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Articles 1 - 30 of 34
Full-Text Articles in Physical Sciences and Mathematics
Precision Frequency Measurements With Interferometric Weak Values, David J. Starling, P. Ben Dixon, Andrew N. Jordan, John C. Howell
Precision Frequency Measurements With Interferometric Weak Values, David J. Starling, P. Ben Dixon, Andrew N. Jordan, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 ± 7 kHz/√Hz with only 2 mW of continuous-wave, single-mode input power. We describe the measurement of a weak value and show how even higher-frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as precision relative frequency measurements and laser locking without the use of atomic lines.
Rethinking Geometrical Exactness, Marco Panza
Rethinking Geometrical Exactness, Marco Panza
MPP Published Research
A crucial concern of early modern geometry was fixing appropriate norms for deciding whether some objects, procedures, or arguments should or should not be allowed into it. According to Bos, this is the exactness concern. I argue that Descartes’s way of responding to this concern was to suggest an appropriate conservative extension of Euclid’s plane geometry (EPG). In Section 2, I outline the exactness concern as, I think, it appeared to Descartes. In Section 3, I account for Descartes’s views on exactness and for his attitude towards the most common sorts of constructions in classical geometry. I also explain in …
Vibrationally Promoted Electron Emission At A Metal Surface: Electron Kinetic Energy Distributions, Jerry L. Larue, Tim Schäfer, Daniel Matsiev, Luis Velarde, N. Hendrick Nahler, Daniel J. Auerbach, Alec M. Wodtke
Vibrationally Promoted Electron Emission At A Metal Surface: Electron Kinetic Energy Distributions, Jerry L. Larue, Tim Schäfer, Daniel Matsiev, Luis Velarde, N. Hendrick Nahler, Daniel J. Auerbach, Alec M. Wodtke
Biology, Chemistry, and Environmental Sciences Faculty Articles and Research
We report the first direct measurement of the kinetic energy of exoelectrons produced by collisions of vibrationally excited molecules with a low work function metal surface exhibiting electron excitations of 64% (most probable) and 95% (maximum) of the initial vibrational energy. This remarkable efficiency for vibrational-to-electronic energy transfer is in good agreement with previous results suggesting the coupling of multiple vibrational quanta to a single electron.
Rapidly Reconfigurable Slow-Light System Based On Off-Resonant Raman Absorption, Praveen K. Vudyasetu, Ryan M. Camacho, John C. Howell
Rapidly Reconfigurable Slow-Light System Based On Off-Resonant Raman Absorption, Praveen K. Vudyasetu, Ryan M. Camacho, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present a slow-light system based on dual Raman absorption resonances in warm rubidium vapor. Each Raman absorption resonance is produced by a control beam in an off-resonant Λ system. This system combines all optical control of the Raman absorption and the low-dispersion broadening properties of the double Lorentzian absorption slow light. The bandwidth, group delay, and central frequency of the slow-light system can all be tuned dynamically by changing the properties of the control beam. We demonstrate multiple pulse delays with low distortion and show that such a system has fast switching dynamics and thus fast reconfiguration rates.
Breathing Fresh Air Into The Philosophy Of Mathematics, Marco Panza
Breathing Fresh Air Into The Philosophy Of Mathematics, Marco Panza
MPP Published Research
A review of Paolo Mancosu (ed.): The Philosophy of Mathematical Practice.
