transition, the correlations of the order parameter become long-ranged. Fluctuations of diverging size and duration (and vanishing energy) take the system between two distinct ground states across the critical point. When are quantum effects significant? Surprisingly, all n ...
... As we approach the phase transition, the correlations of the order parameter become long-ranged. Fluctuations of diverging size and duration (and vanishing energy) take the system between two distinct ground states across the critical point. When are quantum effects significant? Surprisingly, all n ...
The Quantum World
... reflects the rest. A black body is one that perfectly absorbs, and then re-emits, all radiation falling upon it. Not only are there good approximations to such an object available in nature but also it is an ideal subject for theoretical consideration. A classic problem is posed by asking what form ...
... reflects the rest. A black body is one that perfectly absorbs, and then re-emits, all radiation falling upon it. Not only are there good approximations to such an object available in nature but also it is an ideal subject for theoretical consideration. A classic problem is posed by asking what form ...
Renormalization
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.Renormalization specifies relationships between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in infinities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, this continuum limit, the removal of the ""construction scaffolding"" of lattices at various scales, has to be taken carefully, as detailed below.Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through ""effective"" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each.