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Articles 31 - 60 of 206
Full-Text Articles in Physics
Watching The Clocks: Interpreting The Page-Wootters Formalism And The Internal Quantum Reference Frame Programme, Emily Adlam
Watching The Clocks: Interpreting The Page-Wootters Formalism And The Internal Quantum Reference Frame Programme, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
We discuss some difficulties that arise in attempting to interpret the Page–Wootters and Internal Quantum Reference Frames formalisms, then use a ‘final measurement’ approach to demonstrate that there is a workable single-world realist interpretation for these formalisms. We note that it is necessary to adopt some interpretation before we can determine if the ‘reference frames’ invoked in these approaches are operationally meaningful, and we argue that without a clear operational interpretation, such reference frames might not be suitable to define an equivalence principle. We argue that the notion of superposition should take into account the way in which an instantaneous …
Weakness Of Weak Values: Incompatibility Of Anomalous Pulse-Spectrum Amplification And Optical Frequency Combs, John C. Howell
Weakness Of Weak Values: Incompatibility Of Anomalous Pulse-Spectrum Amplification And Optical Frequency Combs, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We probe the use of optical frequency combs to place lower bounds on anomalous amplification of a weak-value-measured pulse delay, potentially reaching a theoretical temporal resolution of better than 10−34 s. Owing to the interferometric behavior of weak values, we show that anomalous weak value amplification of a time delay is not equivalent to a temporal linear phase ramp. We show that the anomalous weak value is a rearrangement of amplitudes that generates an apparent shift that can be measured in direct detection, but does not change the actual frequency offset of a spectral distribution measurable in coherent detection. …
On Superoscillations And Supershifts In Several Variables, Yakir Aharonov, Fabrizio Colombo, Andrew N. Jordan, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen
On Superoscillations And Supershifts In Several Variables, Yakir Aharonov, Fabrizio Colombo, Andrew N. Jordan, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The aim of this paper is to study a class of superoscillatory functions in several variables, removing some restrictions on the functions that we introduced in a previous paper. Since the tools that we used with our approach are not common knowledge we will give detailed proof for the case of two variables. The results proved for superoscillatory functions in several variables can be further extended to supershifts in several variables.
Monitoring Fast Superconducting Qubit Dynamics Using A Neural Network, G. Koolstra, N. Stevenson, S. Barzili, L. Burns, K. Siva, S. Greenfield, W. Livingston, A. Hashim, R. K. Naik, J. M. Kreikebaum, K. P. O'Brien, D. I. Santiago, Justin Dressel, I. Siddiqi
Monitoring Fast Superconducting Qubit Dynamics Using A Neural Network, G. Koolstra, N. Stevenson, S. Barzili, L. Burns, K. Siva, S. Greenfield, W. Livingston, A. Hashim, R. K. Naik, J. M. Kreikebaum, K. P. O'Brien, D. I. Santiago, Justin Dressel, I. Siddiqi
Mathematics, Physics, and Computer Science Faculty Articles and Research
Weak measurements of a superconducting qubit produce noisy voltage signals that are weakly correlated with the qubit state. To recover individual quantum trajectories from these noisy signals, traditional methods require slow qubit dynamics and substantial prior information in the form of calibration experiments. Monitoring rapid qubit dynamics, e.g., during quantum gates, requires more complicated methods with increased demand for prior information. Here, we experimentally demonstrate an alternative method for accurately tracking rapidly driven superconducting qubit trajectories that uses a long short-term memory (LSTM) artificial neural network with minimal prior information. Despite few training assumptions, the LSTM produces trajectories that include …
Symmetry And Control In Thermodynamics, Emily Adlam, L. Uribarri, N. Allen
Symmetry And Control In Thermodynamics, Emily Adlam, L. Uribarri, N. Allen