Site-Specific Photocatalytic Splitting Of Methanol On Tio2(110), Chuanyao Zhou, Zefeng Ren, Shijing Tan, Zhibo Ma, Xinchun Mao, Dongxu Dai, Hongjun Fan, Xueming Yang, Jerry L. Larue, Russell Cooper, Alec M. Wodtke, Zhou Wang, Zhenyu Li, Bing Wang, Jinlong Yang, Jianguo Hou
Site-Specific Photocatalytic Splitting Of Methanol On Tio2(110), Chuanyao Zhou, Zefeng Ren, Shijing Tan, Zhibo Ma, Xinchun Mao, Dongxu Dai, Hongjun Fan, Xueming Yang, Jerry L. Larue, Russell Cooper, Alec M. Wodtke, Zhou Wang, Zhenyu Li, Bing Wang, Jinlong Yang, Jianguo Hou
Biology, Chemistry, and Environmental Sciences Faculty Articles and Research
Clean hydrogen production is highly desirable for future energy needs, making the understanding of molecular-level phenomena underlying photocatalytic hydrogen production both fundamentally and practically important. Water splitting on pure TiO2 is inefficient, however, adding sacrificial methanol could significantly enhance the photocatalyzed H2 production. Therefore, understanding the photochemistry of methanol on TiO2 at the molecular level could provide important insights to its photocatalytic activity. Here, we report the first clear evidence of photocatalyzed splitting of methanol on TiO2 derived from time-dependent two-photon photoemission (TD-2PPE) results in combination with scanning tunneling microscopy (STM). STM tip induced molecular manipulation …
Heralded Single-Photon Partial Coherence, P. Ben Dixon, Gregory A. Howland, Mehul Malik, David J. Starling, R. W. Boyd, John C. Howell
Heralded Single-Photon Partial Coherence, P. Ben Dixon, Gregory A. Howland, Mehul Malik, David J. Starling, R. W. Boyd, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study transverse spatial coherence of approximately localized single-photon states. We demonstrate nonlocal control over single-photon spatial coherence via projective measurements of an entangled twin and provide a theoretical interpretation from quantum coherence theory. Our results show that the spatial coherence of a single-photon state behaves similarly to that of a classical optical field, although the coincidence measurement adds a degree of freedom.
A Surface Femtosecond Two-Photon Photoemission Spectrometer For Excited Electron Dynamics And Time-Dependent Photochemical Kinetics, Zefeng Ren, Chuanyao Zhou, Zhibo Ma, Chun-Lei Xhao, Xinchun Mao, Dongxu Dai, Jerry L. Larue, Russell Cooper, Alec M. Wodtke, Xueming Yang
A Surface Femtosecond Two-Photon Photoemission Spectrometer For Excited Electron Dynamics And Time-Dependent Photochemical Kinetics, Zefeng Ren, Chuanyao Zhou, Zhibo Ma, Chun-Lei Xhao, Xinchun Mao, Dongxu Dai, Jerry L. Larue, Russell Cooper, Alec M. Wodtke, Xueming Yang
Biology, Chemistry, and Environmental Sciences Faculty Articles and Research
A surface femtosecond two-photon photoemission (2PPE) spectrometer devoted to the study of ultrafast excited electron dynamics and photochemical kinetics on metal and metal oxide surfaces has been constructed. Low energy photoelectrons are measured using a hemispheri- cal electron energy analyzer with an imaging detector that allows us to detect the energy and the angular distributions of the photoelectrons simultaneously. A Mach-Zehnder interferom- eter was built for the time-resolved 2PPE (TR-2PPE) measurement to study ultrafast surface excited electron dynamics, which was demonstrated on the Cu(111) surface. A scheme for measuring time-dependent 2PPE (TD-2PPE) spectra has also been developed for studies of …
Agnostic Science. Towards A Philosophy Of Data Analysis, Domenico Napoletani, Marco Panza, Daniele C. Struppa
Agnostic Science. Towards A Philosophy Of Data Analysis, Domenico Napoletani, Marco Panza, Daniele C. Struppa
MPP Published Research
In this paper we will offer a few examples to illustrate the orientation of contemporary research in data analysis and we will investigate the corresponding role of mathematics. We argue that the modus operandi of data analysis is implicitly based on the belief that if we have collected enough and sufficiently diverse data, we will be able to answer most relevant questions concerning the phenomenon itself. This is a methodological paradigm strongly related, but not limited to, biology, and we label it the microarray paradigm. In this new framework, mathematics provides powerful techniques and general ideas which generate new …
Effects Of Variable Oceanographic Conditions On Forage Fish Lipid Content And Fatty Acid Composition In The Northern California Current, Marisa N. C. Litz, Richard D. Brodeur, Robert L. Emmett, Selina S. Heppell, Rosalee S. Hellberg, Linda O'Higgins, Matthew S. Morris
