What is quantum unique ergodicity?
... The first major theorem proved in this subject was the quantum ergodicity theorem proved by Schnirelman, Zelditch and Colin de Verdière for manifolds without boundary (Example 1.3), and for manifolds with boundary by Gérard–Leichtnam and Zelditch–Zworski [11], [15], [4], [6], [16]. Theorem 4.1 (Qu ...
... The first major theorem proved in this subject was the quantum ergodicity theorem proved by Schnirelman, Zelditch and Colin de Verdière for manifolds without boundary (Example 1.3), and for manifolds with boundary by Gérard–Leichtnam and Zelditch–Zworski [11], [15], [4], [6], [16]. Theorem 4.1 (Qu ...
How to test the “quantumness” of a quantum computer?
... and quantum annealing (SCA and SQA, respectively). The surprising result was that the operation of D-Wave One produced a bimodal statistical distribution of success probabilities, corresponding to clearly distinct groups of “easy” and “hard” problems, similar to the one produced by SQA, but drastica ...
... and quantum annealing (SCA and SQA, respectively). The surprising result was that the operation of D-Wave One produced a bimodal statistical distribution of success probabilities, corresponding to clearly distinct groups of “easy” and “hard” problems, similar to the one produced by SQA, but drastica ...
The Logic of Complementarity - Philsci
... Kalckar also keeps off the view claimed by some writers who have sustained that Bohr was motivated by sources outside physics, like the readings of Kierkegaard or of the Danish philosopher H. Høffding. According to Kalckar, the very origins of such an idea came from physics itself and, to reinforce ...
... Kalckar also keeps off the view claimed by some writers who have sustained that Bohr was motivated by sources outside physics, like the readings of Kierkegaard or of the Danish philosopher H. Høffding. According to Kalckar, the very origins of such an idea came from physics itself and, to reinforce ...
Emergence, Reduction, and Theoretical Principles
... for the reductionist hypothesis is that results of the sort mentioned above (e.g., infinite conductivity) would continue to be accurate even in the face of significant changes to our microphysical theories. In other words, we might have an entirely different model from the current one(s) of how SSB ...
... for the reductionist hypothesis is that results of the sort mentioned above (e.g., infinite conductivity) would continue to be accurate even in the face of significant changes to our microphysical theories. In other words, we might have an entirely different model from the current one(s) of how SSB ...
The Philosophy behind Quantum Gravity
... reductionism, and discuss how the enterprise of quantum gravity is related to the interpretation of quantum mechanics. I then (section 3) briefly review an argument for the necessity of a quantized theory of gravity, and argue that such a theory is necessary neither for consistency reasons nor (at l ...
... reductionism, and discuss how the enterprise of quantum gravity is related to the interpretation of quantum mechanics. I then (section 3) briefly review an argument for the necessity of a quantized theory of gravity, and argue that such a theory is necessary neither for consistency reasons nor (at l ...
How Quantum Theory Helps Us Explain
... quantum theory: single particle interference phenomena in section 7, the stability of matter in section 8, and Bose-Einstein condensation in section 9. In conclusion I note some open problems and relate the present account of explanation in quantum theory to alternative approaches that emphasize th ...
... quantum theory: single particle interference phenomena in section 7, the stability of matter in section 8, and Bose-Einstein condensation in section 9. In conclusion I note some open problems and relate the present account of explanation in quantum theory to alternative approaches that emphasize th ...
Algebraic aspects of topological quantum field theories
... study of topological quantum field theory. The notion of a topological quantum field theory (TQFT) was coined by Witten [Wit88] in 1988. The physically motivated idea is to provide a mathematical framework for studying quantum field theory which does not depend on the Riemannian metric of the underl ...
... study of topological quantum field theory. The notion of a topological quantum field theory (TQFT) was coined by Witten [Wit88] in 1988. The physically motivated idea is to provide a mathematical framework for studying quantum field theory which does not depend on the Riemannian metric of the underl ...
