Explore the relationship between quantummechanics and information-age applications This volume takes an altogether unique approach to quantummechanics. Providing an in-depth exposition of quantummechanicsfundamentals, it shows how these concepts are applied to most of today's information technologies, whether they are electronic devices or materials. No other text makes this critical, essential leap from theory to real-world applications. The book's lively discussion of the mathematics involved fits right in with contemporary multidisciplinary trends in education: Once the basic formulation has been derived in a given chapter, the connection to important technological problems is summarily described. The many helpful features include * Twenty-eight application-oriented sections that focus on lasers, transistors, magnetic memories, superconductors, nuclear magnetic resonance (NMR), and other important technology-driving materials and devices * One hundred solved examples, with an emphasis on numerical results and the connection between the physics and its applications * End-of-chapter problems that ground the student in both fundamental and applied concepts * Numerous figures and tables to clarify the various topics and provide a global view of the problems under discussion * Over two hundred illustrations to highlight problems and text A book for the information age, QuantumMechanics: Fundamentals and Applications to Technology promises to become a standard in departments of electrical engineering, applied physics, and materials science, as well as physics. It is an excellent text for senior undergraduate and graduate students, and a helpful reference for practicing scientists, engineers, and chemists in the semiconductor and electronic industries.
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ R { ξ}, where R 3 and R { ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.
mechanics, which is assumed, but to examine whether it gives a consistent account of measurement. The conclusion is that after a measurement, interference terms are ‘effectively’ absent; the set of ‘one-to-one correlations between states of the apparatus and the object’ has the same form as that of everyday statistics and is thus a probability distribution. This probability distribution refers to potentialities, only one of which is actually realized in any one trial. Opinions may differ on whether their treatment is any less vulnerable to criticisms such as those of Bell. To sum up, Gottfried and Yan’s book contains a vast amount of knowledge and understanding. As well as explaining the way in which quantum theory works, it attempts to illuminate fundamental aspects of the theory. A typical example is the ‘fable’ elaborated in Gottfried’s article in Nature cited above, that if Newton were shown Maxwell’s equations and the Lorentz force law, he could deduce the meaning of E and B, but if Maxwell were shown Schrödinger’s equation, he could not deduce the meaning of Psi. For use with a well-constructed course (and, of course, this is the avowed purpose of the book; a useful range of problems is provided for each chapter), or for the relative expert getting to grips with particular aspects of the subject or aiming for a deeper understanding, the book is certainly ideal. It might be suggested, though, that, even compared to the first edition, the isolated learner might find the wide range of topics, and the very large number of mathematical and conceptual techniques, introduced in necessarily limited space, somewhat overwhelming. The second book under consideration, that of Schwabl, contains ‘Advanced’ elements of quantum theory; it is designed for a course following on from one for which Gottfried and Yan, or Schwabl’s own `QuantumMechanics' might be recommended. It is the second edition in English, and is a translation of the third German edition
In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantummechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, non-perturbative quantum theory for a Lorentzian gravitational field on a four-dimensional manifold. In the approach, the principles of quantummechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete on the fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory. In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of the kinematical Ashtekar-Isham-Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to
Describes a presentation of basic quantummechanics for nonscience majors that relies on a computer-generated graphic display to circumvent the usual mathematical difficulties. It allows a detailed treatment of free-particle motion in a wave picture. (MLH)
There is great interest in quantummechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantummechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantummechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications
We present a theoretical framework for the dynamics of bosonic Bogoliubov quasiparticles. We call it Lorentz quantummechanics because the dynamics is a continuous complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantummechanics, the dynamics is the unitary transformation in Hilbert space. In our Lorentz quantummechanics, three types of state exist: space-like, light-like and time-like. Fundamental aspects are explored in parallel to the usual quantummechanics, such as a matrix form of a Lorentz transformation, and the construction of Pauli-like matrices for spinors. We also investigate the adiabatic evolution in these mechanics, as well as the associated Berry curvature and Chern number. Three typical physical systems, where bosonic Bogoliubov quasi-particles and their Lorentz quantum dynamics can arise, are presented. They are a one-dimensional fermion gas, Bose-Einstein condensate (or superfluid), and one-dimensional antiferromagnet.
For the first time, we introduce so-called fundamental entangling operators e^{iQ1 P2} and e^{iP1 Q2 } for composing bipartite entangled states of continuum variables, where Q i and P i ( i = 1, 2) are coordinate and momentum operator, respectively. We then analyze how these entangling operators naturally appear in the quantum image of classical quadratic coordinate transformation ( q 1, q 2) → ( A q 1 + B q 2, C q 1 + D q 2), where A D- B C = 1, which means even the basic coordinate transformation ( Q 1, Q 2) → ( A Q 1 + B Q 2, C Q 1 + D Q 2) involves entangling mechanism. We also analyse their Lie algebraic properties and use the integration technique within an ordered product of operators to show they are also one- and two- mode combinatorial squeezing operators.
We present a generally covariant approach to quantummechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime". We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantummechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantummechanics.
Quantum communications promises reliable transmission of quantum information, efficient distribution of entanglement and generation of completely secure keys. For all these tasks, we need to determine the optimal point-to-point rates that are achievable by two remote parties at the ends of a quantum channel, without restrictions on their local operations and classical communication, which can be unlimited and two-way. These two-way assisted capacities represent the ultimate rates that are reachable without quantum repeaters. Here, by constructing an upper bound based on the relative entropy of entanglement and devising a dimension-independent technique dubbed ‘teleportation stretching', we establish these capacities for many fundamental channels, namely bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels in arbitrary dimension. In particular, we exactly determine the fundamental rate-loss tradeoff affecting any protocol of quantum key distribution. Our findings set the limits of point-to-point quantum communications and provide precise and general benchmarks for quantum repeaters. PMID:28443624
Quantum communications promises reliable transmission of quantum information, efficient distribution of entanglement and generation of completely secure keys. For all these tasks, we need to determine the optimal point-to-point rates that are achievable by two remote parties at the ends of a quantum channel, without restrictions on their local operations and classical communication, which can be unlimited and two-way. These two-way assisted capacities represent the ultimate rates that are reachable without quantum repeaters. Here, by constructing an upper bound based on the relative entropy of entanglement and devising a dimension-independent technique dubbed 'teleportation stretching', we establish these capacities for many fundamental channels, namely bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels in arbitrary dimension. In particular, we exactly determine the fundamental rate-loss tradeoff affecting any protocol of quantum key distribution. Our findings set the limits of point-to-point quantum communications and provide precise and general benchmarks for quantum repeaters.
We explore quantummechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantummechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantummechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit.more » In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.« less
Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here we show the implementation of quantum feedback control of a micro-mechanical oscillator using squeezed probe light. This allows quantum-enhanced feedback cooling with a measurement rate greater than it is possible with classical light, and a consequent reduction in the final oscillator temperature. Our results have significance for future applications in areas ranging from quantum information networks, to quantum-enhanced force and displacement measurements and fundamental tests of macroscopic quantummechanics.
in metrology (acceleration sensing, vibrometry, gravity wave detection) and in quantum information processing (continuous-variables quantum ...AFRL-OSR-VA-TR-2015-0009 FUNDAMENTAL PRINCIPLES OF COHERENT-FEEDBACK QUANTUM CONTROL Hideo Mabuchi LELAND STANFORD JUNIOR UNIV CA Final Report 12/08...foundations and potential applications of coherent-feedback quantum control. We have focused on potential applications in quantum -enhanced metrology and
Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantummechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantummechanics is more fundamental than classical mechanics, the quantum description of classically chaoticmore » nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.« less
Pergamon Press. Bell , J. S . 1966 On the problem of hidden variables in quantummechanics. Rev. of Modern Phys., 38, 447. Berndl, K., Daumer, M...fluid dynamics based on two quantummechanical perspectives; Schrödinger’s wave mechanics and quantum fluid dynamics based on Hamilton-Jacoby...References 8 2). Direct Problems a). Quantum fluid dynamics formalism based on Hamilton-Jacoby equation are adapted for the numerical
Newton's mechanics in the 17th century increased the lethality of artillery. Thermodynamics in the 19th led to the steam-powered industrial revolution. Maxwell's unification of electricity, magnetism and light gave us electrical power, the telegraph, radio and television. The discovery of quantummechanics in the 20th century by Planck, Bohr, Einstein, Schrodinger, Heisenberg led to the creation of the atomic and hydrogen bombs as well as computer chips, the world-wide-web and Silicon Valley's multibillion dollar corporations. The lesson is that breakthroughs in fundamental physics, both theoretical and experimental, have always led to profound technological wealth-creating industries and will continue to do so. There is now a new revolution brewing in quantummechanics that can be divided into three periods. The first quantum revolution was from 1900 to about 1975. The second quantum information/computer revolution was from about 1975 to 2015. (The early part of this story is told by Kaiser in his book, How the Hippies Saved Physics, how a small group of Berkeley/San Francisco physicists triggered that second revolution.) The third quantum revolution is how an extension of quantummechanics may lead to the understanding of consciousness as a natural physical phenomenon that can emerge in many material substrates, not only in our carbon-based biochemistry. In particular, this new post-quantummechanics may lead to naturally conscious artificial intelligence in nano-electronic machines, as well as perhaps extending human life spans to hundreds of years and more.
Modir, Bahar; Thompson, John D.; Sayre, Eleanor C.
2017-01-01
Students' difficulties in quantummechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantummechanics problems in an upper-division physics course. Using the lens of epistemological framing, we investigated four…
This paper presents a new technology program, within the fundamental physics, focusing on four quantum technology areas: quantum atomics, quantum optics, space superconductivity and quantum sensor technology, and quantum field based sensor and modeling technology.
These three lectures consider the questions of reality, causality, and probability in quantum theory, from quantummechanics to quantum field theory. They do so in part by exploring the ideas of the key founding figures of the theory, such N. Bohr, W. Heisenberg, E. Schrödinger, or P. A. M. Dirac. However, while my discussion of these figures aims to be faithful to their thinking and writings, and while these lectures are motivated by my belief in the helpfulness of their thinking for understanding and advancing quantum theory, this project is not driven by loyalty to their ideas. In part for that reason, these lectures also present different and even conflicting ways of thinking in quantum theory, such as that of Bohr or Heisenberg vs. that of Schrödinger. The lectures, most especially the third one, also consider new physical, mathematical, and philosophical complexities brought in by quantum field theory vis-à-vis quantummechanics. I close by briefly addressing some of the implications of the argument presented here for the current state of fundamental physics.
Where does quantummechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantummechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantummechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.
This paper presents a new technology program, within the fundamental physics research program, focusing on four quantum technology areas: quantum atomics, quantum optics, space superconductivity and quantum sensor technology, and quantum fluid based sensor and modeling technology.
Chattopadhyay, Swapan; Falcone, Roger; Walsworth, Ronald
Over the last twenty years, there has been a boom in quantum science - i.e., the development and exploitation of quantum systems to enable qualitatively and quantitatively new capabilities, with high-impact applications and fundamental insights that can range across all areas of science and technology.
Space platforms offer unique environment for and measurements of quantum world and fundamental physics. Quantum technology and measurements enhance measurement capabilities in space and result in greater science returns.
Reed, A. P.; Mayer, K. H.; Teufel, J. D.; Burkhart, L. D.; Pfaff, W.; Reagor, M.; Sletten, L.; Ma, X.; Schoelkopf, R. J.; Knill, E.; Lehnert, K. W.
2017-12-01
The motion of micrometre-sized mechanical resonators can now be controlled and measured at the fundamental limits imposed by quantummechanics. These resonators have been prepared in their motional ground state or in squeezed states, measured with quantum-limited precision, and even entangled with microwave fields. Such advances make it possible to process quantum information using the motion of a macroscopic object. In particular, recent experiments have combined mechanical resonators with superconducting quantum circuits to frequency-convert, store and amplify propagating microwave fields. But these systems have not been used to manipulate states that encode quantum bits (qubits), which are required for quantum communication and modular quantum computation. Here we demonstrate the conversion of propagating qubits encoded as superpositions of zero and one photons to the motion of a micromechanical resonator with a fidelity in excess of the classical bound. This ability is necessary for mechanical resonators to convert quantum information between the microwave and optical domains or to act as storage elements in a modular quantum information processor. Additionally, these results are an important step towards testing speculative notions that quantum theory may not be valid for sufficiently massive systems.
It is widely held that quantummechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory does not present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the formalisms of older physical theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantummechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given to measurement by the “projection postulate.” But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantummechanics. A realistic interpretation is possible in which only the reality of one (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory.
In quantummechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantummechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
A common understanding of quantummechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
The Einstein-Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantummechanics. Both the wave and particle aspects of the Einstein fluctuation formula are interpreted in terms of the fundamental absorption and emission processes. (Author/SK)
This paper presents a minimal formulation of nonrelativistic quantummechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called "microscopic theory", applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen-Specker-Bell theorem and Gleason's theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantummechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.
Many textbooks on QuantumMechanics are not very precise as to the meaning of making a measurement: as a consequence, they frequently make assertions which are not based on a dynamical description of the measurement process. A model proposed by von Neumann allows a dynamical description of measurement in QuantumMechanics, including the measuring instrument in the formalism. In this article we apply von Neumann's model to illustrate the measurement of an observable by means of a measuring instrument and show how various results, which are sometimens postulated without a dynamical basis, actually emerge. We also investigate the more complex, intriguing and fundamental problem of two successive measurements in QuantumMechanics, extending von Neumann's model to two measuring instruments. We present a description which allows obtaining, in a unified way, various results that have been given in the literature.
Quantum optomechanics provides a universal tool to achieve the quantum control of mechanical motion. It does that in devices spanning a vast range of parameters, with mechanical frequencies from a few Hertz to GHz, and with masses from 10-20 g to several kilos. Its underlying ideas can be traced back to the study of gravitational wave antennas, quantum optics, cavity QED and laser cooling which, when combined with the recent availability of advanced micromechanical and nanomechanical devices, opens a path to the realization of macroscopic mechanical systems that operate deep in the quantum regime. At the fundamental level this development paves the way to experiments that will lead to a more profound understanding of quantummechanics; and from the point of view of applications, quantum optomechanical techniques will provide motion and force sensing near the fundamental limit imposed by quantummechanics (quantum metrology) and significantly expand the toolbox of quantum information science. After a brief summary of key historical developments, the talk will give a broad overview of the current state of the art of quantum optomechanics, and comment on future prospects both in applied and in fundamental science. Work supported by NSF, ARO and the DARPA QuASAR and ORCHID programs.
Tomamichel, Marco; Martinez-Mateo, Jesus; Pacher, Christoph; Elkouss, David
2017-11-01
The security of quantum key distribution protocols is guaranteed by the laws of quantummechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that one-way information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during information reconciliation is not generally valid. We propose an improved approximation that takes into account finite key effects and numerically test it against codes for two probability distributions, that we call binary-binary and binary-Gaussian, that typically appear in quantum key distribution protocols.
The quantum internet holds promise for achieving quantum communication--such as quantum teleportation and quantum key distribution (QKD)--freely between any clients all over the globe, as well as for the simulation of the evolution of quantum many-body systems. The most primitive function of the quantum internet is to provide quantum entanglement or a secret key to two points efficiently, by using intermediate nodes connected by optical channels with each other. Here we derive a fundamental rate-loss trade-off for a quantum internet protocol, by generalizing the Takeoka-Guha-Wilde bound to be applicable to any network topology. This trade-off has essentially no scaling gap with the quantum communication efficiencies of protocols known to be indispensable to long-distance quantum communication, such as intercity QKD and quantum repeaters. Our result--putting a practical but general limitation on the quantum internet--enables us to grasp the potential of the future quantum internet.
The quantum internet holds promise for achieving quantum communication—such as quantum teleportation and quantum key distribution (QKD)—freely between any clients all over the globe, as well as for the simulation of the evolution of quantum many-body systems. The most primitive function of the quantum internet is to provide quantum entanglement or a secret key to two points efficiently, by using intermediate nodes connected by optical channels with each other. Here we derive a fundamental rate-loss trade-off for a quantum internet protocol, by generalizing the Takeoka–Guha–Wilde bound to be applicable to any network topology. This trade-off has essentially no scaling gap with the quantum communication efficiencies of protocols known to be indispensable to long-distance quantum communication, such as intercity QKD and quantum repeaters. Our result—putting a practical but general limitation on the quantum internet—enables us to grasp the potential of the future quantum internet. PMID:27886172
The quantum internet holds promise for achieving quantum communication-such as quantum teleportation and quantum key distribution (QKD)-freely between any clients all over the globe, as well as for the simulation of the evolution of quantum many-body systems. The most primitive function of the quantum internet is to provide quantum entanglement or a secret key to two points efficiently, by using intermediate nodes connected by optical channels with each other. Here we derive a fundamental rate-loss trade-off for a quantum internet protocol, by generalizing the Takeoka-Guha-Wilde bound to be applicable to any network topology. This trade-off has essentially no scaling gap with the quantum communication efficiencies of protocols known to be indispensable to long-distance quantum communication, such as intercity QKD and quantum repeaters. Our result-putting a practical but general limitation on the quantum internet-enables us to grasp the potential of the future quantum internet.
This dissertation begins with the argument that a preferred way of doing metaphysics is through philosophy of physics. An understanding of quantum physics is vital to answering questions such as: What counts as an individual object in physical ontology? Is the universe fundamentally indeterministic? Are indiscernibles identical? This study explores how the various modal interpretations of quantummechanics answer these sorts of questions; modal accounts are one of the two classes of interpretations along with so-called collapse accounts. This study suggests a new alternative within the class of modal views that yields a more plausible ontology, one in which the Principle of the Identity of Indisceribles is necessarily true. Next, it shows that modal interpretations can consistently deny that the universe must be fundamentally indeterministic so long as they accept certain other metaphysical commitments: either a perfect initial distribution of states in the universe or some form of primitive dispositional properties. Finally, the study sketches out a future research project for modal interpretations based on developing quantified quantum logic.
The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the standard quantum limit that arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum nondemolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric gravitational-wave detectors.
Single photon experiments involving a Mach-Zehnder interferometer can illustrate the fundamental principles of quantummechanics, e.g., the wave-particle duality of a single photon, single photon interference, and the probabilistic nature of quantum measurement involving single photons. These experiments explicitly make the connection between the abstract quantum theory and concrete laboratory settings and have the potential to help students develop a solid grasp of the foundational issues in quantummechanics. Here we describe students' conceptual difficulties with these topics in the context of Mach-Zehnder interferometer experiments with single photons and how the difficulties found in written surveys and individual interviews were used as a guide in the development of a Quantum Interactive Learning Tutorial (QuILT). The QuILT uses an inquiry-based approach to learning and takes into account the conceptual difficulties found via research to help upper-level undergraduate and graduate students learn about foundational quantummechanics concepts using the concrete quantum optics context. It strives to help students learn the basics of quantummechanics in the context of single photon experiment, develop the ability to apply fundamentalquantum principles to experimental situations in quantum optics, and explore the differences between classical and quantum ideas in a concrete context. We discuss the findings from in-class evaluations suggesting that the QuILT was effective in helping students learn these abstract concepts.
Bertolami, Orfeu; Bernardini, Alex E.; Leal, Pedro
2018-01-01
Some fundamental aspects related with the construction of Robertson-Schrödinger-like uncertainty-principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum systems in the noncommutative phase-space. Some consequences of the deformed noncommutative algebra are also considered in physical systems of interest.
The basis of this research is obtaining the best quantummechanical structure of carbon nanomaterials and is fundamental in determining their other properties. Therefore, their predictive phototoxicity is directly related to the materials’ structure. The results of this project w...
The central part of Everett's formulation of quantummechanics is a quantummechanical model of memory and of observation as the recording of information in a memory. To use this model as an answer to the measurement problem, Everett has to assume that a conscious observer can be in a superposition of such memory states and be unaware of it. This assumption has puzzled generations of readers. The fundamental aim of this dissertation is to find a set of simpler assumptions which are sufficient to show that Everett's model is empirically adequate. I argue that Everett's model needs three assumptions to account for the process of observation: an assumption of decoherence of observers as quantummechanical systems; an assumption of supervenience of mental states (qualities) over quantummechanical properties; and an assumption about the interpretation of quantummechanical states in general: quantummechanical states describe ensembles of states of affairs coexisting in the same system. I argue that the only plausible understanding of such ensembles is as ensembles of possibilities, and that all standard no-collapse interpretations agree in this reading of quantummechanical states. Their differences can be understood as different theories about what marks the real state within this ensemble, and Everett's theory as the claim that no additional 'mark of reality' is necessary. Using the three assumptions, I argue that introspection cannot determine the objective quantummechanical state of an observer. Rather, the introspective qualities of a quantummechanical state can be represented by a (classical) statistical ensemble of subjective states. An analysis of these subjective states and their dynamics leads to the conclusion that they suffice to give empirically correct predictions. The argument for the empirical adequacy of the subjective state entails that knowledge of the objective quantummechanical state is impossible in principle. Empirical reality for a conscious
The underpinning of the universe is quantummechanics. It can be used to explain the observed particle and wave nature of atoms. Atom interferometry uses the wave characteristics of atoms to investigate fundamental physics and advance our understanding of the macroscopic world. NASA is working with Dr. Mark Kasevich to apply this technology to advance astrophysics and improve navigation. In his seminar, Kasevich will delve into the world of atom interferometry, gravitational waves and quantum sensors.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S. P.
2013-01-01
-symmetric quantummechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter–antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantummechanics. PMID:23509390
For a long time microscopic physical descriptions of biological processes have been based on quantummechanical concepts and tools, and routinely employed by chemical physicists and quantum chemists. However, the last ten years have witnessed new developments on these studies from a different perspective, rooted in the framework of quantum information theory. The process that more, than others, has been subject of intense research is the transfer of excitation energy in photosynthetic light-harvesting complexes, a consequence of the unexpected experimental discovery of oscillating signals in such highly noisy systems. The fundamental interdisciplinary nature of this research makes it extremely fascinating, but can also constitute an obstacle to its advance. Here in this review our objective is to provide an essential summary of the progress made in the theoretical description of excitation energy dynamics in photosynthetic systems from a quantummechanical perspective, with the goal of unifying the language employed by the different communities. This is initially realized through a stepwise presentation of the fundamental building blocks used to model excitation transfer, including protein dynamics and the theory of open quantum system. Afterwards, we shall review how these models have evolved as a consequence of experimental discoveries; this will lead us to present the numerical techniques that have been introduced to quantitatively describe photo-absorbed energy dynamics. Finally, we shall discuss which mechanisms have been proposed to explain the unusual coherent nature of excitation transport and what insights have been gathered so far on the potential functional role of such quantum features.
Conferences and Proceedings: The results were presented at several conferences. These include: 1. M. O. Scully, " Foundations of QuantumMechanics ", in...applications have revealed a strong connection between the fundamental aspects of quantummechanics that governs physical systems and the informational...could be solved in polynomial time using quantum computers. Another set of problems where quantummechanics can carry out computations substantially
We introduce a new and conceptually simple interpretation of quantummechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR-Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantummechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.
A philosophy of physics called "linguistic empiricism" is presented and applied to the interpretation problem of quantummechanics. This philosophical position is based on the works of Jacques Derrida. The main propositions are (i) that meaning, included the meaning attached to observations, are language-dependent and (ii) that mathematics in physics should be considered as a proper language, not necessary translatable to a more basic language of intuition and immediate experience. This has fundamental implications for quantummechanics, which is a mathematically coherent and consistent theory; its interpretation problem is associated with its lack of physical images expressible in ordinary language.
The major title of this dissertation, 'From first principles,' is a phase often heard in the study of thermodynamics and quantummechanics. These words embody a powerful idea in the physical sciences; namely, that it is possible to distill the complexities of nature into a set of simple, well defined mathematical laws from which specific relations can then be derived . In thermodynamics, these fundamental laws are immediately familiar to the physical scientist by their numerical order: the First, Second and Third Laws. However, the subject of the present volume is quantummechanics-specifically, non-relativistic quantummechanics, which is appropriate formore » most systems of chemical interest.« less
Single photon experiments involving a Mach-Zehnder interferometer can illustrate the fundamental principles of quantummechanics, e.g., the wave-particle duality of a single photon, single photon interference, and the probabilistic nature of quantum measurement involving single photons. These experiments explicitly make the connection between the…
The familiar concepts of state vectors and operators in quantummechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantummechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantummechanics with standard magnetic fields.
Herman Feshbach, the organizer of this Symposium in honor of Niels Bohr, asked me, in his original invitation, for a review of the present state of condensed matter physics, with emphasis on major unsolved problems and comments on any overlap with Bohr's ideas regarding the fundamentals of quantummechanics. That is surely a difficult assignment and, indeed, goes well beyond what is attempted here; nevertheless, I will take the liberty of raising one issue of a philosophical or metaphysical flavor.
We discuss foundational issues of quantum information biology (QIB)—one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from "traditional quantum biophysics". The latter is about quantum bio-physical processes, e.g., in cells or brains. QIB models the dynamics of information states of bio-systems. We argue that the information interpretation of quantummechanics (its various forms were elaborated by Zeilinger and Brukner, Fuchs and Mermin, and D' Ariano) is the most natural interpretation of QIB. Biologically QIB is based on two principles: (a) adaptivity; (b) openness (bio-systems are fundamentally open). These principles are mathematically represented in the framework of a novel formalism— quantum adaptive dynamics which, in particular, contains the standard theory of open quantum systems.
Calmet, Xavier; Graesser, Michael; Hsu, Stephen D H
2004-11-19
We derive fundamental limits on measurements of position, arising from quantummechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length lP. This suggests a Planck-size minimum ball of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order lP. Our results imply a device independent limit on possible position measurements.
Physicists routinely claim that the fundamental laws of physics are 'time symmetric' or 'time reversal invariant' or 'reversible'. In particular, it is claimed that the theory of quantummechanics is time symmetric. But it is shown in this paper that the orthodox analysis suffers from a fatal conceptual error, because the logical criterion for judging the time symmetry of probabilistic theories has been incorrectly formulated. The correct criterion requires symmetry between future-directed laws and past-directed laws. This criterion is formulated and proved in detail. The orthodox claim that quantummechanics is reversible is re-evaluated. The property demonstrated in the orthodox analysis is shown to be quite distinct from time reversal invariance. The view of Satosi Watanabe that quantummechanics is time asymmetric is verified, as well as his view that this feature does not merely show a de facto or 'contingent' asymmetry, as commonly supposed, but implies a genuine failure of time reversal invariance of the laws of quantummechanics. The laws of quantummechanics would be incompatible with a time-reversed version of our universe.
Quantummechanics holds a fascination for many students, but its mathematical complexity and counterintuitive results can present major barriers. The QuVis QuantumMechanics Visualization Project (www.st-andrews.ac.uk/physics/quvis) aims to overcome these issues through the development and evaluation of interactive simulations with accompanying activities for the learning and teaching of quantummechanics. Over 90 simulations are now available on the QuVis website. One collection of simulations is embedded in the Institute of Physics Quantum Physics website (quantumphysics.iop.org), which consists of freely available resources for an introductory course in quantummechanics starting from two-level systems. Simulations support model-building by reducing complexity, focusing on fundamental ideas and making the invisible visible. They promote engaged exploration, sense-making and linking of multiple representations, and include high levels of interactivity and direct feedback. Simulations are research-based and evaluation with students informs all stages of the development process. Simulations are iteratively refined using student feedback in individual observation sessions and in-class trials. Evaluation has shown that the simulations can help students learn quantummechanics concepts at both the introductory and advanced undergraduate level and that students perceive simulations to be beneficial to their learning. Recent activity includes the launch of a new collection of HTML5 simulations that run on both desktop and tablet-based devices and the introduction of a goal and reward structure in simulations through the inclusion of challenges. This presentation will give an overview of the QuVis resources, highlight recent work and outline future plans. QuVis is supported by the UK Institute of Physics, the UK Higher Education Academy and the University of St Andrews.
List of papers on quantum philosophy by J. S. Bell; Preface; Acknowledgements; Introduction by Alain Aspect; 1. On the problem of hidden variables in quantummechanics; 2. On the Einstein-Rosen-Podolsky paradox; 3. The moral aspects of quantummechanics; 4. Introduction to the hidden-variable question; 5. Subject and object; 6. On wave packet reduction in the Coleman-Hepp model; 7. The theory of local beables; 8. Locality in quantummechanics: reply to critics; 9. How to teach special relativity; 10. Einstein-Podolsky-Rosen experiments; 11. The measurement theory of Everett and de Broglie's pilot wave; 12. Free variables and local causality; 13. Atomic-cascade photons and quantum-mechanical nonlocality; 14. de Broglie-Bohm delayed choice double-slit experiments and density matrix; 15. Quantummechanics for cosmologists; 16. Bertlmann's socks and the nature of reality; 17. On the impossible pilot wave; 18. Speakable and unspeakable in quantummechanics; 19. Beables for quantum field theory; 20. Six possible worlds of quantummechanics; 21. EPR correlations and EPR distributions; 22. Are there quantum jumps?; 23. Against 'measurement'; 24. La Nouvelle cuisine.
Since 1984, various optical quantum key distribution (QKD) protocols have been proposed and examined. In all of them, the rate of secret key generation decays exponentially with distance. A natural and fundamental question is then whether there are yet-to-be discovered optical QKD protocols (without quantum repeaters) that could circumvent this rate-distance tradeoff. This paper provides a major step towards answering this question. Here we show that the secret key agreement capacity of a lossy and noisy optical channel assisted by unlimited two-way public classical communication is limited by an upper bound that is solely a function of the channel loss, regardless of how much optical power the protocol may use. Our result has major implications for understanding the secret key agreement capacity of optical channels-a long-standing open problem in optical quantum information theory-and strongly suggests a real need for quantum repeaters to perform QKD at high rates over long distances.
A century after its inception, quantummechanics continues to puzzle us with dead-and-alive cats, waves "collapsing" into particles, and "spooky action at a distance." In his first book, What Is Real?, science writer and astrophysicist Adam Becker sets out to explore why the physics community is still arguing today about quantummechanics's true meaning.
Freericks, James; Cutler, Dylan; Vieira-Barbosa, Lucas
2017-01-01
We have launched a MOOC for nonscientists that teaches quantummechanics using the Feynman methodology as outlined in his QED book and in a similar book by Daniel Styer. Using a combination of videos, voice-over powerpoint animations, computer simulations and interactive tutorials, we teach the fundamentals of quantummechanics employing a minimum of math (high school algebra, square roots, and a little trigonometry) but going into detail on a number of complex quantum ideas. We begin with the Stern-Gerlach experiment, including delayed choice and Bell's inequality variants. Then we focus on light developing the quantum theory for partial reflection and diffraction. At this point we demonstrate the complexity of quantum physics by showing how watched and unwatched two-slit experiments behave differently and how quantum particles interfere. The four week course ends with advanced topics in light where we cover the idea of an interaction free measurement, the quantum Zeno effect and indistinguishable particles via the Hong-Ou-Mandel experiment. We hope this MOOC will reach thousands of students interesting in learning quantummechanics without any dumbing down or the need to learn complex math. It can also be used with undergraduates to help with conceptual understanding. Funded by the National Science Foundation under grants numbered PHY-1620555 and PHY-1314295 and by Georgetown University.
Esposito, Giampiero; Marmo, Giuseppe; Miele, Gennaro; Sudarshan, George
2014-11-01
Preface; 1. Introduction: the need for a quantum theory; 2. Experimental foundations of quantum theory; 3. Waves and particles; 4. Schrödinger picture, Heisenberg picture and probabilistic aspects; 5. Integrating the equations of motion; 6. Elementary applications: 1-dimensional problems; 7. Elementary applications: multidimensional problems; 8. Coherent states and related formalism; 9. Introduction to spin; 10. Symmetries in quantummechanics; 11. Approximation methods; 12. Modern pictures of quantummechanics; 13. Formulations of quantummechanics and their physical implications; 14. Exam problems; Glossary of geometric concepts; References; Index.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantummechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantummechanics.
Theoretical physics seems to be in a kind of schizophrenic state. Many phenomena in the observable macroscopic world obey nonlinear evolution equations, whereas the microscopic world is governed by quantummechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. I claim that linearity in quantummechanics is not as essential as it apparently seems since quantummechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown where complex Riccati equations appear in time-dependent quantummechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantummechanics. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation. Finally, it will be shown that (real and complex) Riccati equations also appear in many other fields of physics, like statistical thermodynamics and cosmology.
Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum algorithm is limited to the process of solving the problem. We extend it to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation measurement. This extended, time-symmetric, representation brings in relational quantummechanics. It is with respect to Bob and any external observer and cannot be with respect to Alice. It would tell her the number of the drawer with the ball before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. We show that, mathematically, one can ascribe any part of the selection of the random outcome of the preparation measurement to the final Alice's measurement. Ascribing half of it explains the speedup of the present algorithm. This leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows half of the number of the drawer with the ball in advance. The quantum algorithm turns out to be a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. In the sample of quantum algorithms examined, the part of the random outcome of the initial measurement selected by the final measurement is one half or slightly above it. Conversely, given an oracle problem, the assumption it is one half always corresponds to an existing quantum algorithm and gives the order of magnitude of the number of oracle queries required by the optimal one.
We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantummechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.
States that the major problem in learning quantummechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantummechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)
We investigate the difficulties that undergraduate students in quantummechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting individual interviews. Quantummechanics is abstract and its paradigm is very different from the classical one. A good grasp of the principles of quantummechanics requires creating and organizing a knowledge structure consistent with the quantum postulates. Previously learned concepts such as the principle of superposition and probability can be useful in quantummechanics if students are given opportunity to build associations between new and prior knowledge. We also discuss the need for better alignment between quantummechanics and modern physics courses taken previously because semi-classical models can impede internalization of the quantum paradigm in more advanced courses.
Preface; 1. Introduction: quantum peculiarities; 2. The map vs the territory; 3. The original TI: fundamentals; 4. The new possibilist TI: fundamentals; 5. Challenges, replies, and applications; 6. PTI and relativity; 7. The metaphysics of possibility; 8. PTI and 'spacetime'; 9. Epilogue: more than meets the eye; Appendixes; References; Index.
Preface; 1. Introduction: quantum peculiarities; 2. The map vs the territory; 3. The original TI: fundamentals; 4. The new possibilist TI: fundamentals; 5. Challenges, replies, and applications; 6. PTI and relativity; 7. The metaphysics of possibility; 8. PTI and 'spacetime'; 9. Epilogue: more than meets the eye; Appendixes; References; Index.
Quantummechanics (QMs) is a foundational subject in many science and engineering fields. It is difficult to teach, however, as it requires a fundamental revision of the assumptions and laws of classical physics and probability. Furthermore, introductory QM courses and texts predominantly focus on the mathematical formulations of the subject and…
The large dielectric constant and small effective mass in a semiconductor allows a description of its electronic states in terms of envelope wavefunctions whose energy, time, and length scales are mesoscopic, i.e., halfway between those of atomic and those of condensed matter systems. This property makes it possible to demonstrate and investigate many quantummechanical, many-body, and quantum kinetic phenomena with tabletop experiments that would be nearly impossible in other systems. This, along with the ability to custom-design semiconductor nanostructures, makes semiconductors an ideal laboratory for experimental investigations. We present an overview of some of the most exciting results obtained in semiconductors in recent years using the technique of ultrafast nonlinear optical spectrocopy. These results show that Coulomb correlation plays a major role in semiconductors and makes them behave more like a strongly interacting system than like an atomic system. The results provide insights into the physics of strongly interacting systems that are relevant to other condensed matter systems, but not easily accessible in other materials. PMID:10716981
The rampant success of quantum theory is the result of applications of the 'new' quantummechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantummechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantummechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained
The purpose of this study was to construct a valid and reliable multiple-choice achievement test to assess students' understanding of core concepts of introductory quantummechanics. Development of the QuantumMechanics Visualization Instrument (QMVI) occurred across four successive semesters in 1999--2001. During this time 213 undergraduate and graduate students attending the Pennsylvania State University (PSU) at University Park and Arizona State University (ASU) participated in this development and validation study. Participating students were enrolled in four distinct groups of courses: Modern Physics, Undergraduate QuantumMechanics, Graduate QuantumMechanics, and Chemistry QuantumMechanics. Expert panels of professors of physics experienced in teaching quantummechanics courses and graduate students in physics and science education established the core content and assisted in the validating of successive versions of the 24-question QMVI. Instrument development was guided by procedures outlined in the Standards for Educational and Psychological Testing (AERA-APA-NCME, 1999). Data gathered in this study provided information used in the development of successive versions of the QMVI. Data gathered in the final phase of administration of the QMVI also provided evidence that the intended score interpretation of the QMVI achievement test is valid and reliable. A moderate positive correlation coefficient of 0.49 was observed between the students' QMVI scores and their confidence levels. Analyses of variance indicated that students' scores in Graduate QuantumMechanics and Undergraduate QuantumMechanics courses were significantly higher than the mean scores of students in Modern Physics and Chemistry QuantumMechanics courses (p < 0.05). That finding is consistent with the additional understanding and experience that should be anticipated in graduate students and junior-senior level students over sophomore physics majors and majors in another field. The moderate
Scale relativity is a new approach to the problem of the origin of fundamental scales and of scaling laws in physics, which consists in generalizing Einstein's principle of relativity to the case of scale transformations of resolutions. We recall here how it leads one to the concept of fractal space-time, and to introduce a new complex time derivative operator which allows to recover the Schrödinger equation, then to generalize it. In high energy quantum physics, it leads to the introduction of a Lorentzian renormalization group, in which the Planck length is reinterpreted as a lowest, unpassable scale, invariant under dilatations. These methods are successively applied to two problems: in quantummechanics, that of the mass spectrum of elementary particles; in chaotic dynamics, that of the distribution of planets in the Solar System.
Quantummechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantummechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantummechanics. More recent proposals intend to complete quantummechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se, suffers from a very limited understanding that is even more severe than that of quantummechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces. Quantummechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space---not unlike the motion of a classical N-particle system in its 6N-dimensional phase-space. Unfortunately, we need an inside and an outside view, we need an external reference frame, we need an observer. This unavoidable partition is the origin of most of the troubles we have with quantummechanics. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on `instantaneous' projections within some externally selected measurement basis. As a result, the theory becomes essentially statistical rather than deterministic
Quantummechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamentalquantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantummechanics. Comprehensive account Written by one of the main figures in the field Paperback edition of successful work on philosophy of quantummechanics
Learning physics is challenging at all levels. Students' difficulties in the introductory level physics courses have been widely studied and many instructional strategies have been developed to help students learn introductory physics. However, research shows that there is a large diversity in students' preparation and skills in the upper-level physics courses and it is necessary to provide scaffolding support to help students learn advanced physics. This thesis explores issues related to students' common difficulties in learning upper-level undergraduate quantummechanics and how these difficulties can be reduced by research-based learning tutorials and peer instruction tools. We investigated students' difficulties in learning quantummechanics by administering written tests and surveys to many classes and conducting individual interviews with a subset of students. Based on these investigations, we developed Quantum Interactive Learning Tutorials (QuILTs) and peer instruction tools to help students build a hierarchical knowledge structure of quantummechanics through a guided approach. Preliminary assessments indicate that students' understanding of quantummechanics is improved after using the research-based learning tools in the junior-senior level quantummechanics courses. We also designed a standardized conceptual survey that can help instructors better probe students' understanding of quantummechanics concepts in one spatial dimension. The validity and reliability of this quantummechanics survey is discussed.
We analyze the fundamental security significance of the quantitative criteria on the final generated key K in quantum key generation including the quantum criterion d, the attacker's mutual information on K, and the statistical distance between her distribution on K and the uniform distribution. For operational significance a criterion has to produce a guarantee on the attacker's probability of correctly estimating some portions of K from her measurement, in particular her maximum probability of identifying the whole K. We distinguish between the raw security of K when the attacker just gets at K before it is used in a cryptographicmore » context and its composition security when the attacker may gain further information during its actual use to help get at K. We compare both of these securities of K to those obtainable from conventional key expansion with a symmetric key cipher. It is pointed out that a common belief in the superior security of a quantum generated K is based on an incorrect interpretation of d which cannot be true, and the security significance of d is uncertain. Generally, the quantum key distribution key K has no composition security guarantee and its raw security guarantee from concrete protocols is worse than that of conventional ciphers. Furthermore, for both raw and composition security there is an exponential catch-up problem that would make it difficult to quantitatively improve the security of K in a realistic protocol. Some possible ways to deal with the situation are suggested.« less
Scan QuantumMechanics is a novel interpretation of some aspects of quantummechanics in which the superposition of states is only an approximate effective concept. Quantum systems scan all possible states in the superposition and switch randomly and very rapidly among them. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia Iq reaches a critical value Icr for an observable, the switching among its different eigenvalues stops and the corresponding superposition comes to an end, leaving behind a system with a well defined value of that observable. Consequently, increasing the mass, temperature, gravitational strength, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. Moreover, the process could be reversible. Entanglement can only occur between quantum systems because an exact synchronization between the switchings of the systems involved must be established in the first place and classical systems do not have any switchings to start with. Future experiments might determine the critical inertia Icr corresponding to different observables, which translates into a critical mass Mcr for fixed environmental conditions as well as critical temperatures, critical electric and magnetic fields, etc. In addition, this proposal implies a new radiation mechanism from astrophysical objects with strong gravitational fields, giving rise to non-thermal synchrotron emission, that could contribute to neutron star formation. Superconductivity, superfluidity, Bose-Einstein condensates, and any other physical phenomena at very low temperatures must be reanalyzed in the light of this interpretation, as well as mesoscopic systems in general.
Over the past 40 years, a number of discoveries in quantum physics have completely transformed our vision of fundamental metrology. This revolution starts with the frequency stabilization of lasers using saturation spectroscopy and the redefinition of the metre by fixing the velocity of light c. Today, the trend is to redefine all SI base units from fundamental constants and we discuss strategies to achieve this goal. We first consider a kinematical frame, in which fundamental constants with a dimension, such as the speed of light c, the Planck constant h, the Boltzmann constant k(B) or the electron mass m(e) can be used to connect and redefine base units. The various interaction forces of nature are then introduced in a dynamical frame, where they are completely characterized by dimensionless coupling constants such as the fine structure constant alpha or its gravitational analogue alpha(G). This point is discussed by rewriting the Maxwell and Dirac equations with new force fields and these coupling constants. We describe and stress the importance of various quantum effects leading to the advent of this new quantum metrology. In the second part of the paper, we present the status of the seven base units and the prospects of their possible redefinitions from fundamental constants in an experimental perspective. The two parts can be read independently and they point to these same conclusions concerning the redefinitions of base units. The concept of rest mass is directly related to the Compton frequency of a body, which is precisely what is measured by the watt balance. The conversion factor between mass and frequency is the Planck constant, which could therefore be fixed in a realistic and consistent new definition of the kilogram based on its Compton frequency. We discuss also how the Boltzmann constant could be better determined and fixed to replace the present definition of the kelvin.
Bell showed that assuming locality leads to a disagreement with quantummechanics. Here the nature of the nonlocality that follows from quantummechanics is investigated. Note by the Editor—Readers will recognize Professor Rosen, author of this paper, as one of the co-authors of the famous EPR paper, Albert Einstein, Boris Podolsky, and Nathan Rosen, ``Can Quantum-Mechanical Description of Physical Reality be considered Complete?'', Phys. Rev. 47, 770-780 (1935). Robert H. Romer, Editor
Hooge parameter. 2. 1 / f Noise of the Recombination Current Generated in the Depletion Region The quantum i/ f ...theory. There are two forms of quantum 11f noise . In the first place C~ and Cn4 p n to quantum 1 / f noise theory. This would yield Hooge parameters S...FundamentalQuantum 1 / f Noise in Ultrasmall S~ iodcrD’vesadOtm.Dsgn P in. 12. PERSONAL AUTHOR(S) Handel, Peter H. (Princioal investiaat r) 13a. TYPE
Mesa Pascasio, J.; Fussy, S.; Schwabl, H.; Grössing, G.
2016-03-01
We present our model of an Emergent QuantumMechanics which can be characterized by “realism without pre-determination”. This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like “surreal” trajectories, which are obtained classically, i.e. without the use of any quantummechanical tool such as wavefunctions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantummechanics in a high-low intesity double slit scenario gives rise to the “quantum sweeper effect” with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques.
de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.
2018-02-01
Symplectic QuantumMechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantummechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantummechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.
The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantummechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantummechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism).
We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantummechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for b → ∞ and therefore Hartman effect doesn't exist in space fractional quantummechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantummechanics as compared to the case of standard quantummechanics. We recover the Hartman effect of standard quantummechanics as a special case of space fractional quantummechanics.
Ellis, John; Hagelin, John S.; Nanopoulos, D. V.; ...
1984-07-01
The treatment of quantum effects in gravitational fields indicates that pure states may evolve into mixed states, and Hawking has proposed modification of the axioms of field theory which incorporate the corresponding violation of quantummechanics. In this study we propose a modified hamiltonian equation of motion for density matrices and use it to interpret upper bounds on the violation of quantummechanics in different phenomenological situations. We apply our formalism to the K 0-K 0 system and to long baseline neutron interferometry experiments. In both cases we find upper bounds of about 2 × 10 -21 GeV on contributionsmore » to the single particle “hamiltonian” which violate quantummechanical coherence. We discuss how these limits might be improved in the future, and consider the relative significance of other successful tests of quantummechanics. Finally, an appendix contains model estimates of the magnitude of effects violating quantummechanics.« less
Macroscopic objects, although quantummechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantummechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantummechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantummechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantummechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.
A potential application of a superfluid gyroscope is for real-time measurements of the small variations in the rotational speed of the Earth, the Moon, and Mars. Such rotational jitter, if not measured and corrected for, will be a limiting factor on the resolution potential of a GPS system. This limitation will prevent many automation concepts in navigation, construction, and biomedical examination from being realized. We present the calculation of thermal and quantum-mechanical phase noise across the Josephson junction of a superfluid gyroscope. This allows us to derive the fundamental limits on the performance of a superfluid gyroscope. We show that the fundamental limit on real-time GPS due to rotational jitter can be reduced to well below 1 millimeter/day. Other limitations and their potential mitigation will also be discussed.
I ask the question: What can we infer about the nature and structure of the physical world (a) from experiments already done to test the predictions of quantummechanics (b) from the assumption that all future experiments will agree with those predictions? I discuss existing and projected experiments related to the two classic paradoxes of quantummechanics, named respectively for EPR and Schrödinger's Cat, and show in particular that one natural conclusion from both types of experiment implies the abandonment of the concept of macroscopic counterfactual definiteness.
Hydration reactions are fundamental to many biological functions and environmental processes. The energetics of hydration of inorganic and organic chemical species influences their fate and transport behavior in the environment. In this study, gas-phase quantummechanical calcula...
Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr
2011-09-01
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0≤t<∞, with the puzzling result that there is a quantummechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantummechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantummechanics.
A general noncommutative quantummechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantummechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.
In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantummechanics. First line of study concerns the violations of the noncontextual realist models by quantummechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantummechanics.
The physical description of all materials is rooted in quantummechanics, which describes how atoms bond and electrons interact at a fundamental level. Although these quantum effects can in many cases be approximated by a classical description at the macroscopic level, in recent years there has been growing interest in material systems where quantum effects remain manifest over a wider range of energy and length scales. Such quantum materials include superconductors, graphene, topological insulators, Weyl semimetals, quantum spin liquids, and spin ices. Many of them derive their properties from reduced dimensionality, in particular from confinement of electrons to two-dimensional sheets. Moreover, they tend to be materials in which electrons cannot be considered as independent particles but interact strongly and give rise to collective excitations known as quasiparticles. In all cases, however, quantum-mechanical effects fundamentally alter properties of the material. This Review surveys the electronic properties of quantum materials through the prism of the electron wavefunction, and examines how its entanglement and topology give rise to a rich variety of quantum states and phases; these are less classically describable than conventional ordered states also driven by quantummechanics, such as ferromagnetism.
In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantummechanics. Quantummechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantummechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantummechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantummechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantummechanics.
The recently developed Irreversible QuantumMechanics formalism describes physical reality both at the statistical and the particle levels and voices have been heard suggesting that it be used in fundamental physics. Two examples are sketched in which similar steps were taken and proved to be terrible errors: Aristotle's rejection of the vacuum because "nature does not tolerate it", replacing it by a law of force linear in velocity and Chew's rejection of Quantum Field Theory because "it is not unitary off-mass-shell". In Particle Physics, I suggest using the new representation as an "effective" picture without abandoning the canonical background.
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantummechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantummechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown
Conventional approach to quantummechanics in phase space (q,p), is to take the operator based quantummechanics of Schroedinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantummechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of themore » formalism are demonstrated throughout the text.« less
Quantummechanics is widely recognised as an important and difficult subject, and many studies have been published focusing on students’ conceptual difficulties. However, the sociocultural aspects of studying such an emblematic subject have not been researched to any large extent. This study explores students’ experiences of undergraduate quantummechanics using qualitative analysis of semi-structured interview data. The results inform discussions about the teaching of quantummechanics by adding a sociocultural dimension. Students pictured quantummechanics as an intriguing subject that inspired them to study physics. The study environment they encountered when taking their first quantummechanics course was however not always as inspiring as expected. Quantummechanics instruction has commonly focused on the mathematical framework of quantummechanics, and this kind of teaching was also what the interviewees had experienced. Two ways of handling the encounter with a traditional quantummechanics course were identified in the interviews; either students accept the practice of studying quantummechanics in a mathematical, exercise-centred way or they distance themselves from these practices and the subject. The students who responded by distancing themselves experienced a crisis and disappointment, where their experiences did not match the way they imagined themselves engaging with quantummechanics. The implications of these findings are discussed in relation to efforts to reform the teaching of undergraduate quantummechanics.
Presents a new research-based course on quantummechanics in which the conceptual issues of quantummechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
Hernandez, Hector H.; Chacon-Acosta, Guillermo; Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120
In this work we study the quantum pendulum within the framework of momentous quantummechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources. PMID:28674011
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.
The last five years have witnessed an amazing development in the field of nano- and micromechanics. What was widely considered fantasy ten years ago is about to become an experimental reality: the quantum regime of mechanical systems is within reach of current experiments. Two factors (among many) have contributed significantly to this situation. As part of the widespread effort into nanoscience and nanofabrication, it is now possible to produce high-quality nanomechanical and micromechanical resonators, spanning length scales of millimetres to nanometres, and frequencies from kilohertz to gigahertz. Researchers coupled these mechanical elements to high-sensitivity actuation and readout systems such as single-electron transistors, quantum dots, atomic point contacts, SQUID loops, high-finesse optical or microwave-cavities etc. Some of these ultra-sensitive readout schemes are in principle capable of detection at the quantum limit and a large part of the experimental effort is at present devoted to achieving this. On the other hand, the fact that the groups working in the field come from various different physics backgrounds—the authors of this editorial are a representative sample—has been a constant source of inspiration for helpful theoretical and experimental tools that have been adapted from other fields to the mechanical realm. To name just one example: ideas from quantum optics have led to the recent demonstration (both in theory and experiment) that coupling a mechanical resonator to a high-finesse optical cavity can be fully analogous to the well-known sideband-resolved laser cooling of ions and hence is capable in principle of cooling a mechanical mode into its quantum ground state. There is no doubt that such interdisciplinarity has been a crucial element for the development of the field. It is interesting to note that a very similar sociological phenomenon occurred earlier in the quantum information community, an area which is deeply enriched by the
Here, we present a silver atomic-scale device fabricated and operated by a combined technique of electrochemical control (EC) and mechanically controllable break junction (MCBJ). With this EC-MCBJ technique, we can perform mechanically controllable bistable quantum conductance switching of a silver quantum point contact (QPC) in an electrochemical environment at room temperature. Furthermore, the silver QPC of the device can be controlled both mechanically and electrochemically, and the operating mode can be changed from 'electrochemical' to 'mechanical', which expands the operating mode for controlling QPCs. These experimental results offer the perspective that a silver QPC may be used as a contact for a nanoelectromechanical relay.
Quantummechanics is often taken to be necessarily probabilistic. However, this view of quantummechanics appears to be more the result of historical accident than of careful analysis. Moreover, quantummechanics in its usual form faces serious problems. Although the mathematical core of quantummechanics--quantum probability theory- -does not face conceptual difficulties, the application of quantum probability to the physical world leads to problems. In particular, quantummechanics seems incapable of describing our everyday macroscopic experience. Therefore, several authors have proposed new interpretations --including (but not limited to) modal interpretations, spontaneous localization interpretations, the consistent histories approach, and the Bohm theory--each of which deals with quantum-mechanical probabilities differently. Each of these interpretations promises to describe our macroscopic experience and, arguably, each succeeds. Is there any way to compare them? Perhaps, if we turn to another troubling aspect of quantummechanics, non-locality. Non -locality is troubling because prima facie it threatens the compatibility of quantummechanics with special relativity. This prima facie threat is mitigated by the no-signalling theorems in quantummechanics, but nonetheless one may find a 'conflict of spirit' between nonlocality in quantummechanics and special relativity. Do any of these interpretations resolve this conflict of spirit?. There is a strong relation between how an interpretation deals with quantum-mechanical probabilities and how it deals with non-locality. The main argument here is that only a completely deterministic interpretation can be completely local. That is, locality together with the empirical predictions of quantummechanics (specifically, its strict correlations) entails determinism. But even with this entailment in hand, comparison of the various interpretations requires a look at each, to see how non-locality arises, or in the case of
The transactional interpretation of quantummechanics [1] was originally published in 1986 and is now about 14 years old. It is an explicitly nonlocal and Lorentz invariant alternative to the Copenhagen interpretation. It interprets the formalism for a quantum interaction as describing a "handshake" between retarded waves (ψ) and advanced waves (ψ*) for each quantum event or "transaction" in which energy, momentum, angular momentum, and other conserved quantities are transferred. The transactional interpretation offers the advantages that (1) it is actually "visible" in the formalism of quantummechanics, (2) it is economical, involving fewer independent assumptions than its rivals, (3) it is paradox-free, resolving all of the paradoxes of standard quantum theory including nonlocality and wave function collapse, (4) it does not give a privileged role to observers or measurements, and (5) it permits the visualization of quantum events. We will review the transactional interpretation and some of its applications to "quantum paradoxes."
life with biochemical make-up resembling that of known life. Whilst the experimental search for a second sample of life - possibly by detecting a chiral "anomaly" - continues, some theoretical investigations may be pursued to narrow down the options. Chiral determinism would be an intrinsically quantum process. There are hints that quantummechanics plays a key role in biology, but the claim remains contentious. Here I review some of the evidence for quantum aspects of biology. I also summarize some proposals for testing biological determinism by seeking evidence for a multiple genesis events on Earth, and for identifying extant "alien microbes" - micro-organisms descended from an independent origin from familiar life.
Das, Siddhartha; Khatri, Sumeet; Siopsis, George; Wilde, Mark M.
2018-01-01
It is well known in the realm of quantummechanics and information theory that the entropy is non-decreasing for the class of unital physical processes. However, in general, the entropy does not exhibit monotonic behavior. This has restricted the use of entropy change in characterizing evolution processes. Recently, a lower bound on the entropy change was provided in the work of Buscemi, Das, and Wilde [Phys. Rev. A 93(6), 062314 (2016)]. We explore the limit that this bound places on the physical evolution of a quantum system and discuss how these limits can be used as witnesses to characterize quantum dynamics. In particular, we derive a lower limit on the rate of entropy change for memoryless quantum dynamics, and we argue that it provides a witness of non-unitality. This limit on the rate of entropy change leads to definitions of several witnesses for testing memory effects in quantum dynamics. Furthermore, from the aforementioned lower bound on entropy change, we obtain a measure of non-unitarity for unital evolutions.
Research in physics has its impact on world view; physics influences the image of nature. On the other hand philosophy thinks about nature and the role of man. The insight that philosophy might indicate the frontiers of human possibilities of thought makes it highly desirable to teach these aspects in physics education. One of the most exciting examples is quantum theory which v. Weizsäcker called a fundamental philosophical advance. I give some hints to implementing philosophical aspects into a course on quantum theory. For this purpose I designed a dialogue between three philosophers - from the Antique, the Enlightenment and a quantum philosopher - discussing results of quantum theory on the background of important philosophical terms. Especially the views of Aristotle are reviewed. This idea has been carried out in a supplementary course on quantum theory for interested teacher students and for in-service training of teachers.
Preface; Notation; 1. Historical introduction; 2. Particle states in a central potential; 3. General principles of quantummechanics; 4. Spin; 5. Approximations for energy eigenstates; 6. Approximations for time-dependent problems; 7. Potential scattering; 8. General scattering theory; 9. The canonical formalism; 10. Charged particles in electromagnetic fields; 11. The quantum theory of radiation; 12. Entanglement; Author index; Subject index.
In PT-symmetric quantummechanics a fundamental principle of quantummechanics, that the Hamiltonian must be Hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P denotes parity and T denotes time reversal. Here we study the role of boundary conditions in PT-symmetric quantummechanics by constructing a simple model that is the PT-symmetric analog of a particle in a box. The model has the usual particle-in-a-box Hamiltonian but boundary conditions that respect PT symmetry rather than Hermiticity. We find that for a broad class of PT-symmetric boundary conditions the model respects the condition of unbroken PT symmetry, namely, that the Hamiltonian and the symmetry operator PT have simultaneous eigenfunctions, implying that the energy eigenvalues are real. We also find that the Hamiltonian is self-adjoint under the PT-symmetric inner product. Thus we obtain a simple soluble model that fulfills all the requirements of PT-symmetric quantummechanics. In the second part of this paper we formulate a variational principle for PT-symmetric quantummechanics that is the analog of the textbook Rayleigh-Ritz principle. Finally we consider electromagnetic analogs of the PT-symmetric particle in a box. We show that the isolated particle in a box may be realized as a Fabry-Perot cavity between an absorbing medium and its conjugate gain medium. Coupling the cavity to an external continuum of incoming and outgoing states turns the energy levels of the box into sharp resonances. Remarkably we find that the resonances have a Breit-Wigner line shape in transmission and a Fano line shape in reflection; by contrast, in the corresponding Hermitian case the line shapes always have a Breit-Wigner form in both transmission and reflection.
In 1935, Einstein, Podolsky and Rosen published their influential paper proposing a now famous paradox (the EPR paradox) that threw doubt on the completeness of quantummechanics. Two fundamental concepts: entanglement and steering, were given in the response to the EPR paper by Schrodinger, which both reflect the nonlocal nature of quantummechanics. In 1964, John Bell obtained an experimentally testable inequality, in which its violation contradicts the prediction of local hidden variable models and agrees with that of quantummechanics. Since then, great efforts have been made to experimentally investigate the nonlocal feature of quantummechanics and many distinguished quantum properties were observed. In this work, along with the discussion of the development of quantum nonlocality, we would focus on our recent experimental efforts in investigating quantum correlations and their applications with optical systems, including the study of entanglement-assisted entropic uncertainty principle, Einstein-Podolsky-Rosen steering and the dynamics of quantum correlations.
Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantummechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantummechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantummechanics in terms of Kripke's semantics. We thus show how three different theories — quantummechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantummechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantummechanics itself.
We propose giving the mathematical concept of the pseudospectrum a central role in quantummechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantummechanics.
Preface; 1. Introduction; Part I. The Emergence of QuantumMechanics: 2. Quantummechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of QuantumMechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Preface; 1. Introduction; Part I. The Emergence of QuantumMechanics: 2. Quantummechanics and the principle of observability; 3. The problem of interpretation; Part II. The Heisenberg-Bohr Dialogue: 4. The wave-particle duality; 5. Indeterminacy and the limits of classical concepts: the turning point in Heisenberg's thought; 6. Heisenberg and Bohr: divergent viewpoints of complementarity; Part III. Heisenberg's Epistemology and Ontology of QuantumMechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.
Ontic structural realism refers to the novel, exciting, and widely discussed basic idea that the structure of physical reality is genuinely relational. In its radical form, the doctrine claims that there are, in fact, no objects but only structure, i.e., relations. More moderate approaches state that objects have only relational but no intrinsic properties. In its most moderate and most tenable form, ontic structural realism assumes that at the most fundamental level of physical reality there are only relational properties. This means that the most fundamental objects only possess relational but no non-reducible intrinsic properties. The present paper will argue that our currently best physics refutes even this most moderate form of ontic structural realism. More precisely, I will claim that 1) according to quantum field theory, the most fundamental objects of matter are quantum fields and not particles, and show that 2) according to the Standard Model, quantum fields have intrinsic non-relational properties.
A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantummechanics. Our studies suggest this notoriously difficult task may be frustrated by the intuitively "realist" perspectives of introductory…
A sketch of the quantummechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.
Non-commutativity appears in physics almost hand in hand with quantummechanics. Non-commuting operators corresponding to observables lead to Heisenberg's Uncertainty Principle, which is often used as a prime example of how quantummechanics transcends 'common sense', while the operators that generate a symmetry group are usually given in terms of their commutation relations. This thesis discusses a number of new developments which go beyond the usual stopping point of non-commuting quantities as matrices with complex elements. Chapter 2 shows how certain generalisations of quantummechanics, from using complex numbers to using other (often non-commutative) algebras, can still be written as linear systems with symplectic phase flows. Chapter 3 deals with Adler's trace dynamics, a non-linear graded generalisation of Hamiltonian dynamics with supersymmetry applications, where the phase space coordinates are (generally non-commuting) operators, and reports on aspects of a demonstration that the statistical averages of the dynamical variables obey the rules of complex quantum field theory. The last two chapters discuss specific aspects of quaternionic quantummechanics. Chapter 4 reports a generalised projective representation theory and presents a structure theorem that categorises quaternionic projective representations. Chapter 5 deals with a generalisation of the coherent states formalism and examines how it may be applied to two commonly used groups.
The sialyltransferase is an enzyme that transfers the sialic acid moiety from cytidine 5'-monophospho-N-acetyl-neuraminic acid (CMP-NeuAc) to the terminal position of glycans. To elucidate the catalytic mechanism of sialyltransferase, we explored the potential energy surface along the sialic acid transfer reaction coordinates by the hybrid quantummechanics/molecular mechanics method on the basis of the crystal structure of sialyltransferase CstII. Our calculation demonstrated that CstII employed an S N 1-like reaction mechanism via the formation of a short-lived oxocarbenium ion intermediate. The computational barrier height was 19.5 kcal/mol, which reasonably corresponded with the experimental reaction rate. We also found that two tyrosine residues (Tyr156 and Tyr162) played a vital role in stabilizing the intermediate and the transition states by quantummechanical interaction with CMP.
Here, we present a silver atomic-scale device fabricated and operated by a combined technique of electrochemical control (EC) and mechanically controllable break junction (MCBJ). With this EC-MCBJ technique, we can perform mechanically controllable bistable quantum conductance switching of a silver quantum point contact (QPC) in an electrochemical environment at room temperature. Furthermore, the silver QPC of the device can be controlled both mechanically and electrochemically, and the operating mode can be changed from ‘electrochemical’ to ‘mechanical’, which expands the operating mode for controlling QPCs. These experimental results offer the perspective that a silver QPC may be used as a contact for a nanoelectromechanical relay.
The SU(2) Yang-Mills matrix model coupled to fundamental fermions is studied in the adiabatic limit, and quantum critical behavior is seen at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. The SU(2) Yang-Mills matrix model coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase. This paper is an extended version of the lectures given by the second author (SV) at the International Workshop on Quantum Physics: Foundations and Applications, Bangalore, in February 2016, and is based on [1].
The article considers the implications of the experiment of A. Einstein, B. Podolsky, and N. Rosen (EPR), and of the exchange (concerning this experiment) between EPR and Bohr concerning the incompleteness, or else nonlocality, of quantummechanics for our understanding of quantum phenomena and quantum probability. The article specifically argues that in the case of quantum phenomena, including those involved in the experiments of the EPR type, the probabilistic considerations are important even when the predictions concerned can be made with certainty, due to the impossibility, in general, to repeat any given quantum experiment with the same outcome. The article argue that this fact, not properly considered or taken into account by EPR, makes it difficult and ultimately impossible to sustain their argument, which it is consistent with Bohr's counterargument to EPR and with his view of quantum phenomena and quantummechanics.
Nonrelativistic quantummechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantummechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is inducedmore » by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.« less
The emergence of quantum chemistry in the early twentieth century was an international as well as an interdisciplinary affair, involving dialogue between physicists and chemists in Germany, the United States, and Britain. Historians of science have recently documented both the causes and effects of this internationalism and interdisciplinarity. Chemists and physicists involved in the development of quantum chemistry in its first few decades tended to argue for opposing views on acceptable standards of explanation in their field, although the debate did not divide along disciplinary lines. The purpose of this paper is to investigate these different positions, through the methodological reflections of John Clarke Slater, Linus Pauling, and Charles Coulson. Slater tended to argue for quantum-mechanical rigor and the application of fundamental principles as the values guiding models of molecular bonding. Although they were on different sides of the debate between the valence-bond and molecular-orbital approaches, Pauling and Coulson both emphasized the recovery of traditional chemical explanations and systematic explanatory power within chemistry.
Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.
1974-01-01
Exact numerical calculations are made for scattering of quantummechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantummechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantummechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.
Historians have convincingly shown the close ties U.S. physicists had with the military during the Cold War and have raised the question of whether this alliance affected the content of physics. Some have asserted that it distorted physics, shifting attention from fundamental problems to devices. Yet the papers of physicists in quantum electronics and quantum optics, fields that have been exemplary for those who hold the distortion thesis, show that the same scientists who worked on military devices simultaneously pursued fundamental and foundational topics. This essay examines one such physicist, Marlan O. Scully, with attention to both his extensive foundational studies and the way in which his applied and basic researches played off each other.
Synchronizability of space and time experiences between different inhabitants of a spacetime is abstracted as a fundamental premise of Classical physics. Absence thereof i.e. desynchronization between space and time experiences of a system under study and the observer is then studied for a single dimension single particle system. Desynchronization fundamentally makes probability concepts enter physics ab-initio and not as secondary tools to deal with situations wherein incomplete information in situation following perfectly deterministic dynamics demands its introduction. Desynchronization model based on Poisson distribution of events vis-à-vis an observer, leads to expectation of particle's motion as a Brownian motion deriving Nelson's quantum diffusion coefficient naturally, without needing to postulate it. This model also incorporates physical effects akin to those of Bohm's Quantum Potential, again without needing any sub-quantum medium. Schrodinger's equation is shown to be derivable incorporating desynchronization only of space while Quantum Field Theory is shown to model desynchronization of time as well. Fundamental suggestion of the study is that it is desynchronization that is at the root of quantum phenomena rather than sub-micro scales of spacetime. Absence of possibility of synchronization between system's space and time and those of observer is studied. Mathematical modeling of desynchronized evolution explains some intriguing aspects of QuantumMechanical theory.
Korichi, Z.; Meftah, M. T., E-mail: mewalid@yahoo.com
2014-03-15
The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantummechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantummechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.
In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantummechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.
Two physical approaches—as distinct, under the classification of Mittelstaedt, from formal approaches—to the problem of individuation of quantum objects are considered, one formulated in spatiotemporal terms and one in quantummechanical terms. The spatiotemporal approach itself has two forms: one attributed to Einstein and based on the ontology of space-time points, and the other proposed by Howard and based on intersections of world lines. The quantummechanical approach is also provided here in two forms, one based on interference and another based on a new Quantum Principle of Individuation (QPI). It is argued that the space-time approach to individuation fails and that the quantum approach offers several advantages over it, including consistency with Leibniz’s Principle of Identity of Indiscernibles.
We discuss an explicit realization of the dissipative dynamics anticipated in the proof of 't Hooft's existence theorem, which states that 'For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization'. - There is an energy-parity symmetry hidden in the Liouville equation, which mimics the Kaplan-Sundrum protective symmetry for the cosmological constant. This symmetry may be broken by the coarse-graining inherent in physics at scales much larger than the Planck length. We correspondingly modify classical ensemble theory by incorporating dissipative fluctuations (information loss) - which are caused by discrete spacetime continually 'measuring' matter. In this way, aspects of quantummechanics, such as the von Neumann equation, including a Lindblad term, arise dynamically and expectations of observables agree with the Born rule. However, the resulting quantum coherence is accompanied by an intrinsic decoherence and continuous localization mechanism. Our proposal leads towards a theory that is linear and local at the quantummechanical level, but the relation to the underlying classical degrees of freedom is nonlocal.
Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.
2017-12-01
Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp (1 |2 ) superconformal symmetry. We study the problem of constructing all quantummechanical models with a hidden osp (1 |2 ) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantummechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models—both oscillator and particlelike—realize all possible unitary irreducible representations of osp (1 |2 ).
The gravitational equivalence principle in quantummechanics is of considerable importance, but it is generally not included in physics textbooks. In this note, we present a precise quantum formulation of this principle and comment on its verification in a neutron diffraction experiment. The solution of the time dependent Schrödinger equation for this problem also gives the wave function for the motion of a charged particle in a homogeneous electric field, which is also usually ignored in textbooks on quantummechanics.
Quantum cryptography allows one to distribute a secret key between two remote parties using the fundamental principles of quantummechanics. The well-known established paradigm for the quantum key distribution relies on the actual transmission of signal particle through a quantum channel. In this Letter, we show that the task of a secret key distribution can be accomplished even though a particle carrying secret information is not in fact transmitted through the quantum channel. The proposed protocols can be implemented with current technologies and provide practical security advantages by eliminating the possibility that an eavesdropper can directly access the entire quantum system of each signal particle.
Quantum cryptography allows one to distribute a secret key between two remote parties using the fundamental principles of quantummechanics. The well-known established paradigm for the quantum key distribution relies on the actual transmission of signal particle through a quantum channel. In this Letter, we show that the task of a secret key distribution can be accomplished even though a particle carrying secret information is not in fact transmitted through the quantum channel. The proposed protocols can be implemented with current technologies and provide practical security advantages by eliminating the possibility that an eavesdropper can directly access the entire quantum system of each signal particle.
Fritz London's seminal idea of ;quantummechanisms of macroscopic scale;, first articulated in 1946, was the unanticipated result of two decades of research, during which London pursued quantum-mechanical explanations of various kinds of systems of particles at different scales. He started at the microphysical scale with the hydrogen molecule, generalized his approach to chemical bonds and intermolecular forces, then turned to macrophysical systems like superconductors and superfluid helium. Along this path, he formulated a set of concepts-the quantummechanism of exchange, the rigidity of the wave function, the role of quantum statistics in multi-particle systems, the possibility of order in momentum space-that eventually coalesced into a new conception of systems of equal particles. In particular, it was London's clarification of Bose-Einstein condensation that enabled him to formulate the notion of superfluids, and led him to the recognition that quantummechanics was not, as it was commonly assumed, relevant exclusively as a micromechanics.
A fundamental physical principle that has consequences for the topology of space-time is the principle of Einstein-Weyl causality. This also has quantummechanical manifestations. Borchers and Sen have rigorously investigated the mathematical implications of Einstein-Weyl causality and shown the denumerable space-time Q2 would be implied. They were left with important philosophical paradoxes regarding the nature of the physical real line E, e.g., whether E = R, the real line of mathematics. In order to remove these paradoxes an investigation into a constructible foundation is suggested. We have pursued such a program and find it indeed provides a dense, denumerable space-time and, moreover, an interesting connection with quantummechanics. We first show that this constructible theory contains polynomial functions which are locally homeomorphic with a dense, denumerable metric space R* and are inherently quantized. Eigenfunctions governing fields can then be effectively obtained by computational iteration. Postulating a Lagrangian for fields in a compactified space-time, we get a general description of which the Schrodinger equation is a special case. From these results we can then also show that this denumerable space-time is relational (in the sense that space is not infinitesimally small if and only if it contains a quantized field) and, since Q2 is imbedded in R*2, it directly fulfills the strict topological requirements for Einstein-Weyl causality. Therefore, the theory predicts that E = R*.
The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantummechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene – the molecular biological view and the epigenetic view – are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantummechanics that are interesting to consider. PMID:22639577
This review paper is devoted to the understanding of free-electron lasers (FEL) as devices for fundamental physics (FP) studies. After clarifying what FP stands for, we select some aspects of the FEL physics which can be viewed as fundamental. Furthermore, we discuss the perspective uses of the FEL in FP experiments. Regarding the FP aspects of the FEL, we analyze the quantum electrodynamics (QED) nature of the underlying laser mechanism. We look for the truly quantum signature in a process whose phenomenology is dominated by classical effects. As to the use of FEL as a tool for FP experiments we discuss the realization of a device dedicated to the study of non-linear effects in QED such as photon-photon scattering and shining-through-the-wall experiments planned to search for dark matter candidates like axions.
The most significant characteristic of nilpotent quantummechanics is that the quantum system (fermion state) and its environment (vacuum) are, in mathematical terms, mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has applications well beyond quantum physics. The nilpotent structure has also been identified as being constructed from two commutative vector spaces. This construction has a number of identifiable characteristics which we can expect to find in systems where self-organization is dominant, and a case presented after the publication of a paper by us on ‘The ‘Logic’ of Self-Organizing Systems’,1 in the organization of the neurons in the visual cortex. We expect to find many more complex systems where our general principles, based, by analogy, on nilpotent quantummechanics, will apply.
Sachtleben, Kewin; Mazon, Kahio T.; Rego, Luis G. C.
2017-09-01
We propose the equivalence of superconducting qubits with a pistonlike mechanicalquantum engine. The work reports a study on the nature of the nonequilibrium work exchanged with the quantum-nonadiabatic working medium, which is modeled as a multilevel coupled quantum well system subject to an external control parameter. The quantum dynamics is solved for arbitrary control protocols. It is shown that the work output has two components: one that depends instantaneously on the level populations and another that is due to the quantum coherences built in the system. The nonadiabatic coherent dynamics of the quantum engine gives rise to a resistance (friction) force that decreases the work output. We consider the functional equivalence of such a device and a rf-SQUID flux qubit.