Effects Of Variable Oceanographic Conditions On Forage Fish Lipid Content And Fatty Acid Composition In The Northern California Current, Marisa N. C. Litz, Richard D. Brodeur, Robert L. Emmett, Selina S. Heppell, Rosalee S. Hellberg, Linda O'Higgins, Matthew S. Morris
Food Science Faculty Articles and Research
Lipids and fatty acids (FA) were investigated in 4 species of forage fish: northern anchovy Engraulis mordax, Pacific sardine Sardinops sagax, Pacific herring Clupea pallasi, and whitebait smelt Allosmerus elongatus, for their ability to serve as biological indicators of ocean conditions in the California Current large marine ecosystem (CCLME). Samples were collected during the oceanographically contrasting years of 2005 and 2006. Upwelling was severely curtailed in the spring and early summer of 2005, leading to delayed biological productivity, whereas upwelling was relatively normal in spring 2006. Principal components analysis described 78% of the variance within the …
Interferometric Weak Value Deflections: Quantum And Classical Treatments, John C. Howell, David J. Starling, P. Ben Dixon, Praveen K. Vudyasetu, Andrew N. Jordan
Interferometric Weak Value Deflections: Quantum And Classical Treatments, John C. Howell, David J. Starling, P. Ben Dixon, Praveen K. Vudyasetu, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
We derive the weak value deflection given in an article by Dixon et al. [P. B. Dixon et al. Phys. Rev. Lett. 102 173601 (2009)] both quantum mechanically and classically, including diffraction effects. This article is meant to cover some of the mathematical details omitted in that article owing to space constraints.
Analysis Of An All-Optical Sbs Avalanche Detector, D. Walker, M. Steiner, Armen Gulian
Analysis Of An All-Optical Sbs Avalanche Detector, D. Walker, M. Steiner, Armen Gulian
Mathematics, Physics, and Computer Science Faculty Articles and Research
Seeding Brillouin scattering with a sufficiently efficient source of coherent phonons has the potential to produce energy-sensitive photon detectors. Based on this idea, we propose and analyze some possible designs for such a detector.
Post-Coring Entrapment Of Modern Air In Some Shallow Ice Cores Collected Near The Firn-Ice Transition: Evidence From Cfc-12 Measurements In Antarctic Firn Air And Ice Cores, Murat Aydin, S. A. Montzka, M. O. Battle, M. B. Williams, Warren J. De Bruyn, J. H. Butler, K. R. Verhulst, C. Tatum, B. K. Gun, D. A. Plotkin, B. D. Hall, Eric S. Saltzman
Post-Coring Entrapment Of Modern Air In Some Shallow Ice Cores Collected Near The Firn-Ice Transition: Evidence From Cfc-12 Measurements In Antarctic Firn Air And Ice Cores, Murat Aydin, S. A. Montzka, M. O. Battle, M. B. Williams, Warren J. De Bruyn, J. H. Butler, K. R. Verhulst, C. Tatum, B. K. Gun, D. A. Plotkin, B. D. Hall, Eric S. Saltzman
Biology, Chemistry, and Environmental Sciences Faculty Articles and Research
In this study, we report measurements of CFC-12 (CCl2F2) in firn air and in air extracted from shallow ice cores from three Antarctic sites. The firn air data are consistent with the known atmospheric history of CFC-12. In contrast, some of the ice core samples collected near the firn-ice transition exhibit anomalously high CFC-12 levels. Together, the ice core and firn air data provide evidence for the presence of modern air entrapped in the shallow ice core samples that likely contained open pores at the time of collection. We propose that this is due to closure of the open pores …
Polystyrene-Supported Aluminum Chloride As An Efficient And Reusable Catalyst For Condensation Of Indole With Various Carbonyl Compounds, Bahman Tamami, Amir Nasrolahi Shirazi, Kaveh Parvanak Borujeni
Polystyrene-Supported Aluminum Chloride As An Efficient And Reusable Catalyst For Condensation Of Indole With Various Carbonyl Compounds, Bahman Tamami, Amir Nasrolahi Shirazi, Kaveh Parvanak Borujeni
Pharmacy Faculty Articles and Research
Crosslinked polystyrene-supported aluminum chloride (PS-AlCl3) is a stable, recyclable and environmental friendly heterogeneous catalyst for the condensation of indole with aldehydes and ketones to afford diindolylmethanes. In addition, PS-AlCl3 shows satisfactory selectivity in the reaction of mixtures of an aldehyde and a ketone with indole. Although AlCl3 is a water sensitive, corrosive and environmentally harmful compound, PS-AlCl3 is a stable and water-tolerant species. The mild reaction conditions, short reaction times, easy work-up, high to excellent yields, chemoselectivity, reuse of the catalyst for at least ten times without significant change in its catalytic activity, low cost, and easy preparation and handling …
