Quantum Physics Commons^™

Spin-Dependent Two-Color Kapitza-Dirac Effects, Scot Mcgregor, Wayne Cheng-Wei Huang, Herman Batelaan, Bradley Allan Shadwick

Department of Physics and Astronomy: Faculty Publications

In this paper we present an analysis of the spin behavior of electrons propagating through a laser field. We present an experimentally realizable scenario in which spin-dependent effects of the interaction between the laser and the electrons are dominant. The laser interaction strength and incident electron velocity are in the nonrelativistic domain. This analysis may thus lead to novel methods of creating and characterizing spin-polarized nonrelativistic femtosecond electron pulses.

Discrete Excitation Spectrum Of A Classical Harmonic Oscillator In Zero-Point Radiation, Wayne Cheng-Wei Huang, Herman Batelaan

Department of Physics and Astronomy: Faculty Publications

We report that upon excitation by a single pulse, a classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation exhibits a discrete harmonic spectrum in agreement with that of its quantum counterpart. This result is interesting in view of the fact that the vacuum field is needed in the classical calculation to obtain the agreement.

Differentiability Of Correlations In Realistic Quantum Mechanics, Alejandro Cabrera, Edson De Faria, Enrique Pujals, Charles Tresser

Publications and Research

We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumed …

Weak Values Obtained In Matter-Wave Interferometry, Stephan Sponar, Tobias Denkmayr, Hermann Geppert, Hartmutt Lemmel, Alexandre Matzkin, Jeff Tollaksen, Yuji Hasegawa

Mathematics, Physics, and Computer Science Faculty Articles and Research

Weak values, introduced more than 25 years ago, underwent a metamorphosis from a theoretical curiosity to a powerful resource in photonics for exploring foundations of quantum mechanics, as well as a practical laboratory tool. Due to the tiny coherence volume of particles used in matter-wave optics, a straightforward implementation of weak measurements is not feasible. We have overcome this hurdle by developing a method to weakly measure a massive particle's spin component. A neutron optical approach is realized by utilizing neutron interferometry, where the neutron's spin is coupled weakly to its spatial degree of freedom. Here, we present how one …

Fundamental Mathematics Of Consciousness, Menas Kafatos

Mathematics, Physics, and Computer Science Faculty Articles and Research

We explore a mathematical formalism that ties together the observer with the observed in the view that Consciousness is primary, operating through three principles which apply at all levels, the essence of qualia of experience. The formalism is a simplified version of Hilbert space mathematics encountered in quantum mechanics. It does, however, go beyond specific interpretations of quantum mechanics and has strong philosophical foundations in Western philosophy as well as monistic systems of the East. The implications are explored and steps for the full development of this axiomatic mathematical approach to Consciousness are discussed.

Weak Measurement And Bohmian Conditional Wave Functions, Travis Norsen

Physics: Faculty Publications

It was recently pointed out (and demonstrated experimentally) by Lundeen et al. that the wave function of a particle (more precisely, the wave function possessed by each member of an ensemble of identically-prepared particles) can be "directly measured" using weak measurement. Here it is shown that if this same technique is applied, with appropriate post-selection, to one particle from a (perhaps entangled) multi-particle system, the result is precisely the so-called "conditional wave function" of Bohmian mechanics. Thus, a plausibly operationalist method for defining the wave function of a quantum mechanical sub-system corresponds to the natural definition of a sub-system wave …

Mapping The Optimal Route Between Two Quantum States, S. J. Weber, A. Chantasri, Justin Dressel, Andrew N. Jordan, K. W. Murch, I. Siddiqi

Mathematics, Physics, and Computer Science Faculty Articles and Research

A central feature of quantum mechanics is that a measurement result is intrinsically probabilistic. Consequently, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system in the presence of these fluctuations is of increasing importance in quantum information processing and finds application in fields ranging from nuclear magnetic resonance¹ to chemical synthesis². A detailed understanding of this stochastic evolution is essential for the development of optimized control methods. Here we reconstruct the individual quantum trajectories^{3, 4, 5} of a superconducting circuit that evolves under the …

On Electromagnetic And Quantum Invisibility, Pattabhiraju Chowdary Mundru

Doctoral Dissertations

The principle objective of this dissertation is to investigate the fundamental properties of electromagnetic wave interactions with artificially fabricated materials i.e., metamaterials for application in advanced stealth technology called electromagnetic cloaking. The main goal is to theoretically design a metamaterial shell around an object that completely eliminates the dipolar and higher order multipolar scattering, thus making the object invisible.

