Session D-6: Teaching Modern Physics,
2012
Illinois Mathematics and Science Academy
Session D-6: Teaching Modern Physics, Peter Dong
Professional Learning Day
Modern physics is an excellent way to get students interested in physics – the “weirdness” of relativity and quantum mechanics captures the imagination. This presentation discusses how to teach the subject in a way that encourages this interest. This year’s session will focus on teaching quantum mechanics in a way that is interesting to students and avoids common misconceptions.
Contextual-Value Approach To The Generalized Measurement Of Observables,
2012
Chapman University
Contextual-Value Approach To The Generalized Measurement Of Observables, Justin Dressel, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present a detailed motivation for and definition of the contextual values of an observable, which were introduced by Dressel et al. [Phys. Rev. Lett. 104, 240401 (2011)]. The theory of contextual values is a principled approach to the generalized measurement of observables. It extends the well-established theory of generalized statemeasurements by bridging the gap between partial state collapse and the observables that represent physically relevant information about the system. To emphasize the general utility of the concept, we first construct the full theory of contextual values within an operational formulation of classical probability theory, paying special attention to observable …
Significance Of The Imaginary Part Of The Weak Value,
2012
Chapman University
Significance Of The Imaginary Part Of The Weak Value, Justin Dressel, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
Unlike the real part of the generalized weak value of an observable, which can in a restricted sense be operationally interpreted as an idealized conditioned average of that observable in the limit of zero measurement disturbance, the imaginary part of the generalized weak value does not provide information pertaining to the observable being measured.What it does provide is direct information about howthe initial statewould be unitarily disturbed by the observable operator. Specifically, we provide an operational interpretation for the imaginary part of the generalized weak value as the logarithmic directional derivative of the postselection probability along the unitary flow generated …
Measuring Which-Path Information With Coupled Electronic Mach-Zehnder Interferometers,
2012
Chapman University
Measuring Which-Path Information With Coupled Electronic Mach-Zehnder Interferometers, Justin Dressel, Y. Choi, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
We theoretically investigate a generalized “which-path” measurement on an electronic Mach-Zehnder Interferometer (MZI) implemented via Coulomb coupling to a second electronic MZI acting as a detector. The use of contextual values, or generalized eigenvalues, enables the precise construction of which-path operator averages that are valid for any measurement strength from the available drain currents. The form of the contextual values provides direct physical insight about the measurement being performed, providing information about the correlation strength between system and detector, the measurement inefficiency, and the proper background removal. We find that the detector interferometer must display maximal wavelike behavior to optimally …
Majorana Modes In Time-Reversal Invariant S -Wave Topological Superconductors,
2012
Dartmouth College
Majorana Modes In Time-Reversal Invariant S -Wave Topological Superconductors, Shusa Deng, Lorenza Viola, Gerardo Ortiz
Dartmouth Scholarship
We present a time-reversal invariant s-wave superconductor supporting Majorana edge modes. The multiband character of the model together with spin-orbit coupling are key to realizing such a topological superconductor. We characterize the topological phase diagram by using a partial Chern number sum, and show that the latter is physically related to the parity of the fermion number of the time-reversal invariant modes. By taking the self-consistency constraint on the s-wave pairing gap into account, we also establish the possibility of a direct topological superconductor-to-topological insulator quantum phase transition.
Colloquium : Stimulating Uncertainty: Amplifying The Quantum Vacuum With Superconducting Circuits,
2012
University of Michigan-Ann Arbor
Colloquium : Stimulating Uncertainty: Amplifying The Quantum Vacuum With Superconducting Circuits, P. D. Nation, J. R. Johansson, M. P. Blencowe, Franco Nori
Dartmouth Scholarship
The ability to generate particles from the quantum vacuum is one of the most profound consequences of Heisenberg’s uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable quantum computer, have been used in the experimental demonstration of the dynamical Casimir effect, and may soon be able to realize the elusive verification of analog Hawking radiation. This Colloquium article describes several mechanisms for generating photons from the quantum vacuum and …
Topspin Networks In Loop Quantum Gravity,
2012
Merrimack
Topspin Networks In Loop Quantum Gravity, Christopher L. Duston
Physics Faculty Publications
We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert space of cylindrical functions. We will also discuss the area and Hamiltonian operators, and show how they depend on the topology. This extends the idea of 'background independence' in loop quantum gravity to include topology as well as geometry. It is hoped this work will confirm the usefulness of the topspin network formalism and open up several new avenues for research into …
Analysis Of Entanglement And Logic Gate Implementation In Generic Two-Level Systems,
2012
Eastern Illinois University
Analysis Of Entanglement And Logic Gate Implementation In Generic Two-Level Systems, Jonathan Jones
Undergraduate Honors Theses
An N-atom quantum system interacting with a single cavity field mode serves as an intuitive and useful model for many areas of quantum information science. We extend this model to describe artificial systems composed of quantum dots and Josephson junction devices as well. In addition, we include the dipole interactions characteristic of such systems. We use Bell-type inequalities and concurrence to examine the development of entanglement in the specific cases of two- and three-atom systems, and find that the effect of dipole interactions on entanglement generation depends heavily on the initial state of the system. Finally, we propose a …
Response To Griffiths,
2012
Chapman University
Response To Griffiths, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
"First of all, I would like to thank Prof. Griffith for his comments. The exchange has reminded me of the series of letters that appeared in Physics Today following the publication of an article by Chandralekha Singh, Mario Belloni, and Wolfgang Christian on improving the teaching of undergraduate quantum mechanics (see http://ptonline.aip.org/ journals/doc/PHTOAD-ft/vol_60/iss_3/8_1.shtml). In those responses, both Griffiths and Travis Norsen argued that students’ understanding of quantum mechanics would be vastly improved if they were taught more about the foundations of quantum theory, and I wholeheartedly agree with that sentiment. The thing is, Griffiths argued vociferously that this should be …
Everything Is Entangled,
2012
Chapman University
Everything Is Entangled, Roman V. Buniy, Stephen D. H. Hsu
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other - the reduced density matrix describing any pair is likely to be separable.