Major Challenges For The Modern Chemistry In Particular And Science In General, Vuk Uskoković
Major Challenges For The Modern Chemistry In Particular And Science In General, Vuk Uskoković
Pharmacy Faculty Articles and Research
In the past few hundred years, science has exerted an enormous influence on the way the world appears to human observers. Despite phenomenal accomplishments of science, science nowadays faces numerous challenges that threaten its continued success. As scientific inventions become embedded within human societies, the challenges are further multiplied. In this critical review, some of the critical challenges for the field of modern chemistry are discussed, including: (a) interlinking theoretical knowledge and experimental approaches; (b) implementing the principles of sustainability at the roots of the chemical design; (c) defining science from a philosophical perspective that acknowledges both pragmatic and realistic …
Bitopological Duality For Distributive Lattices And Heyting Algebras, Guram Bezhanishvili, Nick Bezhanishvili, David Gabelaia, Alexander Kurz
Bitopological Duality For Distributive Lattices And Heyting Algebras, Guram Bezhanishvili, Nick Bezhanishvili, David Gabelaia, Alexander Kurz
Engineering Faculty Articles and Research
We introduce pairwise Stone spaces as a natural bitopological generalization of Stone spaces—the duals of Boolean algebras—and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important for the study …
On Universal Algebra Over Nominal Sets, Alexander Kurz, Daniela Petrişan
On Universal Algebra Over Nominal Sets, Alexander Kurz, Daniela Petrişan
Engineering Faculty Articles and Research
We investigate universal algebra over the category Nom of nominal sets. Using the fact that Nom is a full re ective subcategory of a monadic category, we obtain an HSP-like theorem for algebras over nominal sets. We isolate a `uniform' fragment of our equational logic, which corresponds to the nominal logics present in the literature. We give semantically invariant translations of theories for nominal algebra and NEL into `uniform' theories and systematically prove HSP theorems for models of these theories.
Algebraic Theories Over Nominal Sets, Alexander Kurz, Daniela Petrişan, Jiří Velebil
Algebraic Theories Over Nominal Sets, Alexander Kurz, Daniela Petrişan, Jiří Velebil
Engineering Faculty Articles and Research
We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to introduce new notions of finitary based monads and uniform monads. In a second part we spell out these notions in the language of universal algebra, show how to recover the logics of Gabbay-Mathijssen and Clouston-Pitts, and apply classical results from universal algebra.
A Time-Symmetric Formulation Of Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Jeff Tollaksen
A Time-Symmetric Formulation Of Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Jeff Tollaksen
Mathematics, Physics, and Computer Science Faculty Articles and Research
Quantum mechanics allows one to independently select both the initial and final states of a single system. Such pre- and postselection reveals novel effects that challenge our ideas about what time is and how it flows.
Upper Limits On A Possible Gluon Mass, Shmuel Nussinov, Robert Shrock
Upper Limits On A Possible Gluon Mass, Shmuel Nussinov, Robert Shrock
Mathematics, Physics, and Computer Science Faculty Articles and Research
We analyze upper limits on a possible gluon mass, mg. We first discuss various ways to modify quantum chromodynamics to include m(g) not equal 0, including a bare mass, a Higgs mechanism, and dynamical breaking of color SU(3)(c). From an examination of experimental data, we infer an upper limit m(g) < O(1) MeV. As part of our analysis, we show that a claim, hitherto unrefuted in the literature, of a much stronger upper limit on m(g), is invalid. We discuss subtleties in interpreting gluon mass limits in view of the fact that at scales below Lambda(QCD), quantum chromodynamics is strongly coupled, perturbation theory is not reliable, and the physics is not accurately described in terms of the Lagrangian degrees of freedom, including gluons. We also point out a fundamental difference in the behavior of quantum chromodynamics with a nonzero gluon mass and a weakly coupled gauge theory with a gauge boson mass.