Mathematics, Physics, and Computer Science Faculty Articles and Research
We explore the relationship between symmetry and entropy, distinguishing between symmetries of state and dynamical symmetries, and in the context of quantum thermodynamics between symmetries of pure and mixed states. Ultimately, we will argue that symmetry in thermodynamics is best understood as a means of control within the control theory paradigm, and we will describe an interesting technological application of symmetry-based control in the context of a quantum coherence capacitor. Symmetry, the concept from which Noether derived the conservation laws of physics, is one of the most important guiding principles of modern physics. Moreover, symmetry is often regarded as a …
Experimental Demonstration Of Continuous Quantum Error Correction, William P. Livingston, Machiel S. Blok, Emmanuel Flurin, Justin Dressel, Andrew N. Jordan, Irfan Siddiqi
Experimental Demonstration Of Continuous Quantum Error Correction, William P. Livingston, Machiel S. Blok, Emmanuel Flurin, Justin Dressel, Andrew N. Jordan, Irfan Siddiqi
Mathematics, Physics, and Computer Science Faculty Articles and Research
The storage and processing of quantum information are susceptible to external noise, resulting in computational errors. A powerful method to suppress these effects is quantum error correction. Typically, quantum error correction is executed in discrete rounds, using entangling gates and projective measurement on ancillary qubits to complete each round of error correction. Here we use direct parity measurements to implement a continuous quantum bit-flip correction code in a resource-efficient manner, eliminating entangling gates, ancillary qubits, and their associated errors. An FPGA controller actively corrects errors as they are detected, achieving an average bit-flip detection efficiency of up to 91%. Furthermore, …
A Unified Spproach To Schrödinger Evolution Of Superoscillations And Supershifts, Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser
A Unified Spproach To Schrödinger Evolution Of Superoscillations And Supershifts, Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser
Mathematics, Physics, and Computer Science Faculty Articles and Research
Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time-dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of superoscillations during the evolution is the (more general) supershift property of the solution. In this paper, we give a unified approach to determine the supershift property for the solution of the time-dependent one-dimensional Schrödinger equation. The main advantage and novelty of our results is that they only require suitable estimates and regularity assumptions on the Green’s function, but not its …
Laws Of Nature As Constraints, Emily Adlam
Laws Of Nature As Constraints, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
The laws of nature have come a long way since the time of Newton: quantum mechanics and relativity have given us good reasons to take seriously the possibility of laws which may be non-local, atemporal, ‘all-at-once,’ retrocausal, or in some other way not well-suited to the standard dynamical time evolution paradigm. Laws of this kind can be accommodated within a Humean approach to lawhood, but many extant non-Humean approaches face significant challenges when we try to apply them to laws outside the time evolution picture. Thus for proponents of non-Humean approaches to lawhood there is a clear need for a …
Gravitational Wave Sensors Based On Superconducting Transducers, Armen Gulian, Joe Foreman, Vahan Nikoghosyan, Louis Sica, Pablo Abramian-Barco, Jeff Tollaksen, Gurgen Melkonyan, Iris Mowgood, Chris Burdette, Rajendra Dulal, Serafim Teknowijoyo, Sara Chahid, Shmuel Nussinov
Gravitational Wave Sensors Based On Superconducting Transducers, Armen Gulian, Joe Foreman, Vahan Nikoghosyan, Louis Sica, Pablo Abramian-Barco, Jeff Tollaksen, Gurgen Melkonyan, Iris Mowgood, Chris Burdette, Rajendra Dulal, Serafim Teknowijoyo, Sara Chahid, Shmuel Nussinov
Mathematics, Physics, and Computer Science Faculty Articles and Research