In this context, we developed a quasi-effective medium theory that determines the optical properties of multi-layered-composites beyond the quasi-static limit. The proposed theory exactly reproduces the far-field scattering/extinction cross sections through an iterative process in which mode-dependent quasi-effective impedances of the …

New Insights On Emergence From The Perspective Of Weak Values And Dynamical Non-Locality, Jeff Tollaksen

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this article, we will examine new fundamental aspects of "emergence" and "information" using novel approaches to quantum mechanics which originated from the group around Aharonov. The two-state vector formalism provides a complete description of pre- and post-selected quantum systems and has uncovered a host of new quantum phenomena which were previously hidden. The most important feature is that any weak coupling to a pre- and post-selected system is effectively a coupling to a "weak value" which is given by a simple expression depending on the two-state vector. In particular, weak values, are the outcomes of so called "weak measurements" …

Quantum Non-Barking Dogs, Sara Imari Walker, Paul C. W. Davies, Prasant Samantray, Yakir Aharonov

Mathematics, Physics, and Computer Science Faculty Articles and Research

Quantum weak measurements with states both pre- and post-selected offer a window into a hitherto neglected sector of quantum mechanics. A class of such systems involves time dependent evolution with transitions possible. In this paper we explore two very simple systems in this class. The first is a toy model representing the decay of an excited atom. The second is the tunneling of a particle through a barrier. The post-selection criteria are chosen as follows: at the final time, the atom remains in its initial excited state for the first example and the particle remains behind the barrier for the …

Point–Counterpoint: Can Anything Be Learned From Surveys On The Interpretations Of Quantum Mechanics?, Matthew S. Leifer, Nathan Harshman

Mathematics, Physics, and Computer Science Faculty Articles and Research

"In what follows, Matt Leifer and Nathan Harshman present opposing views on the value of surveys on foundational attitudes towards quantum mechanics. Three such surveys were recently published and their results are summarized in Table 1. Matt takes the `point,’ arguing that such surveys are not useful, while Nathan takes the `counterpoint.’ A complete set of references for both is given at the end."

Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu

Physics: Faculty Publications and Other Works

We review solvable models within the framework of supersymmetric quantum mechanics (SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum mechanical problems. We review shape invariance and its connection to a consequent potential algebra. The additive shape invariance condition is specified by a difference-differential equation; we show that this equation is equivalent to an infinite set of partial differential equations. Solving these equations, we show that the known list of h-independent superpotentials is complete. We then describe how these equations could be extended to include superpotentials that do depend on h.

The Quantum Mechanics Of Supersymmetry, Joshua Gearhart

Physics

No abstract provided.

Holism And Non-Separability Applied To Quantum Mechanics, Catherine E. Nisson

Senior Honors Projects, 2010-2019

Einstein was never satisfied with quantum mechanics. He argued that quantum mechanics was incomplete for two main reasons; it violated the locality principle and the separability principle. The violation of separability is an unavoidable consequence of quantum interactions. Non-separability can be seen in quantum entanglement. Non-locality, however, is more controversial. Einstein and his associates published the EPR paper in order to argue for the incompleteness of quantum mechanics. Years later, John Bell formulated what became known as the Bell Inequalities in response to the EPR paper. The Bell Inequalities are seen as a major obstacle for quantum locality. I will …

