Axioms for quantum mechanics: relativistic causality, retrocausality, and the existence of a classical limit

NASA Astrophysics Data System (ADS)

Rohrlich, Daniel

Y. Aharonov and A. Shimony both conjectured that two axioms - relativistic causality (``no superluminal signalling'') and nonlocality - so nearly contradict each other that only quantum mechanics reconciles them. Can we indeed derive quantum mechanics, 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 quantum mechanics has a classical limit, so must any generalization of quantum mechanics. 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 quantum mechanics) from the three axioms of relativistic causality, retrocausality and the existence of a classical limit. Although the derivation does not assume quantum mechanics, 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.

Insights into Teaching Quantum Mechanics in Secondary and Lower Undergraduate Education

ERIC Educational Resources Information Center

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 quantum mechanics in secondary and lower undergraduate education. A conceptual approach to quantum mechanics is being implemented in more and more introductory physics courses around the world. Because of the differences between the conceptual nature of quantum mechanics and…

Investigating and Improving Student Understanding of Key Ideas in Quantum Mechanics throughout Instruction

NASA Astrophysics Data System (ADS)

Emigh, Paul Jeffrey

This dissertation describes research on student understanding of quantum mechanics across multiple levels of instruction. The primary focus has been to identify patterns in student reasoning related to key concepts in quantum mechanics. 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: Quantum Mechanics, 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 quantum mechanics.

Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices

NASA Astrophysics Data System (ADS)

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 quantum mechanics: in fact, we derive all its four postulates from the generalized Bayesian theory. This implies that quantum mechanics is self-consistent. It also leads us to reinterpret the main operations in quantum mechanics as probability rules: Bayes' rule (measurement), marginalization (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantum mechanics is the Bayesian theory in the complex numbers.

Teaching Quantum Mechanics on an Introductory Level.

ERIC Educational Resources Information Center

Muller, Rainer; Wiesner, Hartmut

2002-01-01

Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics 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)

Gaussian effective potential: Quantum mechanics

NASA Astrophysics Data System (ADS)

Stevenson, P. M.

1984-10-01

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 quantum mechanics. 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.

Facets of contextual realism in quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Alok Kumar; Home, Dipankar

2011-09-23

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 quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.

Local quantum measurement and no-signaling imply quantum correlations.

PubMed

Barnum, H; Beigi, S; Boixo, S; Elliott, M B; Wehner, S

2010-04-09

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the tensor product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond quantum mechanics, quantum theory would be invalidated even locally.

Cognitive Issues in Learning Advanced Physics: An Example from Quantum Mechanics

NASA Astrophysics Data System (ADS)

Singh, Chandralekha; Zhu, Guangtian

2009-11-01

We are investigating cognitive issues in learning quantum mechanics 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 quantum mechanics and for ensuring that the learning tools help students build a robust knowledge structure. We discuss the cognitive aspects of quantum mechanics that are similar or different from those of introductory physics and their implications for developing strategies to help students develop a good grasp of quantum mechanics.

Quantum optics, cavity QED, and quantum optomechanics

NASA Astrophysics Data System (ADS)

Meystre, Pierre

2013-05-01

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 quantum mechanics; and from the point of view of applications, quantum optomechanical techniques will provide motion and force sensing near the fundamental limit imposed by quantum mechanics (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.

Testing Nonassociative Quantum Mechanics.

PubMed

Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut

2015-11-27

The familiar concepts of state vectors and operators in quantum mechanics 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 quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.

From Einstein-Podolsky-Rosen paradox to quantum nonlocality: experimental investigation of quantum correlations

NASA Astrophysics Data System (ADS)

Xu, Jin-Shi; Li, Chuan-Feng; Guo, Guang-Can

2016-11-01

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 quantum mechanics. Two fundamental concepts: entanglement and steering, were given in the response to the EPR paper by Schrodinger, which both reflect the nonlocal nature of quantum mechanics. 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 quantum mechanics. Since then, great efforts have been made to experimentally investigate the nonlocal feature of quantum mechanics 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.

Improving students' understanding of quantum mechanics

NASA Astrophysics Data System (ADS)

Zhu, Guangtian

2011-12-01

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 quantum mechanics and how these difficulties can be reduced by research-based learning tutorials and peer instruction tools. We investigated students' difficulties in learning quantum mechanics 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 quantum mechanics through a guided approach. Preliminary assessments indicate that students' understanding of quantum mechanics is improved after using the research-based learning tools in the junior-senior level quantum mechanics courses. We also designed a standardized conceptual survey that can help instructors better probe students' understanding of quantum mechanics concepts in one spatial dimension. The validity and reliability of this quantum mechanics survey is discussed.

Search for violations of quantum mechanics

DOE PAGES

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 quantum mechanics. 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 quantum mechanics 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 quantum mechanical coherence. We discuss how these limits might be improved in the future, and consider the relative significance of other successful tests of quantum mechanics. Finally, an appendix contains model estimates of the magnitude of effects violating quantum mechanics.« less

Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction.