Measurement Theories in Quantum Mechanics Cortland M. Setlow March 3, 2006
... offers a deeper understanding of electromagnetic phenomena, Mermin's correlations may offer some new structure to quantum mechanics, but here I seek only to analyze some aspects of measurement. What, then, is QM trying to tell us? With its Hilbert space structure and associated operators, we can des ...
... offers a deeper understanding of electromagnetic phenomena, Mermin's correlations may offer some new structure to quantum mechanics, but here I seek only to analyze some aspects of measurement. What, then, is QM trying to tell us? With its Hilbert space structure and associated operators, we can des ...
High performance quantum computing
... simply present an example partition structure for the resource lattice, hopefully demonstrating some of the essential features that would be needed for this model. We will approach this analysis with some basic numerical estimates to give an idea of the resource costs and physical lattice sizes for ...
... simply present an example partition structure for the resource lattice, hopefully demonstrating some of the essential features that would be needed for this model. We will approach this analysis with some basic numerical estimates to give an idea of the resource costs and physical lattice sizes for ...
Information measures of hydrogenic systems, Laguerre polynomials
... them. To do that we only use known properties of Laguerre polynomials and spherical harmonics (which are the elements which basically conform the hydrogenic wavefunctions) and, for the Shannon case, an isoperimetric inequality [16,5,14]. The structure of the paper is as follows. First, the necessary ...
... them. To do that we only use known properties of Laguerre polynomials and spherical harmonics (which are the elements which basically conform the hydrogenic wavefunctions) and, for the Shannon case, an isoperimetric inequality [16,5,14]. The structure of the paper is as follows. First, the necessary ...
Frenkel-Reshetikhin
... interplay between various ideas of both sciences (see [0] for a partial bibliography). Mathematical roots of these theories lie in the representation theory of infinite dimensional Lie algebras and groups, algebraic geometry and Hamiltonian mechanics. The physical intuition arises from quantum field ...
... interplay between various ideas of both sciences (see [0] for a partial bibliography). Mathematical roots of these theories lie in the representation theory of infinite dimensional Lie algebras and groups, algebraic geometry and Hamiltonian mechanics. The physical intuition arises from quantum field ...
file
... allegedly “first” phenomenological enterprise. For example, Heidegger famously emphasized the role of a “pre-structure” of understanding e the idea being that our experience of meaningfulness is always based on background assumptions and pre-established ways of structuring (Backman 2001: 71). However ...
... allegedly “first” phenomenological enterprise. For example, Heidegger famously emphasized the role of a “pre-structure” of understanding e the idea being that our experience of meaningfulness is always based on background assumptions and pre-established ways of structuring (Backman 2001: 71). However ...
The Unruh effect revisited - Department of Mathematics and Statistics
... anthropomorphic terminology used above and in much of the literature as well as of all reference to particles or quanta, which turn out to be irrelevant to the discussion. This is what we will do below. It is worth pointing out in this connection that already in [U], “detection of a particle” is def ...
... anthropomorphic terminology used above and in much of the literature as well as of all reference to particles or quanta, which turn out to be irrelevant to the discussion. This is what we will do below. It is worth pointing out in this connection that already in [U], “detection of a particle” is def ...
Introduction
... Even though Klein’s viewpoint was generally accepted by the mathematical community, its re-interpretation in the light of modern geometries, and especially of modern theories of physics, is central today. There are no books on the modern developments of this program. Our book is one modest step towa ...
... Even though Klein’s viewpoint was generally accepted by the mathematical community, its re-interpretation in the light of modern geometries, and especially of modern theories of physics, is central today. There are no books on the modern developments of this program. Our book is one modest step towa ...
Particle Physics and the LHC
... • If there are very large/small parameters in a quantum theory, there must be a good reason why they are so small…. • In general, there will be large quantum corrections to such parameters in higher orders of perturbation theory, in terms of other parameters which are not so small. • These quantum c ...
... • If there are very large/small parameters in a quantum theory, there must be a good reason why they are so small…. • In general, there will be large quantum corrections to such parameters in higher orders of perturbation theory, in terms of other parameters which are not so small. • These quantum c ...