An Algebraic Classification Of Entangled States,
2012
Chapman University
An Algebraic Classification Of Entangled States, Roman V. Buniy, Thomas W. Kephart
Mathematics, Physics, and Computer Science Faculty Articles and Research
We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the invariants and sets of equivalent classes of entangled states. The new method works for an arbitrary finite number of finite-dimensional state subspaces. As an application of the method, we considered a large selection of cases of three subspaces of various dimensions. We also obtain an entanglement classification of four qubits, where we find 27 fundamental sets of classes.
Entropy And Information Causality In General Probabilistic Theories (Addendum),
2012
University of New Mexico
Entropy And Information Causality In General Probabilistic Theories (Addendum), Howard Barnum, Jonathan Barrett, Lisa Orloff Clark, Matthew S. Leifer, Robert Spekkens, Nicholas Stepanik, Alex Wilce, Robin Wilke
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this addendum to our paper (2010 New J. Phys. 12 033024), we point out that an elementary consequence of the strong subadditivity inequality allows us to strengthen one of the main conclusions of that paper.
Teleportation In General Probabilistic Theories,
2012
Los Alamos National Laboratory
Teleportation In General Probabilistic Theories, Howard Barnum, Jonathan Barrett, Matthew S. Leifer, Alex Wilce
Mathematics, Physics, and Computer Science Faculty Articles and Research
In a previous paper, we showed that many important quantum information-theoretic phenomena, including the no-cloning and no-broadcasting theorems, are in fact generic in all non-classical probabilistic theories. An exception is teleportation, which most such theories do not support. In this paper, we investigate which probabilistic theories, and more particularly, which composite systems, do support a teleportation protocol. We isolate a natural class of composite systems that we term regular, and establish necessary and sufficient conditions for a regular tripartite system to support a conclusive, or post-selected, teleportation protocol. We also establish a sufficient condition for deterministic teleportation that yields …
Review Of Elegance And Enigma: The Quantum Interviews,
2012
Chapman University
Review Of Elegance And Enigma: The Quantum Interviews, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
A review of Elegance and Enigma: The Quantum Interviews, edited by Maximilian Schlosshauer.
Pbr, Epr, And All That Jazz,
2012
Chapman University
Pbr, Epr, And All That Jazz, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
"In the past couple of months, the quantum foundations world has been abuzz about a new preprint entitled "The Quantum State Cannot be Interpreted Statistically" by Matt Pusey, Jon Barrett and Terry Rudolph (henceforth known as PBR). Since I wrote a blog post explaining the result, I have been inundated with more correspondence from scientists and more requests for comment from science journalists than at any other point in my career. Reaction to the result amongst quantum researchers has been mixed, with many people reacting negatively to the title, which can be misinterpreted as an attack on the Born rule. …
A Dialogue Between Contemporary Perspectives And Ellen White On Divine Action And Quantum Physics,
2012
Andrews University
A Dialogue Between Contemporary Perspectives And Ellen White On Divine Action And Quantum Physics, Michael F. Younker
Journal of the Adventist Theological Society
No abstract provided.
Review Of The Mathematical Language Of Quantum Theory: From Uncertainty To Entanglement,
2012
Chapman University
Review Of The Mathematical Language Of Quantum Theory: From Uncertainty To Entanglement, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
A book review of The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement by Teiko Heinosaari and Mario Ziman.
New Invariants For Entangled States,
2012
Chapman University
New Invariants For Entangled States, Roman V. Buniy, Thomas W. Kephart
Mathematics, Physics, and Computer Science Faculty Articles and Research
We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured in the literature.
On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization,
2012
University of Houston
On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization, Evert Jan Post, Stan Sholar, Hooman Rahimizadeh, Michael Berg
Mathematics, Statistics and Data Science Faculty Works
The purpose of the present article is to demonstrate that by adopting a unifying differential geometric perspective on certain themes in physics one reaps remarkable new dividends in both microscopic and macroscopic domains. By replacing algebraic objects by tensor-transforming objects and introducing methods from the theory of differentiable manifolds at a very fundamental level we obtain a Kottler-Cartan metric-independent general invariance of the Maxwell field, which in turn makes for a global quantum superstructure for Gauss-Amp`ere and Aharonov-Bohm “quantum integrals.” Beyond this, our approach shows that postulating a Riemannian metric at the quantum level is an unnecessary concept and our …
The Double Cover Of The Real Symplectic Group And A Theme From Feynman’S Quantum Mechanics,
2012
Loyola Marymount University
The Double Cover Of The Real Symplectic Group And A Theme From Feynman’S Quantum Mechanics, Michael Berg
Mathematics, Statistics and Data Science Faculty Works
We present a direct connection between the 2-cocycle defining the double cover of the real symplectic group and a Feynman path integral describing the time evolution of a quantum mechanical system.