The Weyl-Wigner map yields the entire structure of Moyal quantummechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantummechanics, was presented in the literature many years ago. However, a derivation of the formalism directly from standard operator quantummechanics, clarifying the relation between the two formulations, is still missing. In this article we present a covariant generalization of the Weyl order prescription and of the Weyl-Wigner map and use them to derive Vey quantummechanics directly from the standard operator formulation. The procedure displays some interesting features: it yields all the key ingredients and provides a more straightforward interpretation of the Vey theory including a direct implementation of unitary operator transformations as phase space coordinate transformations in the Vey idiom. These features are illustrated through a simple example.
Humble, Travis S [Knoxville, TN; Bennink, Ryan S [Knoxville, TN; Grice, Warren P [Oak Ridge, TN
2011-12-13
The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.
We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can forever locally remember information about their local initial conditions and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL) and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveal dynamically stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality, where equilibrium ordering is forbidden.
In quantummechanics, quantum coherence of a state relative to a quantum measurement can be identified with the quantumness that has to be destroyed by the measurement. In particular, quantum coherence of a bipartite state relative to a local quantum measurement encodes quantum correlations in the state. If one takes minimization with respect to the local measurements, then one is led to quantifiers which capture quantum correlations from the perspective of coherence. In this vein, quantum discord, which quantifies the minimal correlations that have to be destroyed by quantum measurements, can be identified as the minimal coherence, with the coherence measured by the relative entropy of coherence. To advocate and formulate this idea in a general context, we first review coherence relative to Lüders measurements which extends the notion of coherence relative to von Neumann measurements (or equivalently, orthonomal bases), and highlight the observation that quantum discord arises as minimal coherence through two prototypical examples. Then, we introduce some novel measures of quantum correlations in terms of coherence, illustrate them through examples, investigate their fundamental properties and implications, and indicate their applications to quantum metrology.
In some circles of quantum physicists, a view is maintained that the nonseparability of quantum systems-i.e., the entanglement-is a characteristic feature of quantummechanics. According to this view, the entanglement plays a crucial role in the solution of quantum measurement problem, the origin of the “classicality” from the quantum physics, the explanation of the EPR paradox by a nonlocal character of the quantum world. Besides, the entanglement is regarded as a cornerstone of such modern disciplines as quantum computation, quantum cryptography, quantum information, etc. At the same time, entangled states are well known and widely used in various physics areas. In particular, this notion is widely used in nuclear, atomic, molecular, solid state physics, in scattering and decay theories as well as in other disciplines, where one has to deal with many-body quantum systems. One of the methods, how to construct the basis states of a composite many-body quantum system, is the so-called genealogical decomposition method. Genealogical decomposition allows one to construct recurrently by particle number the basis states of a composite quantum system from the basis states of its forming subsystems. These coupled states have a structure typical for entangled states. If a composite system is stable, the internal structure of its forming basis states does not manifest itself in measurements. However, if a composite system is unstable and decays onto its forming subsystems, then the measurables are the quantum numbers, associated with these subsystems. In such a case, the entangled state has a dynamical origin, determined by the Hamiltonian of the corresponding decay process. Possible correlations between the quantum numbers of resulting subsystems are determined by the symmetries-conservation laws of corresponding dynamical variables, and not by the quantum entanglement feature.
We show how a quantum computer can be employed to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical-computer simulations for such problems, to significantly increase their accuracy and enable hitherto intractable simulations. Detailed resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. This demonstrates that quantum computers will realistically be able to tackle important problems in chemistry that are both scientifically and economically significant.
Numerous molecular systems, including solutions, proteins, and composite materials, can be modeled using mixed-resolution representations, of which the quantummechanics/molecular mechanics (QM/MM) approach has become the most widely used. However, the QM/MM approach often faces a number of challenges, including the high cost of repetitive QM computations, the slow sampling even for the MM part in those cases where a system under investigation has a complex dynamics, and a difficulty in providing a simple, qualitative interpretation of numerical results in terms of the influence of the molecular environment upon the active QM region. In this paper, we address these issues by combining QM/MM modeling with the methodology of "bottom-up" coarse-graining (CG) to provide the theoretical basis for a systematic quantum-mechanical/coarse-grained molecular mechanics (QM/CG-MM) mixed resolution approach. A derivation of the method is presented based on a combination of statistical mechanics and quantummechanics, leading to an equation for the effective Hamiltonian of the QM part, a central concept in the QM/CG-MM theory. A detailed analysis of different contributions to the effective Hamiltonian from electrostatic, induction, dispersion, and exchange interactions between the QM part and the surroundings is provided, serving as a foundation for a potential hierarchy of QM/CG-MM methods varying in their accuracy and computational cost. A relationship of the QM/CG-MM methodology to other mixed resolution approaches is also discussed.
Numerous molecular systems, including solutions, proteins, and composite materials, can be modeled using mixed-resolution representations, of which the quantummechanics/molecular mechanics (QM/MM) approach has become the most widely used. However, the QM/MM approach often faces a number of challenges, including the high cost of repetitive QM computations, the slow sampling even for the MM part in those cases where a system under investigation has a complex dynamics, and a difficulty in providing a simple, qualitative interpretation of numerical results in terms of the influence of the molecular environment upon the active QM region. In this paper, we address these issues by combining QM/MM modeling with the methodology of "bottom-up" coarse-graining (CG) to provide the theoretical basis for a systematic quantum-mechanical/coarse-grained molecular mechanics (QM/CG-MM) mixed resolution approach. A derivation of the method is presented based on a combination of statistical mechanics and quantummechanics, leading to an equation for the effective Hamiltonian of the QM part, a central concept in the QM/CG-MM theory. A detailed analysis of different contributions to the effective Hamiltonian from electrostatic, induction, dispersion, and exchange interactions between the QM part and the surroundings is provided, serving as a foundation for a potential hierarchy of QM/CG-MM methods varying in their accuracy and computational cost. A relationship of the QM/CG-MM methodology to other mixed resolution approaches is also discussed.
It has been recently shown that in the presence of an applied voltage, hydrogen and deuterium nuclei can be separated from one another using graphene membranes as a nuclear sieve, resulting in a 10-fold enhancement in the concentration of the lighter isotope. While previous studies, both experimental and theoretical, have attributed this effect mostly to differences in vibrational zero point energy (ZPE) of the various isotopes near the membrane surface, we propose that multi-dimensional quantummechanical tunneling of nuclei through the graphene membrane influences this proton permeation process in a fundamental way. We perform ring polymer molecular dynamics calculations in which we include both ZPE and tunneling effects of various hydrogen isotopes as they permeate the graphene membrane and compute rate constants across a range of temperatures near 300 K. While capturing the experimentally observed separation factor, our calculations indicate that the transverse motion of the various isotopes across the surface of the graphene membrane is an essential part of this sieving mechanism. An understanding of the multi-dimensional quantummechanical nature of this process could serve to guide the design of other such isotopic enrichment processes for a variety of atomic and molecular species of interest.
It has been recently shown that in the presence of an applied voltage, hydrogen and deuterium nuclei can be separated from one another using graphene membranes as a nuclear sieve, resulting in a 10-fold enhancement in the concentration of the lighter isotope. While previous studies, both experimental and theoretical, have attributed this effect mostly to differences in vibrational zero point energy (ZPE) of the various isotopes near the membrane surface, we propose that multi-dimensional quantummechanical tunneling of nuclei through the graphene membrane influences this proton permeation process in a fundamental way. We perform ring polymer molecular dynamics calculations in which we include both ZPE and tunneling effects of various hydrogen isotopes as they permeate the graphene membrane and compute rate constants across a range of temperatures near 300 K. While capturing the experimentally observed separation factor, our calculations indicate that the transverse motion of the various isotopes across the surface of the graphene membrane is an essential part of this sieving mechanism. An understanding of the multi-dimensional quantummechanical nature of this process could serve to guide the design of other such isotopic enrichment processes for a variety of atomic and molecular species of interest.
Segal, D. M.; Lorent, V.; Dubessy, R.; Darquié, B.
2018-03-01
The text below was written during two visits that Daniel Segal made at Université Paris 13. Danny stayed at Laboratoire de Physique des Lasers the summers of 2008 and 2009 to participate in the exploration of a novel lead in the field of ultra-high resolution spectroscopy. Our idea was to probe trapped molecular ions using Quantum Logic Spectroscopy (QLS) in order to advance our understanding of a variety of fundamental processes in nature. At that time, QLS, a ground-breaking spectroscopic technique, had only been demonstrated with atomic ions. Our ultimate goals were new approaches to the observation of parity violation in chiral molecules and tests of time variations of the fundamental constants. This text is the original research proposal written eight years ago. We have added a series of notes to revisit it in the light of what has been since realized in the field.
Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr; Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in
2016-02-15
We first study a class of fundamentalquantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamentalquantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculusmore » extends the Hudson-Parthasarathy quantum stochastic calculus.« less
Quantummechanics imposes a fundamental trade-off between the accuracy of time measurements and the size of the systems used as clocks. When the measurements of different time intervals are combined, the errors due to the finite clock size accumulate, resulting in an overall inaccuracy that grows with the complexity of the set-up. Here, we introduce a method that, in principle, eludes the accumulation of errors by coherently transferring information from a quantum clock to a quantum memory of the smallest possible size. Our method could be used to measure the total duration of a sequence of events with enhanced accuracy, and to reduce the amount of quantum communication needed to stabilize clocks in a quantum network.
Empirical studies persistently indicate that the usual explanatory strategies used in quantummechanics (QM) instruction fail, in general, to yield understanding. In this study, we propose an instructional intervention, which: (a) incorporates into its subject matter a critical comparison of QM scientific content with the fundamental epistemological and ontological commitments of the prominent philosophical theories of explanation, a weak form of which we meet in QM teaching; (b) illuminates the reasons of their failure in the quantum domain; and (c) implements an explanatory strategy highly inspired by the epistemological pathways through which, during the birth-process of QM, science has gradually reached understanding. This strategy, an inherent element of which is the meta-cognitive and meta-scientific thinking, aims at leading learners not only to an essential understanding of QM worldview, but to a deep insight into the ‘Nature of Science’ as well.
In this paper we apply the last developments of the theory of measurement in quantummechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantummechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.
A fully functional quantum computer must contain at least two important components: a quantum memory for storing and manipulating quantum information and a quantum data bus to securely transfer information between quantum memories. Typically, a quantum memory is composed of a matter system, such as an atom or an electron spin, due to their prolonged quantum coherence. Alternatively, a quantum data bus is typically composed of some propagating degree of freedom, such as a photon, which can retain quantum information over long distances. Therefore, a quantum computer will likely be a hybrid quantum device, consisting of two or more disparate quantum systems. However, there must be a reliable and controllable quantum interface between the memory and bus in order to faithfully interconvert quantum information. The current engineering challenge for quantum computers is scaling the device to large numbers of controllable quantum systems, which will ultimately depend on the choice of the quantum elements and interfaces utilized in the device. In this thesis, we present and characterize a hybrid quantum device comprised of single nitrogen-vacancy (NV) centers embedded in a high quality factor diamond mechanical oscillator. The electron spin of the NV center is a leading candidate for the realization of a quantum memory due to its exceptional quantum coherence times. On the other hand, mechanical oscillators are highly sensitive to a wide variety of external forces, and have the potential to serve as a long-range quantum bus between quantum systems of disparate energy scales. These two elements are interfaced through crystal strain generated by vibrations of the mechanical oscillator. Importantly, a strain interface allows for a scalable architecture, and furthermore, opens the door to integration into a larger quantum network through coupling to an optical interface. There are a few important engineering challenges associated with this device. First, there have been no
We develop a quantum information protocol that models the biological behaviours of individuals living in a natural selection scenario. The artificially engineered evolution of the quantum living units shows the fundamental features of life in a common environment, such as self-replication, mutation, interaction of individuals, and death. We propose how to mimic these bio-inspired features in a quantum-mechanical formalism, which allows for an experimental implementation achievable with current quantum platforms. This study paves the way for the realization of artificial life and embodied evolution with quantum technologies.
We develop a quantum information protocol that models the biological behaviours of individuals living in a natural selection scenario. The artificially engineered evolution of the quantum living units shows the fundamental features of life in a common environment, such as self-replication, mutation, interaction of individuals, and death. We propose how to mimic these bio-inspired features in a quantum-mechanical formalism, which allows for an experimental implementation achievable with current quantum platforms. This study paves the way for the realization of artificial life and embodied evolution with quantum technologies. PMID:26853918
The word 'uncertainty', in the context of quantummechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantummechanics to represent an absolute truth. But they do not cause us to put that very 'truth' into question. This article addresses the issue of quantum 'uncertainty' from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications.
In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called
The realization of devices which harness the laws of quantummechanics represents an exciting challenge at the interface of modern technology and fundamental science. An exemplary paragon of the power of such quantum primitives is the concept of ``quantum money.'' A dishonest holder of a quantum bank-note will invariably fail in any forging attempts; indeed, under assumptions of ideal measurements and decoherence-free memories such security is guaranteed by the no-cloning theorem. In any practical situation, however, noise, decoherence and operational imperfections abound. Thus, the development of secure ``quantum money''-type primitives capable of tolerating realistic infidelities is of both practical and fundamental importance. Here, we propose a novel class of such protocols and demonstrate their tolerance to noise; moreover, we prove their rigorous security by determining tight fidelity thresholds. Our proposed protocols require only the ability to prepare, store and measure single qubit quantum memories, making their experimental realization accessible with current technologies.
Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with any thermodynamic bath, on the work cost for the implementation of any logical process. This limit is given by a new information measure—the coherent relative entropy—which accounts for the Gibbs weight of each microstate. The coherent relative entropy enjoys a collection of natural properties justifying its interpretation as a measure of information and can be understood as a generalization of a quantum relative entropy difference. As an application, we show that the standard first and second laws of thermodynamics emerge from our microscopic picture in the macroscopic limit. Finally, our results have an impact on understanding the role of the observer in thermodynamics: Our approach may be applied at any level of knowledge—for instance, at the microscopic, mesoscopic, or macroscopic scales—thus providing a formulation of thermodynamics that is inherently relative to the observer. We obtain a precise criterion for when the laws of thermodynamics can be applied, thus making a step forward in determining the exact extent of the universality of thermodynamics and enabling a systematic treatment of Maxwell-demon-like situations.
We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantummechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.
A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantummechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.
Quantum heat engines employ as working agents multilevel systems instead of classical gases. We show that under some conditions quantum heat engines are equivalent to a series of reservoirs at different altitudes containing balls of various weights. A cycle consists of picking up at random a ball from one reservoir and carrying it to the next, thereby performing or absorbing some work. In particular, quantum heat engines, employing two-level atoms as working agents, are modeled by reservoirs containing balls of weight 0 or 1. The mechanical model helps us prove that the maximum efficiency of quantum heat engines is the Carnot efficiency. Heat pumps and negative temperatures are considered.
The interpretation of quantummechanics presented in this paper is inspired by two ideas that are fundamental in Bohr's writings: indivisibility and complementarity. Further basic assumptions of the proposed interpretation are completeness, universality and conceptual economy. In the interpretation, decoherence plays a fundamental role for the understanding of measurement. A general and precise conception of complementarity is proposed. It is fundamental in this interpretation to make a distinction between ontological reality, constituted by everything that does not depend at all on the collectivity of human beings, nor on their decisions or limitations, nor on their existence, and empirical reality constituted by everything that not being ontological is, however, intersubjective. According to the proposed interpretation, neither the dynamical properties, nor the constitutive properties of microsystems like mass, charge and spin, are ontological. The properties of macroscopic systems and space-time are also considered to belong to empirical reality. The acceptance of the above mentioned conclusion does not imply a total rejection of the notion of ontological reality. In the paper, utilizing the Aristotelian ideas of general cause and potentiality, a relation between ontological reality and empirical reality is proposed. Some glimpses of ontological reality, in the form of what can be said about it, are finally presented.
In the condensed phase, quantum chemical properties such as many-body effects and intermolecular charge fluctuations are critical determinants of the solvation structure and dynamics. Thus, a quantummechanical (QM) molecular description is required for both solute and solvent to incorporate these properties. However, it is challenging to conduct molecular dynamics (MD) simulations for condensed systems of sufficient scale when adapting QM potentials. To overcome this problem, we recently developed the size-consistent multi-partitioning (SCMP) quantummechanics/molecular mechanics (QM/MM) method and realized stable and accurate MD simulations, using the QM potential to a benchmark system. In the present study, as the first application of the SCMP method, we have investigated the structures and dynamics of Na + , K + , and Ca 2+ solutions based on nanosecond-scale sampling, a sampling 100-times longer than that of conventional QM-based samplings. Furthermore, we have evaluated two dynamic properties, the diffusion coefficient and difference spectra, with high statistical certainty. Furthermore the calculation of these properties has not previously been possible within the conventional QM/MM framework. Based on our analysis, we have quantitatively evaluated the quantum chemical solvation effects, which show distinct differences between the cations.
This book covers relativistic quantum theory from the point of view of a particle theory, based on the irreducible representations of the Poincaré group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; this book develops what is called relativistic point form quantummechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A chapter is devoted to applications of point form quantummechanics to nuclear physics.
A scheme for constructing quantummechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantummechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.
Hanada, Masanori; Hyakutake, Yoshifumi; Ishiki, Goro; Nishimura, Jun
2014-05-01
Black holes have been predicted to radiate particles and eventually evaporate, which has led to the information loss paradox and implies that the fundamental laws of quantummechanics may be violated. Superstring theory, a consistent theory of quantum gravity, provides a possible solution to the paradox if evaporating black holes can actually be described in terms of standard quantummechanical systems, as conjectured from the theory. Here, we test this conjecture by calculating the mass of a black hole in the corresponding quantummechanical system numerically. Our results agree well with the prediction from gravity theory, including the leading quantum gravity correction. Our ability to simulate black holes offers the potential to further explore the yet mysterious nature of quantum gravity through well-established quantummechanics.
The authors show that requiring diffeomorphic equivalence for one-dimensional stationary states implies that the reduced action S{sub 0} satisfies the quantum Hamilton-Jacobi equation with the Planck constant playing the role of a covariantizing parameter. The construction shows the existence of a fundamental initial condition which is strictly related to the Moebius symmetry of the Legendre transform and to its involutive character. The universal nature of the initial condition implies the Schroedinger equation in any dimension.
The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that other aspects (such as the operational prescriptions that are an integral part of experimental physics) have been largely ignored. This has undoubtedly exacerbated attempts to find a solution to the "measurement problem". How the measurement problem is defined depends to some extent on how the theoretical concepts introduced by the theory are interpreted. In this paper, we fully embrace the minimalist statistical (ensemble) interpretation of quantummechanics espoused by Einstein, Ballentine, and others. According to this interpretation, the quantum state description applies only to a statistical ensemble of similarly prepared systems rather than representing an individual system. Thus, the statistical interpretation obviates the need to entertain reduction of the state vector, one of the primary dilemmas of the measurement problem. The other major aspect of the measurement problem, the necessity of describing measurements in terms of classical concepts that lay outside of quantum theory, remains. A consistent formalism for interacting quantum and classical systems, like the one based on ensembles on configuration space that we refer to in this paper, might seem to eliminate this facet of the measurement problem; however, we argue that the ultimate interface with experiments is described by operational prescriptions and not in terms of the concepts of classical theory. There is no doubt that attempts to address the measurement problem have yielded important advances in fundamental physics; however, it is also very clear that the measurement problem is still far from being resolved. The pedestrian approach presented here suggests that this state of affairs is in part the result of searching for a theoretical/mathematical solution to what is fundamentally an experimental/observational question. It
Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph
2014-06-19
Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via 'magic state' distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple 'hidden variable' model of quantummechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms.
The ever-decreasing size of electronic components is leading to a fundamental change in the way computers operate, as at the few-nanometer scale, resistive heating and quantummechanics prohibit efficient and stable operation. One of the most promising next-generation computing paradigms is Spintronics, which uses the spin of the electron to manipulate and store information in the form of magnetic thin films. I will present our optical studies of the fundamentalmechanisms by which we can efficiently manipulate magnetization using electrical current. Although electron spin is a quantum-mechanical property, Spintronics relies on macroscopic magnetization and thus does not take advantage of quantummechanics in the algorithms used to encode and transmit information. For the second part of my talk, I will present our work under the umbrella of new computing and communication technologies based on the quantummechanical properties of photons. Quantum technologies often require the carriers of information, or qubits, to have specific properties. Photonic quantum states are good information carriers because they travel fast and are robust to environmental fluctuations, but characterizing and controlling photonic sources so the photons have just the right properties is still a challenge. I will describe our work towards enabling quantum-physics-based secure long-distance communication using photons.
Quantummechanics in terms of interactive holography appears as `normal' science [1]. With the holography quantum behavior is determined by the interplay of material formations and their conjugate images. To begin with, this effortlessly elucidates the nonlocality in quantum entanglements. Then, it has been shown that Schr"odinger's dynamics for a single particle arises from Bi-Fragmental random walks of the particle itself and its holographic image. For many particles this picture blurs with fragments merging as bosons or fermions. In biomolecules, swapping of particles and their holographic placeholders leads to self-replication of the living matter. Because of broad interpretations of quantum formalism direct experiments attributing it to holography may not be very compelling. The holographic mechanism better reveals as an absolute frame of reference. A number of physical and biological events exhibit annual variations when Earth orbital position changes with respect to the universal holographic mechanism. The well established calendar variations of heart attacks can be regarded as a positive outcome of a generalization of the Michelson experiment, where holography is interferometry and ailing hearts are detectors of pathologically replicated proteins. Also, there have been already observed calendar changes in radioactive decay rates. The same could be expected for various fine quantum experiences, like, e.g., Josephson tunneling. In other words, QuantumMechanics (February) QuantumMechanics (August). [1] S. Berkovich, ``A comprehensive explanation of quantummechanics,'' www.cs.gwu.edu/research/technical-report/170 .
First, exact definitions are supplied for the terms: position, velocity, energy, etc. (of the electron, for instance), such that they are valid also in quantummechanics. Canonically conjugated variables are determined simultaneously only with a characteristic uncertainty. This uncertainty is the intrinsic reason for the occurrence of statistical relations in quantummechanics. Mathematical formulation is made possible by the Dirac-Jordan theory. Beginning from the basic principles thus obtained, macroscopic processes are understood from the viewpoint of quantummechanics. Several imaginary experiments are discussed to elucidate the theory.
We outline a programme for an axiomatic reconstruction of quantummechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field. This article is part of the themed issue `Second quantum revolution: foundational questions'.
Quantum effects in solute-solvent interactions, such as the many-body effect and the dipole-induced dipole, are known to be critical factors influencing the infrared spectra of species in the liquid phase. For accurate spectrum evaluation, the surrounding solvent molecules, in addition to the solute of interest, should be treated using a quantummechanical method. However, conventional quantummechanics/molecular mechanics (QM/MM) methods cannot handle free QM solvent molecules during molecular dynamics (MD) simulation because of the diffusion problem. To deal with this problem, we have previously proposed an adaptive QM/MM "size-consistent multipartitioning (SCMP) method". In the present study, as the first application of the SCMP method, we demonstrate the reproduction of the infrared spectrum of liquid-phase water, and evaluate the quantum effect in comparison with conventional QM/MM simulations.
Oliva, Maxime; Kakofengitis, Dimitris; Steuernagel, Ole
2018-07-01
Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantummechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches to quantum phase space studies. We first demonstrate the absence of trajectories in general terms. We then give an explicit proof for all quantum phase space distributions with negative values: we show that the generation of coherences in anharmonic quantummechanical systems is responsible for the occurrence of singularities in their phase space velocity fields, and vice versa. This explains numerical problems repeatedly reported in the literature, and provides deeper insight into the nature of quantum phase space dynamics.
Krijtenburg-Lewerissa, K.; Pol, H. J.; Brinkman, A.; van Joolingen, W. R.
2017-06-01
This study presents a review of the current state of research on teaching quantummechanics in secondary and lower undergraduate education. A conceptual approach to quantummechanics is being implemented in more and more introductory physics courses around the world. Because of the differences between the conceptual nature of quantummechanics and classical physics, research on misconceptions, testing, and teaching strategies for introductory quantummechanics is needed. For this review, 74 articles were selected and analyzed for the misconceptions, research tools, teaching strategies, and multimedia applications investigated. Outcomes were categorized according to their contribution to the various subtopics of quantummechanics. Analysis shows that students have difficulty relating quantum physics to physical reality. It also shows that the teaching of complex quantum behavior, such as time dependence, superposition, and the measurement problem, has barely been investigated for the secondary and lower undergraduate level. At the secondary school level, this article shows a need to investigate student difficulties concerning wave functions and potential wells. Investigation of research tools shows the necessity for the development of assessment tools for secondary and lower undergraduate education, which cover all major topics and are suitable for statistical analysis. Furthermore, this article shows the existence of very diverse ideas concerning teaching strategies for quantummechanics and a lack of research into which strategies promote understanding. This article underlines the need for more empirical research into student difficulties, teaching strategies, activities, and research tools intended for a conceptual approach for quantummechanics.
We are investigating cognitive issues in learning quantummechanics in order to develop effective teaching and learning tools. The analysis of cognitive issues is particularly important for bridging the gap between the quantitative and conceptual aspects of quantummechanics and for ensuring that the learning tools help students build a robust knowledge structure. We discuss the cognitive aspects of quantummechanics that are similar or different from those of introductory physics and their implications for developing strategies to help students develop a good grasp of quantummechanics.
Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.
Kantner, Markus; Mittnenzweig, Markus; Koprucki, Thomas
2017-11-01
The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantummechanics. We connect the well-established fields of semiclassical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we introduce a new hybrid quantum-classical modeling approach, which provides a comprehensive description of quantum dot devices on multiple scales: it enables the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single quantum dot in the stationary and transient operation regime.
Fundamentally binary theories are nonsignaling theories in which measurements of many outcomes are constructed by selecting from binary measurements. They constitute a sensible alternative to quantum theory and have never been directly falsified by any experiment. Here we show that fundamentally binary theories are experimentally testable with current technology. For that, we identify a feasible Bell-type experiment on pairs of entangled qutrits. In addition, we prove that, for any n , quantum n -ary correlations are not fundamentally (n -1 ) -ary. For that, we introduce a family of inequalities that hold for fundamentally (n -1 ) -ary theories but are violated by quantum n -ary correlations.
The time evolution of quantum states is arguably one of the more difficult ideas in quantummechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…
Krijtenburg-Lewerissa, K.; Pol, H. J.; Brinkman, A.; van Joolingen, W. R.
2017-01-01
This study presents a review of the current state of research on teaching quantummechanics in secondary and lower undergraduate education. A conceptual approach to quantummechanics is being implemented in more and more introductory physics courses around the world. Because of the differences between the conceptual nature of quantummechanics and…
In this work, we first solve complex Morse flow equations for the simplest case of a bosonic harmonic oscillator to discuss localization in the context of Picard-Lefschetz theory. We briefly touch on the exact non-BPS solutions of the bosonized supersymmetric quantummechanics on algebraic geometric grounds and report that their complex phases can be accessed through the cohomology of WKB 1-form of the underlying singular spectral curve subject to necessary cohomological corrections for nonzero genus. Motivated by Picard-Lefschetz theory, we write down a general formula for the index of N =4 quantummechanics with background R -symmetry gauge fields. We conjecture that certain symmetries of the refined Witten index and singularities of the moduli space may be used to determine the correct intersection coefficients. A few examples, where this conjecture holds, are shown in both linear and closed quivers with rank-one quiver gauge groups. The R -anomaly removal along the "Morsified" relative homology cycles also called "Lefschetz thimbles" is shown to lead to the appearance of Stokes lines. We show that the Fayet-Iliopoulos parameters appear in the intersection coefficients for the relative homology of the quiver quantummechanics resulting from dimensional reduction of 2 d N =(2 ,2 ) gauge theory on a circle and explicitly calculate integrals along the Lefschetz thimbles in N =4 C Pk -1 model. The Stokes jumping of coefficients and its relation to wall crossing phenomena is briefly discussed. We also find that the notion of "on-the-wall" index is related to the invariant Lefschetz thimbles under Stokes phenomena. An implication of the Lefschetz thimbles in constructing knots from quiver quantummechanics is indicated.
Pastawski, Fernando; Yao, Norman Y.; Jiang, Liang; Lukin, Mikhail D.; Cirac, J. Ignacio
2012-01-01
The realization of devices that harness the laws of quantummechanics represents an exciting challenge at the interface of modern technology and fundamental science. An exemplary paragon of the power of such quantum primitives is the concept of “quantum money” [Wiesner S (1983) ACM SIGACT News 15:78–88]. A dishonest holder of a quantum bank note will invariably fail in any counterfeiting attempts; indeed, under assumptions of ideal measurements and decoherence-free memories such security is guaranteed by the no-cloning theorem. In any practical situation, however, noise, decoherence, and operational imperfections abound. Thus, the development of secure “quantum money”-type primitives capable of tolerating realistic infidelities is of both practical and fundamental importance. Here, we propose a novel class of such protocols and demonstrate their tolerance to noise; moreover, we prove their rigorous security by determining tight fidelity thresholds. Our proposed protocols require only the ability to prepare, store, and measure single quantum bit memories, making their experimental realization accessible with current technologies.
Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne
2017-12-01
Mathematical sense-making—looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world—is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and "science studies" have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level—upper division physics students—especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantummechanics question to illustrate what mathematical sense-making can look like in quantummechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantummechanics. Mathematical sense-making in quantummechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantummechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.
Berry phases and gauge structures are fundamentalquantum phenomena. In linear quantummechanics the gauge field in parameter space presents monopole singularities where the energy levels become degenerate. In nonlinear quantummechanics, which is an effective theory of interacting quantum systems, there can be phase transitions and hence critical surfaces in the parameter space. We find that these critical surfaces result in a new type of gauge field singularity, namely, a conic singularity that resembles the big bang of a 2 + 1 dimensional de Sitter universe, with the fundamental frequency of Bogoliubov excitations acting as the cosmic scale, and mode softening at the critical surface, where the fundamental frequency vanishes, causing a causal singularity. Such conic singularity may be observed in various systems such as Bose-Einstein condensates and molecular magnets. This finding offers a new approach to quantum simulation of fundamental physics.
This article is a revision of two papers submitted to the APS in the past two and a half years. In these papers, arguments and proofs are summarized for the following: (1) The wrong conclusion by EPR that QuantumMechanics is incomplete, perhaps requiring the addition of ``hidden variables'' for completion. Theorems that assume such ``hidden variables,'' such as Bell's theorem, are also wrong. (2) Quantum entanglement is not a realizable physical phenomenon and is based entirely on assuming a probability superposition model for quantum spin. Such a model directly violates conservation of angular momentum. (3) Simultaneous multiple-paths followed by a quantum particle traveling through space also cannot possibly exist. Besides violating Noether's theorem, the multiple-paths theory is based solely on probability calculations. Probability calculations by themselves cannot possibly represent simultaneous physically real events. None of the reviews of the submitted papers actually refuted the arguments and evidence that was presented. These analyses should therefore be carefully evaluated since the conclusions reached have such important impact in quantummechanics and quantum information theory.
Although the presentation of quantummechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantummechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…
Einstein's equivalence principle (EP) states the complete physical equivalence of a gravitational field and corresponding inertial field in an accelerated reference frame. However, to what extent the EP remains valid in non-relativistic quantummechanics is a controversial issue. To avoid violation of the EP, Bargmann's superselection rule forbids a coherent superposition of states with different masses. Here we suggest a quantum simulation of non-relativistic Schrödinger particle dynamics in non-inertial reference frames, which is based on the propagation of polarization-entangled photon pairs in curved and birefringent optical waveguides and Hong-Ou-Mandel quantum interference measurement. The photonic simulator can emulate superposition of mass states, which would lead to violation of the EP.
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantummechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.
We discuss the categorization of 20 quantummechanics problems by physics professors and undergraduate students from two honours-level quantummechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…
Kohnle, Antje; Douglass, Margaret; Edwards, Tom J.; Gillies, Alastair D.; Hooley, Christopher A.; Sinclair, Bruce D.
2010-01-01
In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantummechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantummechanics concepts. They focus on known areas of student difficulty and misconceptions by…
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
2016-10-01
We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalized to the space of Hermitian matrices. This very theory is quantummechanics: in fact, we derive all its four postulates from the generalized Bayesian theory. This implies that quantummechanics is self-consistent. It also leads us to reinterpret the main operations in quantummechanics as probability rules: Bayes' rule (measurement), marginalization (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantummechanics is the Bayesian theory in the complex numbers.
Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantummechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantummechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantummechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.
[This paper is part of the Focused Collection on Upper Division Physics Courses.] Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantummechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantummechanics. The framework posits that the challenges many students face in developing expertise in quantummechanics are analogous to the challenges introductory students face in developing expertise in introductory classical mechanics. This framework incorporates both the effects of diversity in upper-level students' prior preparation, goals, and motivation in general (i.e., the facts that even in upper-level courses, students may be inadequately prepared, have unclear goals, and have insufficient motivation to excel) as well as the "paradigm shift" from classical mechanics to quantummechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantummechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantummechanics and introductory classical mechanics are discussed to illustrate how the patterns of difficulties are analogous as students learn to unpack the respective principles and grasp the formalism in each knowledge domain during the development of expertise. Embracing such a framework and contemplating the parallels between the difficulties in these two knowledge domains can enable researchers to leverage the extensive literature for introductory physics education research to guide the design of teaching and learning tools for helping students develop expertise in quantummechanics.
One of the most widely known building blocks of modern physics is Heisenberg’s indeterminacy principle. Among the different statements of this fundamental property of the full quantummechanical nature of physical reality, the uncertainty relation for energy and time has a special place. Its interpretation and its consequences have inspired continued research efforts for almost a century. In its modern formulation, the uncertainty relation is understood as setting a fundamental bound on how fast any quantum system can evolve. In this topical review we describe important milestones, such as the Mandelstam-Tamm and the Margolus-Levitin bounds on the quantum speed limit, and summarise recent applications in a variety of current research fields—including quantum information theory, quantum computing, and quantum thermodynamics amongst several others. To bring order and to provide an access point into the many different notions and concepts, we have grouped the various approaches into the minimal time approach and the geometric approach, where the former relies on quantum control theory, and the latter arises from measuring the distinguishability of quantum states. Due to the volume of the literature, this topical review can only present a snapshot of the current state-of-the-art and can never be fully comprehensive. Therefore, we highlight but a few works hoping that our selection can serve as a representative starting point for the interested reader.
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantummechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
In this study, students' conceptual difficulties about some basic concepts in quantummechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named QuantumMechanics Conceptual Test has been developed by one of the researchers of this study…
It is argued that, although in the Many-Worlds Interpretation of quantummechanics there is no "probability" for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence between an illegitimate question: "What is the probability of an outcome of a quantum measurement?" with a legitimate question: "What is the probability that `I' am in the world corresponding to that outcome?"; (b) A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and (c) Relativistic causality, which together with (b) explain the Born rule of standard quantummechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing probability measure are discussed.
During the past decades, quantummechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles calculations of systems containing up to a few hundred atoms have become a standard in many branches of science. The sizes of the systems which can be simulated have increased even further during recent years, and quantum-mechanical calculations of systems up to many thousands of atoms are nowadays possible. This opens up new appealing possibilities, in particular for interdisciplinary work, bridging together communities of different needs andmore » sensibilities. In this review we will present the current status of this topic, and will also give an outlook on the vast multitude of applications, challenges and opportunities stimulated by electronic structure calculations, making this field an important working tool and bringing together researchers of many different domains.« less
The QuantumMechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantummechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included…
Lin, Hai; Zhao, Yan; Tishchenko, Oksana; Truhlar, Donald G
2006-09-01
The multiconfiguration molecular mechanics (MCMM) method is a general algorithm for generating potential energy surfaces for chemical reactions by fitting high-level electronic structure data with the help of molecular mechanical (MM) potentials. It was previously developed as an extension of standard MM to reactive systems by inclusion of multidimensional resonance interactions between MM configurations corresponding to specific valence bonding patterns, with the resonance matrix element obtained from quantummechanical (QM) electronic structure calculations. In particular, the resonance matrix element is obtained by multidimensional interpolation employing a finite number of geometries at which electronic-structure calculations of the energy, gradient, and Hessian are carried out. In this paper, we present a strategy for combining MCMM with hybrid quantummechanical molecular mechanical (QM/MM) methods. In the new scheme, electronic-structure information for obtaining the resonance integral is obtained by means of hybrid QM/MM calculations instead of fully QM calculations. As such, the new strategy can be applied to the studies of very large reactive systems. The new MCMM scheme is tested for two hydrogen-transfer reactions. Very encouraging convergence is obtained for rate constants including tunneling, suggesting that the new MCMM method, called QM/MM-MCMM, is a very general, stable, and efficient procedure for generating potential energy surfaces for large reactive systems. The results are found to converge well with respect to the number of Hessians. The results are also compared to calculations in which the resonance integral data are obtained by pure QM, and this illustrates the sensitivity of reaction rate calculations to the treatment of the QM-MM border. For the smaller of the two systems, comparison is also made to direct dynamics calculations in which the potential energies are computed quantummechanically on the fly.