On Relational Quantum Mechanics, Oscar Acosta

Open Access Theses & Dissertations

A problem facing quantum mechanics is that there are a number of views or interpretations available that purport to 'explain' quantum mechanics. In this paper I discuss and analyze the view of relational quantum mechanics by Carlo Rovelli in the context of theoretical underdetermination. I will show that even though Rovelli offers a view that consolidates some of the aspects of competing theories it still falls short of breaking out of the theoretical underdetermination. The criteria that I have used to consider a theory successful in this context is one that increases the predictive output of quantum theory. Lacking an …

Visualizing Atomic Orbitals Using Second Life, Andrew Lang, David C. Kobilnyk

College of Science and Engineering Faculty Research and Scholarship

We demonstrate the usefulness of Second Life as a platform for enlivening major concepts in chemistry education. These concepts include absorption spectra, selection rules, quantum numbers, and atomic orbital shapes. We have built several exhibits in Second Life which provide 3-dimensional interactivity for each of those areas: an interactive experiment showing the absorption spectrum of hydrogen, an interactive model of selection rules showing allowed and forbidden transitions for each state, a 3-dimensional grid of orbitals showing the constraints on the values of quantum numbers, and a large-scale interactive orbital display allowing the user to choose and rotate to-scale atomic orbitals …

Feynman’S Relativistic Electrodynamics Paradox And The Aharonov-Bohm Effect, Adam Caprez, Herman Batelaan

Department of Physics and Astronomy: Faculty Publications

An analysis is done of a relativistic paradox posed in the Feynman Lectures of Physics involving two interacting charges. The physical system presented is compared with similar systems that also lead to relativistic paradoxes. The momentum conservation problem for these systems is presented. The relation between the presented analysis and the ongoing debates on momentum conservation in the Aharonov-Bohm problem is discussed.

The E.P.R. Paradox, George Levesque

Undergraduate Review

No abstract provided.

Vortices And Chaos In The Quantum Fluid, D. A. Wisniacki, E. R. Pujals, F. Borondo

Publications and Research

The motion of a single vortex originates chaos in the quantum fluid defined in Bohm's interpretation of quantum mechanics. Here we analize this situation in a very simple case: one single vortex in a rectangular billiard.

Renormalons As Dilation Modes In The Functional Space, A. Babansky, I. Balitsky

Physics Faculty Publications

There are two possible sources of the factorial large-order behavior of a typical perturbative series. First, the number of different Feynman diagrams may be large; second, there may be abnormally large diagrams known as renormalons. It is well known that the large combinatorial number of diagrams is described by instanton-type solutions of the classical equations. We demonstrate that, from the functional-integral viewpoint, the renormalons do not correspond to a particular configuration but manifest themselves as dilatation modes in the functional space.

Vibrational Properties Of A Loaded String, Samantha Parmley, Tom Zobrist, Terry Clough, Anthony Perez-Miller, Mark Makela

All Faculty Scholarship for the College of the Sciences

In this paper we discuss our study of a string–mass chain and its anology to quantum mechanical systems. Theoretical predictions are made based upon the numerical solution to the wave equation. These predictions are tested experimentally using both normal mode analysis and pulse analysis. The frequency band structures for periodic and disordered string mass chains are studied as well as their corresponding eigenfunctions. The theoretical and experimental results are in accord. This experiment, suitable for advanced physics majors, demonstrates many important features of quantum mechanics: eigenvalues, superposition principle, band structure, gap modes, and Anderson localization.

Path Integral Study Of The Correlated Electronic States Of Na4–Na6, Randall W. Hall

Collected Faculty Scholarship

Feynman’s path integral formulation of quantum mechanics is used to study the correlated electronic states of Na4–Na6. Two types of simulations are performed: in the first, the nuclei are allowed to move at finite temperature in order to find the most stable geometries. In agreement with previous calculations, we find that planar structures are the most stable and that there is significant vibrational amplitude at finite temperatures, indicating that the Born–Oppenheimer surface is relatively flat. In the second type of simulation, the nuclei are held fixed at symmetric and asymmetric geometries and the correlated electron density is found. Our 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 …