Krein Systems And Canonical Systems On A Finite Interval: Accelerants With A Jump Discontinuity At The Origin And Continuous Potentials, Daniel Alpay, I. Gohberg, M. A. Kaashoek, L. Lerer, A. Sakhnovich
Krein Systems And Canonical Systems On A Finite Interval: Accelerants With A Jump Discontinuity At The Origin And Continuous Potentials, Daniel Alpay, I. Gohberg, M. A. Kaashoek, L. Lerer, A. Sakhnovich
Mathematics, Physics, and Computer Science Faculty Articles and Research
This paper is devoted to connections between accelerants and potentials of Krein systems and of canonical systems of Dirac type, both on a finite interval. It is shown that a continuous potential is always generated by an accelerant, provided the latter is continuous with a possible jump discontinuity at the origin. Moreover, the generating accelerant is uniquely determined by the potential. The results are illustrated on pseudo-exponential potentials. The paper is a continuation of the earlier paper of the authors [1] dealing with the direct problem for Krein systems.
Entropy And Information Causality In General Probabilistic Theories, Howard Barnum, Jonathan Barrett, Lisa Orloff Clark, Matthew S. Leifer, Robert Spekkens, Nicholas Stepanik, Alex Wilce, Robin Wilke
Entropy And Information Causality In General Probabilistic Theories, 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
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state …
Is The Notion Of Mathematical Object An Historical Notion?, Marco Panza
Is The Notion Of Mathematical Object An Historical Notion?, Marco Panza
MPP Published Research
"Both historians and philosophers of mathematics frequently speak of mathematical objects. Are they speaking of the same or of similar things? Better: are they appealing to the same notion or to similar notions?"
On Coalgebras Over Algebras, Adriana Balan, Alexander Kurz
On Coalgebras Over Algebras, Adriana Balan, Alexander Kurz
Engineering Faculty Articles and Research
We extend Barr’s well-known characterization of the final coalgebra of a Set-endofunctor as the completion of its initial algebra to the Eilenberg-Moore category of algebras for a Set-monad M for functors arising as liftings. As an application we introduce the notion of commuting pair of endofunctors with respect to the monad M and show that under reasonable assumptions, the final coalgebra of one of the endofunctors involved can be obtained as the free algebra generated by the initial algebra of the other endofunctor.
Families Of Symmetries As Efficient Models Of Resource Binding, Vincenzo Ciancia, Alexander Kurz, Ugo Montanari
Families Of Symmetries As Efficient Models Of Resource Binding, Vincenzo Ciancia, Alexander Kurz, Ugo Montanari
Engineering Faculty Articles and Research
Calculi that feature resource-allocating constructs (e.g. the pi-calculus or the fusion calculus) require special kinds of models. The best-known ones are presheaves and nominal sets. But named sets have the advantage of being finite in a wide range of cases where the other two are infinite. The three models are equivalent. Finiteness of named sets is strictly related to the notion of finite support in nominal sets and the corresponding presheaves. We show that named sets are generalisd by the categorical model of families, that is, free coproduct completions, indexed by symmetries, and explain how locality of interfaces gives good …
Climatological Aspects Of The Optical Properties Of Fine/Coarse Mode Aerosol Mixtures, Thomas F. Eck, B. N. Holben, Aliaksandyr Sinyuk, R. T. Pinker, P. Goloub, H. Chen, B. Chatenet, Z. Li, Ramesh P. Singh, Sachchida N. Tripathi, J. S. Reid, D. M. Giles, O. Dubovik, N. T. O'Neill, A. Smirnov, P. Wang, X. Xia
Climatological Aspects Of The Optical Properties Of Fine/Coarse Mode Aerosol Mixtures, Thomas F. Eck, B. N. Holben, Aliaksandyr Sinyuk, R. T. Pinker, P. Goloub, H. Chen, B. Chatenet, Z. Li, Ramesh P. Singh, Sachchida N. Tripathi, J. S. Reid, D. M. Giles, O. Dubovik, N. T. O'Neill, A. Smirnov, P. Wang, X. Xia
Mathematics, Physics, and Computer Science Faculty Articles and Research