Following the initial success of LIGO, new advances in gravitational wave (GW) detector systems are planned to reach fruition during the next decades. These systems are interferometric and large. Here we suggest different, more compact detectors of GW radiation with competitive sensitivity. These nonresonant detectors are not interferometric. They use superconducting Cooper pairs in a magnetic field to transform mechanical motion induced by GW into detectable magnetic flux. The detectors can be oriented relative to the source of GW, so as to maximize the signal output and help determine the direction of nontransient sources. In this design an incident GW …
A Dynamical Quantum Cheshire Cat Effect And Implications For Counterfactual Communication, Yakir Aharonov, Eliahu Cohen, Sandu Popescu
A Dynamical Quantum Cheshire Cat Effect And Implications For Counterfactual Communication, Yakir Aharonov, Eliahu Cohen, Sandu Popescu
Mathematics, Physics, and Computer Science Faculty Articles and Research
Here we report a type of dynamic effect that is at the core of the so called “counterfactual computation” and especially “counterfactual communication” quantum effects that have generated a lot of interest recently. The basic feature of these counterfactual setups is the fact that particles seem to be affected by actions that take place in locations where they never (more precisely, only with infinitesimally small probability) enter. Specifically, the communication/computation takes place without the quantum particles that are supposed to be the information carriers travelling through the communication channel or entering the logic gates of the computer. Here we show …
Macroscopic Superposition States In Isolated Quantum Systems, Roman V. Buniy, Stephen D. H. Hsu
Macroscopic Superposition States In Isolated Quantum Systems, Roman V. Buniy, Stephen D. H. Hsu
Mathematics, Physics, and Computer Science Faculty Articles and Research
For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrödinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann’s 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, despite their seeming fragility, macroscopic superposition states are ubiquitous consequences of quantum evolution. We discuss the connection to many worlds quantum mechanics.
A New Method To Generate Superoscillating Functions And Supershifts, Yakir Aharonov, Fabrizio Colombo, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen
A New Method To Generate Superoscillating Functions And Supershifts, Yakir Aharonov, Fabrizio Colombo, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen
Mathematics, Physics, and Computer Science Faculty Articles and Research
Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics and in many fields of science and technology such as optics, signal processing and antenna theory. In this paper, we introduce a new method to generate superoscillatory functions that allows us to construct explicitly a very large class of superoscillatory functions.
Failed Attempt To Escape From The Quantum Pigeon Conundrum, Yakir Aharonov, Shrobona Bagchi, Justin Dressel, Gregory Reznik, Michael Ridley, Lev Vaidman
Failed Attempt To Escape From The Quantum Pigeon Conundrum, Yakir Aharonov, Shrobona Bagchi, Justin Dressel, Gregory Reznik, Michael Ridley, Lev Vaidman
Mathematics, Physics, and Computer Science Faculty Articles and Research
A recent criticism by Kunstatter et al. [Phys. Lett. A 384, 126686 (2020)] of a quantum setup violating the pigeon counting principle [Aharonov et al. PNAS 113, 532 (2016)] is refuted. The quantum nature of the violation of the pigeonhole principle with pre- and postselection is clarified.
On Conservation Laws In Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich
On Conservation Laws In Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich
Mathematics, Physics, and Computer Science Faculty Articles and Research
Conservation laws are one of the most important aspects of nature. As such, they have been intensively studied and extensively applied, and are considered to be perfectly well established. We, however, raise fundamental question about the very meaning of conservation laws in quantum mechanics. We argue that, although the standard way in which conservation laws are defined in quantum mechanics is perfectly valid as far as it goes, it misses essential features of nature and has to be revisited and extended.
