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Articles 1 - 30 of 38
Full-Text Articles in Physical Sciences and Mathematics
Weak Values Are Universal In Von Neumann Measurements, Justin Dressel, Andrew N. Jordan
Weak Values Are Universal In Von Neumann Measurements, Justin Dressel, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system observable. For any coupling strength, any initial states, and any choice of conditioning, the averages of the detector position and momentum are completely described by the real parts of three generalized weak values in the joint Hilbert space. Higher-order detector moments also have similar weak value expansions. Using the Wigner distribution of the initial detector state, we find compact expressions for …
Logistic Curves, Extraction Costs And Peak Oil, Robert J. Brecha
Logistic Curves, Extraction Costs And Peak Oil, Robert J. Brecha
Physics Faculty Publications
Debates about the possibility of a near-term maximum in world oil production have become increasingly prominent over the past decade, with the focus often being on the quantification of geologically available and technologically recoverable amounts of oil in the ground. Economically, the important parameter is not a physical limit to resources in the ground, but whether market price signals and costs of extraction will indicate the efficiency of extracting conventional or nonconventional resources as opposed to making substitutions over time for other fuels and technologies. We present a hybrid approach to the peak-oil question with two models in which the …
Electron-Phonon Coupling And Structural Phase Transitions On Au/Mo(112), Keisuke Fukutani
Electron-Phonon Coupling And Structural Phase Transitions On Au/Mo(112), Keisuke Fukutani
Department of Physics and Astronomy: Dissertations, Theses, and Student Research
The electronic structures, many-body interactions and Fermi surface topologies of Au/Mo(112) were investigated in detail and were found to play important roles in the newly discovered order-disorder structural phase transition of the system. First, the high-resolution angle-resolved photoemission spectroscopy was utilized to characterize the electronic band structure of Mo(112) in far greater details than before. This elucidated the existence of several surface-derived states and their dispersion relations in high precisions near the Fermi level, as well as the symmetries of the bulk and surface electronic states, which are in good quantitative agreement with the ab-initio calculations. Such thorough understanding of …
Automated Synthesis Of Dynamically Corrected Quantum Gates, Kaveh Khodjasteh, Hendrik Bluhm, Lorenza Viola
Automated Synthesis Of Dynamically Corrected Quantum Gates, Kaveh Khodjasteh, Hendrik Bluhm, Lorenza Viola
Dartmouth Scholarship
Dynamically corrected gates are extended to non-Markovian open quantum systems where limitations on the available controls and/or the presence of control noise make existing analytical approaches unfeasible. A computational framework for the synthesis of dynamically corrected gates is formalized that allows sensitivity against non-Markovian decoherence and control errors to be perturbatively minimized via numerical search, resulting in robust gate implementations. Explicit sequences for achieving universal high-fidelity control in a singlet-triplet spin qubit subject to realistic system and control constraint are provided, which simultaneously cancel to the leading order the dephasing due to non-Markovian nuclear-bath dynamics and voltage noise affecting the …
Hohenberg-Kohn Theorem Including Electron Spin, Xiao-Yin Pan, Viraht Sahni
Hohenberg-Kohn Theorem Including Electron Spin, Xiao-Yin Pan, Viraht Sahni
Publications and Research
The Hohenberg-Kohn theorem is generalized to the case of a finite system of N electrons in external electrostatic epsilon(r) = -del nu(r) and magnetostatic B(r) = del x A(r) fields in which the interaction of the latter with both the orbital and spin angular momentum is considered. For a nondegenerate ground state a bijective relationship is proved between the gauge invariant density rho(r) and physical current density j(r) and the potentials {nu(r), A(r)}. The possible many-to-one relationship between the potentials {v(r), A(r)} and the wave function is explicitly accounted for in the proof. With the knowledge that the basic variables …
Nanomechanical Resonator Coupled Linearly Via Its Momentum To A Quantum Point Contact, Latchezar L. Benatov, Miles P. Blencowe
Nanomechanical Resonator Coupled Linearly Via Its Momentum To A Quantum Point Contact, Latchezar L. Benatov, Miles P. Blencowe
Dartmouth Scholarship
We use a Born-Markov approximated master equation approach to study the symmetrized-in-frequency current noise spectrum and the oscillator steady state of a nanoelectromechanical system where a nanoscale resonator is coupled linearly via its momentum to a quantum point contact (QPC). Our current noise spectra exhibit clear signatures of the quantum correlations between the QPC current and the back-action force on the oscillator at a value of the relative tunneling phase (η=−π/2) where such correlations are expected to be maximized. We also show that the steady state of the oscillator obeys a classical Fokker-Planck equation, but can experience thermomechanical noise squeezing …
Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu
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.