Recently we hear more and more physicists saying, `spacetime is doomed', `spacetime is a mirage', the `end of spacetime', `spacetime is not fundamental but emergent' etc. "Henceforth space by itself and time by itself are doomed to fade into the mere shadows, and only a union of the two will preserve an independent reality." - 1908 Hermann Minkowski. We have come full circle from the time of Minkowski's 1908 statement to the brink of an imminent new age of discovery. The basis of our understanding of the natural world has evolved in modern times from Newtonian Mechanics to the 2nd regime of QuantumMechanics; and now to the threshold of a 3rd regime - Unified Field Mechanics (UFM). The Planck scale stochastic quantum realm can no longer be considered the `basement' or fundamental level of reality. As hard as quantum reality was to imagine so is the fact that the quantum domain is a manifold of finite radius; and that the `sacrosanct - indelible' Quantum Uncertainty Principle can now be surmounted. For decades main stream physicists have been stymied by efforts to reconcile General Relativity with QuantumMechanics. The stumbling block lies with the two theories conflicting views of space and time: For quantum theory, space and time offer a fixed backcloth against which particles move. In Einstein's relativities, space and time are not only inextricably linked, but the resultant spacetime is warped by the matter within it. In our nascent UFM paradigm for arcane reasons the quantum manifold is not the regime of integration with gravity; it is instead integrated with the domain of the unified field where the forces of nature are deemed to unify. We give a simplistic survey of the fundamental premises of UFM and summarize experimental protocols to falsify the model at this stage of the paradigm's development.
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantummechanics and non-relativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantummechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/|x|^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantummechanics. We describe a theoretical framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantummechanics. The framework posits that the challenges many students face in developing expertise in quantummechanics are analogous to the challenges introductory students face in developing expertise in introductory classical mechanics. This framework incorporates the effects of diversity in students' prior preparation, goals and motivation for taking upper-level physics courses in general as well as the ``paradigm shift'' from classical mechanics to quantummechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantummechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantummechanics and introductory classical mechanics will be discussed to illustrate how the patterns of difficulties are analogous as students learn to unpack the respective principles and grasp the formalism in each knowledge domain during the development of expertise. Embracing such a theoretical framework and contemplating the parallels between the difficulties in these two knowledge domains can enable researchers to leverage the extensive literature for introductory physics education research to guide the design of teaching and learning tools for helping students develop expertise in quantummechanics. Support from the National Science Foundation is gratefully acknowledged.
Learning quantummechanics is challenging, even for upper-level undergraduate and graduate students. Research-validated interactive tutorials that build on students' prior knowledge can be useful tools to enhance student learning. We have been investigating student difficulties with quantummechanics pertaining to the double-slit experiment in…
States that the existence of an essential underdetermination in the interpretation of the formalism of quantummechanics, in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics, legitimizes the analysis of hermeneutics in science education. (LZ)
We discuss the question of the dynamical meaning of the second law of thermodynamics in the framework of quantummechanics. Previous discussion of the problem in the framework of classical dynamics has shown that the second law can be given a dynamical meaning in terms of the existence of so-called Lyapounov variables—i.e., dynamical variables varying monotonically in time without becoming contradictory. It has been found that such variables can exist in an extended framework of classical dynamics, provided that the dynamical motion is suitably unstable. In this paper we begin to extend these results to quantummechanics. It is found that no dynamical variable with the characteristic properties of nonequilibrium entropy can be defined in the standard formulation of quantummechanics. However, if the Hamiltonian has certain well-defined spectral properties, such variables can be defined but only as a nonfactorizable superoperator. Necessary nonfactorizability of such entropy operators M has the consequence that they cannot preserve the class of pure states. Physically, this means that the distinguishability between pure states and corresponding mixtures must be lost in the case of a quantal system for which the algebra of observables can be extended to include a new dynamical variable representing nonequilibrium entropy. We discuss how this result leads to a solution of the quantum measurement problem. It is also found that the question of existence of entropy of superoperators M is closely linked to the problem of defining an operator of time in quantummechanics. PMID:16578757
We discuss the generation mechanism of fundamental rogue wave structures in N-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N-component coupled nonlinear Schrödinger equation. Furthermore, our results show that N-component coupled nonlinear Schrödinger systems may possess N different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.
Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic QuantumMechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantummechanics, we develop a unified mathematical framework for classical and quantummechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantummechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantummechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantummechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence
[This paper is part of the Focused Collection on Upper Division Physics Courses.] The time evolution of quantum states is arguably one of the more difficult ideas in quantummechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing the key role of the energy eigenbasis in determining the time dependence of wave functions. Through analysis of student responses to a set of four interrelated tasks, we categorize some of the difficulties that underlie common errors. The conceptual and reasoning difficulties that have been identified are illustrated through student responses to four sets of questions administered at different points in a junior-level course on quantummechanics. Evidence is also given that the problems persist throughout undergraduate instruction and into the graduate level.
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantummechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
Stubbs, Christopher [Harvard University, Cambridge, Massachusetts, USA
2017-12-09
Astrophysical observations provide robust evidence that our current picture of fundamental physics is incomplete. The discovery in 1998 that the expansion of the Universe is accelerating (apparently due to gravitational repulsion between regions of empty space!) presents us with a profound challenge, at the interface between gravity and quantummechanics. This "Dark Energy" problem is arguably the most pressing open question in modern fundamental physics. The first talk will describe why the Dark Energy problem constitutes a crisis, with wide-reaching ramifications. One consequence is that we should probe our understanding of gravity at all accessible scales, and the second talk will present experiments and observations that are exploring this issue.
The Heisenberg-James-Stapp (quantummechanical) mind model is surveyed and criticized briefly. The criticism points out that the model, while being essentially consistent concerning (human) consciousness, fundamentally lacks the evolutional point of view both onto- and phylogenetically. Ethology and other than Jamesian psychology is quoted and a quantummechanical theoretical scheme is suggested to essentially extend Stapp's frame in an evolutionary context. It is proposed that its central supposition, spontaneous quantum measurement can be better utilized in an investigation of the origin of the "subjective" process, having come about concomitantly with the chemistry of the origin of life. We dwell on its applicability at this latter process, at its heart standing, it is supposed, the endophysical nonlinear "self-measurement" of (quantummechanically describable) matter, and so our investigation is extended to this primeval phenomenon. It is suggested that the life phenomenon is an indirect C* → (W*) → C* quantum algebraic process transition, where the (W*) system would represent the living state. Summarized also are our previous results on an internalized, "reversed", time process, introduced originally by Gunji, which is subordinated to the external "forwards" time evolution, driving towards symmetry by gradual space-mappings, where the original splitting-up must have come about in a spontaneous symmetry breaking nonlinear "self-measurement" of matter in an endophysical World.
The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantummechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantummechanics and fractional quantummechanics has been presented to emphasize the features of fractional quantummechanics and to avoid misinterpretations of the fractional uncertainty relation. It has been shown that the fractional probability current equation is correct in the area of its applicability. Further studies have to be done to find meaningful quantum physics problems with involvement of the fractional probability current density vector and the extra term emerging in the framework of fractional quantummechanics.
We study the relative importance of deterioration of material quantum yield and charge balance to the electroluminescence stability of PHOLEDs, with a special emphasis on blue devices. Investigations show that the quantum yields of both host and emitter in the emission layer degrade due to exciton-polaron interactions and that the deterioration in material quantum yield plays the primary role in device degradation under operation. On the other hand, the results show that the charge balance factor is also affected by exciton-polaron interactions but only plays a secondary role in determining device stability. Finally, we show that the degradation mechanisms in blue PHOLEDs are fundamentally the same as those in green PHOLEDs. The limited stability of the blue devices is a result of faster deterioration in the quantum yield of the emitter.
Enzymes have evolved to increase the rate of biological reactions using fundamental physical processes. Until recently, the nature of catalysis has been based upon a classical model but it has since been considered that certain aspects of catalysis, particularly those concerning the transfer of a hydrogen species, may be accounted for using the theory of quantummechanics. This thesis reports the use of reaction paths obtained using QMMM (combined quantummechanics-molecular mechanics), combined with canonical variational transition state theory and multidimensional tunnelling corrections, to study two dehydrogenase enzymes, Liver Alcohol Dehydrogenase (LADH) and Methylamine Dehydrogenase (MADH). These methods are used to investigate the nature of these models in explaining reported experimental data indicative of quantummechanical tunnelling within these enzymes. The results obtained are in good agreement with experimental data indicating the presence of tunnelling in LADH and, to a greater degree, in MADH, reflected in the magnitude of the calculated kinetic isotope effects (KIEs). For LADH, a primary tritium KIE of 5.6 is reported, calculated using transition state theory (TST) with a Wigner tunnelling correction, and compares favourably with an experimental value of 7.1. For MADH, a KIE of 11.1 was determined using canonical variational theory (CVT) with a small curvature tunnelling (SCT) correction, and compared favourably with an experimental value of 16.8. In addition, a relationship is observed between the contribution due to tunnelling in each system and the geometric positioning of the donating and accepting atoms of the transferring species, and is in qualitative agreement with current opinion concerning tunnelling and the dynamic nature of catalysis. Potential energy barriers have been obtained for both systems using QMMM. For LADH, barriers of 8.2 kcal mol-1 and 22.0 kcal mol-1, and reaction energies of -25.7 kcal mol-1 and +3.4 kcal mol-1, are
Zollman, Dean A.; Rebello, N. Sanjay; Hogg, Kirsten
2002-01-01
Explains a hands-on approach to teaching quantummechanics that challenges the belief shared by many physics instructors that quantummechanics is a very abstract subject that cannot be understood until students have learned much of the classical physics. (Contains 23 references.) (Author/YDS)
The transactional interpretation of quantummechanics (TI) is summarized and various points concerning the TI and its relation to the Copenhagen interpretation (CI) are considered. Questions concerning mapping the TI onto the CI, of advanced waves as solutions to proper wave equations, of collapse and the QM formalism, and of the relation of quantummechanical interpretations to experimental tests and results are discussed.
We summarize the transactional interpretation (TI) of quantummechanics (QM) and consider various points concerning the TI and its relation to the Copenhagen interpretation (CI). Questions concerning mapping the TI onto the CI, of advanced waves as solutions to proper wave equations, of collapse and the QM formalism, and of the relation of quantummechanical interpretations to experimental tests and results are discussed.
fundamental The atom Is the atom fundamental? Is the nucleus fundamental? Are protons and neutrons fundamental decay What is the Mechanism giving mass to fundamental particles? What is the Mechanism giving mass to fundamental particles? Part 2 How Does the Higgs Boson get its Mass? Finding the Mass of the Higgs Boson
A long-standing debate over the interpretation of quantummechanics has centered on the meaning of Schroedinger's wave function {psi} for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school(led by Bohr, Heisenberg and Pauli) holds that {psi} provides a complete description of a single electron state; hence the probability interpretation of {psi}{psi}* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school(led by Einstein, de Broglie, Bohm and Jaynes) holds that {psi} represents a statistical ensemble of possible electron states; hence it ismore » an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung(first noticed by Schroedinger) opens a window to particle substructure in quantummechanics that explains the physical significance of the complex phase factor in {psi}. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantummechanics have been foreseen by Lewis Carroll in The Hunting of the Snark{exclamation_point}.« less
The author has previously pointed out some similarities between selforganizing neural networks and quantummechanics. These types of neural networks were originally conceived of as away of emulating the cognitive capabilities of the human brain. Recently extensions of these networks, collectively referred to as deep learning networks, have strengthened the connection between self-organizing neural networks and human cognitive capabilities. In this note we consider whether hardware quantum devices might be useful for emulating neural networks with human-like cognitive capabilities, or alternatively whether implementations of deep learning neural networks using conventional computers might lead to better algorithms for solving the many body Schrodinger equation.
Li, Pengfei; Soudackov, Alexander V; Hammes-Schiffer, Sharon
2018-02-28
The proton-coupled electron transfer (PCET) reaction catalyzed by soybean lipoxygenase has served as a prototype for understanding hydrogen tunneling in enzymes. Herein this PCET reaction is studied with mixed quantummechanical/molecular mechanical (QM/MM) free energy simulations. The free energy surfaces are computed as functions of the proton donor-acceptor (C-O) distance and the proton coordinate, and the potential of mean force is computed as a function of the C-O distance, inherently including anharmonicity. The simulation results are used to calculate the kinetic isotope effects for the wild-type enzyme (WT) and the L546A/L754A double mutant (DM), which have been measured experimentally to be ∼80 and ∼700, respectively. The PCET reaction is found to be exoergic for WT and slightly endoergic for the DM, and the equilibrium C-O distance for the reactant is found to be ∼0.2 Å greater for the DM than for WT. The larger equilibrium distance for the DM, which is due mainly to less optimal substrate binding in the expanded binding cavity, is primarily responsible for its higher kinetic isotope effect. The calculated potentials of mean force are anharmonic and relatively soft at shorter C-O distances, allowing efficient thermal sampling of the shorter distances required for effective hydrogen tunneling. The primarily local electrostatic field at the transferring hydrogen is ∼100 MV/cm in the direction to facilitate proton transfer and increases dramatically as the C-O distance decreases. These simulations suggest that the overall protein environment is important for conformational sampling of active substrate configurations aligned for proton transfer, but the PCET reaction is influenced primarily by local electrostatic effects that facilitate conformational sampling of shorter proton donor-acceptor distances required for effective hydrogen tunneling.
We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize what can be learned from different approaches to a theory of quantum gravity. Then we discuss some models that have been developed to implement a minimal length scale in quantummechanics and quantum field theory. These models have entered the literature as the generalized uncertainty principle or the modified dispersion relation, and have allowed the study of the effects of a minimal length scale in quantummechanics, quantum electrodynamics, thermodynamics, black-hole physics and cosmology. Finally, we touch upon the question of ways to circumvent the manifestation of a minimal length scale in short-distance physics.
Pedersen, Mads Kock; Skyum, Birk; Heck, Robert; Müller, Romain; Bason, Mark; Lieberoth, Andreas; Sherson, Jacob F.
2016-06-01
A virtual learning environment can engage university students in the learning process in ways that the traditional lectures and lab formats cannot. We present our virtual learning environment StudentResearcher, which incorporates simulations, multiple-choice quizzes, video lectures, and gamification into a learning path for quantummechanics at the advanced university level. StudentResearcher is built upon the experiences gathered from workshops with the citizen science game Quantum Moves at the high-school and university level, where the games were used extensively to illustrate the basic concepts of quantummechanics. The first test of this new virtual learning environment was a 2014 course in advanced quantummechanics at Aarhus University with 47 enrolled students. We found increased learning for the students who were more active on the platform independent of their previous performances.
Zhang, Xu; Xiang, Hongping; Zhang, Mingliang; Lu, Gang
2017-09-01
Plasmonic resonance of metallic nanoparticles results from coherent motion of its conduction electrons, driven by incident light. For the nanoparticles less than 10 nm in diameter, localized surface plasmonic resonances become sensitive to the quantum nature of the conduction electrons. Unfortunately, quantummechanical simulations based on time-dependent Kohn-Sham density functional theory are computationally too expensive to tackle metal particles larger than 2 nm. Herein, we introduce the recently developed time-dependent orbital-free density functional theory (TD-OFDFT) approach which enables large-scale quantummechanical simulations of plasmonic responses of metallic nanostructures. Using TD-OFDFT, we have performed quantummechanical simulations to understand size-dependent plasmonic response of Na nanoparticles and plasmonic responses in Na nanoparticle dimers and trimers. An outlook of future development of the TD-OFDFT method is also presented.
This dissertation describes research on student understanding of quantummechanics across multiple levels of instruction. The primary focus has been to identify patterns in student reasoning related to key concepts in quantummechanics. The specific topics include quantum measurements, time dependence, vector spaces, and angular momentum. The research has spanned a variety of different quantum courses intended for introductory physics students, upper-division physics majors, and graduate students in physics. The results of this research have been used to develop a set of curriculum, Tutorials in Physics: QuantumMechanics, for addressing the most persistent student difficulties. We document both the development of this curriculum and how it has impacted and improved student understanding of quantummechanics.
Quantum computing promises an unprecedented ability to solve intractable problems by harnessing quantummechanical effects such as tunneling, superposition, and entanglement. The Quantum Artificial Intelligence Laboratory (QuAIL) at NASA Ames Research Center is the space agency's primary facility for conducting research and development in quantum information sciences. QuAIL conducts fundamental research in quantum physics but also explores how best to exploit and apply this disruptive technology to enable NASA missions in aeronautics, Earth and space sciences, and space exploration. At the same time, machine learning has become a major focus in computer science and captured the imagination of the public as a panacea to myriad big data problems. In this talk, we will discuss how classical machine learning can take advantage of quantum computing to significantly improve its effectiveness. Although we illustrate this concept on a quantum annealer, other quantum platforms could be used as well. If explored fully and implemented efficiently, quantum machine learning could greatly accelerate a wide range of tasks leading to new technologies and discoveries that will significantly change the way we solve real-world problems.
The principle of superposition is an intriguing feature of quantummechanics, which is regularly exploited in many different circumstances. A recent work [M. Oszmaniec et al., Phys. Rev. Lett. 116, 110403 (2016), 10.1103/PhysRevLett.116.110403] shows that the fundamentals of quantummechanics restrict the process of superimposing two unknown pure states, even though it is possible to superimpose two quantum states with partial prior knowledge. The prior knowledge imposes geometrical constraints on the choice of input states. We discuss an experimentally feasible protocol to superimpose multiple pure states of a d -dimensional quantum system and carry out an explicit experimental realization for two single-qubit pure states with partial prior information on a two-qubit NMR quantum information processor.
Laser-cooled atoms are used as freefall test masses. The gravitational acceleration on atoms is measured by atom-wave interferometry. The fundamental concept behind atom interferometry is the quantummechanical particle-wave duality. One can exploit the wave-like nature of atoms to construct an atom interferometer based on matter waves analogous to laser interferometers.
In early 1925, Wolfgang Pauli (1900-1958) published the paper for which he is now most famous and for which he received the Nobel Prize in 1945. The paper detailed what we now know as his "exclusion principle." This essay situates the work leading up to Pauli's principle within the traditions of the "Sommerfeld School," led by Munich University's renowned theorist and teacher, Arnold Sommerfeld (1868-1951). Offering a substantial corrective to previous accounts of the birth of quantummechanics, which have tended to sideline Sommerfeld's work, it is suggested here that both the method and the content of Pauli's paper drew substantially on the work of the Sommerfeld School in the early 1920s. Part One describes Sommerfeld's turn away from a faith in the power of model-based (modellmässig) methods in his early career towards the use of a more phenomenological emphasis on empirical regularities (Gesetzmässigkeiten) during precisely the period that both Pauli and Werner Heisenberg (1901-1976), among others, were his students. Part two delineates the importance of Sommerfeld's phenomenology to Pauli's methods in the exclusion principle paper, a paper that also eschewed modellmässig approaches in favour of a stress on Gesetzmässigkeiten. In terms of content, a focus on Sommerfeld's work reveals the roots of Pauli's understanding of the fundamental Zweideutigkeit (ambiguity) involving the quantum number of electrons within the atom. The conclusion points to the significance of these results to an improved historical understanding of the origin of aspects of Heisenberg's 1925 paper on the "Quantum-theoretical Reformulation (Umdeutung) of Kinematical and Mechanical Relations."
Togan, E; Chu, Y; Trifonov, A S; Jiang, L; Maze, J; Childress, L; Dutt, M V G; Sørensen, A S; Hemmer, P R; Zibrov, A S; Lukin, M D
2010-08-05
Quantum entanglement is among the most fascinating aspects of quantum theory. Entangled optical photons are now widely used for fundamental tests of quantummechanics and applications such as quantum cryptography. Several recent experiments demonstrated entanglement of optical photons with trapped ions, atoms and atomic ensembles, which are then used to connect remote long-term memory nodes in distributed quantum networks. Here we realize quantum entanglement between the polarization of a single optical photon and a solid-state qubit associated with the single electronic spin of a nitrogen vacancy centre in diamond. Our experimental entanglement verification uses the quantum eraser technique, and demonstrates that a high degree of control over interactions between a solid-state qubit and the quantum light field can be achieved. The reported entanglement source can be used in studies of fundamentalquantum phenomena and provides a key building block for the solid-state realization of quantum optical networks.
Why is quantummechanics considered a hard and inaccessible subject? Part of the difficulty is due to the nature of the subject itself. However, no small part of the difficulty is its pedagogy, which often relies on out-of-date historical motivation and experimental evidence that is disconnected from day-to-day experiences. In this first talk, we explore ways in which video games are well-suited to teaching quantummechanics, in particular with regards to building intuition, as well as some of their limitations. We then illustrate these considerations through qCraft, an extension for Minecraft that incorporates aspects of quantummechanics into the game.
Kohnle, Antje; Benfield, Cory; Hahner, Georg; Paetkau, Mark
2017-01-01
The QuVis QuantumMechanics Visualization Project provides freely available research-based interactive simulations with accompanying activities for the teaching and learning of quantummechanics across a wide range of topics and levels. This article gives an overview of some of the simulations and describes their use in an introductory physical…
Partanen, Matti; Tan, Kuan Yen; Govenius, Joonas; Lake, Russell E.; Mäkelä, Miika K.; Tanttu, Tuomo; Möttönen, Mikko
2016-05-01
The emerging quantum technological apparatuses, such as the quantum computer, call for extreme performance in thermal engineering. Cold distant heat sinks are needed for the quantized electric degrees of freedom owing to the increasing packaging density and heat dissipation. Importantly, quantummechanics sets a fundamental upper limit for the flow of information and heat, which is quantified by the quantum of thermal conductance. However, the short distance between the heat-exchanging bodies in the previous experiments hinders their applicability in quantum technology. Here, we present experimental observations of quantum-limited heat conduction over macroscopic distances extending to a metre. We achieved this improvement of four orders of magnitude in the distance by utilizing microwave photons travelling in superconducting transmission lines. Thus, it seems that quantum-limited heat conduction has no fundamental distance cutoff. This work establishes the integration of normal-metal components into the framework of circuit quantum electrodynamics, which provides a basis for the superconducting quantum computer. Especially, our results facilitate remote cooling of nanoelectronic devices using faraway in situ-tunable heat sinks. Furthermore, quantum-limited heat conduction is important in contemporary thermodynamics. Here, the long distance may lead to ultimately efficient mesoscopic heat engines with promising practical applications.
Quantum information theory deals with quantum noise in order to protect physical quantum bits (qubits) from its effects. A single electron is an emblematic example of a qubit, and today it is possible to experimentally produce polarized ensembles of electrons. In this paper, the theory of the polarization of electron beams elastically scattered by atoms is briefly summarized. Then the POLARe program suite, a set of computer programs aimed at the calculation of the spin-polarization parameters of electron beams elastically interacting with atomic targets, is described. Selected results of the program concerning Ar, Kr, and Xe atoms are presented together with the comparison with experimental data about the Sherman function for low kinetic energy of the incident electrons (1.5eV-350eV). It is demonstrated that the quantum-relativistic theory of the polarization of electron beams elastically scattered by atoms is in good agreement with experimental data down to energies smaller than a few eV.
Nwokoye, Chidubem; Siddique, Abid; Bennett, Lawrence; Della Torre, Edward; IMR Team
Quantum entanglement is a unique quantummechanical effect that arises from the correlation between two or more quantum systems. The fundamental aspects of magnon entanglement has been theoretical studied and the interest in developing technologies that exploits quantum entanglement is growing. We discuss the results of an experimental study of magnon entanglement in multilayered CoPd ferromagnets. Our findings are interesting and will aid in developing novel magnonic devices. Office of Naval Research.
Time dynamics of isolated many-body quantum systems has long been an elusive subject, perhaps most urgently needed in the foundations of quantum statistical mechanics. In generic systems, one expects the nonequilibrium dynamics to lead to thermalization: a relaxation to states where the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable through the time-tested recipe of statistical mechanics. The relaxation mechanism is not obvious, however; dynamical chaos cannot play the key role as it does in classical systems since quantum evolution is linear. Here we demonstrateootnotetextM. Rigol, V. Dunjko, and M. Olshanii, to appear in Nature (2008), using the results of an ab initio numerical experiment with 5 hard-core bosons moving in a 5x5 lattice, that in quantum systems thermalization happens not in course of time evolution but instead at the level of individual eigenstates, as first proposed by DeutschootnotetextJ. M. Deutsch, Phys.Rev. A 43, 2046 (1991) and SrednickiootnotetextM. Srednicki, Phys. Rev. E 50, 888 (1994).
We study two different models of optomechanical systems where a temperature gradient between two radiation baths is exploited for inducing self-sustained coherent oscillations of a mechanical resonator. From a thermodynamic perspective, such systems represent quantum instances of self-contained thermal machines converting heat into a periodic mechanical motion and thus they can be interpreted as nano-scale analogues of macroscopic piston engines. Our models are potentially suitable for testing fundamental aspects of quantum thermodynamics in the laboratory and for applications in energy efficient nanotechnology.
Why, despite all efforts to the contrary, have attempts at unification based on the supposedly more fundamentalquantum theory failed miserably? The truth is that the essential idea or concept of the quantum itself has never been fully understood. What is the quantum, or rather, what is its ultimate nature? Science may be able to work adequately with the quantum; in a sense science is quite articulate in the language of the quantum, i.e., its mathematical interpretation of the quantummechanics, but science has no idea of the true physical nature of the quantum. Scientists and philosophers have wasted energy and efforts on irrelevant issues such as the debate over determinism and indeterminism instead of carefully analyzing the physical source of the quantum. Only with a true understanding of the physical nature of the quantum will the unification of the quantum and relativity ever become a reality.
Quantum geometrodynamics with intrinsic time development and momentric variables is presented. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together with its ground state and primordial quantum fluctuations. Cotton-York potential dominates at early times when the universe was small; the ground state naturally resolves Penrose's Weyl curvature hypothesis, and thermodynamic and gravitational "arrows of time" point in the same direction. Ricci scalar potential corresponding to Einstein's general relativity emerges as a zero-point energy contribution. A new set of fundamental commutation relations without Planck's constant emerges from the unification of gravitation and quantummechanics.
Eagle, Forrest W.; Seaney, Kyser D.; Grubb, Michael P.
2017-01-01
Quantummechanics is a notoriously difficult subject to learn, due to a lack of real-world analogies that might help provide an intuitive grasp of the underlying ideas. Discrete energy levels and absorption and emission wavelengths in atoms are sometimes described as uniquely quantum phenomena, but are actually general to spatially confined waves…
Quantummechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of `time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on re ection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantummechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.
The development of quantum optics was part and parcel of the formation of modern physics following the fundamental work of Max Planck and Albert Einstein, which gave rise to quantummechanics. The possibility of working with pure quantum objects, like single atoms and single photons, has turned quantum optics into the main tool for testing the fundamentals of quantum physics. Thus, despite a long history, quantum optics nowadays remains an extremely important branch of physics. It represents a natural base for the development of advanced technologies, like quantum information processing and quantum computing. Previous Central European Workshops on Quantum Optics (CEWQO) took place in Palermo (2007), Vienna (2006), Ankara (2005), Trieste (2004), Rostock (2003), Szeged (2002), Prague (2001), Balatonfüred (2000), Olomouc (1999), Prague (1997), Budmerice (1995, 1996), Budapest (1994) and Bratislava (1993). Those meetings offered excellent opportunities for the exchange of knowledge and ideas between leading scientists and young researchers in quantum optics, foundations of quantummechanics, cavity quantum electrodynamics, photonics, atom optics, condensed matter optics, and quantum informatics, etc. The collaborative spirit and tradition of CEWQO were a great inspiration and help to the Institute of Physics, Belgrade, and the Serbian Academy of Sciences and Arts, as the organizers of CEWQO 2008. The 16th CEWQO will take place in 2009 in Turku, Finland, and the 17th CEWQO will be organized in 2010 in St Andrews, United Kingdom. The 15th CEWQO was organized under the auspices and support of the Ministry of Science of the Republic of Serbia, the Serbian Physical Society, the European Physical Society with sponsorship from the University of Belgrade, the Central European Initiative, the FP6 Program of the European Commission under INCO project QUPOM No 026322, the FP7 Program of the European Commission under project NANOCHARM, Europhysics Letters (EPL), The European
The second of six instructional blocks in automotive mechanics, the lessons and supportive information in the document provide a guide for teachers in planning an instructional program in engine fundamentals at the secondary and postsecondary level. The material, as organized, is a suggested sequence of instruction within each block. Each lesson…
The lectures that follow were originally given in 1992, and written up only slightly later. Since then there have been dramatic developments in the quantum theory of black holes, especially in the context of string theory. None of these are reflected here. The concept of quantum hair, which is discussed at length in the lectures, is certainly of permanent interest, and I continue to believe that in some generalized form it will prove central to the whole question of how information is stored in black holes. The discussion of scattering and emission modes from various classes of black holes could be substantially simplified using modern techniques, and from currently popular perspectives the choice of examples might look eccentric. On the other hand fashions have changed rapidly in the field, and the big questions as stated and addressed here, especially as formulated for "real" black holes (nonextremal, in four-dimensional, asymptotically flat space-time, with supersymmetry broken), remain pertinent even as the tools to address them may evolve. The four lectures I gave at the school were based on two lengthy papers that have now been published, "Black Holes as Elementary Particles," Nuclear Physics B380, 447 (1992) and "Quantum Hair on Black Holes," Nuclear Physics B378, 175 (1992). The unifying theme of this work is to help make plausible the possibility that black holes, although they are certainly unusual and extreme states of matter, may be susceptible to a description using concepts that are not fundamentally different from those we use in describing other sorts of quantum-mechanical matter. In the first two lectures I discussed dilaton black holes. The fact that apparently innocuous changes in the "matter" action can drastically change the properties of a black hole is already very significant: it indicates that the physical properties of small black holes cannot be discussed reliably in the abstract, but must be considered with due regard to the rest of
Astrophysical observations provide robust evidence that our current picture of fundamental physics is incomplete. The discovery in 1998 that the expansion of the Universe is accelerating (apparently due to gravitational repulsion between regions of empty space!) presents us with a profound challenge, at the interface between gravity and quantummechanics. This "Dark Energy" problem is arguably the most pressing open question in modern fundamental physics. The first talk will describe why the Dark Energy problem constitutes a crisis, with wide-reaching ramifications. One consequence is that we should probe our understanding of gravity at all accessible scales, and the second talkmore » will present experiments and observations that are exploring this issue.« less
The faithful storage of a quantum bit (qubit) of light is essential for long-distance quantum communication, quantum networking and distributed quantum computing. The required optical quantum memory must be able to receive and recreate the photonic qubit; additionally, it must store an unknown quantum state of light better than any classical device. So far, these two requirements have been met only by ensembles of material particles that store the information in collective excitations. Recent developments, however, have paved the way for an approach in which the information exchange occurs between single quanta of light and matter. This single-particle approach allows the material qubit to be addressed, which has fundamental advantages for realistic implementations. First, it enables a heralding mechanism that signals the successful storage of a photon by means of state detection; this can be used to combat inevitable losses and finite efficiencies. Second, it allows for individual qubit manipulations, opening up avenues for in situ processing of the stored quantum information. Here we demonstrate the most fundamental implementation of such a quantum memory, by mapping arbitrary polarization states of light into and out of a single atom trapped inside an optical cavity. The memory performance is tested with weak coherent pulses and analysed using full quantum process tomography. The average fidelity is measured to be 93%, and low decoherence rates result in qubit coherence times exceeding 180 microseconds. This makes our system a versatile quantum node with excellent prospects for applications in optical quantum gates and quantum repeaters.
Yuan, Gangcheng; Gómez, Daniel E; Kirkwood, Nicholas; Boldt, Klaus; Mulvaney, Paul
2018-04-24
Many potential applications of quantum dots (QDs) can only be realized once the luminescence from single nanocrystals (NCs) is understood. These applications include the development of quantum logic devices, single-photon sources, long-life LEDs, and single-molecule biolabels. At the single-nanocrystal level, random fluctuations in the QD photoluminescence occur, a phenomenon termed blinking. There are two competing models to explain this blinking: Auger recombination and surface trap induced recombination. Here we use lifetime scaling on core-shell chalcogenide NCs to demonstrate that both types of blinking occur in the same QDs. We prove that Auger-blinking can yield single-exponential on/off times in contrast to earlier work. The surface passivation strategy determines which blinking mechanism dominates. This study summarizes earlier studies on blinking mechanisms and provides some clues that stable single QDs can be engineered for optoelectronic applications.
Y. Aharonov and A. Shimony both conjectured that two axioms - relativistic causality (``no superluminal signalling'') and nonlocality - so nearly contradict each other that only quantummechanics reconciles them. Can we indeed derive quantummechanics, at least in part, from these two axioms? No: ``PR-box'' correlations show that quantum correlations are not the most nonlocal correlations consistent with relativistic causality. Here we replace ``nonlocality'' with ``retrocausality'' and supplement the axioms of relativistic causality and retrocausality with a natural and minimal third axiom: the existence of a classical limit, in which macroscopic observables commute. That is, just as quantummechanics has a classical limit, so must any generalization of quantummechanics. In this limit, PR-box correlations violaterelativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound (a theorem of quantummechanics) from the three axioms of relativistic causality, retrocausality and the existence of a classical limit. Although the derivation does not assume quantummechanics, it points to the Hilbert space structure that underlies quantum correlations. I thank the John Templeton Foundation (Project ID 43297) and the Israel Science Foundation (Grant No. 1190/13) for support.
Kleinmann, Matthias; Osborne, Tobias J.; Scholz, Volkher B.; Werner, Albert H.
2013-01-01
What singles out quantummechanics as the fundamental theory of nature? Here we study local measurements in generalized probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantummechanics. Our result makes use of a generalization of Dvoretzky’s theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantummechanics, however.
Multiscale modeling has become a popular tool for research applying to different areas including materials science, microelectronics, biology, chemistry, etc. In this tutorial review, we describe a newly developed multiscale computational method, incorporating quantummechanics into electronic device modeling with the electromagnetic environment included through classical electrodynamics. In the quantummechanics/electromagnetics (QM/EM) method, the regions of the system where active electron scattering processes take place are treated quantummechanically, while the surroundings are described by Maxwell's equations and a semiclassical drift-diffusion model. The QM model and the EM model are solved, respectively, in different regions of the system in a self-consistent manner. Potential distributions and current densities at the interface between QM and EM regions are employed as the boundary conditions for the quantummechanical and electromagnetic simulations, respectively. The method is illustrated in the simulation of several realistic systems. In the case of junctionless field-effect transistors, transfer characteristics are obtained and a good agreement between experiments and simulations is achieved. Optical properties of a tandem photovoltaic cell are studied and the simulations demonstrate that multiple QM regions are coupled through the classical EM model. Finally, the study of a carbon nanotube-based molecular device shows the accuracy and efficiency of the QM/EM method.
Of course, there is no one- or two-week shortcut by which nonspecialists can master enough quantummechanics to become informed users of quantum chemical techniques. Nevertheless, a text that integrated the fundamentals of quantum theory with a rigorous introduction to quantum chemistry could help instructors design a class that would benefit both these nonspecialists and graduate students in physical chemistry. Could such a class overcome the (undeserved) stigma associated with the physical chemistry curriculum? That remains to be seen.
A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr-Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit G\\to 0, where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.
In this Perspective, several developments in the field of quantummechanics/molecular mechanics (QM/MM) approaches are reviewed. Emphasis is placed on the use of correlated wavefunction theory and new state of the art methods for the treatment of large quantum systems. Until recently, computational chemistry approaches to large/complex chemical problems have seldom been considered as tools for quantitative predictions. However, due to the tremendous development of computational resources and new quantum chemical methods, it is nowadays possible to describe the electronic structure of biomolecules at levels of theory which a decade ago were only possible for system sizes of up to 20 atoms. These advances are here outlined in the context of QM/MM. The article concludes with a short outlook on upcoming developments and possible bottlenecks for future applications.
Correa, Luis A.; Palao, José P.; Alonso, Daniel; Adesso, Gerardo
2014-01-01
Thermodynamics is a branch of science blessed by an unparalleled combination of generality of scope and formal simplicity. Based on few natural assumptions together with the four laws, it sets the boundaries between possible and impossible in macroscopic aggregates of matter. This triggered groundbreaking achievements in physics, chemistry and engineering over the last two centuries. Close analogues of those fundamental laws are now being established at the level of individual quantum systems, thus placing limits on the operation of quantum-mechanical devices. Here we study quantum absorption refrigerators, which are driven by heat rather than external work. We establish thermodynamic performance bounds for these machines and investigate their quantum origin. We also show how those bounds may be pushed beyond what is classically achievable, by suitably tailoring the environmental fluctuations via quantum reservoir engineering techniques. Such superefficient quantum-enhanced cooling realises a promising step towards the technological exploitation of autonomous quantum refrigerators. PMID:24492860
Quantum physics revolutionized classical disciplines of mechanics, statistical physics, and electrodynamics. One branch of scientific knowledge however seems untouched: thermodynamics. Major motivation behind thermodynamics is to develop efficient heat engines. Technology has a trend to miniaturize engines, reaching to quantum regimes. Development of quantum heat engines (QHEs) requires emerging field of quantum thermodynamics. Studies of QHEs debate whether quantum coherence can be used as a resource. We explore an alternative where it can function as an effective catalyst. We propose a QHE which consists of a photon gas inside an optical cavity as the working fluid and quantum coherent atomic clusters as the fuel. Utilizing the superradiance, where a cluster can radiate quadratically faster than a single atom, we show that the work output becomes proportional to the square of the number of the atoms. In addition to practical value of cranking up QHE, our result is a fundamental difference of a quantum fuel from its classical counterpart.