Aerosol mixtures composed of coarse mode desert dust combined with fine mode combustion generated aerosols (from fossil fuel and biomass burning sources) were investigated at three locations that are in and/or downwind of major global aerosol emission source regions. Multiyear monitoring data at Aerosol Robotic Network sites in Beijing (central eastern China), Kanpur (Indo-Gangetic Plain, northern India), and Ilorin (Nigeria, Sudanian zone of West Africa) were utilized to study the climatological characteristics of aerosol optical properties. Multiyear climatological averages of spectral single scattering albedo (SSA) versus fine mode fraction (FMF) of aerosol optical depth at 675 nm at all three …
Complementary Nature Of Surface And Atmospheric Parameters Associated With Haiti Earthquake Of 12 January 2010, Ramesh P. Singh, Waseem Mehdi, Manish Sharma
Complementary Nature Of Surface And Atmospheric Parameters Associated With Haiti Earthquake Of 12 January 2010, Ramesh P. Singh, Waseem Mehdi, Manish Sharma
Mathematics, Physics, and Computer Science Faculty Articles and Research
The present paper describes surface (surface air temperature) and atmospheric parameters (relative humidity, surface latent heat flux) over the epicenter (18A degrees 27A ' 25A ' A ' N 72A degrees 31A ' 59A ' A ' W) of Haiti earthquake of 12 January 2010. Our analysis shows pronounced changes in surface and atmospheric parameters few days prior to the main earthquake event. Changes in relative humidity are found from the surface up to an altitude of 500 hPa clearly show atmospheric perturbations associated with the earthquake event. The purpose of this paper is to show complementary nature of the …
Limit On Continuous Neutrino Emission From Neutron Stars, Itzhak Goldman, Shmuel Nussinov
Limit On Continuous Neutrino Emission From Neutron Stars, Itzhak Goldman, Shmuel Nussinov
Mathematics, Physics, and Computer Science Faculty Articles and Research
The timing data of the binary pulsar PSR1913+16, are used to establish an upper limit on the rate of continuous neutrino emission from neutron stars. Neutrino emission from each of the neutron stars of the binary system, increases the star binding energy and thus translates to a decrease in their masses. This in turn implies an increase with time of the binary period. Using the pulsar data we obtain an upper limit on the allowed rate of mass reduction: vertical bar M vertical bar < 1.1 x 10(-12) yr(-1) M, where M is the total mass of the binary. This constrains exotic nuclear equations of state that predict continuous neutrino emissions. The limit applies also to other channels of energy loss, e. g. axion emission. Continued timing measurements of additional binary pulsars, should yield a stronger limit in the future.
Quantum Interference Experiments, Modular Variables And Weak Measurements, Jeff Tollaksen, Yakir Aharonov, Aharon Casher, Tirzah Kaufherr, Shmuel Nussinov
Quantum Interference Experiments, Modular Variables And Weak Measurements, Jeff Tollaksen, Yakir Aharonov, Aharon Casher, Tirzah Kaufherr, Shmuel Nussinov
Mathematics, Physics, and Computer Science Faculty Articles and Research
We address the problem of interference using the Heisenberg picture and highlight some new aspects through the use of pre-selection, post-selection, weak measurements and modular variables. We present a physical explanation for the different behaviors of a single particle when the distant slit is open or closed; instead of having a quantum wave that passes through all slits, we have a localized particle with non-local interactions with the other slit(s). We introduce a Gedanken experiment to measure this non-local exchange. While the Heisenberg and Schrodinger pictures are equivalent formulations of quantum mechanics, nevertheless, the results discussed here support a new …
Linear Stochastic State Space Theory In The White Noise Space Setting, Daniel Alpay, David Levanony, Ariel Pinhas
Linear Stochastic State Space Theory In The White Noise Space Setting, Daniel Alpay, David Levanony, Ariel Pinhas
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this commutative ring, and are characterized in a number of ways. A major feature in our approach is the observation that key characteristics of a linear, time invariant, stochastic system are determined by the corresponding characteristics associated with the deterministic part of the system, namely its average behavior.