What Is Nonlocal In Counterfactual Quantum Communication?, Yakir Aharonov, Daniel Rohrlich
What Is Nonlocal In Counterfactual Quantum Communication?, Yakir Aharonov, Daniel Rohrlich
Mathematics, Physics, and Computer Science Faculty Articles and Research
We revisit the “counterfactual quantum communication” of Salih et al. [1], who claim that an observer “Bob” can send one bit of information to a second observer “Alice” without any physical particle traveling between them. We show that a locally conserved, massless current—specifically, a current of modular angular momentum, Lz mod 2ℏ—carries the one bit of information. We integrate the flux of Lz mod 2ℏ from Bob to Alice and show that it equals one of the two eigenvalues of Lz mod 2ℏ, either 0 or ℏ, thus precisely accounting for the one bit of information he sends her.We previously …
Always-On Quantum Error Tracking With Continuous Parity Measurements, Razieh Mohseninia, Jing Yang, Irfan Siddiqi, Andrew N. Jordan, Justin Dressel
Always-On Quantum Error Tracking With Continuous Parity Measurements, Razieh Mohseninia, Jing Yang, Irfan Siddiqi, Andrew N. Jordan, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
We investigate quantum error correction using continuous parity measurements to correct bit-flip errors with the three-qubit code. Continuous monitoring of errors brings the benefit of a continuous stream of information, which facilitates passive error tracking in real time. It reduces overhead from the standard gate-based approach that periodically entangles and measures additional ancilla qubits. However, the noisy analog signals from continuous parity measurements mandate more complicated signal processing to interpret syndromes accurately. We analyze the performance of several practical filtering methods for continuous error correction and demonstrate that they are viable alternatives to the standard ancilla-based approach. As an optimal …
The Operational Choi-Jamio Lkowski Isomorphism, Emily Adlam
The Operational Choi-Jamio Lkowski Isomorphism, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this article, I use an operational formulation of the Choi–Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi–Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded …
A Twist On Broken U(3) × U(3) Supersymmetry, Scott Chapman
A Twist On Broken U(3) × U(3) Supersymmetry, Scott Chapman
Mathematics, Physics, and Computer Science Faculty Articles and Research
What symmetry breaking would be required for gauginos from a supersymmetric theory to behave like left-handed quarks of the Standard Model? Starting with a supersymmetric SU(3)xSU(3)xU(1)xU(1) gauge theory, the 18 adjoint-representation gauginos are replaced with 2 families of 9 gauginos in the (3,3*) representation of the group. After this explicit breaking of supersymmetry, two-loop quadratic divergences still cancel at a unification scale. Coupling constant unification is supported by deriving the theory from an SU(3)xSU(3)xSU(3)xSU(3) Grand Unified Theory (GUT). Sin2 of the Weinberg angle for the GUT is 1/4 rather than 3/8, leading to a lower unification scale than usually …
Noncontextuality Inequalities From Antidistinguishability, Matthew S. Leifer, Cristhiano Duarte
Noncontextuality Inequalities From Antidistinguishability, Matthew S. Leifer, Cristhiano Duarte
Mathematics, Physics, and Computer Science Faculty Articles and Research
Noncontextuality inequalities are usually derived from the distinguishability properties of quantum states, i.e., their orthogonality. Here, we show that antidistinguishability can also be used to derive noncontextuality inequalities. The Yu-Oh 13-ray noncontextuality inequality can be rederived and generalized as an instance of our antidistinguishability method. For some sets of states, the antidistinguishability method gives tighter bounds on noncontextual models than just considering orthogonality, and the Hadamard states provide an example of this. We also derive noncontextuality inequalities based on mutually unbiased bases and symmetric informationally complete positive operator-valued measures. Antidistinguishability based inequalities were initially discovered as overlap bounds for the …
Magnetic Forces In The Absence Of A Classical Magnetic Field, Ismael L. Paiva, Yakir Aharonov, Jeff Tollaksen, Mordecai Waegell
Magnetic Forces In The Absence Of A Classical Magnetic Field, Ismael L. Paiva, Yakir Aharonov, Jeff Tollaksen, Mordecai Waegell
Mathematics, Physics, and Computer Science Faculty Articles and Research
