Physics Commons^™

Patrick Aidan Heelan’S The Observable: Heisenberg’S Philosophy Of Quantum Mechanics, Paul Downes

Research Resources

The publication of Patrick Aidan Heelan’s The Observable, with forewords from Michel Bitbol, editor Babette Babich and the author himself, offers a timely invitation to reconsider the relation between quantum physics and continental philosophy.

Patrick Heelan does so, as a contemporary of and interlocutor with Werner Heisenberg on these issues, as a physicist himself who trained with leading figures of quantum mechanics (QM), Erwin Schrödinger and Eugene Wigner. Moreover, Heelan highlights Heisenberg’s interest in phenomenology as ‘a friend and frequent visitor of Martin Heidegger’ (55). Written originally in 1970 and unpublished then for reasons Babich explicates in her foreword, …

Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation investigates the properties of unbounded derivations on C*-algebras, namely the density of their analytic vectors and a property we refer to as "kernel stabilization." We focus on a weakly-defined derivation δ_D which formalizes commutators involving unbounded self-adjoint operators on a Hilbert space. These commutators naturally arise in quantum mechanics, as we briefly describe in the introduction.

A first application of kernel stabilization for δ_D shows that a large class of abstract derivations on unbounded C*-algebras, defined by O. Bratteli and D. Robinson, also have kernel stabilization. A second application of kernel stabilization provides a sufficient condition …

Random-Field Critical And Spin-Flop Behavior Of The Anisotropic Heisenberg Antiferromagnet Fe0.9mg0.1br2 In Axial Magnetic Fields, Christian Binek

Christian Binek

Faraday optical measurements on the dilute hexagonal antiferromagnet Fe0.85Mg0.15Br2 in an external axial field reveal a spin-flop phase line ending at a multicritical point (Tm=8.1 K, Hm=1050 kA m-1) and crossover from random-exchange to random-field Ising criticality with an exponent Phi =1.40+or-0.04 in the vicinity of TN=11.1 K. Cusp-like behaviour of the specific heat at TN is discussed in view of recent Monte Carlo results.

Thermodynamics And Phase Transitions For The Heisenberg Model On The Pinwheel Distorted Kagome Lattice, Ehsan Khatami, Rajiv Singh, Marcos Rigol

Faculty Publications

We study the Heisenberg model on the pinwheel distorted kagome lattice as observed in the material Rb2Cu3SnF12. Experimentally relevant thermodynamic properties at finite temperatures are computed utilizing numerical linked-cluster expansions. We also develop a Lanczos-based, zero-temperature, numerical linked-cluster expansion to study the approach of the pinwheel distorted lattice to the uniform kagome-lattice Heisenberg model. We find strong evidence for a phase transition before the uniform limit is reached, implying that the ground state of the kagome-lattice Heisenberg model is likely not pinwheel dimerized and is stable to finite pinwheel-dimerizing perturbations.

The Quantum Dialectic, Logan Kelley

Pitzer Senior Theses

A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part …

Thermodynamics Of The Antiferromagnetic Heisenberg Model On The Checkerboard Lattice, Ehsan Khatami, Maros Rigol

Faculty Publications

Employing numerical linked-cluster expansions (NLCEs) along with exact diagonalizations of finite clusters with periodic boundary condition, we study the energy, specific heat, entropy, and various susceptibilities of the antiferromagnetic Heisenberg model on the checkerboard lattice. NLCEs, combined with extrapolation techniques, allow us to access temperatures much lower than those accessible to exact diagonalization and other series expansions. We show that the high-temperature peak in specific heat decreases as the frustration increases, consistent with the large amount of unquenched entropy in the region around maximum classical frustration, where the nearest-neighbor and next-nearest-neighbor exchange interactions (J and J′, respectively) have the same …

Random-Field Critical And Spin-Flop Behavior Of The Anisotropic Heisenberg Antiferromagnet Fe0.9mg0.1br2 In Axial Magnetic Fields, Christian Binek

Christian Binek Publications

Faraday optical measurements on the dilute hexagonal antiferromagnet Fe0.85Mg0.15Br2 in an external axial field reveal a spin-flop phase line ending at a multicritical point (Tm=8.1 K, Hm=1050 kA m-1) and crossover from random-exchange to random-field Ising criticality with an exponent Phi =1.40+or-0.04 in the vicinity of TN=11.1 K. Cusp-like behaviour of the specific heat at TN is discussed in view of recent Monte Carlo results.

The Discovery Of Quantum Mechanics, Patrick A. Heelan

Research Resources

In this chapter Heelan discusses how Heisenberg's insight of 1925, that physics should concern itself henceforth only with relations between observables, changed the intentionality-structure of physics. This insight led Heisenberg to the construction of a quantum mechanics of observables. Heelan briefly discusses the significance of his insighand of his rejection of Schrödinger's wave mechanics; the novelty of quantum mechanics as a physical theory, and the meaning he attributed to its most surprising result, viz., the Indeterminacy Relations. The crisis was a crisis of the rationalism inherent in the outlook of classical physics, and Heisenberg's insistence on "observable quantities" was a …