Styer, Daniel F.; Balkin, Miranda S.; Becker, Kathryn M.; Burns, Matthew R.; Dudley, Christopher E.; Forth, Scott T.; Gaumer, Jeremy S.; Kramer, Mark A.; Oertel, David C.; Park, Leonard H.; Rinkoski, Marie T.; Smith, Clait T.; Wotherspoon, Timothy D.
2002-03-01
Nine formulations of nonrelativistic quantummechanics are reviewed. These are the wavefunction, matrix, path integral, phase space, density matrix, second quantization, variational, pilot wave, and Hamilton-Jacobi formulations. Also mentioned are the many-worlds and transactional interpretations. The various formulations differ dramatically in mathematical and conceptual overview, yet each one makes identical predictions for all experimental results.
The Horizon QuantumMechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon QuantumMechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem disfavoured.
Bond, Rachael L.; He, Yang-Hui; Ormerod, Thomas C.
The ability to calculate precise likelihood ratios is fundamental to science, from Quantum Information Theory through to Quantum State Estimation. However, there is no assumption-free statistical methodology to achieve this. For instance, in the absence of data relating to covariate overlap, the widely used Bayes’ theorem either defaults to the marginal probability driven “naive Bayes’ classifier”, or requires the use of compensatory expectation-maximization techniques. This paper takes an information-theoretic approach in developing a new statistical formula for the calculation of likelihood ratios based on the principles of quantum entanglement, and demonstrates that Bayes’ theorem is a special case of a more general quantummechanical expression.
These proceedings comprise the invited lectures of the second international symposium on Emergent QuantumMechanics (EmQM13), which was held at the premises of the Austrian Academy of Sciences in Vienna, Austria, 3-6 October 2013. The symposium was held at the ''Theatersaal'' of the Academy of Sciences, and was devoted to the open exploration of emergent quantummechanics, a possible ''deeper level theory'' that interconnects three fields of knowledge: emergence, the quantum, and information. Could there appear a revised image of physical reality from recognizing new links between emergence, the quantum, and information? Could a novel synthesis pave the way towards a 21st century, ''superclassical'' physics? The symposium provided a forum for discussing (i) important obstacles which need to be overcome as well as (ii) promising developments and research opportunities on the way towards emergent quantummechanics. Contributions were invited that presented current advances in both standard as well as unconventional approaches to quantummechanics. The EmQM13 symposium was co-organized by Gerhard Grössing (Austrian Institute for Nonlinear Studies (AINS), Vienna), and by Jan Walleczek (Fetzer Franklin Fund, USA, and Phenoscience Laboratories, Berlin). After a very successful first conference on the same topic in 2011, the new partnership between AINS and the Fetzer Franklin Fund in producing the EmQM13 symposium was able to further expand interest in the promise of emergent quantummechanics. The symposium consisted of two parts, an opening evening addressing the general public, and the scientific program of the conference proper. The opening evening took place at the Great Ceremonial Hall (Grosser Festsaal) of the Austrian Academy of Sciences, and it presented talks and a panel discussion on ''The Future of QuantumMechanics'' with three distinguished speakers: Stephen Adler (Princeton), Gerard 't Hooft (Utrecht) and Masanao Ozawa (Nagoya). The articles contained in
We give a review of the basic themes of my recent book: Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press). We first give motivations for considering the possibility that quantummechanics is not exact, but is instead an accurate asymptotic approximation to a deeper level theory. For this deeper level, we propose a non-commutative generalization of classical mechanics, that we call "trace dynamics", and we give a brief survey of how it works, considering for simplicity only the bosonic case. We then discuss the statistical mechanics of trace dynamics and give our argument that with suitable approximations, the Ward identities for trace dynamics imply that ensemble averages in the canonical ensemble correspond to Wightman functions in quantum field theory. Thus, quantum theory emerges as the statistical thermodynamics of trace dynamics. Finally, we argue that Brownian motion corrections to this thermodynamics lead to stochastic corrections to the Schrödinger equation, of the type that have been much studied in the "continuous spontaneous localization" model of objective state vector reduction. In appendices to the talk, we give details of the existence of a conserved operator in trace dynamics that encodes the structure of the canonical algebra, of the derivation of the Ward identities, and of the proof that the stochastically-modified Schrödinger equation leads to state vector reduction with Born rule probabilities.
Research-based tools to educate college students in physics courses from introductory level to graduate level are essential for helping students with a diverse set of goals and backgrounds learn physics. This thesis explores issues related to student common difficulties with some topics in undergraduate quantummechanics and thermodynamics courses. Student difficulties in learning quantummechanics and thermodynamics are investigated by administering written tests and surveys to many classes and conducting individual interviews with a subset of students outside the class to unpack the cognitive mechanisms of the difficulties. The quantummechanics research also focuses on using the research on student difficulties for the development and evaluation of a Quantum Interactive Learning Tutorial (QuILT) to help students learn about the time-dependence of expectation values using the context of Larmor precession of spin and evaluating the role of asking students to self-diagnose their mistakes on midterm examination on their performance on subsequent problem solving. The QuILT on Larmor precession of spin has both paper-pencil activities and a simulation component to help students learn these foundational issues in quantummechanics. Preliminary evaluations suggest that the QuILT, which strives to help students build a robust knowledge structure of time-dependence of expectation values in quantummechanics using a guided approach, is successful in helping students learn these topics in the junior-senior level quantummechanics courses. The technique to help upper-level students in quantummechanics courses effectively engage in the process of learning from their mistakes is also found to be effective. In particular, research shows that the self-diagnosis activity in upper-level quantummechanics significantly helps students who are struggling and this activity can reduce the gap between the high and low achieving students on subsequent problem solving. Finally, a survey
Walter, Stefan; Nunnenkamp, Andreas; Bruder, Christoph
2014-03-07
Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical self-sustained oscillator coupled to an external harmonic drive. Using the power spectrum we analyze synchronization in terms of frequency entrainment and frequency locking in close analogy to the classical case. We show that there is a steplike crossover to a synchronized state as a function of the driving strength. In contrast to the classical case, there is a finite threshold value in driving. Quantum noise reduces the synchronized region and leads to a deviation from strict frequency locking.
Quantummechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantummechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantummechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.
Quantummechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantummechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantummechanics is constructed usingmore » geometrical quantities. This suggests that quantum theory has its roots in information geometry.« less
Assuming a background in basic classical physics, multivariable calculus, and differential equations, A Concise Introduction to QuantumMechanics provides a self-contained presentation of the mathematics and physics of quantummechanics. The relevant aspects of classical mechanics and electrodynamics are reviewed, and the basic concepts of wave-particle duality are developed as a logical outgrowth of experiments involving blackbody radiation, the photoelectric effect, and electron diffraction. The Copenhagen interpretation of the wave function and its relation to the particle probability density is presented in conjunction with Fourier analysis and its generalization to function spaces. These concepts are combined to analyze the system consisting of a particle confined to a box, developing the probabilistic interpretation of observations and their associated expectation values. The Schrödinger equation is then derived by using these results and demanding both Galilean invariance of the probability density and Newtonian energy-momentum relations. The general properties of the Schrödinger equation and its solutions are analyzed, and the theory of observables is developed along with the associated Heisenberg uncertainty principle. Basic applications of wave mechanics are made to free wave packet spreading, barrier penetration, the simple harmonic oscillator, the Hydrogen atom, and an electric charge in a uniform magnetic field. In addition, Dirac notation, elements of Hilbert space theory, operator techniques, and matrix algebra are presented and used to analyze coherent states, the linear potential, two state oscillations, and electron diffraction. Applications are made to photon and electron spin and the addition of angular momentum, and direct product multiparticle states are used to formulate both the Pauli exclusion principle and quantum decoherence. The book concludes with an introduction to the rotation group and the general properties of angular momentum.
Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.
Proteasome is the major component of the crucial nonlysosomal protein degradation pathway in the cells, but the detailed reaction pathway is unclear. In this study, first-principles quantummechanical/molecular mechanical free energy calculations have been performed to explore, for the first time, possible reaction pathways for proteasomal proteolysis/hydrolysis of a representative peptide, succinyl-leucyl-leucyl-valyl-tyrosyl-7-amino-4-methylcoumarin (Suc-LLVY-AMC). The computational results reveal that the most favorable reaction pathway consists of six steps. The first is a water-assisted proton transfer within proteasome, activating Thr1-Oγ. The second is a nucleophilic attack on the carbonyl carbon of a Tyr residue of substrate by the negatively charged Thr1-Oγ, followed by the dissociation of the amine AMC (third step). The fourth step is a nucleophilic attack on the carbonyl carbon of the Tyr residue of substrate by a water molecule, accompanied by a proton transfer from the water molecule to Thr1-Nz. Then, Suc-LLVY is dissociated (fifth step), and Thr1 is regenerated via a direct proton transfer from Thr1-Nz to Thr1-Oγ. According to the calculated energetic results, the overall reaction energy barrier of the proteasomal hydrolysis is associated with the transition state (TS3b) for the third step involving a water-assisted proton transfer. The determined most favorable reaction pathway and the rate-determining step have provided a reasonable interpretation of the reported experimental observations concerning the substituent and isotopic effects on the kinetics. The calculated overall free energy barrier of 18.2 kcal/mol is close to the experimentally-derived activation free energy of ~18.3–19.4 kcal/mol, suggesting that the computational results are reasonable. PMID:24111489
Coherently manipulating multipartite quantum correlations leads to remarkable advantages in quantum information processing. A fundamental question is whether such quantum advantages persist only by exploiting multipartite correlations, such as entanglement. Recently, Dale, Jennings, and Rudolph negated the question by showing that a randomness processing, quantum Bernoulli factory, using quantum coherence, is strictly more powerful than the one with classical mechanics. In this Letter, focusing on the same scenario, we propose a theoretical protocol that is classically impossible but can be implemented solely using quantum coherence without entanglement. We demonstrate the protocol by exploiting the high-fidelity quantum state preparation and measurement with a superconducting qubit in the circuit quantum electrodynamics architecture and a nearly quantum-limited parametric amplifier. Our experiment shows the advantage of using quantum coherence of a single qubit for information processing even when multipartite correlation is not present.
Han, Jaebeom; Mazack, Michael J M; Zhang, Peng; Truhlar, Donald G; Gao, Jiali
2013-08-07
A quantummechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantummechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantummechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantummechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantummechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 × 10(6) self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across
Partanen, Matti; Tan, Kuan Yen; Govenius, Joonas; Lake, Russell E.; Mäkelä, Miika K.; Tanttu, Tuomo; Möttönen, Mikko
2016-01-01
The emerging quantum technological apparatuses1, 2, such as the quantum computer3–6, call for extreme performance in thermal engineering7. Cold distant heat sinks are needed for the quantized electric degrees of freedom due to the increasing packaging density and heat dissipation. Importantly, quantummechanics sets a fundamental upper limit for the flow of information and heat, which is quantified by the quantum of thermal conductance8–10. However, the short distance between the heat-exchanging bodies in the previous experiments11–14 hinders their applicability in quantum technology. Here, we present experimental observations of quantum-limited heat conduction over macroscopic distances extending to a metre. We achieved this improvement of four orders of magnitude in the distance by utilizing microwave photons travelling in superconducting transmission lines. Thus, it seems that quantum-limited heat conduction has no fundamental distance cutoff. This work establishes the integration of normal-metal components into the framework of circuit quantum electrodynamics15–17 which provides a basis for the superconducting quantum computer18–21. Especially, our results facilitate remote cooling of nanoelectronic devices using far-away in-situ-tunable heat sinks22, 23. Furthermore, quantum-limited heat conduction is important in contemporary thermodynamics24, 25. Here, the long distance may lead to ultimately efficient mesoscopic heat engines with promising practical applications26. PMID:27239219
Sinitskiy, Anton V.; Voth, Gregory A., E-mail: gavoth@uchicago.edu
2015-09-07
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionistmore » perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantummechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.« less
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantummechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantummechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for themore » quantum evolution (the existence of which has been proved for certain classes of quantummechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.« less
During his famous 1943 lecture series at Trinity College Dublin, the reknown physicist Erwin Schrodinger discussed the failure and challenges of interpreting life by classical physics alone and that a new approach, rooted in Quantum principles, must be involved. Quantum events are simply a level of organization below the molecular level. This includes the atomic and subatomic makeup of matter in microbial metabolism and structures, as well as the organic, genetic information code of DNA and RNA. Quantum events at this time do not elucidate, for example, how specific genetic instructions were first encoded in an organic genetic code in microbial cells capable of growth and division, and its subsequent evolution over 3.6 to 4 billion years. However, due to recent technological advances, biologists and physicists are starting to demonstrate linkages between various quantum principles like quantum tunneling, entanglement and coherence in biological processes illustrating that nature has exerted some level quantum control to optimize various processes in living organisms. In this article we explore the role of quantum events in microbial processes and endeavor to show that after nearly 67 years, Schrödinger was prophetic and visionary in his view of quantum theory and its connection with some of the fundamentalmechanisms of life.
ödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantummechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantummechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.
Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantummechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantummechanics. The framework posits that…
Motivated by recent work in density matrix embedding theory, we define exact link orbitals that capture all quantummechanical (QM) effects across arbitrary quantummechanics/molecular mechanics (QM/MM) boundaries. Exact link orbitals are rigorously defined from the full QM solution, and their number is equal to the number of orbitals in the primary QM region. Truncating the exact set yields a smaller set of link orbitals optimal with respect to reproducing the primary region density matrix. We use the optimal link orbitals to obtain insight into the limits of QM/MM boundary treatments. We further analyze the popular general hybrid orbital (GHO) QM/MM boundary across a test suite of molecules. We find that GHOs are often good proxies for the most important optimal link orbital, although there is little detailed correlation between the detailed GHO composition and optimal link orbital valence weights. The optimal theory shows that anions and cations cannot be described by a single link orbital. However, expanding to include the second most important optimal link orbital in the boundary recovers an accurate description. The second optimal link orbital takes the chemically intuitive form of a donor or acceptor orbital for charge redistribution, suggesting that optimal link orbitals can be used as interpretative tools for electron transfer. We further find that two optimal link orbitals are also sufficient for boundaries that cut across double bonds. Finally, we suggest how to construct "approximately" optimal link orbitals for practical QM/MM calculations.
The long-standing conceptual controversies concerning the interpretation of nonrelativistic quantummechanics are argued, on one hand, to be due to its incompleteness, as affirmed by Einstein. But on the other hand, it appears to be possible to complete it at least partially, as Bohr might have appreciated it, in the framework of its standard mathematical formalism with observables as appropriately defined self-adjoint operators. This completion of quantummechanics is based on the requirement on laboratory physics to be effectively confined to a bounded space region and on the application of the von Neumann deficiency theorem to properly define a set of self-adjoint extensions of standard observables, e.g. the momenta and the Hamiltonian, in terms of certain isometries on the region boundary. This is formalized mathematically in the setting of a boundary ontology for the so-called Qbox in which the wave function acquires a supplementary dependence on a set of Additional Boundary Variables (ABV). It is argued that a certain geometric subset of the ABV parametrizing Quasi-Periodic Translational Isometries (QPTI) has a particular physical importance by allowing for the definition of an ontic wave function, which has the property of epitomizing the spatial wave function “collapse.” Concomitantly the standard wave function in an unbounded geometry is interpreted as an epistemic wave function, which together with the ontic QPTI wave function gives rise to the notion of two-wave duality, replacing the standard concept of wave-particle duality. More generally, this approach to quantum physics in a bounded geometry provides a novel analytical basis for a better understanding of several conceptual notions of quantummechanics, including reality, nonlocality, entanglement and Heisenberg’s uncertainty relation. The scope of this analysis may be seen as a foundational update of the multiple versions 1.x of the Copenhagen interpretation of quantummechanics, which is
It is a fundamental problem in physics of what principle limits the correlations as predicted by our current description of nature, based on quantummechanics. One possible explanation is the "global exclusivity" principle recently discussed in Phys. Rev. Lett. 110, 060402 (2013). In this work we show that this principle actually has a much stronger restriction on the probability distribution. We provide a tight constraint inequality imposed by this principle and prove that this principle singles out quantum correlations in scenarios represented by any graph. Our result implies that the exclusivity principle might be one of the fundamental principles of nature.
Precise control over quantum systems can enable the realization of fascinating applications such as powerful computers, secure communication devices, and simulators that can elucidate the physics of complex condensed matter systems. However, the fragility of quantum effects makes it very difficult to harness the power of quantummechanics. In this thesis, we present novel systems and tools for gaining fundamental insights into the complex quantum world and for bringing practical applications of quantummechanics closer to reality. We first optimize and show equivalence between a wide range of techniques for storage of photons in atomic ensembles. We describe experiments demonstrating the potential of our optimization algorithms for quantum communication and computation applications. Next, we combine the technique of photon storage with strong atom-atom interactions to propose a robust protocol for implementing the two-qubit photonic phase gate, which is an important ingredient in many quantum computation and communication tasks. In contrast to photon storage, many quantum computation and simulation applications require individual addressing of closely-spaced atoms, ions, quantum dots, or solid state defects. To meet this requirement, we propose a method for coherent optical far-field manipulation of quantum systems with a resolution that is not limited by the wavelength of radiation. While alkali atoms are currently the system of choice for photon storage and many other applications, we develop new methods for quantum information processing and quantum simulation with ultracold alkaline-earth atoms in optical lattices. We show how multiple qubits can be encoded in individual alkaline-earth atoms and harnessed for quantum computing and precision measurements applications. We also demonstrate that alkaline-earth atoms can be used to simulate highly symmetric systems exhibiting spin-orbital interactions and capable of providing valuable insights into strongly
Like rocket science or brain surgery, quantummechanics is pigeonholed as a daunting and inaccessible topic, which is best left to an elite or peculiar few. This classification was not earned without some degree of merit. Depending on perspective; quantummechanics is a discipline or philosophy, a convention or conundrum, an answer or question. Authors have run the gamut from hand waving to heavy handed in the hope to dispel the common beliefs about quantummechanics, but perhaps they continue to promulgate the stigma. The focus of this particular effort is to give the reader an introduction, if not at least an appreciation, of the role that linear algebra techniques play in the practical application of quantummechanical methods. It interlaces aspects of the classical and quantum picture, including a number of both worked and parallel applications. Students with no prior experience in quantummechanics, motivated graduate students, or researchers in other areas attempting to gain some introduction to quantum theory will find particular interest in this book. Part of Series on wave phenomena in the physical sciences
A brief introduction to discrete quantummechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantummechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.
Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We show here that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures, and quantum retrodiction, thus exemplifying the paradigm of quantum biology, satisfies the Ozawa bound as well as the Lanford-Robinson bound on information extraction. By considering Groenewold's information, the quantum information extracted during the reaction, we reproduce the known and unravel other magnetic-field effects not conveyed by reaction yields.
The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical
In this study, for the first time, the energies of two-electron Hulthen quantum dots (TEHQdots) embedded in Debye and quantum plasmas modeled by the more general exponential cosine screened Coulomb (MGECSC) potential under the combined influence of electric and magnetic fields are investigated by numerically solving the Schrödinger equation using the asymptotic iteration method. To do this, the four different forms of the MGECSC potential, which set through the different cases of the potential parameters, are taken into consideration. We propose that plasma environments form considerable quantummechanical effects for quantum dots and other atomic systems and that plasmas are important experimental arguments. In this study, by considering the quantum dot parameters, the external field parameters, and the plasma screening parameters, a control mechanism of the confinement on energies of TEHQdots and the frequency of the radiation emitted by TEHQdots as a result of any excitation is discussed. In this mechanism, the behaviors, similarities, the functionalities of the control parameters, and the influences of plasmas on these quantities are explored.
We show that the quantum Jarzynski equality generalizes to PT -symmetric quantummechanics with unbroken PT -symmetry. In the regime of broken PT -symmetry the Jarzynski equality does not hold as also the CPT -norm is not preserved during the dynamics. These findings are illustrated for an experimentally relevant system – two coupled optical waveguides. It turns out that for these systems the phase transition between the regimes of unbroken and broken PT -symmetry is thermodynamically inhibited as the irreversible work diverges at the critical point.
Cyclobutadiene has a four-membered carbon ring with two double bonds, but this highly strained molecular configuration is almost square and, via a coordinated motion, the nuclei quantummechanically tunnels through the high-energy square state to a configuration equivalent to the initial configuration under a 90° rotation. This results in a square ground state, comprising a superposition of two molecular configurations, that is driven by quantum tunneling. Using a quantummechanical model, and an effective nuclear potential from density functional theory, we calculate the vibrational energy spectrum and the accompanying wavefunctions. We use the wavefunctions to identify the motions of the molecule and detail how different motions can enhance or suppress the tunneling rate. This is relevant for kinematics of tunneling-driven reactions, and we discuss these implications. We are also able to provide a qualitative account of how the molecule will respond to an external perturbation and how this may enhance or suppress infra-red-active vibrational transitions.
Although the usual way of representing Markov processes is time asymmetric, there is a way of describing Markov processes, due to Schrodinger, which is time symmetric. This observation provides a link between quantummechanics and the layered Bayesian networks that are often used in automated pattern recognition systems. In particular, there is a striking formal similarity between quantummechanics and a particular type of Bayesian network, the Helmholtz machine, which provides a plausible model for how the mammalian brain recognizes important environmental situations. One interesting aspect of this relationship is that the "wake-sleep" algorithm for training a Helmholtz machine is very similar to the problem of finding the potential for the multi-channel Schrodinger equation. As a practical application of this insight it may be possible to use inverse scattering techniques to study the relationship between human brain wave patterns, pattern recognition, and learning. We also comment on whether there is a relationship between quantum measurements and consciousness.
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantummechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantummechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.
completion of the theory requires a macroscopic mechanism for selecting a physical framework, which is part of the macroscopic theory (MAQM). The selection of a physical framework involves the breaking of the microscopic ‘framework symmetry’, which can proceed either phenomenologically as in the standard quantum measurement theory, or more fundamentally by considering the quantum system under study to be a subsystem of a macroscopic quantum system. The decoherent histories formulation of Gell-Mann and Hartle, as well as that of Omnès, are theories of this fundamental type, where the physical framework is selected by a coarse-graining procedure in which the physical phenomenon of decoherence plays an essential role. Various well-known interpretations of QM are described from the perspective of CQT. Detailed definitions and proofs are presented in the appendices.
The principle of sufficient reason asserts that anything that happens does so for a reason: no definite state of affairs can come into being unless there is a sufficient reason why that particular thing should happen. This principle is usually attributed to Leibniz, although the first recorded Western philosopher to use it was Anaximander of Miletus. The demand that nature be rational, in the sense that it be compatible with the principle of sufficient reason, conflicts with a basic feature of contemporary orthodox physical theory, namely the notion that nature's response to the probing action of an observer is determined by pure chance, and hence on the basis of absolutely no reason at all. This appeal to pure chance can be deemed to have no rational fundamental place in reason-based Western science. It is argued here, on the basis of the other basic principles of quantum physics, that in a world that conforms to the principle of sufficient reason, the usual quantum statistical rules will naturally emerge at the pragmatic level, in cases where the reason behind nature's choice of response is unknown, but that the usual statistics can become biased in an empirically manifest way when the reason for the choice is empirically identifiable. It is shown here that if the statistical laws of quantummechanics were to be biased in this way then the basically forward-in-time unfolding of empirical reality described by orthodox quantummechanics would generate the appearances of backward-time-effects of the kind that have been reported in the scientific literature.
After a quarter century of discoveries that rattled the foundations of classical mechanics and electrodynamics, the year 1926 saw the publication of two works intended to provide a theoretical structure to support new quantum explanations of the subatomic world. Heisenberg's matrix mechanics and Schrödinger's wave mechanics provided compatible but mathematically disparate ways of unifying the discoveries of Planck, Einstein, Bohr and many others. Efforts began immediately to prove the equivalence of these two structures, culminated successfully by John von Neumann's 1932 volume Mathematical Foundations of QuantumMechanics. This forms the springboard for the current effort. We begin with a presentation of a minimal set of von Neumann postulates while introducing language and notation to facilitate subsequent discussion of quantum calculations based in finite dimensional Hilbert spaces. Chapters that follow address two-state quantum systems (with spin one-half as the primary example), entanglement of multiple two-state systems, quantum angular momentum theory and quantum approaches to statistical mechanics. A concluding chapter gives an overview of issues associated with quantummechanics in continuous infinite-dimensional Hilbert spaces. [Planck1900] PlanckM1900Zur Teorie des Gesetzes der Energieverteilung in NormalspektrumVerhandlung der Deutscher Physikalischen Gesellschaft 2 237[Heisenberg1925] HeisenbergW1925
The quantummechanical periodic Toda lattice is studied by the direct diagonalization of the Hamiltonian. The eigenstates are classified according to the irreducible representations of the dihedral group D[sub N]. It is shown that Gutzwiller's quantization conditions are satisfied and they have a one-to-one correspondence to the irreducible representation of the D[sub N] group. The authors have also carried out the semiclassical quantization of the periodic Toda lattice by the EBK formulation. The eigenvalues of the semiclassical quantization have a one-to-one correspondence to the integer quantum numbers, and those quantum numbers also have a close relationship to the symmetry ofmore » the state. Numerical calculations have been done for N = 3, 4, 5, and 6 particle periodic Toda lattices. The distributions of the eigenvalues are systematic and distinguished by the symmetry of the state. As illustrative examples, amplitudes of the wave functions and density distributions are shown. 14 refs., 8 figs., 11 tabs.« less
Recently, a new formulation of quantummechanics, based on the concept of signed particles, has been suggested. In this paper, we introduce a cellular automaton which mimics the dynamics of quantum objects in the phase-space in a time-dependent fashion. This is twofold: it provides a simplified and accessible language to non-physicists who wants to simulate quantummechanical systems, at the same time it enables a different way to explore the laws of Physics. Moreover, it opens the way towards hybrid simulations of quantum systems by combining full quantum models with cellular automata when the former fail. In order to show the validity of the suggested cellular automaton and its combination with the signed particle formalism, several numerical experiments are performed, showing very promising results. Being this article a preliminary study on quantum simulations in phase-space by means of cellular automata, some conclusions are drawn about the encouraging results obtained so far and the possible future developments.
The principle of sufficient reason asserts that anything that happens does so for a reason: no definite state of affairs can come into being unless there is a sufficient reason why that particular thing should happen. This principle is usually attributed to Leibniz, although the first recorded Western philosopher to use it was Anaximander of Miletus. The demand that nature be rational, in the sense that it be compatible with the principle of sufficient reason, conflicts with a basic feature of contemporary orthodox physical theory, namely the notion that nature's response to the probing action of an observer is determinedmore » by pure chance, and hence on the basis of absolutely no reason at all. This appeal to pure chance can be deemed to have no rational fundamental place in reason-based Western science. It is argued here, on the basis of the other basic principles of quantum physics, that in a world that conforms to the principle of sufficient reason, the usual quantum statistical rules will naturally emerge at the pragmatic level, in cases where the reason behind nature's choice of response is unknown, but that the usual statistics can become biased in an empirically manifest way when the reason for the choice is empirically identifiable. It is shown here that if the statistical laws of quantummechanics were to be biased in this way then the basically forward-in-time unfolding of empirical reality described by orthodox quantummechanics would generate the appearances of backward-time-effects of the kind that have been reported in the scientific literature.« less
This article presents the results of glottal open-quotient measurements in the case of singing voice production. It explores the relationship between open quotient and laryngeal mechanisms, vocal intensity, and fundamental frequency. The audio and electroglottographic signals of 18 classically trained male and female singers were recorded and analyzed with regard to vocal intensity, fundamental frequency, and open quotient. Fundamental frequency and open quotient are derived from the differentiated electroglottographic signal, using the DECOM (DEgg Correlation-based Open quotient Measurement) method. As male and female phonation may differ in respect to vocal-fold vibratory properties, a distinction is made between two different glottal configurations, which are called laryngeal mechanisms: mechanism 1 (related to chest, modal, and male head register) and mechanism 2 (related to falsetto for male and head register for female). The results show that open quotient depends on the laryngeal mechanisms. It ranges from 0.3 to 0.8 in mechanism 1 and from 0.5 to 0.95 in mechanism 2. The open quotient is strongly related to vocal intensity in mechanism 1 and to fundamental frequency in mechanism 2. .
Ever since Schrödinger, Time in quantum theory is postulated Newtonian for every reference frame. With the help of certain known mathematical results, we show that the concept of the so-called Local Time allows avoiding the postulate. In effect, time appears as neither fundamental nor universal on the quantum-mechanical level while being consistently attributable to every, at least approximately, closed quantum system as well as to every of its (conservative or not) subsystems.
As a fundamental primitive, Secure Multiparty Summation and Multiplication can be used to build complex secure protocols for other multiparty computations, specially, numerical computations. However, there is still lack of systematical and efficient quantum methods to compute Secure Multiparty Summation and Multiplication. In this paper, we present a novel and efficient quantum approach to securely compute the summation and multiplication of multiparty private inputs, respectively. Compared to classical solutions, our proposed approach can ensure the unconditional security and the perfect privacy protection based on the physical principle of quantummechanics.
As a fundamental primitive, Secure Multiparty Summation and Multiplication can be used to build complex secure protocols for other multiparty computations, specially, numerical computations. However, there is still lack of systematical and efficient quantum methods to compute Secure Multiparty Summation and Multiplication. In this paper, we present a novel and efficient quantum approach to securely compute the summation and multiplication of multiparty private inputs, respectively. Compared to classical solutions, our proposed approach can ensure the unconditional security and the perfect privacy protection based on the physical principle of quantummechanics. PMID:26792197
In this paper I discuss the work on quantum physics and wave mechanics by Charles Galton Darwin, a Cambridge wrangler of the last generation, as a case study to better understand the early reception of quantum physics in Britain. I argue that his proposal in the early 1920s to abandon the strict conservation of energy, as well as his enthusiastic embracement of wave mechanics at the end of the decade, can be easily understood by tracing his ontological and epistemological commitments to his early training in the Cambridge Mathematical Tripos. I also suggest that Darwin's work cannot be neglected in a study of quantum physics in Britain, since he was one of very few fellows of the Royal Society able to judge and explain quantum physics and quantummechanics.
Venugopal, R.; Paulsson, M.; Goasguen, S.; Datta, S.; Lundstrom, M. S.
2003-05-01
We present a computationally efficient, two-dimensional quantummechanical simulation scheme for modeling dissipative electron transport in thin body, fully depleted, n-channel, silicon-on-insulator transistors. The simulation scheme, which solves the nonequilibrium Green's function equations self consistently with Poisson's equation, treats the effect of scattering using a simple approximation inspired by the "Büttiker probes," often used in mesoscopic physics. It is based on an expansion of the active device Hamiltonian in decoupled mode space. Simulation results are used to highlight quantum effects, discuss the physics of scattering and to relate the quantummechanical quantities used in our model to experimentally measured low field mobilities. Additionally, quantum boundary conditions are rigorously derived and the effects of strong off-equilibrium transport are examined. This paper shows that our approximate treatment of scattering, is an efficient and useful simulation method for modeling electron transport in nanoscale, silicon-on-insulator transistors.
Lundeen, J. S.; Feito, A.; Coldenstrodt-Ronge, H.; Pregnell, K. L.; Silberhorn, Ch.; Ralph, T. C.; Eisert, J.; Plenio, M. B.; Walmsley, I. A.
2009-01-01
Measurement connects the world of quantum phenomena to the world of classical events. It has both a passive role-in observing quantum systems-and an active one, in preparing quantum states and controlling them. In view of the central status of measurement in quantummechanics, it is surprising that there is no general recipe for designing a detector that measures a given observable. Compounding this, the characterization of existing detectors is typically based on partial calibrations or elaborate models. Thus, experimental specification (that is, tomography) of a detector is of fundamental and practical importance. Here, we present the realization of quantum detector tomography. We identify the positive-operator-valued measure describing the detector, with no ancillary assumptions. This result completes the triad, state, process and detector tomography, required to fully specify an experiment. We characterize an avalanche photodiode and a photon-number-resolving detector capable of detecting up to eight photons. This creates a new set of tools for accurately detecting and preparing non-classical light.
The Visual QuantumMechanics project has created a series of teaching/learning units to introduce quantum physics to a variety of audiences ranging from high school students who normally would not study these topics to undergraduate physics majors. Most recently we have been developing materials relating modern medical procedures and contemporary physics. In all of these materials interactive computer visualizations are coupled with hands-on experiences to create a series of activities which help students learn about some aspects of quantummechanics. Our goal is to enable students to obtain a qualitative and, where appropriate, a quantitative understanding of contemporary ideas in physics. Included in the instructional materials are student-centered activities that address a variety of concepts in quantum physics and applications to devices such as the light emitting diode, the electron microscope, an inexpensive infrared detection card, and the Star Trek Transporter. Whenever possible the students begin the study of a new concept with an experiment using inexpensive equipment. They, then, build models of the physical phenomenon using interactive computer visualization and conclude by applying those models to new situations. For physics students these visualizations are usually followed by a mathematical approach. For others the visualizations provide a framework for understanding the concepts. Thus, Visual QuantumMechanics allows a wide range of students to begin to understand the basic concepts, implications and interpretations of quantum physics. At present we are building on this foundation to create materials which show the connection between contemporary physics and modern medical diagnosis. Additional information is available at http://web.phys.ksu.edu/.
Classical mechanics challenges students to use their intuitions and experiences as a basis for understanding, in effect to approach learning as "a refinement of everyday thinking'' (Einstein, 1936). Moving on to quantummechanics (QM), students, like physicists, need to adjust this approach, in particular with respect to the roles that…
Understanding the molecular basis of drug action has been an important objective for pharmaceutical scientists. With the increasing speed of computers and the implementation of quantum chemistry methodologies, pharmacodynamic and pharmacokinetic problems have become more computationally tractable. Historically the former has been the focus of drug design, but within the last two decades efforts to understand the latter have increased. It takes about fifteen years and over $1 billion dollars for a drug to go from laboratory hit, through lead optimization, to final approval by the U.S. Food and Drug Administration. While the costs have increased substantially, the overall clinical success rate for a compound to emerge from clinical trials is approximately 10%. Most of the attrition rate can be traced to ADMET (absorption, distribution, metabolism, excretion, and toxicity) problems, which is a powerful impetus to study these issues at an earlier stage in drug discovery. Quantummechanics offers pharmaceutical scientists the opportunity to investigate pharmacokinetic problems at the molecular level prior to laboratory preparation and testing. This review will provide a perspective on the use of quantummechanics or a combination of quantummechanics coupled with other classical methods in the pharmacokinetic phase of drug discovery. A brief overview of the essential features of theory will be discussed, and a few carefully selected examples will be given to highlight the computational methods.
In an earlier paper written in loving memory of Asher Peres, we gave a critical analysis of the celebrated 1935 paper in which Einstein, Podolsky and Rosen (EPR) challenged the completeness of quantummechanics. There, we had pointed out logical shortcomings in the EPR paper. Now, we raise additional questions concerning their suggested program to find a theory that would “provide a complete description of the physical reality”. In particular, we investigate the extent to which the EPR argumentation could have lead to the more dramatic conclusion that quantummechanics is in fact incorrect. With this in mind, we propose a speculation, made necessary by a logical shortcoming in the EPR paper caused by the lack of a necessary condition for “elements of reality”, and surmise that an eventually complete theory would either be inconsistent with quantummechanics, or would at least violate Heisenberg’s Uncertainty Principle.
Teaching physics implies making choices. In the case of teaching quantum physics, besides an educational choice - the didactic strategy - another choice must be made, an epistemological one, concerning the interpretation of quantum theory itself. These two choices are closely connected. We have chosen a didactic strategy that privileges the phenomenological-conceptual approach, with emphasis upon quantum features of the systems, instead of searching for classical analogies. This choice has led us to present quantum theory associated with an orthodox, yet realistic, interpretation of the concept of quantum state, considered as the key concept of quantum theory, representing the physical reality of a system, independent of measurement processes. The results of the mplementation of this strategy, with three groups of engineering students, showed that more than a half of them attained a reasonable understanding of the basics of quantummechanics (QM) for this level. In addition, a high degree of satisfaction was attained with the classes as 80% of the students of the experimental groups claimed to have liked it and to be interested in learning more about QM.