It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine quantum systems in specially designed configurations. This generalizes a previous work where such energy barriers arose from flux lines with half-integer fluxons. Furthermore, it is shown how the Landau levels can be obtained from a two-dimensional grid of flux lines. These results suggest …
Footprints Of Quantum Pigeons, Gregory Reznick, Shrobona Bagchi, Justin Dressel, Lev Vaidman
Footprints Of Quantum Pigeons, Gregory Reznick, Shrobona Bagchi, Justin Dressel, Lev Vaidman
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show that in the mathematical framework of the quantum theory, the classical pigeonhole principle can be violated more directly than previously suggested, i.e., in a setting closer to the traditional statement of the principle. We describe how the counterfactual reasoning of the paradox may be operationally grounded in the analysis of the tiny footprints left in the environment by the pigeons. After identifying the drawbacks of recent experiments of the quantum pigeonhole effect, we argue that a definitive experimental violation of the pigeonhole principle is still needed and propose such an implementation using modern quantum computing hardware: a superconducting …
Reformulating Bell's Theorem: The Search For A Truly Local Quantum Theory, Mordecai Waegell, Kelvin J. Mcqueen
Reformulating Bell's Theorem: The Search For A Truly Local Quantum Theory, Mordecai Waegell, Kelvin J. Mcqueen
Philosophy Faculty Articles and Research
The apparent nonlocality of quantum theory has been a persistent concern. Einstein et al. (1935) and Bell (1964) emphasized the apparent nonlocality arising from entanglement correlations. While some interpretations embrace this nonlocality, modern variations of the Everett-inspired many worlds interpretation try to circumvent it. In this paper, we review Bell's “no-go” theorem and explain how it rests on three axioms, local causality, no superdeterminism, and one world. Although Bell is often taken to have shown that local causality is ruled out by the experimentally confirmed entanglement correlations, we make clear that it is the conjunction of the …
Optimizing Measurement Strengths For Qubit Quasiprobabilities Behind Out-Of-Time-Ordered Correlators, Razieh Mohseninia, José Raúl González Alonso, Justin Dressel
Optimizing Measurement Strengths For Qubit Quasiprobabilities Behind Out-Of-Time-Ordered Correlators, Razieh Mohseninia, José Raúl González Alonso, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
Out-of-time-ordered correlators (OTOCs) have been proposed as a tool to witness quantum information scrambling in many-body system dynamics. These correlators can be understood as averages over nonclassical multitime quasiprobability distributions (QPDs). These QPDs have more information and their nonclassical features witness quantum information scrambling in a more nuanced way. However, their high dimensionality and nonclassicality make QPDs challenging to measure experimentally. We focus on the topical case of a many-qubit system and show how to obtain such a QPD in the laboratory using circuits with three and four sequential measurements. Averaging distinct values over the same measured distribution reveals either …
Schrödinger Evolution Of Superoscillations With Δ - And Δ′ -Potentials, Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser
Schrödinger Evolution Of Superoscillations With Δ - And Δ′ -Potentials, Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we study the time persistence of superoscillations as the initial data of the time-dependent Schrödinger equation with δ- and δ′-potentials. It is shown that the sequence of solutions converges uniformly on compact sets, whenever the initial data converge in the topology of the entire function space A1(C). Convolution operators acting in this space are our main tool. In particular, a general result about the existence of such operators is proven. Moreover, we provide an explicit formula as well as the large time asymptotics for the time evolution of a plane wave under δ- and δ′-potentials.
Topological Bound States For Quantum Charges, Yakir Aharonov, Ismael L. Paiva, Jeff Tollaksen, Mordecai Waegell
Topological Bound States For Quantum Charges, Yakir Aharonov, Ismael L. Paiva, Jeff Tollaksen, Mordecai Waegell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We discuss how, in appropriately designed configurations, solenoids carrying a semifluxon can be used as topological energy barriers for charged quantum systems. We interpret this phenomenon as a consequence of the fact that such solenoids induce nodal lines in the wave function describing the charge, which on itself is a consequence of the Aharonov-Bohm effect. Moreover, we present a thought experiment with a cavity where two solenoids are sufficient to create bound states.