In Quantum Physics, Free Will Leads To Nonconservation Of Energy, Vladik Kreinovich
In Quantum Physics, Free Will Leads To Nonconservation Of Energy, Vladik Kreinovich
Departmental Technical Reports (CS)
Modern physical theories are deterministic in the sense that once we know the current state of the world, we can, in principle, predict all the future states. This was true for classical (pre-quantum) theories, this is true for modern quantum physics. On the other hand, we all know that we can make decision that change the state of the world -- even if, for most of us, a little bit. This intuitive idea of free will permeates all our life, all our activities -- and it seems to contradict the determinism of modern physics. It is therefore desirable to incorporate …
Top-Quark Production And Qcd, Nikolaos Kidonakis, Ben D. Pecjak
Top-Quark Production And Qcd, Nikolaos Kidonakis, Ben D. Pecjak
Faculty and Research Publications
We review theoretical calculations for top-quark production that include complete next-to-leading-order QCD corrections as well as higher-order soft-gluon corrections from threshold resummation. We discuss in detail the differences between various approaches that have appeared in the literature and review results for top-quark total cross sections and differential distributions at the Tevatron and the LHC.
Szilard Engine Reversibility As Quantum Gate Function, F. Matthew Mihelic
Szilard Engine Reversibility As Quantum Gate Function, F. Matthew Mihelic
Faculty Publications
A quantum gate is a logically and thermodynamically reversible situation that effects a unitary transformation of qubits of superimposed information, and essentially constitutes a situation for a reversible quantum decision. A quantum decision is a symmetry break, and the effect of the function of a Szilard engine is a symmetry break. A quantum gate is a situation in which a reversible quantum decision can be made, and so if a logically and thermodynamically reversible Szilard engine can be theoretically constructed then it would function as a quantum gate. While the traditionally theorized Szilard engine is not thermodynamically reversible, if one …
Hohenberg-Kohn And Percus-Levy-Lieb Proofs Of Density-Functional Theory, Viraht Sahni, Xiao-Yin Pan
Hohenberg-Kohn And Percus-Levy-Lieb Proofs Of Density-Functional Theory, Viraht Sahni, Xiao-Yin Pan
Publications and Research
The premise of density-functional theory is that knowledge of the ground-state density uniquely determines the Hamiltonian, and thereby, via solution of the corresponding time-independent Schrodinger equation, all the properties of the system. The density therefore constitutes a basic variable of quantum mechanics. There are at present two paths from the density to the Hamiltonian: the Hohenberg and Kohn proof of the bijectivity between the external potential and the basic variable, and the Percus, Levy, and Lieb constrained-search proof. We argue the Hohenberg- and Kohn-type proof to be the more fundamental, and that this is the case in general when both …
Quantum Mutual Information Capacity For High-Dimensional Entangled States, P. Ben Dixon, Gregory A. Howland, James Schneeloch, John C. Howell
Quantum Mutual Information Capacity For High-Dimensional Entangled States, P. Ben Dixon, Gregory A. Howland, James Schneeloch, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
High-dimensional Hilbert spaces used for quantum communication channels offer the possibility of large data transmission capabilities. We propose a method of characterizing the channel capacity of an entangled photonic state in high-dimensional position and momentum bases. We use this method to measure the channel capacity of a parametric down-conversion state by measuring in up to 576 dimensions per detector. We achieve a channel capacity over 7 bits/photon in either the position or momentum basis. Furthermore, we provide a correspondingly high-dimensional separability bound that suggests that the channel performance cannot be replicated classically.