Presents an explanation, without mathematical equations, of the basic principles of quantummechanics. Includes wave-particle duality, the probability character of the wavefunction, and the uncertainty relations. (MLH)
Quantummechanics in noncommutative space modifies the standard result of the Aharonov-Bohm effect for electrons and other recent quantum effects. Here we obtain the phase in noncommutative space for the Spavieri effect, a generalization of Aharonov-Bohm effect which involves a coherent superposition of particles with opposite charges moving along a single open interferometric path. By means of the experimental considerations a limit √{θ }≃(0.13TeV)-1 is achieved, improving by 10 orders of magnitude the results derived by Chaichian et al. [Phys. Lett. B 527, 149 (2002), 10.1016/S0370-2693(02)01176-0] for the Aharonov-Bohm effect. It is also shown that the noncommutative phases of the Aharonov-Casher and He-McKellar-Willkens effects are nullified in the current experimental tests.
We introduce a method to evaluate the relative populations of different conformers of molecular species in solution, aiming at quantummechanical accuracy, while keeping the computational cost at a nearly molecular-mechanics level. This goal is achieved by combining long classical molecular-dynamics simulations to sample the free-energy landscape of the system, advanced clustering techniques to identify the most relevant conformers, and thermodynamic perturbation theory to correct the resulting populations, using quantum-mechanical energies from density functional theory. A quantitative criterion for assessing the accuracy thus achieved is proposed. The resulting methodology is demonstrated in the specific case of cyanin (cyanidin-3-glucoside) in water solution.
The problem of an electron moving perpendicular to an intense magnetic field is approached from the framework of quantummechanics. A numerical solution to the related rate equations describing the probabilities of occupation of the electron's energy states is put forth along with the expected errors involved. The quantum-mechanical approach is found to predict a significant amount of energy broadening with time for an initially monoenergetic electron beam entering a region of an intense magnetic field as long as the product of initial energy and magnetic field is of order 50 MG BeV or larger.
Erker, Paul; Mitchison, Mark T.; Silva, Ralph; Woods, Mischa P.; Brunner, Nicolas; Huber, Marcus
2017-07-01
Time remains one of the least well-understood concepts in physics, most notably in quantummechanics. A central goal is to find the fundamental limits of measuring time. One of the main obstacles is the fact that time is not an observable and thus has to be measured indirectly. Here, we explore these questions by introducing a model of time measurements that is complete and autonomous. Specifically, our autonomous quantum clock consists of a system out of thermal equilibrium—a prerequisite for any system to function as a clock—powered by minimal resources, namely, two thermal baths at different temperatures. Through a detailed analysis of this specific clock model, we find that the laws of thermodynamics dictate a trade-off between the amount of dissipated heat and the clock's performance in terms of its accuracy and resolution. Our results furthermore imply that a fundamental entropy production is associated with the operation of any autonomous quantum clock, assuming that quantum machines cannot achieve perfect efficiency at finite power. More generally, autonomous clocks provide a natural framework for the exploration of fundamental questions about time in quantum theory and beyond.
It is shown within the Hilbert space formulation of quantummechanics that the total noncommutativity of any two physical quantities is necessary for their satisfying the uncertainty relation or for their being complementary. The importance of these results is illustrated with the canonically conjugate position and momentum of a free particle and of a particle closed in a box.
Ngaojampa, C.; Nimmanpipug, P.; Yu, L. D.; Anuntalabhochai, S.; Lee, V. S.
2011-02-01
In order to promote understanding of the fundamentals of ultra-low-energy ion interaction with DNA, molecular dynamics simulations using combined quantum-mechanics/molecular-mechanics of poly-AT and poly-GC A-DNA double strands irradiated by <200 eV carbon ions were performed to investigate the molecular implications of mutation bias. The simulations were focused on the responses of the DNA backbones and nitrogenous bases to irradiation. Analyses of the root mean square displacements of the backbones and non-hydrogen atoms of base rings of the simulated DNA structure after irradiation revealed a potential preference of DNA double strand separation, dependent on the irradiating energy. The results show that for the backbones, the large difference in the displacement between poly-GC and poly-AT in the initial time period could be the reason for the backbone breakage; for the nitrogenous base pairs, A-T is 30% more sensitive or vulnerable to ion irradiation than G-C, demonstrating a preferential, instead of random, effect of irradiation-induced mutation.
The internal phase dynamics of a quantum system interacting with an electromagnetic field is revealed in details. Theoretical and experimental evidences of a causal relation of the phase of the wave function to the dynamics of the quantum system are presented sistematically for the first time. A dynamics-statistical interpretation of the quantummechanics is introduced.
Benítez Rodríguez, E.; Arévalo Aguilar, L. M.; Piceno Martínez, E.
2017-03-01
To the quantummechanics specialists community it is a well-known fact that the famous original Stern-Gerlach experiment (SGE) produces entanglement between the external degrees of freedom (position) and the internal degree of freedom (spin) of silver atoms. Despite this fact, almost all textbooks on quantummechanics explain this experiment using a semiclassical approach, where the external degrees of freedom are considered classical variables, the internal degree is treated as a quantum variable, and Newton's second law is used to describe the dynamics. In the literature there are some works that analyze this experiment in its full quantummechanical form. However, astonishingly, to the best of our knowledge the original experiment, where the initial states of the spin degree of freedom are randomly oriented coming from the oven, has not been analyzed yet in the available textbooks using the Schrödinger equation (to the best of our knowledge there is only one paper that treats this case: Hsu et al (2011 Phys. Rev. A 83 012109)). Therefore, in this contribution we use the time-evolution operator to give a full quantummechanics analysis of the SGE when the initial state of the internal degree of freedom is completely random, i.e. when it is a statistical mixture. Additionally, as the SGE and the development of quantummechanics are heavily intermingled, we analyze some features and drawbacks in the current teaching of quantummechanics. We focus on textbooks that use the SGE as a starting point, based on the fact that most physicist do not use results from physics education research, and comment on traditional pedagogical attitudes in the physics community.
Learning quantummechanics is challenging, even for upper-level undergraduate and graduate students. Research-validated interactive tutorials that build on students' prior knowledge can be useful tools to enhance student learning. We have been investigating student difficulties with quantummechanics pertaining to the double-slit experiment in various situations that appear to be counterintuitive and contradict classical notions of particles and waves. For example, if we send single electrons through the slits, they may behave as a "wave" in part of the experiment and as a "particle" in another part of the same experiment. Here we discuss the development and evaluation of a research-validated Quantum Interactive Learning Tutorial (QuILT) which makes use of an interactive simulation to improve student understanding of the double-slit experiment and strives to help students develop a good grasp of foundational issues in quantummechanics. We discuss common student difficulties identified during the development and evaluation of the QuILT and analyze the data from the pretest and post test administered to the upper-level undergraduate and first-year physics graduate students before and after they worked on the QuILT to assess its effectiveness. These data suggest that on average, the QuILT was effective in helping students develop a more robust understanding of foundational concepts in quantummechanics that defy classical intuition using the context of the double-slit experiment. Moreover, upper-level undergraduates outperformed physics graduate students on the post test. One possible reason for this difference in performance may be the level of student engagement with the QuILT due to the grade incentive. In the undergraduate course, the post test was graded for correctness while in the graduate course, it was only graded for completeness.
In this article, Scattering states of Klein-Gordon equation for three scatter potentials of single and double Dirac delta and a potential well in the q-deformed formalism of relativistic quantummechanics have been derived. At first, we discussed how q-deformed formalism can be constructed and used. Postulates of this q-deformed quantummechanics are noted. Then scattering problems for spin-zero bosons are studied.
Quantum walks are fundamentally different from random walks due to the quantum superposition property of quantum objects. Quantum walk process was found to be very useful for quantum information and quantum computation applications. In this paper we demonstrate how to use quantum walks as a tool to generate high-dimensional two-particle fermionic entanglement. The generated entanglement can survive longer in the presence of depolorazing noise due to the periodicity of quantum walk dynamics. The possibility to create two distinguishable qudits in a system of tunnel-coupled semiconductor quantum dots is discussed.
Are the standard laws of Physics really fundamental principles? Does the physical vacuum have a more primordial internal structure? Are quarks, leptons, gauge bosons… ultimate elementary objects? These three basic questions are actually closely related. If the deep vacuum structure and dynamics turn out to be less trivial than usually depicted, the conventional "elementary" particles will most likely be excitations of such a vacuum dynamics that remains by now unknown. We then expect relativity and quantummechanics to be low-energy limits of a more fundamental dynamical pattern that generates them at a deeper level. It may even happen that vacuum drives the expansion of the Universe from its own inner dynamics. Inside such a vacuum structure, the speed of light would not be the critical speed for vacuum constituents and propagating signals. The natural scenario would be the superbradyon (superluminal preon) pattern we postulated in 1995, with a new critical speed cs much larger than the speed of light c just as c is much larger than the speed of sound. Superbradyons are assumed to be the bradyons of a super-relativity associated to cs (a Lorentz invariance with cs as the critical speed). Similarly, the standard relativistic space-time with four real coordinates would not necessarily hold beyond low-energy and comparatively local distance scales. Instead, the spinorial space-time (SST) with two complex coordinates we introduced in 1996-97 may be the suitable one to describe the internal structure of vacuum and standard "elementary" particles and, simultaneously, Cosmology at very large distance scales. If the constituents of the preonic vacuum are superluminal, quantum entanglement appears as a natural property provided cs ≫ c . The value of cs can even be possibly found experimentally by studying entanglement at large distances. It is not excluded that preonic constituents of vacuum can exist in our Universe as free particles ("free" superbradyons), in which
The so-called non-locality theorems aim to show that QuantumMechanics is not consistent with the Locality Principle. Their proofs require, besides the standard postulates of Quantum Theory, further conditions, as for instance the Criterion of Reality, which cannot be formulated in the language of Standard Quantum Theory; this difficulty makes the proofs not verifiable according to usual logico-mathematical methods, and therefore it is a source of the controversial debate about the real implications of these theorems. The present work addresses this difficulty for Bell-type and Stapp's arguments of non-locality. We supplement the formalism of QuantumMechanics with formal statements inferred from the further conditions in the two different cases. Then an analysis of the two arguments is performed according to ordinary mathematical logic.
Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com; Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8; Ali, S. Twareque, E-mail: twareque.ali@concordia.ca
This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantummechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantummechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and thosemore » of momentum not commuting, the position operators not commuting and finally, the case of standard quantummechanics, obeying the canonical commutation relations only.« less
We present hybrid symbolic-numerical tools to generate optimized numerical code for rapid prototyping and fast numerical computation starting from a computer algebra system (CAS) and tailored to any given quantummechanical problem. Although a major focus concerns the quantum chemistry methods of H. Nakatsuji which has yielded successful and very accurate eigensolutions for small atoms and molecules, the tools are general and may be applied to any basis set calculation with a variational principle applied to its linear and non-linear parameters.
Raedt, H. D.; Hams, A. H.; Michielsen, K.; Miyashita, S.; Saito, K.
We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum computer for the case of an antiferromagnetic Heisenberg model on triangular lattices of different size.
This dissertation is a phenomenological investigation of the measurement problem in quantummechanics. The primary subject matter for description and analysis is scientific instruments and their use in experiments which elicit the measurement problem. A methodological critique is mounted against the ontological commitments taken for granted in the canonical interpretations of quantum theory and the scientific activity of measurement as the necessary interface between theoretical interest and perceptual results. I argue that an aesthetic dimension of reality functions as aproto-scientific establishment of sense-making that constantly operates to set integratively all other cognitively neat determinations, including scientifically rendered objects that are intrinsically non-visualizable. The way in which data "key in" to the original and originative register of the sensible in observation is clarified by examining prostheses, measuring apparatuses and instruments that are sense-conveying and -integrative with the human sensorium. Experiments, technology and instrumentation are examined in order to understand how knowing and that which is known is bonded by praxis-aisthesis. Quantum measurement is a praxic-dynamie activity and homologically structured and structur ing functional engagement in terms of instantiation, quantifiability, and spatiotemporal differentiation. The distinctions between a beauty-aesthetic and praxis-aisthesis are delineated. It is argued that a beauty-aesthetic is a construal of the economic dimension of scientific objects and work, and is not the primary manner in which the aesthetic dimension is disclosed. The economic dimension of abstractions reduces to an austere aesthetic of calculative economy. Nature itself, however, is not stingy; it is intrinsically capacious, extravagant, full of surprise, nuance, ambiguity and allusiveness. The capaciousness of Nature and the way in which we are integratively set within Nature in a materiality
In 1974, the British physicist Stephen Hawking discovered that black holes have a characteristic temperature and are therefore capable of emitting radiation. Given the scientific importance of this discovery, there is a profuse literature on the subject. Nevertheless, the available literature ends up being either too simple, which does not convey the true physical significance of the issue, or too technical, which excludes an ample segment of the audience interested in science, such as physics teachers and their students. The present article seeks to remedy this shortcoming. It develops a simple and plausible argument that provides insight into the fundamental aspects of Hawking’s discovery, which leads to an approximate equation for the so-called Hawking temperature. The exposition is mainly intended for physics teachers and their students, and it only requires elementary algebra, as well as basic notions of Newtonian mechanics and quantum theory.
Camblong, Horacio E.; Epele, Luis N.; Fanchiotti, Huner
2015-06-15
The analytic structure of the S-matrix of singular quantummechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter (Ω) that determines the boundary conditions. Specifically, a characterization is given in terms of salient mathematical and physical properties governing its behavior. These properties involve unitarity and associated current-conserving Wronskian relations, time-reversal invariance, and Blaschke factorization. The approach leads to an interpretation of effective nonunitary solutions in singular quantummechanics and their determination from the unitary family.
Samosvat, D. M.; Chikalova-Luzina, O. P.; Vyatkin, V. M.; Zegrya, G. G.
2016-11-01
In present work the energy transfer between quantum dots by the exchange (Dexter) mechanism is analysed. The interdot Coulomb interaction is taken into consideration. It is assumed that the quantum dot-donor and the quantum dot-acceptor are made from the same compound A3B5 and embedded in the matrix of other material creating potential barriers for electron and holes. The dependences of the energy transfer rate on the quantum-dot system parameters are found using the Kane model that provides the most adequate description spectra of semiconductors A3B5. Numerical calculations show that the rate of the energy transfer by Dexter mechanism is comparable to the rate of the energy transfer by electrostatic mechanism at the distances approaching to the contact ones.
The article explores some of the basic findings of quantum physics and information theory and their possible usefulness in offering new vistas for understanding psychoanalysis and the patient-analyst interchange. Technical terms are explained and placed in context, and examples of applying quantum models to clinical experience are offered. Given the complexity of the findings of quantummechanics and information theory, the article aims only to introduce some of the major concepts from these disciplines. Within this framework the article also briefly addresses the question of mind as well as the problematic of reducing the experience of consciousness to neurological brain functioning.
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
Classic Mechanics and Electromagnetism, conventionally taken as time-reversible, share the same concept of motion (either of mass or charge) as the basis of the time reversibility in their own fields. This paper focuses on the relationship between mobile geometry and motion reversibility. The goal is to extrapolate the conclusions to the quantum frame, where matter and radiation behave just as elementary mobiles. The possibility that the asymmetry of Time (Time’s arrow) is an effect of a fundamentalquantum asymmetry of elementary particles, turns out to be a consequence of the discussion.
Steuernagel, Ole; Kakofengitis, Dimitris; Ritter, Georg
2013-01-18
The behavior of classical mechanical systems is characterized by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why traditionally only the time evolution of wave functions is studied in quantum dynamics. These studies are quite insensitive to the underlying structure of quantum phase space dynamics. We identify the flow that is the quantum analog of classical particle flow along phase portrait lines. It reveals hidden features of quantum dynamics and extra complexity. Being constrained by conserved flow winding numbers, it also reveals fundamental topological order in quantum dynamics that has so far gone unnoticed.
The application of the basic formalistic elements of wave mechanics theory is discussed. The theory is used to describe the physical phenomena on the microscopic level, the fluid dynamics of gases and liquids, and the analysis of physical phenomena on the macroscopic (visually observable) level. The practical advantages of relating the two fields of wave mechanics and fluid mechanics through the use of the Schroedinger equation constitute the approach to this relationship. Some of the subjects include: (1) fundamental aspects of wave mechanics theory, (2) laminarity of flow, (3) velocity potential, (4) disturbances in fluids, (5) introductory elements of the bifurcation theory, and (6) physiological aspects in fluid dynamics.
Comparisons are made for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. A classical uncertainty principle is derived and compared with its quantum-mechanical counterpart. The results are discussed in terms of the statistical interpretation of the uncertainty principle. (Author/BB)
The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantummechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantummechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations. In classical mechanics the phase space description can be considered as the ontic description, here states are given by points λ =(x , p) of phase space. The dynamics of the ontic state is given by the system of Hamiltonian equations.We can also consider probability distributions on the phase space (or equivalently random variables valued in it). We call them probabilistic ontic states. Dynamics of probabilistic ontic states is given by the Liouville equation.In classical physics we can (at least in principle) measure both the coordinate and momentum and hence ontic states can be treated as epistemic states as well (or it is better to say that here epistemic states can be treated as ontic states). Probabilistic ontic states represent probabilities for outcomes of joint measurement of position and momentum.However, this was
We analyze the effects of noncommutativity in conformal quantummechanics (CQM) using the κ-deformed space-time as a prototype. Up to the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved but the coupling in a canonical model of the CQM gets deformed. We show that the boundary conditions that ensure a unitary time evolution in the noncommutative CQM can break the scale invariance, leading to a quantummechanical scaling anomaly. We calculate the scaling dimensions of the two and three point functions in the noncommutative CQM which are shown to be deformed. The AdS2 / CFT1 duality for the CQM suggests that the corresponding correlation functions in the holographic duals are modified. In addition, the Breitenlohner-Freedman bound also picks up a noncommutative correction. The strongly attractive regime of a canonical model of the CQM exhibit quantum instability. We show that the noncommutativity softens this singular behaviour and its implications for the corresponding holographic duals are discussed.
I develop a new analysis of Niels Bohr's Copenhagen interpretation of quantummechanics by examining the development of his views from his earlier use of the correspondence principle in the so-called 'old quantum theory' to his articulation of the idea of complementarity in the context of the novel mathematical formalism of quantummechanics. I argue that Bohr was motivated not by controversial and perhaps dispensable epistemological ideas---positivism or neo-Kantianism, for example---but by his own unique perspective on the difficulties of creating a new working physics of the internal structure of the atom. Bohr's use of the correspondence principle in the old quantum theory was associated with an empirical methodology that used this principle as an epistemological bridge to connect empirical phenomena with quantum models. The application of the correspondence principle required that one determine the validity of the idealizations and approximations necessary for the judicious use of classical physics within quantum theory. Bohr's interpretation of the new quantummechanics then focused on the largely unexamined ways in which the developing abstract mathematical formalism is given empirical content by precisely this process of approximation. Significant consistency between his later interpretive framework and his forms of argument with the correspondence principle indicate that complementarity is best understood as a relationship among the various approximations and idealizations that must be made when one connects otherwise meaningless quantummechanical symbols to empirical situations or 'experimental arrangements' described using concepts from classical physics. We discover that this relationship is unavoidable not through any sort of a priori analysis of the priority of classical concepts, but because quantummechanics incorporates the correspondence approach in the way in which it represents quantum properties with matrices of transition probabilities, the
Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex
2016-08-08
Here, we show that the proper inclusion of soft reparameterization modes in the Sachdev–Ye–Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantummechanics.
We find the covariant deformed Heisenberg algebra and the Laplace-Beltrami operator on the extended h-deformed quantum plane and solve the Schrödinger equations explicitly for some physical systems on the quantum plane. In the commutative limit the behaviour of a quantum particle on the quantum plane becomes that of the quantum particle on the Poincaré half-plane, a surface of constant negative Gaussian curvature. We show that the bound state energy spectra for particles under specific potentials depend explicitly on the deformation parameter h. Moreover, it is shown that bound states can survive on the quantum plane in a limiting case where bound states on the Poincaré half-plane disappear.
The Darboux transformation in quantummechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics…
A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantummechanics. Our studies suggest this notoriously difficult task may be frustrated by the intuitively realist perspectives of introductory students, and a lack of ontological flexibility in their conceptions of light and matter. We have developed a framework for understanding and characterizing student perspectives on the physical interpretation of quantummechanics, and demonstrate the differential impact on student thinking of the myriad ways instructors approach interpretive themes in their introductory courses. Like expert physicists, students interpret quantum phenomena differently, and these interpretations are significantly influenced by their overall stances on questions central to the so-called measurement problem: Is the wave function physically real, or simply a mathematical tool? Is the collapse of the wave function an ad hoc rule, or a physical transition not described by any equation? Does an electron, being a form of matter, exist as a localized particle at all times? These questions, which are of personal and academic interest to our students, are largely only superficially addressed in our introductory courses, often for fear of opening a Pandora's Box of student questions, none of which have easy answers. We show how a transformed modern physics curriculum (recently implemented at the University of Colorado) may positively impact student perspectives on indeterminacy and wave-particle duality, by making questions of classical and quantum reality a central theme of our course, but also by making the beliefs of our students, and not just those of scientists, an explicit topic of discussion.
Strambini, E; Makarenko, K S; Abulizi, G; de Jong, M P; van der Wiel, W G
2016-01-06
Nonlocality is a key feature discriminating quantum and classical physics. Quantum-interference phenomena, such as Young's double slit experiment, are one of the clearest manifestations of nonlocality, recently addressed as dynamical to specify its origin in the quantum equations of motion. It is well known that loss of dynamical nonlocality can occur due to (partial) collapse of the wavefunction due to a measurement, such as which-path detection. However, alternative mechanisms affecting dynamical nonlocality have hardly been considered, although of crucial importance in many schemes for quantum information processing. Here, we present a fundamentally different pathway of losing dynamical nonlocality, demonstrating that the detailed geometry of the detection scheme is crucial to preserve nonlocality. By means of a solid-state quantum-interference experiment we quantify this effect in a diffusive system. We show that interference is not only affected by decoherence, but also by a loss of dynamical nonlocality based on a local reduction of the number of quantum conduction channels of the interferometer. With our measurements and theoretical model we demonstrate that this mechanism is an intrinsic property of quantum dynamics. Understanding the geometrical constraints protecting nonlocality is crucial when designing quantum networks for quantum information processing.
Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines in free space can then be tested by deriving a lower limit for the probability of finding the particle in a corresponding spatial interval at any intermediate time t . Here, it is shown that this lower limit can be violated by quantum superpositions of states confined within the respective position and momentum intervals. These violations of the particle propagation inequality show that quantummechanics changes the laws of motion at a fundamental level, providing a different perspective on causality relations and time evolution in quantummechanics.
Benenti, Giuliano; Casati, Giulio; Saito, Keiji; Whitney, Robert S.
2017-06-01
In recent years, the study of heat to work conversion has been re-invigorated by nanotechnology. Steady-state devices do this conversion without any macroscopic moving parts, through steady-state flows of microscopic particles such as electrons, photons, phonons, etc. This review aims to introduce some of the theories used to describe these steady-state flows in a variety of mesoscopic or nanoscale systems. These theories are introduced in the context of idealized machines which convert heat into electrical power (heat-engines) or convert electrical power into a heat flow (refrigerators). In this sense, the machines could be categorized as thermoelectrics, although this should be understood to include photovoltaics when the heat source is the sun. As quantummechanics is important for most such machines, they fall into the field of quantum thermodynamics. In many cases, the machines we consider have few degrees of freedom, however the reservoirs of heat and work that they interact with are assumed to be macroscopic. This review discusses different theories which can take into account different aspects of mesoscopic and nanoscale physics, such as coherent quantum transport, magnetic-field induced effects (including topological ones such as the quantum Hall effect), and single electron charging effects. It discusses the efficiency of thermoelectric conversion, and the thermoelectric figure of merit. More specifically, the theories presented are (i) linear response theory with or without magnetic fields, (ii) Landauer scattering theory in the linear response regime and far from equilibrium, (iii) Green-Kubo formula for strongly interacting systems within the linear response regime, (iv) rate equation analysis for small quantum machines with or without interaction effects, (v) stochastic thermodynamic for fluctuating small systems. In all cases, we place particular emphasis on the fundamental questions about the bounds on ideal machines. Can magnetic-fields change the
Theoretical explication of a growing body of empirical data on consciousness-related anomalous phenomena is unlikely to be achieved in terms of known physical processes. Rather, it will first be necessary to formulate the basic role of consciousness in the definition of reality before such anomalous experience can adequately be represented. This paper takes the position that reality is constituted only in the interaction of consciousness with its environment, and therefore that any scheme of conceptual organization developed to represent that reality must reflect the processes of consciousness as well as those of its environment. In this spirit, the concepts and formalisms of elementary quantummechanics, as originally proposed to explain anomalous atomic-scale physical phenomena, are appropriated via metaphor to represent the general characteristics of consciousness interacting with any environment. More specifically, if consciousness is represented by a quantummechanical wave function, and its environment by an appropriate potential profile, Schrödinger wave mechanics defines eigenfunctions and eigenvalues that can be associated with the cognitive and emotional experiences of that consciousness in that environment. To articulate this metaphor it is necessary to associate certain aspects of the formalism, such as the coordinate system, the quantum numbers, and even the metric itself, with various impressionistic descriptors of consciousness, such as its intensity, perspective, approach/avoidance attitude, balance between cognitive and emotional activity, and receptive/assertive disposition. With these established, a number of the generic features of quantummechanics, such as the wave/particle duality, and the uncertainty, indistinguishability, and exclusion principles, display metaphoric relevance to familiar individual and collective experiences. Similarly, such traditional quantum theoretic exercises as the central force field and atomic structure, covalent
If quantum gravity respects the principles of quantummechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. Here, this viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of themore » Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.« less
If quantum gravity respects the principles of quantummechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime. Here, this viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality. In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space. However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of themore » Hilbert space is problematic. Instead it is better to focus on the structure of the algebra of observables, and in particular on its subalgebras corresponding to regions. This paper suggests that study of analogous algebraic structure in gravity gives an important perspective on the nature of the quantum theory. Significant departures from the subalgebra structure of local quantum field theory are found, working in the correspondence limit of long-distances/low-energies. Particularly, there are obstacles to identifying commuting algebras of localized operators. In addition to suggesting important properties of the algebraic structure, this and related observations pose challenges to proposals of a fundamental role for entanglement.« less
We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantummechanics. For one-dimensional supersymmetric quantummechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantummechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.
While historically many quantum-mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a great deal of interest has arisen in quantum effects in nuclear dynamics as well. Due to the computational difficulty of solving the Schrödinger equation in full, these effects are often treated with approximate methods. In this paper, we present an algorithm to tackle these problems using an extension to the many-interacting-worlds approach to quantummechanics. This technique uses a kernel function to rebuild the probability density, and therefore, in contrast with the approximation presented in the original paper, it can be naturally extended to n-dimensional systems. This opens up the possibility of performing quantum ground-state searches with steepest-descent methods, and it could potentially lead to real-time quantum molecular-dynamics simulations. The behavior of the algorithm is studied in different potentials and numbers of dimensions and compared both to the original approach and to exact Schrödinger equation solutions whenever possible.
While photons are ideal for the transmission of quantum information, they require dedicated memories for long-term storage. The challenge for such a photonic quantum memory is the combination of an efficient light-matter interface with a low-decoherence encoding. To increase the time before the quantum information is lost, a thorough analysis of the relevant decoherence mechanisms is indispensable. Our optical quantum memory consists of a single rubidium atom trapped in a two dimensional optical lattice in a high-finesse Fabry-Perot-type optical resonator. The qubit is initially stored in a superposition of Zeeman states, making magnetic field fluctuations the dominant source of decoherence. The impact to this type of noise is greatly reduced by transferring the qubit into a subspace less susceptible to magnetic field fluctuations. In this configuration, the achievable coherence times are no longer limited by those fluctuations, but decoherence mechanisms induced by the trapping beams pose a new limit. We will discuss the origin and magnitude of the relevant effects and strategies for possible resolutions.
It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantummechanical system subjected to a slow periodic variation of parameters. The main example is given by systems (e.g., quantum billiards and quantum graphs) with periodically divided configuration space. In special cases, the process can also lead to a long period of cooling that precedes the acceleration, and to the desertion of the states with a particular value of the quantum number.
Once again, I take advantage of the wonderfully liberal and tolerant mood Andrei Khrennikov sets at his yearly conferences by submitting a nonstandard paper for the proceedings. This pseudo-paper consists of excerpts drawn from two of my samizdats [Quantum States: What the Hell Are They? and Darwinism All the Way Down (and Probabilism All the Way Back Up)] that I think best summarize what I am aiming for on the broadest scale with my quantum foundations program. Section 1 tries to draw a picture of a physical world whose essence is "Darwinism all the way down." Section 2 outlines how quantum theory should be viewed in light of that, i.e., as being an expression of probabilism (in Bruno de Finetti or Richard Jeffrey's sense) all the way back up. Section 3 describes how the idea of "identical" quantum measurement outcomes, though sounding atomistic in character, nonetheless meshes well with a William Jamesian style "radical pluralism." Sections 4 and 5 further detail how quantum theory should not be viewed so much as a "theory of the world," but rather as a theory of decision-making for agents immersed within a quantum world—that is, a world in continual creation. Finally, Sections 6 and 7 attempt to sketch once again the very positive sense in which quantum theory is incomplete, but still just as complete is it can be. In total, I hope these heady speculations convey some of the excitement and potential I see for the malleable world quantummechanics hints of.
Random walks are a powerful tool for the efficient implementation of algorithms in classical computation. Their quantum-mechanical analogues, called quantum walks, hold similar promise. Quantum walks provide a model of quantum computation that has recently been shown to be equivalent in power to the standard circuit model. As in the classical case, quantum walks take place on graphs and can undergo discrete or continuous evolution, though quantum evolution is unitary and therefore deterministic until a measurement is made. This thesis considers the usefulness of continuous-time quantum walks to quantum computation from the perspectives of both their fundamental power under various formulations, and their applicability in practical experiments. In one extant scheme, logical gates are effected by scattering processes. The results of an exhaustive search for single-qubit operations in this model are presented. It is shown that the number of distinct operations increases exponentially with the number of vertices in the scattering graph. A catalogue of all graphs on up to nine vertices that implement single-qubit unitaries at a specific set of momenta is included in an appendix. I develop a novel scheme for universal quantum computation called the discontinuous quantum walk, in which a continuous-time quantum walker takes discrete steps of evolution via perfect quantum state transfer through small 'widget' graphs. The discontinuous quantum-walk scheme requires an exponentially sized graph, as do prior discrete and continuous schemes. To eliminate the inefficient vertex resource requirement, a computation scheme based on multiple discontinuous walkers is presented. In this model, n interacting walkers inhabiting a graph with 2n vertices can implement an arbitrary quantum computation on an input of length n, an exponential savings over previous universal quantum walk schemes. This is the first quantum walk scheme that allows for the application of quantum error correction
Quantum computation and cryptography both involve scenarios in which a user interacts with an imperfectly modelled or 'untrusted' system. It is therefore of fundamental and practical interest to devise tests that reveal whether the system is behaving as instructed. In 1969, Clauser, Horne, Shimony and Holt proposed an experimental test that can be passed by a quantum-mechanical system but not by a system restricted to classical physics. Here we extend this test to enable the characterization of a large quantum system. We describe a scheme that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics. The bipartite system is treated as two black boxes, with no assumptions about their inner workings except that they obey quantum physics. The scheme works even if the system is explicitly designed to undermine it; any misbehaviour is detected. Among its applications, our scheme makes it possible to test whether a claimed quantum computer is truly quantum. It also advances towards a goal of quantum cryptography: namely, the use of 'untrusted' devices to establish a shared random key, with security based on the validity of quantum physics.
Motivated by recent measurements of the lifetime (decay width) of paramagnons in quantum antiferromagnet TlCuCl3, we investigate paramagnon decay in a heat bath and formulate an appropriate quantum theory. Our formulation can be split into two regimes: (i) a nonperturbative, "hot quantum soup" regime where the paramagnon width is comparable to its energy; (ii) a usual perturbative regime where the paramagnon width is significantly lower than its energy. Close to the Neel temperature, the paramagnon width becomes comparable to its energy and falls into the hot quantum soup regime. To describe this regime, we develop a new finite frequency, finite temperature technique for a nonlinear quantum field theory; the "golden rule of quantum kinetics." The formulation is generic and applicable to any three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point. Specifically, we apply our results to TlCuCl3 and find agreement with experimental data. Additionally, we show that logarithmic running of the coupling constant in the upper critical dimension changes the commonly accepted picture of the quantum disordered and quantum critical regimes.
We demonstrate the existence of a novel set of discrete symmetries in the context of the N=2 supersymmetric (SUSY) quantummechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X–Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We showmore » that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N=2 SUSY quantummechanical system can be shown to be a tractable model for the Hodge theory. -- Highlights: •Discrete symmetries of two completely different kinds of N=2 supersymmetric quantummechanical models have been discussed. •The discrete symmetries provide physical realizations of Hodge duality. •The continuous symmetries provide the physical realizations of de Rham cohomological operators. •Our work sheds a new light on the meaning of the above abstract operators.« less
The extension of thermodynamics into the realm of quantummechanics, where quantum fluctuations dominate and systems need not occupy definite states, poses unique challenges. Superconducting quantum circuits offer exquisite control over the environment of simple quantum systems allowing the exploration of thermodynamics at the quantum level through measurement and feedback control. We use a superconducting transmon qubit that is resonantly coupled to a waveguide cavity as an effectively one-dimensional quantum emitter. By driving the emitter and detecting the fluorescence with a near-quantum-limited Josephson parametric amplifier, we track the evolution of the quantum state and characterize the work and heat along single quantum trajectories. By using quantum feedback control to compensate for heat exchanged with the emitter's environment we are able to extract the work statistics associated with the quantum evolution and examine fundamental fluctuation theorems in non-equilibrium thermodynamics. This work was supported by the Alfred P. Sloan Foundation, the National Science Foundation, and the Office of Naval Research.
We present a formalism of Galilean quantummechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantummechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these representations determine the structure of quantummechanics in non-inertialmore » reference frames. Our representations of the Galilean line group contain the usual unitary projective representations of the Galilei group, but have a more intricate cocycle structure. The transformation formula for the Hamiltonian under the Galilean line group shows that in a non-inertial reference frame it acquires a fictitious potential energy term that is proportional to the inertial mass, suggesting the equivalence of inertial mass and gravitational mass in quantummechanics. - Highlights: Black-Right-Pointing-Pointer A formulation of Galilean quantummechanics in non-inertial reference frames is given. Black-Right-Pointing-Pointer The key concept is the Galilean line group, an infinite dimensional group. Black-Right-Pointing-Pointer Unitary, cocycle representations of the Galilean line group are constructed. Black-Right-Pointing-Pointer A non-central extension of the group underlies these representations. Black-Right-Pointing-Pointer Quantum equivalence principle and gravity emerge from these representations.« less
This talk is dedicated to my friend and collaborator, Prof. Dr. Heinz-Dietrich Doebner, on the occasion of his 80th birthday. I shall review some highlights of the approach we have taken in deriving and interpreting an interesting class of nonlinear time-evolution equations for quantum-mechanical wave functions, with few equations; more detail may be found in the references. Then I shall comment on the corresponding hydrodynamical description.
We describe the difficulties advanced undergraduate and graduate students have with concepts related to addition of angular momentum in quantummechanics. We also describe the development and implementation of a research-based learning tool, Quantum Interactive Learning Tutorial (QuILT), to reduce these difficulties. The preliminary evaluation…
Secure communication protocols are becoming increasingly important, e.g. for internet-based communication. Quantum key distribution (QKD) allows two parties, commonly called Alice and Bob, to generate a secret sequence of 0s and 1s called a key that is only known to themselves. Classically, Alice and Bob could never be certain that their communication was not compromised by a malicious eavesdropper. Quantummechanics however makes secure communication possible. The fundamental principle of quantummechanics that taking a measurement perturbs the system (unless the measurement is compatible with the quantum state) also applies to an eavesdropper. Using appropriate protocols to create the key, Alice and Bob can detect the presence of an eavesdropper by errors in their measurements. As part of the QuVis QuantumMechanics Visualisation Project, we have developed a suite of four interactive simulations that demonstrate the basic principles of three different QKD protocols. The simulations use either polarised photons or spin 1/2 particles as physical realisations. The simulations and accompanying activities are freely available for use online or download, and run on a wide range of devices including tablets and PCs. Evaluation with students over three years was used to refine the simulations and activities. Preliminary studies show that the refined simulations and activities help students learn the basic principles of QKD at both the introductory and advanced undergraduate levels.
This article is divided into two parts. In the first part, the atomic unit (au) system is introduced and the scales of time, space (length), and speed, as well as those of mass and energy, in the atomic world are discussed. In the second part, the utility of atomic units in quantummechanical and spectroscopic calculations is illustrated with…
Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.
2016-04-01
The attempt to gain a theoretical understanding of the concept of time in quantummechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Halbertal, D.; Cuppens, J.; Shalom, M. Ben; Embon, L.; Shadmi, N.; Anahory, Y.; Naren, H. R.; Sarkar, J.; Uri, A.; Ronen, Y.; Myasoedov, Y.; Levitov, L. S.; Joselevich, E.; Geim, A. K.; Zeldov, E.