Diffraction-Based Interaction-Free Measurements, Spencer Rogers, Yakir Aharonov, Cyril Elouard, Andrew N. Jordan
Diffraction-Based Interaction-Free Measurements, Spencer Rogers, Yakir Aharonov, Cyril Elouard, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce diffraction-based interaction-free measurements. In contrast with previous work where a set of discrete paths is engaged, good-quality interaction-free measurements can be realized with a continuous set of paths, as is typical of optical propagation. If a bomb is present in a given spatial region—so sensitive that a single photon will set it off—its presence can still be detected without exploding it. This is possible because, by not absorbing the photon, the bomb causes the single photon to diffract around it. The resulting diffraction pattern can then be statistically distinguished from the bomb-free case. We work out the case …
Benchmarks Of Nonclassicality For Qubit Arrays, Mordecai Waegell, Justin Dressel
Benchmarks Of Nonclassicality For Qubit Arrays, Mordecai Waegell, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present a set of practical benchmarks for N-qubit arrays that economically test the fidelity of achieving multi-qubit nonclassicality. The benchmarks are measurable correlators similar to two-qubit Bell correlators, and are derived from a particular set of geometric structures from the N-qubit Pauli group. These structures prove the Greenberger–Horne–Zeilinger (GHZ) theorem, while the derived correlators witness genuine N-partite entanglement and establish a tight lower bound on the fidelity of particular stabilizer state preparations. The correlators need only M ≤ N + 1 distinct measurement settings, as opposed to the 22N − 1 settings that would normally be …
The Nature Of The Heisenberg-Von Neumann Cut: Enhanced Orthodox Interpretation Of Quantum Mechanics, Ashok Narasimhan, Deepak Chopra, Menas Kafatos
The Nature Of The Heisenberg-Von Neumann Cut: Enhanced Orthodox Interpretation Of Quantum Mechanics, Ashok Narasimhan, Deepak Chopra, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
We examine the issue of the Heisenberg-von Neumann cut in light of recent interpretations of quantum eraser experiments which indicate the possibility of a universal Observer outside space-time at an information level of existence. The delayed-choice aspects of observation, measurement, the role of the observer, and information in the quantum framework of the universe are discussed. While traditional double-slit experiments are usually interpreted as indicating that the collapse of the wave function involves choices by an individual observer in space-time, the extension to quantum eraser experiments brings in some additional subtle aspects relating to the role of observation and what …
Roadmap On Superoscillations, Michael Berry, Nicolay Zheludev, Yakir Aharonov, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Jeff Tollaksen, Edward T. F. Rogers, Fei Qin, Minghui Hong, Xiangang Luo, Roei Remez, Ady Arie, Jörg B. Götte, Mark R. Dennis, Alex M. H. Wong, George V. Eleftheriades, Yaniv Eliezer, Alon Bahabad, Gang Chen, Zhongquan Wen, Gaofeng Liang, Chenglong Hao, C-W Qiu, Achim Kempf, Eytan Katzav, Moshe Schwartz
Roadmap On Superoscillations, Michael Berry, Nicolay Zheludev, Yakir Aharonov, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Jeff Tollaksen, Edward T. F. Rogers, Fei Qin, Minghui Hong, Xiangang Luo, Roei Remez, Ady Arie, Jörg B. Götte, Mark R. Dennis, Alex M. H. Wong, George V. Eleftheriades, Yaniv Eliezer, Alon Bahabad, Gang Chen, Zhongquan Wen, Gaofeng Liang, Chenglong Hao, C-W Qiu, Achim Kempf, Eytan Katzav, Moshe Schwartz
Mathematics, Physics, and Computer Science Faculty Articles and Research
Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments.
Realization Of Tensor Product And Of Tensor Factorization Of Rational Functions, Daniel Alpay, Izchak Lewkowicz
Realization Of Tensor Product And Of Tensor Factorization Of Rational Functions, Daniel Alpay, Izchak Lewkowicz
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study the state space realization of a tensor product of a pair of rational functions. At the expense of “inflating” the dimensions, we recover the classical expressions for realization of a regular product of rational functions. Under an additional assumption that the limit at infinity of a given rational function exists and is equal to identity, we introduce an explicit formula for a tensor factorization of this function.