Demonstration Of The Gunnarsson-Lundqvist Theorem And The Multiplicity Of Potentials For Excited States, Yu-Qi Li, Xiao-Yin Pan, Biao Li, Viraht Sahni
Demonstration Of The Gunnarsson-Lundqvist Theorem And The Multiplicity Of Potentials For Excited States, Yu-Qi Li, Xiao-Yin Pan, Biao Li, Viraht Sahni
Publications and Research
The Gunnarsson-Lundqvist (GL) theorem of density functional theory states that there is a one-to-one relationship between the density of the lowest nondegenerate excited state of a given symmetry and the external potential. As a consequence, knowledge of this excited state density determines the external potential uniquely. [The GL theorem is the equivalent for such excited states of theHohenberg-Kohn (HK) theorem for nondegenerate ground states.] For other excited states, there is no equivalent of the GL or HK theorem. For these states, there thus exist multiple potentials that generate the excited-state density. We show, by example, the satisfaction that the GL …
Non-Equilibrium Landauer Transport Model For Hawking Radiation From A Black Hole, P. D. Nation, M. P. Blencowe, Franco Nori
Non-Equilibrium Landauer Transport Model For Hawking Radiation From A Black Hole, P. D. Nation, M. P. Blencowe, Franco Nori
Dartmouth Scholarship
We propose that the Hawking radiation energy and entropy flow rates from a black hole can be viewed as a one-dimensional (1D), non-equilibrium Landauer transport process. Support for this viewpoint comes from previous calculations invoking conformal symmetry in the near-horizon region, which give radiation rates that are identical to those of a single 1D quantum channel connected to a thermal reservoir at the Hawking temperature. The Landauer approach shows in a direct way the particle statistics independence of the energy and entropy fluxes of a black hole radiating into vacuum, as well as one near thermal equilibrium with its environment. …
Contextual-Value Approach To The Generalized Measurement Of Observables, Justin Dressel, Andrew N. Jordan
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, Justin Dressel, Andrew N. Jordan
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, Justin Dressel, Y. Choi, Andrew N. Jordan
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, Shusa Deng, Lorenza Viola, Gerardo Ortiz
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, P. D. Nation, J. R. Johansson, M. P. Blencowe, Franco Nori
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 …
Assessing The Feasibility Of Cosmic-Ray Acceleration By Magnetic Turbulence At The Magnetic Center, M. Fatuzzo, F. Melia
Assessing The Feasibility Of Cosmic-Ray Acceleration By Magnetic Turbulence At The Magnetic Center, M. Fatuzzo, F. Melia
Faculty Scholarship
No abstract provided.
Quantitative Study Of Spin-Flip Co-Tunneling Transport In A Quantum Dot, S. Herbert, T-M. Liu, A. N. Ngo
Quantitative Study Of Spin-Flip Co-Tunneling Transport In A Quantum Dot, S. Herbert, T-M. Liu, A. N. Ngo
Faculty Scholarship
No abstract provided.
Analysis Of Entanglement And Logic Gate Implementation In Generic Two-Level Systems, Jonathan Jones
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 …
Unitary Qubit Lattice Gas Representation Of 2d And 3d Quantum Turbulence, George Vahala, Bo Zhang, Jeffrey Yepez, Linda L. Vahala, Min Soe
Unitary Qubit Lattice Gas Representation Of 2d And 3d Quantum Turbulence, George Vahala, Bo Zhang, Jeffrey Yepez, Linda L. Vahala, Min Soe
Electrical & Computer Engineering Faculty Publications
No abstract provided.
On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization, Evert Jan Post, Stan Sholar, Hooman Rahimizadeh, Michael Berg
On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization, Evert Jan Post, Stan Sholar, Hooman Rahimizadeh, Michael Berg
Mathematics 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 …
Topspin Networks In Loop Quantum Gravity, Christopher L. Duston
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 …
The Double Cover Of The Real Symplectic Group And A Theme From Feynman’S Quantum Mechanics, Michael Berg
The Double Cover Of The Real Symplectic Group And A Theme From Feynman’S Quantum Mechanics, Michael Berg
Mathematics 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.
Pbr, Epr, And All That Jazz, Matthew S. Leifer
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. …
Everything Is Entangled, Roman V. Buniy, Stephen D. H. Hsu
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, Roman V. Buniy, Thomas W. Kephart
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.
New Invariants For Entangled States, Roman V. Buniy, Thomas W. Kephart
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.