2016-11-01
Energy dissipation is a fundamental process governing the dynamics of physical, chemical and biological systems. It is also one of the main characteristics that distinguish quantum from classical phenomena. In particular, in condensed matter physics, scattering mechanisms, loss of quantum information or breakdown of topological protection are deeply rooted in the intricate details of how and where the dissipation occurs. Yet the microscopic behaviour of a system is usually not formulated in terms of dissipation because energy dissipation is not a readily measurable quantity on the micrometre scale. Although nanoscale thermometry has gained much recent interest, existing thermal imaging methods are not sensitive enough for the study of quantum systems and are also unsuitable for the low-temperature operation that is required. Here we report a nano-thermometer based on a superconducting quantum interference device with a diameter of less than 50 nanometres that resides at the apex of a sharp pipette: it provides scanning cryogenic thermal sensing that is four orders of magnitude more sensitive than previous devices—below 1 μK Hz-1/2. This non-contact, non-invasive thermometry allows thermal imaging of very low intensity, nanoscale energy dissipation down to the fundamental Landauer limit of 40 femtowatts for continuous readout of a single qubit at one gigahertz at 4.2 kelvin. These advances enable the observation of changes in dissipation due to single-electron charging of individual quantum dots in carbon nanotubes. They also reveal a dissipation mechanism attributable to resonant localized states in graphene encapsulated within hexagonal boron nitride, opening the door to direct thermal imaging of nanoscale dissipation processes in quantum matter.
Superposition gives rise to the probabilistic nature of quantummechanics and is therefore one of the concepts at the heart of quantummechanics. Although we have found that many students can successfully use the idea of superposition to calculate the probabilities of different measurement outcomes, they are often unable to identify the…
In 1990, Bas C. van Fraassen defined the modal interpretation of quantummechanics as the consideration of it as ``a pure theory of the possible, with testable, empirical implications for what actually happens". This is a narrow, traditional understanding of modality, only in the sense of the concept of possibility (usually denoted in logic by the C. I. Lewis's symbol 3) and the concept of necessity 2 defined by means of 3. In modern logic, however, modality is understood in a much wider sense as any intensional functor (i.e. non-extensional or determined not only by the truth value of a sentence). In the recent (independent of van Fraassen) publications of the author (1997), an attempt was made to apply this wider understanding of modality to interpretation of classical and quantum physics. In the present lecture, these problems are discussed on the background of a brief review of the logical approch to quantummechanics in the recent 7 decades. In this discussion, the new concepts of sub-modality and super-modality of many orders are used.
Alhaidari, A. D., E-mail: haidari@sctp.org.sa; Ismail, M. E. H.
2015-07-15
In the standard formulation of quantummechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which ismore » written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.« less
The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? Here, we address these questions from the standpoint of quantummechanics in a new framework for multipartite correlations that does not assume a pre-defined global causal structure but only the validity of quantummechanics locally. All known situations that respect causal order, including space-like and time-like separated experiments, are captured by this framework in a unified way. Surprisingly, we find correlations that cannot be understood in terms of definite causal order. These correlations violate a 'causal inequality' that is satisfied by all space-like and time-like correlations. We further show that in a classical limit causal order always arises, which suggests that space-time may emerge from a more fundamental structure in a quantum-to-classical transition. PMID:23033068
Friedman, Andrew S.; Kaiser, David I.; Gallicchio, Jason; Team 1: University of Vienna, InstituteQuantum Optics and Quantum Information; Team 2: UC San Diego Cosmology Group; Team 3: NASA/JPL/Caltech
2016-06-01
We report on an in progress "Cosmic Bell" experiment that will leverage cosmology to test quantummechanics and Bell's inequality using astronomical observations. Different iterations of our experiment will send polarization-entangled photons through the open air to detectors ~1-100 kilometers apart, whose settings would be rapidly chosen using real-time telescopic observations of Milky Way stars, and eventually distant, causally disconnected, cosmological sources - such as pairs of quasars or patches of the cosmic microwave background - all while the entangled pair is still in flight. This would, for the first time, attempt to fully close the so-called "setting independence" or "free will" loophole in experimental tests of Bell's inequality, whereby an alternative theory could mimic the quantum predictions if the experimental settings choices shared even a small correlation with unknown, local, causal influences a mere few milliseconds prior to the experiment. A full Cosmic Bell test would push any such influence all the way back to the hot big bang, since the end of any period of inflation, 13.8 billion years ago, an improvement of 20 orders of magnitude compared to the best previous experiments. Redshift z > 3.65 quasars observed at optical wavelengths are the optimal candidate source pairs using present technology. Our experiment is partially funded by the NSF INSPIRE program, in collaboration with MIT, UC San Diego, Harvey Mudd College, NASA/JPL/Caltech, and the University of Vienna. Such an experiment has implications for our understanding of nature at the deepest level. By testing quantummechanics in a regime never before explored, we would at the very least extend our confidence in quantum theory, while at the same time severely constraining large classes of alternative theories. If the experiment were to uncover discrepancies from the quantum predictions, there could be crucial implications for early-universe cosmology, the security of quantum encryption
Given the ubiquity of hydride-transfer reactions in enzyme-catalyzed processes, identifying the appropriate computational method for evaluating such biological reactions is crucial to perform theoretical studies of these processes. In this paper, the hydride-transfer step catalyzed by thymidylate synthase (TSase) is studied by examining hybrid quantummechanics/molecular mechanics (QM/MM) potentials via multiple semiempirical methods and the M06-2X hybrid density functional. Calculations of protium and tritium transfer in these reactions across a range of temperatures allowed calculation of the temperature dependence of kinetic isotope effects (KIE). Dynamics and quantum-tunneling effects are revealed to have little effect on the reaction rate, but are significant in determining the KIEs and their temperature dependence. A good agreement with experiments is found, especially when computed for RM1/MM simulations. The small temperature dependence of quantum tunneling corrections and the quasiclassical contribution term cancel each other, while the recrossing transmission coefficient seems to be temperature-independent over the interval of 5-40 °C.
We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantummechanics 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 assumedmore » to be twice differentiable at the origin, then we arrive at a version of Bell’s theorem. On the one hand, we are showing that any realistic theory of quantummechanics which incorporates the kinematic aspects of relativity must lead to this type of rough correlation function that is once but not twice differentiable. On the other hand, this study brings us a single degree of differentiability away from a relativistic von Neumann no hidden variables theorem.« less
Graph-theoretic quantum system modelling (GTQSM) is facilitated by considering the fundamental unit of quantum computation and information, viz. a quantum bit or qubit as a basic building block. Unit directional vectors "ket 0" and "ket 1" constitute two distinct fundamentalquantum across variable orthonormal basis vectors, for the Hilbert space, specifying the direction of propagation of information, or computation data, while complementary fundamentalquantum through, or flow rate, variables specify probability parameters, or amplitudes, as surrogates for scalar quantum information measure (von Neumann entropy). This paper applies GTQSM in continuum of protein heterodimer tubulin molecules of self-assembling polymers, viz. microtubules in the brain as a holistic system of interacting components representing hierarchical clustered quantum Hopfield network, hQHN, of networks. The quantum input/output ports of the constituent elemental interaction components, or processes, of tunnelling interactions and Coulombic bidirectional interactions are in cascade and parallel interconnections with each other, while the classical output ports of all elemental components are interconnected in parallel to accumulate micro-energy functions generated in the system as Hamiltonian, or Lyapunov, energy function. The paper presents an insight, otherwise difficult to gain, for the complex system of systems represented by clustered quantum Hopfield network, hQHN, through the application of GTQSM construct.
We present an algorithmic extension of a numerical optimization scheme for analytic capping potentials for use in mixed quantum-classical (quantummechanical/molecular mechanical, QM/MM) ab initio calculations. Our goal is to minimize bond-cleavage-induced perturbations in the electronic structure, measured by means of a suitable penalty functional. The optimization algorithm-a variant of the artificial bee colony (ABC) algorithm, which relies on swarm intelligence-couples deterministic (downhill gradient) and stochastic elements to avoid local minimum trapping. The ABC algorithm outperforms the conventional downhill gradient approach, if the penalty hypersurface exhibits wiggles that prevent a straight minimization pathway. We characterize the optimized capping potentials by computing NMR chemical shifts. This approach will increase the accuracy of QM/MM calculations of complex biomolecules.
Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan
2001-01-01
The steady state characteristics of MOSFETS that are of practical Interest are the drive current, off-current, dope of drain current versus drain voltage, and threshold voltage. In this section, we show that quantummechanical simulations yield significantly different results from drift-diffusion based methods. These differences arise because of the following quantummechanical features: (I) polysilicon gate depletion in a manner opposite to the classical case (II) dependence of the resonant levels in the channel on the gate voltage, (III) tunneling of charge across the gate oxide and from source to drain, (IV) quasi-ballistic flow of electrons. Conclusions dI/dV versus V does not increase in a manner commensurate with the increase in number of subbands. - The increase in dI/dV with bias is much smaller then the increase in the number of subbands - a consequence of bragg reflection. Our calculations show an increase in transmission with length of contact, as seen in experiments. It is desirable for molecular electronics applications to have a small contact area, yet large coupling. In this case, the circumferential dependence of the nanotube wave function dictates: - Transmission in armchair tubes saturates around unity - Transmission in zigzag tubes saturates at two.
This paper explains the delayed choice quantum eraser of Kim et al. (A delayed choice quantum eraser, 1999) in terms of the transactional interpretation (TI) of quantummechanics by Cramer (Rev Mod Phys 58:647, 1986, The quantum handshake, entanglement, nonlocality and transactions, 1986). It is kept deliberately mathematically simple to help explain the transactional technique. The emphasis is on a clear understanding of how the instantaneous "collapse" of the wave function due to a measurement at a specific time and place may be reinterpreted as a relativistically well-defined collapse over the entire path of the photon and over the entire transit time from slit to detector. This is made possible by the use of a retarded offer wave, which is thought to travel from the slits (or rather the small region within the parametric crystal where down-conversion takes place) to the detector and an advanced counter wave traveling backward in time from the detector to the slits. The point here is to make clear how simple the transactional picture is and how much more intuitive the collapse of the wave function becomes if viewed in this way. Also, any confusion about possible retro-causal signaling is put to rest. A delayed choice quantum eraser does not require any sort of backward in time communication. This paper makes the point that it is preferable to use the TI over the usual Copenhagen interpretation for a more intuitive understanding of the quantum eraser delayed choice experiment. Both methods give exactly the same end results and can be used interchangeably.
Klink, W.H.; Wickramasekara, S., E-mail: wickrama@grinnell.edu; Department of Physics, Grinnell College, Grinnell, IA 50112
2014-01-15
In previous work we have developed a formulation of quantummechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group that includes transformations amongst non-inertial reference frames. These representations show that in quantummechanics, just as is the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. A special feature of these previously constructed representations is that they all respect the non-relativistic equivalence principle, wherein the fictitious forces associated with linear acceleration canmore » equivalently be described by gravitational forces. In this paper we exhibit a large class of cocycle representations of the Galilean line group that violate the equivalence principle. Nevertheless the classical mechanics analogue of these cocycle representations all respect the equivalence principle. -- Highlights: •A formulation of Galilean quantummechanics in non-inertial reference frames is given. •The key concept is the Galilean line group, an infinite dimensional group. •A large class of general cocycle representations of the Galilean line group is constructed. •These representations show violations of the equivalence principle at the quantum level. •At the classical limit, no violations of the equivalence principle are detected.« less
The theory of dense hydrogen plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. The statistical mechanical calculation of the plasma equation of state is intended for stellar interiors. The general approach is extended to the calculation of the equation of state of the outer layers of large planets.
Intuition from our everyday lives gives rise to the belief that information exchanged between remote parties is carried by physical particles. Surprisingly, in a recent theoretical study [Salih H, Li ZH, Al-Amri M, Zubairy MS (2013) Phys Rev Lett 110:170502], quantummechanics was found to allow for communication, even without the actual transmission of physical particles. From the viewpoint of communication, this mystery stems from a (nonintuitive) fundamental concept in quantummechanics-wave-particle duality. All particles can be described fully by wave functions. To determine whether light appears in a channel, one refers to the amplitude of its wave function. However, in counterfactual communication, information is carried by the phase part of the wave function. Using a single-photon source, we experimentally demonstrate the counterfactual communication and successfully transfer a monochrome bitmap from one location to another by using a nested version of the quantum Zeno effect.
This thesis presents a problem for the foundations of quantummechanics. It arises from the way that theory describes the composition of larger systems in terms of smaller ones, and renders untenable a wide range of interpretations of quantummechanics. That quantummechanics is difficult to interpret is old news, given the well-known Measurement Problem. But the problem I raise is quite different, and in important respects more fundamental. In brief: The physical world exhibits mereological structure: physical objects have parts, which in turn have parts, and so on. A natural way to try to represent this structure is by means of a particle theory, according to which the physical world consists entirely enduring physical objects which themselves have no proper parts, but aggregates of which are, or compose, all physical objects. Elementary, non-relativistic quantummechanics can be cast in this mold--at least, according to the usual expositions of that theory. But herein lies the problem: the standard attempt to give a systematic particle interpretation to elementary quantummechanics results in nonsense, thanks to the well-established principle of Permutation Invariance, which constrains the quantum -mechanical description of systems containing identical particles. Specifically, it follows from the most minimal principles of a particle interpretation (much weaker than those needed to generate the Measurement Problem), together with Permutation Invariance, that systems identical in composition must have the same physical state. In other words, systems which merely have the same numbers of the same types of particles are therefore, at all times, perfect physical duplicates. This conclusion is absurd: e.g., it is quite plausible that some of those particles which compose my body make up a system identical in composition to some pepperoni pizza. Yet no part of me is a qualitative physical duplicate of any pepperoni pizza. Perhaps "you are what you eat" --but not in
Pothos & Busemeyer (P&B) argue that quantum probability (QP) provides a descriptive model of behavior and can also provide a rational analysis of a task. We discuss QP models using Marr's levels of analysis, arguing that they make most sense as algorithmic level theories. We also highlight the importance of having clear interpretations for basic mechanisms such as interference.
Accurate computation of the pKa value of a compound in solution is important but challenging. Here, a new mixing quantummechanical/molecular mechanical (QM/MM) Hamiltonian method is developed to simulate the free-energy change associated with the protonation/deprotonation processes in solution. The mixing Hamiltonian method is designed for efficient quantummechanical free-energy simulations by alchemically varying the nuclear potential, i.e., the nuclear charge of the transforming nucleus. In pKa calculation, the charge on the proton is varied in fraction between 0 and 1, corresponding to the fully deprotonated and protonated states, respectively. Inspired by the mixing potential QM/MM free energy simulation method developed previously [H. Hu and W. T. Yang, J. Chem. Phys. 2005, 123, 041102], this method succeeds many advantages of a large class of λ-coupled free-energy simulation methods and the linear combination of atomic potential approach. Theory and technique details of this method, along with the calculation results of the pKa of methanol and methanethiol molecules in aqueous solution, are reported. The results show satisfactory agreement with the experimental data.
The astonishing, exponentially increasing rates of genome sequencing has led to one of the most significant challenges for the biological and computational sciences in the 21st century: assigning the likely functions of the encoded proteins. Enzymes represent a particular challenge, and a critical one, because the universe of enzymes is likely to contain many novel functions that may be useful for synthetic biology, or as drug targets. Current approaches to protein annotation are largely based on bioinformatics. At the simplest level, this annotation involves transferring the annotations of characterized enzymes to related sequences. In practice, however, there is no simple,more » sequence based criterion for transferring annotations, and bioinformatics alone cannot propose new enzymatic functions. Structure-based computational methods have the potential to address these limitations, by identifying potential substrates of enzymes, as we and others have shown. One successful approach has used in silico 'docking' methods, more commonly applied in structure-based drug design, to identify possible metabolite substrates. A major limitation of this approach is that it only considers substrate binding, and does not directly assess the potential of the enzyme to catalyze a particular reaction using a particular substrate. That is, substrate binding affinity is necessary but not sufficient to assign function. A reaction profile is ultimately what is needed for a more complete quantitative description of function. To address this rather fundamental limitation, they propose to use quantummechanical methods to explicitly compute transition state barriers that govern the rates of catalysis. Although quantummechanical, and mixed quantum/classical (QM/MM), methods have been used extensively to investigate enzymatic reactions, the focus has been primarily on elucidating complex reaction mechanisms. Here, the key catalytic steps are known, and they use these methods quantify
Purdy, T. P.; Grutter, K. E.; Srinivasan, K.; Taylor, J. M.
2017-06-01
The act of position measurement alters the motion of an object being measured. This quantum measurement backaction is typically much smaller than the thermal motion of a room-temperature object and thus difficult to observe. By shining laser light through a nanomechanical beam, we measure the beam’s thermally driven vibrations and perturb its motion with optical force fluctuations at a level dictated by the Heisenberg measurement-disturbance uncertainty relation. We demonstrate a cross-correlation technique to distinguish optically driven motion from thermally driven motion, observing this quantum backaction signature up to room temperature. We use the scale of the quantum correlations, which is determined by fundamental constants, to gauge the size of thermal motion, demonstrating a path toward absolute thermometry with quantummechanically calibrated ticks.
Ameri, V.; Eghbali-Arani, M.; Mari, A.; Farace, A.; Kheirandish, F.; Giovannetti, V.; Fazio, R.
2015-01-01
Spontaneous synchronization is a fundamental phenomenon, important in many theoretical studies and applications. Recently, this effect has been analyzed and observed in a number of physical systems close to the quantum-mechanical regime. In this work we propose mutual information as a useful order parameter which can capture the emergence of synchronization in very different contexts, ranging from semiclassical to intrinsically quantum-mechanical systems. Specifically, we first study the synchronization of two coupled Van der Pol oscillators in both classical and quantum regimes and later we consider the synchronization of two qubits inside two coupled optical cavities. In all these contexts, we find that mutual information can be used as an appropriate figure of merit for determining the synchronization phases independently of the specific details of the system.
Mozaffari, F. S.; Hassanabadi, H.; Sobhani, H.; Chung, W. S.
2018-05-01
In this paper, a conformable fractional quantummechanic has been introduced using three postulates. Then in such a formalism, Schr¨odinger equation, probability density, probability flux and continuity equation have been derived. As an application of considered formalism, a fractional-radial harmonic oscillator has been considered. After obtaining its wave function and energy spectrum, effects of the conformable fractional parameter on some quantities have been investigated and plotted for different excited states.
We study quantumness-generating capability of quantum dynamics, where quantumness refers to the noncommutativity between the initial state and the evolving state. In terms of the commutator of the square roots of the initial state and the evolving state, we define a measure to quantify the quantumness-generating capability of quantum dynamics with respect to initial states. Quantumness-generating capability is absent in classical dynamics and hence is a fundamental characteristic of quantum dynamics. For qubit systems, we present an analytical form for this measure, by virtue of which we analyze several prototypical dynamics such as unitary dynamics, phase damping dynamics, amplitude damping dynamics, and random unitary dynamics (Pauli channels). Necessary and sufficient conditions for the monotonicity of quantumness-generating capability are also identified. Finally, we compare these conditions for the monotonicity of quantumness-generating capability with those for various Markovianities and illustrate that quantumness-generating capability and quantum Markovianity are closely related, although they capture different aspects of quantum dynamics.
Inferring causal relations from experimental observations is of primal importance in science. Instrumental tests provide an essential tool for that aim, as they allow one to estimate causal dependencies even in the presence of unobserved common causes. In view of Bell's theorem, which implies that quantummechanics is incompatible with our most basic notions of causality, it is of utmost importance to understand whether and how paradigmatic causal tools obtained in a classical setting can be carried over to the quantum realm. Here we show that quantum effects imply radically different predictions in the instrumental scenario. Among other results, we show that an instrumental test can be violated by entangled quantum states. Furthermore, we demonstrate such violation using a photonic set-up with active feed-forward of information, thus providing an experimental proof of this new form of non-classical behaviour. Our findings have fundamental implications in causal inference and may also lead to new applications of quantum technologies.
Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schrödinger's equation. In the former, the Hamiltonian is fixed, while in the latter, the Hamiltonian varies with time. As a result, their formulations of Grover's algorithm evolve differently through Hilbert space. We show that this difference is fundamental; they cannot be made to evolve along each other's path without introducing structure more powerful than the standard oracle for unstructured search. For an adiabatic quantum evolution to evolve like the quantum walk search algorithm, it must interpolate between three fixed Hamiltonians, one of which is complex and introduces structure that is stronger than the oracle for unstructured search. Conversely, for a quantum walk to evolve along the path of the adiabatic search algorithm, it must be a chiral quantum walk on a weighted, directed star graph with structure that is also stronger than the oracle for unstructured search. Thus, the two techniques, although similar in being described by Hamiltonians that govern their evolution, compute by fundamentally irreconcilable means.
Quantum electromechanical systems incorporating superconducting qubits have received extensive interest in recent years due to their promising prospects for studying fundamental topics of quantummechanics such as quantum measurement, entanglement and decoherence in new macroscopic limits, also for their potential as elements in technological applications in quantum information network and weak force detector, to name a few. In this presentation we will discuss ours efforts toward to devise an electromechanical circuit to strongly couple a nanomechanical resonator to a superconductor qubit, where a high voltage dc-bias is required, to study quantum behavior of a mechanical resonator. Preliminary results of our latest generation of devices integrating a superconductor qubit into a high-Q voltage biased microwave cavities are presented. Developments in the circuit design to couple a mechanical resonator to a qubit in the high-Q voltage bias CPW cavity is discussed as well prospects of achieving single-phonon measurement resolution. National Science Foundation under Grant No. DMR-1056423 and Grant No. DMR-1312421.
Methods of solution of the inverse scattering problem at fixed energy in quantummechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantummechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.
More than 10 million billion photons of light strike a leaf each second. Incredibly, almost every red-coloured photon is captured by chlorophyll pigments and initiates steps to plant growth. Last year we reported that marine algae use quantummechanics in order to optimize photosynthesis [1], a process essential to its survival. These and other insights from the natural world promise to revolutionize our ability to harness the power of the sun. In a recent review [2] we described the principles learned from studies of various natural antenna complexes and suggested how to utilize that knowledge to shape future technologies. We forecast the need to develop ways to direct and regulate excitation energy flow using molecular organizations that facilitate feedback and control--not easy given that the energy is only stored for a billionth of a second. In this presentation I will describe new results that explain the observation and meaning of quantum-coherent energy transfer. [4pt] [1] Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer, and Gregory D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature 463, 644-648 (2010).[0pt] [2] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro and Rienk van Grondelle, ``Lessons from nature about solar light harvesting'' Nature Chem. 3, 763-774 (2011).
The design of entry vehicles requires predictions of aerothermal environment during the hypersonic phase of their flight trajectories. These predictions are made using computational fluid dynamics (CFD) codes that often rely on physics and chemistry models of nonequilibrium processes. The primary processes of interest are gas phase chemistry, internal energy relaxation, electronic excitation, nonequilibrium emission and absorption of radiation, and gas-surface interaction leading to surface recession and catalytic recombination. NASAs Hypersonics Project is advancing the state-of-the-art in modeling of nonequilibrium phenomena by making detailed spectroscopic measurements in shock tube and arcjets, using ab-initio quantummechanical techniques develop fundamental chemistry and spectroscopic databases, making fundamental measurements of finite-rate gas surface interactions, implementing of detailed mechanisms in the state-of-the-art CFD codes, The development of new models is based on validation with relevant experiments. We will present the latest developments and a roadmap for the technical areas mentioned above
This article presents a general discussion of several aspects of our present understanding of quantummechanics. The emphasis is put on the very special correlations that this theory makes possible: They are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except for very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. For this purpose, orthodox quantummechanics introduces a special postulate: the reduction of the state vector, which comes in addition to the Schrödinger evolution postulate. Nevertheless, the presence in parallel of two evolution processes of the same object (the state vector) may be a potential source for conflicts; various attitudes that are possible to avoid this problem are discussed in this text. After a brief historical introduction, recalling how the very special status of the state vector has emerged in quantummechanics, various conceptual difficulties are introduced and discussed. The Einstein-Podolsky-Rosen (EPR) theorem is presented with the help of a botanical parable, in a way that emphasizes how deeply the EPR reasoning is rooted into what is often called "scientific method." In another section the Greenberger-Horne-Zeilinger argument, the Hardy impossibilities, as well as the Bell-Kochen-Specker theorem are introduced in simple terms. The final two sections attempt to give a summary of the present situation: One section discusses nonlocality and entanglement as we see it presently, with brief mention of recent experiments; the last section contains a (nonexhaustive) list of various attitudes that are found among physicists, and that are helpful to alleviate the conceptual difficulties of quantummechanics.
Spekkens’ toy model is a non-contextual hidden variable model with an epistemic restriction, a constraint on what an observer can know about reality. The aim of the model, developed for continuous and discrete prime degrees of freedom, is to advocate the epistemic view of quantum theory, where quantum states are states of incomplete knowledge about a deeper underlying reality. Many aspects of quantummechanics and protocols from quantum information can be reproduced in the model. In spite of its significance, a number of aspects of Spekkens’ model remained incomplete. Formal rules for the update of states after measurement had not been written down, and the theory had only been constructed for prime-dimensional and infinite dimensional systems. In this work, we remedy this, by deriving measurement update rules and extending the framework to derive models in all dimensions, both prime and non-prime. Stabiliser quantummechanics (SQM) is a sub-theory of quantummechanics with restricted states, transformations and measurements. First derived for the purpose of constructing error correcting codes, it now plays a role in many areas of quantum information theory. Previously, it had been shown that Spekkens’ model was operationally equivalent to SQM in the case of odd prime dimensions. Here, exploiting known results on Wigner functions, we extend this to show that Spekkens’ model is equivalent to SQM in all odd dimensions, prime and non-prime. This equivalence provides new technical tools for the study of technically difficult compound-dimensional SQM.
Quantum field theory (QFT) is the basis of some of the most fundamental theories in modern physics, but it is not an easy subject to learn. In the present article we intend to pave the way from quantummechanics to QFT for students at early graduate or advanced undergraduate level. More specifically, we propose a new way of visualising the wave function Ψ of a linear chain of interacting quantum harmonic oscillators, which can be seen as a model for a simple one-dimensional bosonic quantum field. The main idea is to draw randomly chosen classical states of the chain superimposed upon each other and use a grey scale to represent the value of Ψ at the corresponding coordinates of the quantised system. Our goal is to establish a better intuitive understanding of the mathematical objects underlying quantum field theories and solid state physics.
The ability to manipulate quantum states of light by integrated devices may open new perspectives both for fundamental tests of quantummechanics and for novel technological applications. However, the technology for handling polarization-encoded qubits, the most commonly adopted approach, is still missing in quantum optical circuits. Here we demonstrate the first integrated photonic controlled-NOT (CNOT) gate for polarization-encoded qubits. This result has been enabled by the integration, based on femtosecond laser waveguide writing, of partially polarizing beam splitters on a glass chip. We characterize the logical truth table of the quantum gate demonstrating its high fidelity to the expected one. In addition, we show the ability of this gate to transform separable states into entangled ones and vice versa. Finally, the full accessibility of our device is exploited to carry out a complete characterization of the CNOT gate through a quantum process tomography.
New Delhi metallo-β-lactamase-1 (NDM-1) has emerged as a major global threat to human health for its rapid rate of dissemination and ability to make pathogenic microbes resistant to almost all known β-lactam antibiotics. In addition, effective NDM-1 inhibitors have not been identified to date. In spite of the plethora of structural and kinetic data available, the accurate molecular characteristics of and details on the enzymatic reaction of NDM-1 hydrolyzing β-lactam antibiotics remain incompletely understood. In this study, a combined computational approach including molecular docking, molecular dynamics simulations and quantummechanics/molecular mechanics calculations was performed to characterize the catalytic mechanism of meropenem catalyzed by NDM-1. The quantummechanics/molecular mechanics results indicate that the ionized D124 is beneficial to the cleavage of the C-N bond within the β-lactam ring. Meanwhile, it is energetically favorable to form an intermediate if no water molecule coordinates to Zn2. Moreover, according to the molecular dynamics results, the conserved residue K211 plays a pivotal role in substrate binding and catalysis, which is quite consistent with previous mutagenesis data. Our study provides detailed insights into the catalytic mechanism of NDM-1 hydrolyzing meropenem β-lactam antibiotics and offers clues for the discovery of new antibiotics against NDM-1 positive strains in clinical studies.
Quantummechanics, arguably one of the greatest achievements of modern physics, has not only fundamentally changed our understanding of nature but is also taking an ever increasing role in engineering. Today, the control of quantum systems has already had a far-reaching impact on time and frequency metrology. By gaining further control over a large variety of different quantum systems, many potential applications are emerging. Those applications range from the development of quantum sensors and new quantum metrological approaches to the realization of quantum information processors and quantum networks. Unfortunately most quantum systems are very fragile objects that require tremendous experimental effort to avoid dephasing. Being able to control the interaction between a quantum system with its local environment embodies therefore an important aspect for application and hence is at the focus of this thesis. Nitrogen Vacancy (NV) color centers in diamond have recently attracted attention as a room temperature solid state spin system that expresses long coherence times. The electronic spin associated with NV centers can be efficiently manipulated, initialized and readout using microwave and optical techniques. Inspired by these extraordinary properties, much effort has been dedicated to use NV centers as a building block for scalable room temperature quantum information processing and quantum communication as well as a quantum sensing. In the first part of this thesis we demonstrate that by decoupling the spin from the local environment the coherence time of a NV quantum register can be extended by three order of magnitudes. Employing a novel dissipative mechanism in combination with dynamical decoupling, memory times exceeding one second are observed. The second part shows that, based on quantum control, NV centers in nano-diamonds provide a nanoscale temperature sensor with unprecedented accuracy enabling local temperature measurements in living biological cells
Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg
2015-09-15
A formulation of non-relativistic quantummechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schrödinger time-dependent wave-function. Its classical limit is discussedmore » and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the validity of the suggested approach.« less
In the field of tribology, the ability to predict, and ultimately control, frictional performance is of critical importance for the optimization of tribological systems. As such, understanding the specific mechanisms involved in the lubrication processes for different materials is a fundamental step in tribological system design. In this work, a combination of computational and experimental methods that include classical molecular dynamics (MD) simulations, atomic force microscopy (AFM) experiments, and multivariate statistical analyses provides fundamental insight into the tribological and mechanical properties of carbon-based and inorganic nanostructures, lamellar materials, and inorganic ceramic compounds. One class of materials of modern interest for tribological applications is nanoparticles, which can be employed either as solid lubricating films or as lubricant additives. In experimental systems, however, it is often challenging to attain the in situ observation of tribological interfaces necessary to identify the atomic-level mechanisms involved during lubrication and response to mechanical deformation. Here, classical MD simulations establish the mechanisms occurring during the friction and compression of several types of nanoparticles including carbon nano-onions, amorphous carbon nanoparticles, and inorganic fullerene-like MoS2 nanoparticles. Specifically, the effect of a nanoparticle's structural properties on the lubrication mechanisms of rolling, sliding, and lamellar exfoliation is indicated; the findings quantify the relative impact of each mechanism on the tribological and mechanical properties of these nanoparticles. Beyond identifying the lubrication mechanisms of known lubricating materials, the continual advancement of modern technology necessitates the identification of new candidate materials for use in tribological applications. To this effect, atomic-scale AFM friction experiments on the aluminosilicate mineral pyrophyllite demonstrate that
We discuss common features in mechanical, electromagnetic and quantum systems, supporting identical results for the transmission and reflection coefficients of waves arriving perpendicularly at a plane interface. Also, we briefly discuss the origin of special notions such as refractive index in quantummechanics, massive photons in wave guides and…
Quantum physics and fluid mechanics are the foundation of any understanding of the Earth's climate. In this talk I invoke three well-known aspects of quantummechanics to explore what will happen as the concentrations of greenhouse gases such as carbon dioxide continue to increase. Fluid dynamical models of the Earth's atmosphere, demonstrated here in live simulations, yield further insight into past, present, and future climates. Statistics of geophysical flows can, however, be ascertained directly without recourse to numerical simulation, using concepts borrowed from nonequilibrium statistical mechanicsootnotetextJ. B. Marston, E. Conover, and Tapio Schneider, ``Statistics of an Unstable Barotropic Jet from a Cumulant Expansion,'' arXiv:0705.0011, J. Atmos. Sci. (in press).. I discuss several other ways that theoretical physics may be able to contribute to a deeper understanding of climate changeootnotetextJ. Carlson, J. Harte, G. Falkovich, J. B. Marston, and R. Pierrehumbert, ``Physics of Climate Change'' 2008 Program of the Kavli Institute for Theoretical Physics..
The transport of excitations governs fundamental properties of matter. Particularly rich physics emerges in the interplay between disorder and environmental noise, even in small systems such as photosynthetic biomolecules. Counterintuitively, noise can enhance coherent quantum transport, which has been proposed as a mechanism behind the high transport efficiencies observed in photosynthetic complexes. This effect has been called "environment-assisted quantum transport". Here, we propose a quantum simulation of the excitation transport in an open quantum network, taking advantage of the high controllability of current trapped-ion experiments. Our scheme allows for the controlled study of various different aspects of the excitation transfer, ranging from the influence of static disorder and interaction range, over the effect of Markovian and non-Markovian dephasing, to the impact of a continuous insertion of excitations. Our paper discusses experimental error sources and realistic parameters, showing that it can be implemented in state-of-the-art ion-chain experiments.
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Quantum Finance represents the synthesis of the techniques of quantum theory (quantummechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of options. The ideas are sketched out for simple models, such as the Black-Scholes model, where analytical and numerical results are compared. Application of the method to nonlinear systems is also briefly overviewed. More general models, for exotic or path-dependent options are discussed.
Anquez, M.; Robbins, B. A.; Bharath, H. M.; Boguslawski, M.; Hoang, T. M.; Chapman, M. S.
2016-04-01
The dynamics of a quantum phase transition are explored using slow quenches from the polar to the broken-axisymmetry phases in a small spin-1 ferromagnetic Bose-Einstein condensate. Measurements of the evolution of the spin populations reveal a power-law scaling of the temporal onset of excitations versus quench speed as predicted from quantum extensions of the Kibble-Zurek mechanism. The satisfactory agreement of the measured scaling exponent with the analytical theory and numerical simulations provides experimental confirmation of the quantum Kibble-Zurek model.
This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cells to cognition, ecological and social systems. Mathematically QIB is based on the theory of adaptive quantum systems (which covers also open quantum systems). Ideologically QIB is based on the quantum-like (QL) paradigm: complex bio-systems process information in accordance with the laws of quantum information and probability. This paradigm is supported by plenty of statistical bio-data collected at all bio-scales. QIB re ects the two fundamental principles: a) adaptivity; and, b) openness (bio-systems are fundamentally open). In addition, quantum adaptive dynamics provides the most generally possible mathematical representation of these principles.
Zhang, Baocheng; Cai, Qing-Yu; Zhan, Ming-Sheng; You, Li
2013-06-01
In both classical and quantum world, information cannot appear or disappear. This fundamental principle, however, is questioned for a black hole, by the acclaimed "information loss paradox." Based on the conservation laws of energy, charge, and angular momentum, we recently show the total information encoded in the correlations among Hawking radiations equals exactly to the same amount previously considered lost, assuming the nonthermal spectrum of Parikh and Wilczek. Thus the information loss paradox can be falsified through experiments by detecting correlations, for instance, through measuring the covariances of Hawking radiations from black holes, such as the manmade ones speculated to appear in LHC experiments. The affirmation of information conservation in Hawking radiation will shine new light on the unification of gravity with quantummechanics.
Achuthan, P.; Dept. of Mathematics, Indian Institute of Technology, Madras, 600 036; Narayanankutty, Karuppath
2009-07-02
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantummechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantummechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM,more » though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.« less
As shown in the EPR paper (Einstein, Podolsky e Rosen, 1935), QuantumMechanics is a non-local Theory. The Bell theorem and the successive experiments ruled out the possibility of explaining quantum correlations using only local hidden variables models. Some authors suggested that quantum correlations could be due to superluminal communications that propagate isotropically with velocity vt > c in a preferred reference frame. For finite values of vt and in some special cases, QuantumMechanics and superluminal models lead to different predictions. So far, no deviations from the predictions of QuantumMechanics have been detected and only lower bounds for the superluminal velocities vt have been established. Here we describe a new experiment that increases the maximum detectable superluminal velocities and we give some preliminary results.
``The history of science, to my knowledge,'' wrote Thomas Kuhn, describing the years just prior to the development of matrix and wave mechanics, ``offers no equally clear, detailed, and cogent example of the creative functions of normal science and crisis.'' By 1924, most quantum theorists shared a sense that there was much wrong with all extant atomic models. Yet not all shared equally in the sense that the failure was either terribly surprising or particularly demoralizing. Not all agreed, that is, that a crisis for Bohr-like models was a crisis for quantum theory. This paper attempts to answer four questions: two about history, two about memory. First, which sub-groups of the quantum theoretical community saw themselves and their field in a state of crisis in the early 1920s? Second, why did they do so, and how was a sense of crisis related to their theoretical practices in physics? Third, do we regard the years before 1925 as a crisis because they were followed by the quantummechanical revolution? And fourth, to reverse the last question, were we to call into the question the existence of a crisis (for some at least) does that make a subsequent revolution less revolutionary?
Compares two approaches to strong absorption in elementary quantummechanics; the black sphere and a model based on the continuum theory of nuclear reactions. Examines the application to proton-antiproton interactions at low momenta and concludes that the second model is the appropriate and simplest to use. (Author/GA)
The metric system appeared as the system of units designed for macroscopic (laboratory scale) measurements. The progress in accurate determination of the values of quantum constants (such as the Planck constant) in SI units shows that the capabilities in high-precision measurement of microscopic and macroscopic quantities in terms of the same units have increased substantially recently. At the same time, relative microscopic measurements (for example, the comparison of atomic transition frequencies or atomic masses) are often much more accurate than relative measurements of macroscopic quantities. This is the basis for the strategy to define units in microscopic phenomena and then use them on the laboratory scale, which plays a crucial role in practical methodological applications determined by everyday life and technologies. The international CODATA task group on fundamental constants regularly performs an overall analysis of the precision world data (the so-called Adjustment of the Fundamental Constants) and publishes their recommended values. The most recent evaluation was based on the data published by the end of 2014; here, we review the corresponding data and results. The accuracy in determination of the Boltzmann constant has increased, the consistency of the data on determination of the Planck constant has improved; it is these two dimensional constants that will be used in near future as the basis for the new definition of the kelvin and kilogram, respectively. The contradictions in determination of the Rydberg constant and the proton charge radius remain. The accuracy of determination of the fine structure constant and relative atomic weight of the electron has improved. Overall, we give a detailed review of the state of the art in precision determination of the values of fundamental constants. The mathematical procedure of the Adjustment, the new data and results are considered in detail. The limitations due to macroscopic properties of material
Kim, Yosep; Kim, Yong-Su; Lee, Sang-Yun; Han, Sang-Wook; Moon, Sung; Kim, Yoon-Ho; Cho, Young-Wook
2018-01-15
The weak value concept has enabled fundamental studies of quantum measurement and, recently, found potential applications in quantum and classical metrology. However, most weak value experiments reported to date do not require quantummechanical descriptions, as they only exploit the classical wave nature of the physical systems. In this work, we demonstrate measurement of the sequential weak value of two incompatible observables by making use of two-photon quantum interference so that the results can only be explained quantum physically. We then demonstrate that the sequential weak value measurement can be used to perform direct quantum process tomography of a qubit channel. Our work not only demonstrates the quantum nature of weak values but also presents potential new applications of weak values in analyzing quantum channels and operations.
Aeppli, G.; Department of Physics and Astronomy, University College of London, London
Atomic physics is undergoing a large revival because of the possibility of trapping and cooling ions and atoms both for individual quantum control as well as collective quantum states, such as Bose-Einstein condensates. The present lectures start from the 'atomic' physics of isolated atoms in semiconductors and insulators and proceed to coupling them together to yield magnets undergoing quantum phase transitions as well as displaying novel quantum states with no classical analogs. The lectures are based on: G.-Y. Xu et al., Science 317, 1049-1052 (2007); G. Aeppli, P. Warburton, C. Renner, BT Technology Journal, 24, 163-169 (2006); H. M. Ronnowmore » et al., Science 308, 392-395 (2005) and N. Q. Vinh et al., PNAS 105, 10649-10653 (2008).« less
Röhrig, Robin; Schering, Philipp; Gravert, Lars B.; Fauseweh, Benedikt; Uhrig, Götz S.
2018-04-01
The electronic spin in quantum dots can be described by central spin models (CSMs) with a very large number Neff≈104 to 106 of bath spins posing a tremendous challenge to theoretical simulations. Here, a fully quantummechanical theory is developed for the limit Neff→∞ by means of iterated equations of motion (iEoM). We find that the CSM can be mapped to a four-dimensional impurity coupled to a noninteracting bosonic bath in this limit. Remarkably, even for infinite bath the CSM does not become completely classical. The data obtained by the proposed iEoM approach are tested successfully against data from other, established approaches. Thus the iEoM mapping extends the set of theoretical tools that can be used to understand the spin dynamics in large CSMs.
Gao, Jiali; Truhlar, Donald G; Wang, Yingjie; Mazack, Michael J M; Löffler, Patrick; Provorse, Makenzie R; Rehak, Pavel
2014-09-16
Conspectus Molecular mechanical force fields have been successfully used to model condensed-phase and biological systems for a half century. By means of careful parametrization, such classical force fields can be used to provide useful interpretations of experimental findings and predictions of certain properties. Yet, there is a need to further improve computational accuracy for the quantitative prediction of biomolecular interactions and to model properties that depend on the wave functions and not just the energy terms. A new strategy called explicit polarization (X-Pol) has been developed to construct the potential energy surface and wave functions for macromolecular and liquid-phase simulations on the basis of quantummechanics rather than only using quantummechanical results to fit analytic force fields. In this spirit, this approach is called a quantummechanical force field (QMFF). X-Pol is a general fragment method for electronic structure calculations based on the partition of a condensed-phase or macromolecular system into subsystems ("fragments") to achieve computational efficiency. Here, intrafragment energy and the mutual electronic polarization of interfragment interactions are treated explicitly using quantummechanics. X-Pol can be used as a general, multilevel electronic structure model for macromolecular systems, and it can also serve as a new-generation force field. As a quantum chemical model, a variational many-body (VMB) expansion approach is used to systematically improve interfragment interactions, including exchange repulsion, charge delocalization, dispersion, and other correlation energies. As a quantummechanical force field, these energy terms are approximated by empirical functions in the spirit of conventional molecular mechanics. This Account first reviews the formulation of X-Pol, in the full variationally correct version, in the faster embedded version, and with systematic many-body improvements. We discuss illustrative examples
Deur, Alexandre; Brodsky, Stanley J.; de Teramond, Guy F.
2015-10-01
We establish an explicit connection between the long distance physics of confinement and the dynamical interactions of quarks and gluons at short distances and it has been a long-sought goal of quantum chromodynamics. Using holographic QCD, we derive a direct analytic relation between the scale κ which determines the masses of hadrons and the scale Λ s which controls the predictions of perturbative QCD at very short distances. The resulting prediction Λ s=0.341±0.032 GeV in the MS -scheme agrees well with the experimental average 0.339±0.016 GeV. We also derive a relation between Λs and the QCD string tension σ. Furthermore,more » this connection between the fundamental hadronic scale underlying the physics of quark confinement and the perturbative QCD scale controlling hard collisions can be carried out in any renormalization scheme.« less
Sternberg, James; Ovchinnikov, S. Yu.; Macek, J. H.
2009-05-01
Although the Fermi shuttle was originally proposed as an explanation for highly energetic cosmic rays, it is also a mechanism for the production of high energy electrons in atomic collisions [1]. The Fermi shuttle is usually thought of as a classical effect and most models of this process rely on classical or semi-classical approximations. In this work we explore several quantummechanical models for ion-atom collisions and examine the evidence for the Fermi shuttle in these models. [4pt] [1] B. Sulik, Cs. Koncz, K. Tok'esi, A. Orb'an, and D. Ber'enyi, Phys Rev. Lett. 88 073201 (2002)
Deerfield, David, II; Davis, Charles H.; Wymore, Troy; Stafford, Darrel W.; Pedersen, Lee G.
Possible model, but simplistic, mechanisms for the action of vitamin K epoxide reductase (VKOR) are investigated with quantummechanical methods (B3LYP/6-311G**). The geometries of proposed model intermediates in the mechanisms are energy optimized. Finally, the energetics of the proposed (pseudo-enzymatic) pathways are compared. We find that the several pathways are all energetically feasible. These results will be useful for designing quantummechanical/molecular mechanical method (QM/MM) studies of the enzymatic pathway once three-dimensional structural data are determined and available for VKOR.
The fundamental molecular mechanisms of contractility and tension development in fibrous macromolecules are developed from the point of view of the principles of polymer physical chemistry. The problem is treated in a general manner to encompass the behavior of all macromolecular systems irrespective of their detailed chemical structure and particular function, if any. Primary attention is given to the contractile process which accompanies the crystal-liquid transition in axially oriented macromolecular systems. The theoretical nature of the process is discussed, and many experimental examples are given from the literature which demonstrate the expected behavior. Experimental attention is focused on the contraction of fibrous proteins, and the same underlying molecular mechanism is shown to be operative for a variety of different systems. PMID:6050598
exponent , reflects the screening of an electron in a given orbital by the interior electrons in the atom or molecule. In practice, when studying...Basis sets have evolved over the years in molecular quantummechanics until sets of orbital exponents for the different atoms composing the molecule have...and R. P. Hurst , J. Chem. Phys. 46, 2356 (1967); S. P. LickmannI and J. W. Moskowitz, J. Chem. Phys. 54, 3622 7T971). 26. T. H. Dunning, J. Chem. Phys
The performance in finite time of a quantum-mechanical Brayton engine cycle is discussed, without introduction of temperature. The engine model consists of two quantum isoenergetic and two quantum isobaric processes, and works with a single particle in a harmonic trap. Directly employing the finite-time thermodynamics, the efficiency at maximum power output is determined. Extending the harmonic trap to a power-law trap, we find that the efficiency at maximum power is independent of any parameter involved in the model, but depends on the confinement of the trapping potential.
Perturbative bulk reconstruction in AdS/CFT starts by representing a free bulk field ϕ (0) as a smeared operator in the CFT. A series of 1 /N corrections must be added to ϕ (0) to represent an interacting bulk field ϕ. These corrections have been determined in the literature from several points of view. Here we develop a new perspective. We show that correlation functions involving ϕ (0) suffer from ambiguities due to analytic continuation. As a result ϕ (0) fails to be a well-defined linear operator in the CFT. This means bulk reconstruction can be understood as a procedure for building up well-defined operators in the CFT which thereby singles out the interacting field ϕ. We further propose that the difficulty with defining ϕ (0) as a linear operator can be re-interpreted as a breakdown of associativity. Presumably ϕ (0) can only be corrected to become an associative operator in perturbation theory. This suggests that quantummechanics in the bulk is only valid in perturbation theory around a semiclassical bulk geometry.
Understanding of the electroluminescence (EL) mechanism in optoelectronic devices is imperative for further optimization of their efficiency and effectiveness. Here, a quantummechanical approach is formulated for modeling the EL processes in nanoscale light emitting diodes (LED). Based on non-equilibrium Green's function quantum transport equations, interactions with the electromagnetic vacuum environment are included to describe electrically driven light emission in the devices. The presented framework is illustrated by numerical simulations of a silicon nanowire LED device. EL spectra of the nanowire device under different bias voltages are obtained and, more importantly, the radiation pattern and polarization of optical emission can be determined using the current approach. This work is an important step forward towards atomistic quantummechanical modeling of the electrically induced optical response in nanoscale systems.
This paper describes the effects of a complex scalar scaling field on quantummechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces as structures, at different space time locations. Complex number structures and vector spaces at eachmore » location are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantummechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantummechanics. Here, the lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region, there are no restrictions on the field gradient.« less
As part of an ongoing investigation of students' learning in first semester upper-division quantummechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantummechanics must necessarily follow from the Hamiltonian or Lagrangian formulations of mechanics. Here, we first derive the existing Heisenberg equations of motion from Newton's laws and the uncertainty principle using only the equations F=\\frac{dP}{dt}, P=m\\frac{dV}{dt}, and [X, P] = i. Then, a new expression for the propagator is derived that makes a connection between time evolution in quantummechanics and the motion of a classical particle under Newton's laws. The propagator is solved for three cases where an exact solution is possible: (1) the free particle; (2) the harmonic oscillator; and (3) a constant force, or linear potential in the standard interpretation. We then show that for a general for a general force F(X), by Taylor expanding X(t) in time, we can use this methodology to reproduce the Feynman path integral formula for the propagator. Such a picture may be useful for students as they make the transition from classical to quantummechanics and help solidify the equivalence of the Hamiltonian, Lagrangian, and Newtonian pictures of physics in their minds.
To find the Hermitian phase operator of a single-mode electromagnetic field in quantummechanics, the Schr{umlt o}dinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The Hermitian phase operator is shown to exist on the extended Hilbert space. This operator is naturally considered as the controversial limit of the approximate phase operators on finite dimensional spaces proposed by Pegg and Barnett. The spectral measure of this operator is a Naimark extension of the optimal probability operator-valued measure for the phase parameter found by Helstrom. Eventually, the two promising approaches to themore » statistics of the phase in quantummechanics are synthesized by means of the Hermitian phase operator in the macroscopic extension of the Schr{umlt o}dinger representation. {copyright} 1997 Academic Press, Inc.« less
Since the development of quantum physics in the early part of the 1900s, this field of study has made remarkable contributions to our civilization. Some of these advances include lasers, light-emitting diodes (LED), sensors, spectroscopy, quantum dots, quantum gravity and quantum entanglements. In 1998, the NASA Langley Research Center established a quantum technology committee to monitor the progress in this area and initiated research to determine the potential of quantum technology for future NASA missions. The areas of interest in quantum technology at NASA included fundamentalquantum-optics materials associated with quantum dots and quantum wells, device-oriented photonic crystals, smart optics, quantum conductors, quantum information and computing, teleportation theorem, and quantum energetics. A brief review of the work performed, the progress made in advancing these technologies, and the potential NASA applications of quantum technology will be presented.
While quantum-classical correspondence for a system is a very fundamental problem in modern physics, the understanding of its mechanism is often elusive, so the methods used and the results of detailed theoretical analysis have been accompanied by active debate. In this study, the differences and similarities between quantum and classical behavior for an inverted oscillator have been analyzed based on the description of a complete generalized Airy function-type quantum wave solution. The inverted oscillator model plays an important role in several branches of cosmology and particle physics. The quantum wave packet of the system is composed of many sub-packets that are localized at different positions with regular intervals between them. It is shown from illustrations of the probability density that, although the quantum trajectory of the wave propagation is somewhat different from the corresponding classical one, the difference becomes relatively small when the classical excitation is sufficiently high. We have confirmed that a quantum wave packet moving along a positive or negative direction accelerates over time like a classical wave. From these main interpretations and others in the text, we conclude that our theory exquisitely illustrates quantum and classical correspondence for the system, which is a crucial concept in quantummechanics. Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1A09919503)
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as ‘D-Wave’ chips, promise to solve practical optimization problems potentially faster than conventional ‘classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize ‘temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip. PMID:26483257
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantummechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.
The subjective Everettian approach to quantummechanics presented by Deutsch and Wallace fails to constitute an empirically viable theory of quantum phenomena. The decision theoretic implementation of the Born rule realized in this approach provides no basis for rejecting Everettian quantummechanics in the face of empirical data that contradicts the Born rule. The approach of Greaves and Myrvold, which provides a subjective implementation of the Born rule as well but derives it from empirical data rather than decision theoretic arguments, avoids the problem faced by Deutsch and Wallace and is empirically viable. However, there is good reason to cast doubts on its scientific value.
Pöschl-Teller-driven solutions for quantummechanical fluctuations are triggered off by single scalar field theories obtained through a systematic perturbative procedure for generating deformed defects. The analytical properties concerning the quantum fluctuations in one-dimension, zero-mode states, first- and second-excited states, and energy density profiles are all obtained from deformed topological and non-topological structures supported by real scalar fields. Results are firstly derived from an integrated λϕ4 theory, with corresponding generalizations applied to starting λχ4 and sine-Gordon theories. By focusing our calculations on structures supported by the λϕ4 theory, the outcome of our study suggests an exact quantitative correspondence to Pöschl-Teller-driven systems. Embedded into the perturbative quantummechanics framework, such a correspondence turns into a helpful tool for computing excited states and continuous mode solutions, as well as their associated energy spectrum, for quantum fluctuations of perturbatively deformed structures. Perturbative deformations create distinct physical scenarios in the context of exactly solvable quantum systems and may also work as an analytical support for describing novel braneworld universes embedded into a 5-dimensional gravity bulk.
We study the quantum-mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum-mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric processes, such as the quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of the quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in a one-dimensional box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum-mechanical) foundation for Szilard-Zurek single-molecule engine.
For ``Principle of Indeterminacy''from Heisenberg states: ``one of the fundamental cornerstone of quantummechanics is the Heisenberg uncertainty principle''.whereas canonically conjugate quantities can be determined simultaneously only with a characteristic indeterminacy[M. Arevalo Aguilar, et.al]. Accompanying Alfred North Whitehead conclusion in ``The Aims of Education''that mathematical symbols are artificial before new meanings given, two kinds of fundamental motives: (i) expectation-expectation, (ii) expectation-certainty inherently occurs with determinacy properties of rational expectation equilibrium(REE, henceworth)- Guido Ascari & Tizano Ropele:''Trend inflation, Taylor principle & Indeterminacy'', Kiel Institute, June 2007. Furthers, relative price expression can be compare of their α and (1 - α) configurations in the expression of possible activity. Acknowledgment to Prof[asc]. Dr. Bobby Eka Gunara for ``made a rank through physics'' denotes...
Multi-particle interference is an essential ingredient for fundamentalquantummechanics phenomena and for quantum information processing to provide a computational advantage, as recently emphasized by boson sampling experiments. Hence, developing a reliable and efficient technique to witness its presence is pivotal in achieving the practical implementation of quantum technologies. Here, we experimentally identify genuine many-body quantum interference via a recent efficient protocol, which exploits statistical signatures at the output of a multimode quantum device. We successfully apply the test to validate three-photon experiments in an integrated photonic circuit, providing an extensive analysis on the resources required to perform it. Moreover, drawing upon established techniques of machine learning, we show how such tools help to identify the—a priori unknown—optimal features to witness these signatures. Our results provide evidence on the efficacy and feasibility of the method, paving the way for its adoption in large-scale implementations.
The probability theory used in quantummechanics is currently being employed by psychologists to model the impact of context on decision. Its event space consists of closed subspaces of a Hilbert space, and its probability function sometimes violate the law of the finite additivity of probabilities. Results from the quantummechanics literature indicate that such a "Hilbert space probability theory" cannot be extended in a useful way to standard, finitely additive, probability theory by the addition of new events with specific probabilities. This chapter presents a new kind of probability theory that shares many fundamental algebraic characteristics with Hilbert space probability theory but does extend to standard probability theory by adjoining new events with specific probabilities. The new probability theory arises from considerations about how psychological experiments are related through counterfactual reasoning.
Balygin, K. A.; Klimov, A. N.; Korol'kov, A. V.; Kulik, S. P.; Molotkov, S. N.
2016-06-01
The security of keys in quantum cryptography systems, in contrast to mathematical cryptographic algorithms, is guaranteed by fundamentalquantum-mechanical laws. However, the cryptographic resistance of such systems, which are distributed physical devices, fundamentally depends on the method of their implementation and particularly on the calibration and control of critical parameters. The most important parameter is the number of photons in quasi-single-photon information states in a communication channel. The sensitivity to a bright-pulse attack has been demonstrated in an explicit form for a number of systems. A method guaranteeing the resistance to such attacks has been proposed and implemented. Furthermore, the relation of physical observables used and obtained at the control of quantum states to the length of final secret keys has been obtained for the first time.
Biological macromolecules, such as proteins or nucleic acids, are (still) molecules and thus they follow the same chemical rules that any simple molecule follows, even if their size generally renders accurate studies unhelpful. However, in the context of drug discovery, a detailed analysis of ligand association is required for understanding or predicting their interactions and hybrid quantummechanics/molecular mechanics (QM/MM) computations are relevant tools to help elucidate this process. In this review, the authors explore the use of QM/MM for drug discovery. After a brief description of the molecular mechanics (MM) technique, the authors describe the subtractive and additive techniques for QM/MM computations. The authors then present several application cases in topics involved in drug discovery. QM/MM have been widely employed during the last decades to study chemical processes such as enzyme-inhibitor interactions. However, despite the enthusiasm around this area, plain MM simulations may be more meaningful than QM/MM. To obtain reliable results, the authors suggest fixing several keystone parameters according to the underlying chemistry of each studied system.
Biological macromolecules, such as proteins or nucleic acids, are (still) molecules and thus they follow the same chemical rules that any simple molecule follows, even if their size generally renders accurate studies unhelpful. However, in the context of drug discovery, a detailed analysis of ligand association is required for understanding or predicting their interactions and hybrid quantummechanics/molecular mechanics (QM/MM) computations are relevant tools to help elucidate this process. Areas covered: In this review, the authors explore the use of QM/MM for drug discovery. After a brief description of the molecular mechanics (MM) technique, the authors describe the subtractive and additive techniques for QM/MM computations. The authors then present several application cases in topics involved in drug discovery. Expert opinion: QM/MM have been widely employed during the last decades to study chemical processes such as enzyme-inhibitor interactions. However, despite the enthusiasm around this area, plain MM simulations may be more meaningful than QM/MM. To obtain reliable results, the authors suggest fixing several keystone parameters according to the underlying chemistry of each studied system.
A scheme to achieve strong quantum squeezing of a mechanical resonator in a membrane-in-the-middle optomechanical system is developed. To this end, simultaneous linear and nonlinear coupling between the mechanical resonator and the cavity modes is applied. A two-tone driving light field, comprising unequal red-detuned and blue-detuned sidebands, helps in generating a coherent feedback force through the linear coupling with the membrane resonator. Another driving light field with its amplitude modulated at twice the mechanical frequency drives the mechanical parametric amplification through a second-order coupling with the resonator. The combined effect produces strong quantum squeezing of the mechanical state. The proposed scheme is quite robust to excess second-order coupling observed in coherent feedback operations and can suppress the fluctuations in the mechanical quadrature to far below the zero point and achieve strong squeezing (greater than 10 dB) for realistic parameters.
The known methods, due for instance to G.W. Mackey and T.F. Jordan, which exploit the transformation properties with respect to the Euclidean and Galileian group to determine the formalism of the Quantum Theory of a localizable particle, fail in the case that the considered transformations are not symmetries of the physical system. In the present work we show that the formalism of standard QuantumMechanics for a particle without spin can be completely recovered by exploiting the covariance properties with respect to the group of Euclidean transformations, without requiring that these transformations are symmetries of the physical system.
The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantummechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.
In 1913, when American physicist Arthur Compton was an undergraduate, he invented a simple way to measure the rotation rate of the Earth with a tabletop-sized experiment. The experiment consisted of a large diameter circular ring of thin glass tubing filled with water and oil droplets. After placing the ring in a plane perpendicular to the surface of the Earth and allowing the fluid mixture of oil and water to come to rest, he then abruptly rotated the ring, flipping it 180 degrees about an axis passing through its own plane. The result of the experiment was that the water acquired a measurable drift velocity due to the Coriolis effect arising from the daily rotation of the Earth about its own axis. Compton measured this induced drift velocity by observing the motion of the oil droplets in the water with a microscope. This device, which is now named after him, is known as a Compton generator. The fundamental research objective of this project is to explore the dynamics of a quantum-mechanical analogue to the classical Compton generator experiment through the use of numerical simulations. We present our preliminary results on this system and the future direction of the project. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant Number ACI-1053575.
Wang, Bo; Yang, Ke R; Xu, Xuefei; Isegawa, Miho; Leverentz, Hannah R; Truhlar, Donald G
2014-09-16
Conspectus The development of more efficient and more accurate ways to represent reactive potential energy surfaces is a requirement for extending the simulation of large systems to more complex systems, longer-time dynamical processes, and more complete statistical mechanical sampling. One way to treat large systems is by direct dynamics fragment methods. Another way is by fitting system-specific analytic potential energy functions with methods adapted to large systems. Here we consider both approaches. First we consider three fragment methods that allow a given monomer to appear in more than one fragment. The first two approaches are the electrostatically embedded many-body (EE-MB) expansion and the electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE), which we have shown to yield quite accurate results even when one restricts the calculations to include only electrostatically embedded dimers. The third fragment method is the electrostatically embedded molecular tailoring approach (EE-MTA), which is more flexible than EE-MB and EE-MB-CE. We show that electrostatic embedding greatly improves the accuracy of these approaches compared with the original unembedded approaches. Quantummechanical fragment methods share with combined quantummechanical/molecular mechanical (QM/MM) methods the need to treat a quantummechanical fragment in the presence of the rest of the system, which is especially challenging for those parts of the rest of the system that are close to the boundary of the quantummechanical fragment. This is a delicate matter even for fragments that are not covalently bonded to the rest of the system, but it becomes even more difficult when the boundary of the quantummechanical fragment cuts a bond. We have developed a suite of methods for more realistically treating interactions across such boundaries. These methods include redistributing and balancing the external partial atomic charges and the use of tuned fluorine
The ability to manipulate quantum states of light by integrated devices may open new perspectives both for fundamental tests of quantummechanics and for novel technological applications. The technology for handling polarization-encoded qubits, the most commonly adopted approach, was still missing in quantum optical circuits until the ultrafast laser writing (ULW) technique was adopted for the first time to realize integrated devices able to support and manipulate polarization encoded qubits.1 Thanks to this method, polarization dependent and independent devices can be realized. In particular the maintenance of polarization entanglement was demonstrated in a balanced polarization independent integrated beam splitter1 and an integrated CNOT gate for polarization qubits was realized and carachterized.2 We also exploited integrated optics for quantum simulation tasks: by adopting the ULW technique an integrated quantum walk circuit was realized3 and, for the first time, we investigate how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk. Such experiment has been realized by adopting two-photon entangled states and an array of integrated symmetric directional couplers. The polarization entanglement was exploited to simulate the bunching-antibunching feature of non interacting bosons and fermions. To this scope a novel three-dimensional geometry for the waveguide circuit is introduced, which allows accurate polarization independent behaviour, maintaining a remarkable control on both phase and balancement of the directional couplers.
We review the first successes and failures of a "new wave" of quantum chemistry-based approaches to the treatment of protein/ligand interactions. These approaches share the use of "enhanced", dispersion (D), and/or hydrogen-bond (H) corrected density functional theory (DFT) or semi-empirical quantummechanical (SQM) methods, in combination with ensemble weighting techniques of some form to capture entropic effects. Benchmark and model system calculations in comparison to high-level theoretical as well as experimental references have shown that both DFT-D (dispersion-corrected density functional theory) and SQM-DH (dispersion and hydrogen bond-corrected semi-empirical quantummechanical) perform much more accurately than older DFT and SQM approaches and also standard docking methods. In addition, DFT-D might soon become and SQM-DH already is fast enough to compute a large number of binding modes of comparably large protein/ligand complexes, thus allowing for a more accurate assessment of entropic effects.
The creation of a global quantum network is now a realistic proposition thanks to developments in satellite and fibre links and quantum memory. Applications will range from secure communication and fundamental physics experiments to a future quantum internet.
Fares, H.; Yamada, M.; Chiadroni, E.; Ferrario, M.
2018-05-01
In the previous classical theory of the low-gain free-electron laser (FEL) oscillators, the electron is described as a point-like particle, a delta function in the spatial space. On the other hand, in the previous quantum treatments, the electron is described as a plane wave with a single momentum state, a delta function in the momentum space. In reality, an electron must have statistical uncertainties in the position and momentum domains. Then, the electron is neither a point-like charge nor a plane wave of a single momentum. In this paper, we rephrase the theory of the low-gain FEL where the interacting electron is represented quantummechanically by a plane wave with a finite spreading length (i.e., a wave packet). Using the concepts of the transformation of reference frames and the statistical quantummechanics, an expression for the single-pass radiation gain is derived. The spectral broadening of the radiation is expressed in terms of the spreading length of an electron, the relaxation time characterizing the energy spread of electrons, and the interaction time. We introduce a comparison between our results and those obtained in the already known classical analyses where a good agreement between both results is shown. While the correspondence between our results and the classical results are shown, novel insights into the electron dynamics and the interaction mechanism are presented.
Unconditional security of the BB84 quantum key distribution protocol has been proved by exploiting the fundamental laws of quantummechanics, but the practical quantum key distribution system maybe hacked by considering the imperfect state preparation and measurement respectively. Until now, different attacking schemes have been proposed by utilizing imperfect devices, but the general security analysis model against all of the practical attacking schemes has not been proposed. Here, we demonstrate that the general practical attacking schemes can be divided into the Trojan horse attack, strong randomness attack and weak randomness attack respectively. We prove security of BB84 protocol under randomness attacking models, and these results can be applied to guarantee the security of the practical quantum key distribution system.
Unconditional security of the BB84 quantum key distribution protocol has been proved by exploiting the fundamental laws of quantummechanics, but the practical quantum key distribution system maybe hacked by considering the imperfect state preparation and measurement respectively. Until now, different attacking schemes have been proposed by utilizing imperfect devices, but the general security analysis model against all of the practical attacking schemes has not been proposed. Here, we demonstrate that the general practical attacking schemes can be divided into the Trojan horse attack, strong randomness attack and weak randomness attack respectively. We prove security of BB84 protocol under randomness attacking models, and these results can be applied to guarantee the security of the practical quantum key distribution system.
Unconditional security of the BB84 quantum key distribution protocol has been proved by exploiting the fundamental laws of quantummechanics, but the practical quantum key distribution system maybe hacked by considering the imperfect state preparation and measurement respectively. Until now, different attacking schemes have been proposed by utilizing imperfect devices, but the general security analysis model against all of the practical attacking schemes has not been proposed. Here, we demonstrate that the general practical attacking schemes can be divided into the Trojan horse attack, strong randomness attack and weak randomness attack respectively. We prove security of BB84 protocol under randomness attacking models, and these results can be applied to guarantee the security of the practical quantum key distribution system. PMID:26552359
Geracie, Michael; Haehl, Felix M.; Loganayagam, R.; Narayan, Prithvi; Ramirez, David M.; Rangamani, Mukund
2018-05-01
We examine, in a quantummechanical setting, the Hilbert space representation of the Becchi, Rouet, Stora, and Tyutin (BRST) symmetry associated with Schwinger-Keldysh path integrals. This structure had been postulated to encode important constraints on influence functionals in coarse-grained systems with dissipation, or in open quantum systems. Operationally, this entails uplifting the standard Schwinger-Keldysh two-copy formalism into superspace by appending BRST ghost degrees of freedom. These statements were previously argued at the level of the correlation functions. We provide herein a complementary perspective by working out the Hilbert space structure explicitly. Our analysis clarifies two crucial issues not evident in earlier works: first, certain background ghost insertions necessary to reproduce the correct Schwinger-Keldysh correlators arise naturally, and, second, the Schwinger-Keldysh difference operators are systematically dressed by the ghost bilinears, which turn out to be necessary to give rise to a consistent operator algebra. We also elaborate on the structure of the final state (which is BRST closed) and the future boundary condition of the ghost fields.
In this work, our goal is to examine the attitude of the Greek scientific community towards QuantumMechanics and establish the history of teaching of this theory in Greece. We have examined Physics textbooks written by professors of the University of Athens, as well as records of public speeches, university yearbooks from 1923 to 1970, articles…
We shall argue in this paper that a central piece of modern physics does not really belong to physics at all but to elementary probability theory. Given a joint probability distribution J on a set of random variables containing x and y, define a link between x and y to be the condition x=y on J. Define the {\\it state} D of a link x=y as the joint probability distribution matrix on x and y without the link. The two core laws of quantummechanics are the Born probability rule, and the unitary dynamical law whose best known form is the Schrodinger's equation. Von Neumann formulated these two laws in the language of Hilbert space as prob(P) = trace(PD) and D'T = TD respectively, where P is a projection, D and D' are (von Neumann) density matrices, and T is a unitary transformation. We'll see that if we regard link states as density matrices, the algebraic forms of these two core laws occur as completely general theorems about links. When we extend probability theory by allowing cases to count negatively, we find that the Hilbert space framework of quantummechanics proper emerges from the assumption that all D's are symmetrical in rows and columns. On the other hand, Markovian systems emerge when we assume that one of every linked variable pair has a uniform probability distribution. By representing quantum and Markovian structure in this way, we see clearly both how they differ, and also how they can coexist in natural harmony with each other, as they must in quantum measurement, which we'll examine in some detail. Looking beyond quantummechanics, we see how both structures have their special places in a much larger continuum of formal systems that we have yet to look for in nature.
Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science. Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantummechanics, for increasing the sensitivity of quantum imaging schemes, for improving the robustness and key rate of quantum communication protocols, for enabling a richer variety of quantum simulations, and for achieving more efficient and error-tolerant quantum computation. Integrated photonics has recently become a leading platform for the compact, cost-efficient, and stable generation and processing of non-classical optical states. However, so far, integrated entangled quantum sources have been limited to qubits (D = 2). Here we demonstrate on-chip generation of entangled qudit states, where the photons are created in a coherent superposition of multiple high-purity frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions, formed by two entangled qudits with D = 10. Furthermore, using state-of-the-art, yet off-the-shelf telecommunications components, we introduce a coherent manipulation platform with which to control frequency-entangled states, capable of performing deterministic high-dimensional gate operations. We validate this platform by measuring Bell inequality violations and performing quantum state tomography. Our work enables the generation and processing of high-dimensional quantum states in a single spatial mode.
Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science. Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantummechanics, for increasing the sensitivity of quantum imaging schemes, for improving the robustness and key rate of quantum communication protocols, for enabling a richer variety of quantum simulations, and for achieving more efficient and error-tolerant quantum computation. Integrated photonics has recently become a leading platform for the compact, cost-efficient, and stable generation and processing of non-classical optical states. However, so far, integrated entangled quantum sources have been limited to qubits (D = 2). Here we demonstrate on-chip generation of entangled qudit states, where the photons are created in a coherent superposition of multiple high-purity frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions, formed by two entangled qudits with D = 10. Furthermore, using state-of-the-art, yet off-the-shelf telecommunications components, we introduce a coherent manipulation platform with which to control frequency-entangled states, capable of performing deterministic high-dimensional gate operations. We validate this platform by measuring Bell inequality violations and performing quantum state tomography. Our work enables the generation and processing of high-dimensional quantum states in a single spatial mode.
The double-well potential is arguably one of the most important potentials in quantummechanics, because the solution contains the notion of a state as a linear superposition of "classical" states, a concept which has become very important in quantum information theory. It is therefore desirable to have solutions to simple double-well potentials…
Santos, M F; Cunha, M Terra; Chaves, R; Carvalho, A R R
2012-04-27
Spontaneous emission and the inelastic scattering of photons are two natural processes usually associated with decoherence and the reduction in the capacity to process quantum information. Here we show that, when suitably detected, these photons are sufficient to build all the fundamental blocks needed to perform quantum computation in the emitting qubits while protecting them from deleterious dissipative effects. We exemplify this by showing how to efficiently prepare graph states for the implementation of measurement-based quantum computation.
The masses of the quarks in the Poincaré-invariant quantummechanics are the constituent masses. Even in this framework it is possible to obtain an estimate of the constituent quark masses from the Ward identity for the axial current ant the current quark masses.
The quantum internet holds promise for accomplishing quantum teleportation and unconditionally secure communication freely between arbitrary clients all over the globe, as well as the simulation of quantum many-body systems. For such a quantum internet protocol, a general fundamental upper bound on the obtainable entanglement or secret key has been derived [K. Azuma, A. Mizutani, and H.-K. Lo, Nat. Commun. 7, 13523 (2016), 10.1038/ncomms13523]. Here we consider its converse problem. In particular, we present a universal protocol constructible from any given quantum network, which is based on running quantum repeater schemes in parallel over the network. For arbitrary lossy optical channel networks, our protocol has no scaling gap with the upper bound, even based on existing quantum repeater schemes. In an asymptotic limit, our protocol works as an optimal entanglement or secret-key distribution over any quantum network composed of practical channels such as erasure channels, dephasing channels, bosonic quantum amplifier channels, and lossy optical channels.
Quantum communication provides an absolute security advantage, and it has been widely developed over the past 30 years. As an important branch of quantum communication, quantum secure direct communication (QSDC) promotes high security and instantaneousness in communication through directly transmitting messages over a quantum channel. The full implementation of a quantum protocol always requires the ability to control the transfer of a message effectively in the time domain; thus, it is essential to combine QSDC with quantum memory to accomplish the communication task. In this Letter, we report the experimental demonstration of QSDC with state-of-the-art atomic quantum memory for the first time in principle. We use the polarization degrees of freedom of photons as the information carrier, and the fidelity of entanglement decoding is verified as approximately 90%. Our work completes a fundamental step toward practical QSDC and demonstrates a potential application for long-distance quantum communication in a quantum network.
Quantum communication provides an absolute security advantage, and it has been widely developed over the past 30 years. As an important branch of quantum communication, quantum secure direct communication (QSDC) promotes high security and instantaneousness in communication through directly transmitting messages over a quantum channel. The full implementation of a quantum protocol always requires the ability to control the transfer of a message effectively in the time domain; thus, it is essential to combine QSDC with quantum memory to accomplish the communication task. In this Letter, we report the experimental demonstration of QSDC with state-of-the-art atomic quantum memory for the first time in principle. We use the polarization degrees of freedom of photons as the information carrier, and the fidelity of entanglement decoding is verified as approximately 90%. Our work completes a fundamental step toward practical QSDC and demonstrates a potential application for long-distance quantum communication in a quantum network.