PubMed

Budiyono, Agung; Rohrlich, Daniel

2017-11-03

Where does quantum mechanics 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 quantum mechanics 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 quantum mechanics 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.

Generation of mechanical interference fringes by multi-photon counting

NASA Astrophysics Data System (ADS)

Ringbauer, M.; Weinhold, T. J.; Howard, L. A.; White, A. G.; Vanner, M. R.

2018-05-01

Exploring the quantum behaviour of macroscopic objects provides an intriguing avenue to study the foundations of physics and to develop a suite of quantum-enhanced technologies. One prominent path of study is provided by quantum optomechanics which utilizes the tools of quantum optics to control the motion of macroscopic mechanical resonators. Despite excellent recent progress, the preparation of mechanical quantum superposition states remains outstanding due to weak coupling and thermal decoherence. Here we present a novel optomechanical scheme that significantly relaxes these requirements allowing the preparation of quantum superposition states of motion of a mechanical resonator by exploiting the nonlinearity of multi-photon quantum measurements. Our method is capable of generating non-classical mechanical states without the need for strong single-photon coupling, is resilient against optical loss, and offers more favourable scaling against initial mechanical thermal occupation than existing schemes. Moreover, our approach allows the generation of larger superposition states by projecting the optical field onto NOON states. We experimentally demonstrate this multi-photon-counting technique on a mechanical thermal state in the classical limit and observe interference fringes in the mechanical position distribution that show phase super-resolution. This opens a feasible route to explore and exploit quantum phenomena at a macroscopic scale.

Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2014-12-01

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 quantum mechanics, 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 quantum mechanics 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. Quantum mechanics 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.

Holographic description of a quantum black hole on a computer

NASA Astrophysics Data System (ADS)

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 quantum mechanics 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 quantum mechanical systems, as conjectured from the theory. Here, we test this conjecture by calculating the mass of a black hole in the corresponding quantum mechanical 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 quantum mechanics.

Fundamental Study on Quantum Nanojets

DTIC Science & Technology

2004-08-01

Pergamon Press. Bell , J. S . 1966 On the problem of hidden variables in quantum mechanics. Rev. of Modern Phys., 38, 447. Berndl, K., Daumer, M...fluid dynamics based on two quantum mechanical 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

Faithful conversion of propagating quantum information to mechanical motion

NASA Astrophysics Data System (ADS)

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 quantum mechanics. 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.

Beyond the Quantum

NASA Astrophysics Data System (ADS)

Nieuwenhuizen, Theo M.; Mehmani, Bahar; Špička, Václav; Aghdami, Maryam J.; Khrennikov, Andrei Yu

2007-09-01

pt. A. Introductions. The mathematical basis for deterministic quantum mechanics / G.'t Hooft. What did we learn from quantum gravity? / A. Ashtekar. Bose-Einstein condensates and EPR quantum non-locality / F. Laloe. The quantum measurement process: lessons from an exactly solvable model / A.E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen -- pt. B. Quantum mechanics and quantum information. POVMs: a small but important step beyond standard quantum mechanics / W. M. de Muynck. State reduction by measurements with a null result / G. Nienhuis. Solving open questions in the Bose-Einstein condensation of an ideal gas via a hybrid mixture of laser and statistical physics / M. Kim, A. Svidzinsky and M.O. Scully. Twin-Photon light scattering and causality / G. Puentes, A. Aiello and J. P. Woerdman. Simultaneous measurement of non-commuting observables / G. Aquino and B. Mehmani. Quantum decoherence and gravitational waves / M.T. Jaekel ... [et al.]. Role of various entropies in the black hole information loss problem / Th. M. Nieuwenhuizen and I.V. Volovich. Quantum and super-quantum correlations / G.S. Jaeger -- pt. C. Long distance correlations and bell inequalities. Understanding long-distance quantum correlations / L. Marchildon. Connection of probability models to EPR experiments: probability spaces and Bell's theorem / K. Hess and W. Philipp. Fair sampling vs no-signalling principle in EPR experiments / G. Adenier and A. Yu. Khrennikov -- pt. D. Mathematical foundations. Where the mathematical structure of quantum mechanics comes from / G.M. D'Ariano. Phase space description of quantum mechanics and non-commutative geometry: Wigner-Moyal and Bohm in a wider context / B.J. Hiley. Quantum mechanics as simple algorithm for approximation of classical integrals / A. Yu. Khrennikov. Noncommutative quantum mechanics viewed from Feynman Formalism / J. Lages ... [et al.]. Beyond the quantum in Snyder space / J.F.S. van Huele and M. K. Transtrum -- pt. E. Stochastic electrodynamics. Some quantum experiments from the point of view of Stochastic electrodynamics / V. Spicka ... [et al.]. On the ergodic behaviour of atomic systems under the action of the zero-point radiation field / L. De La Peña and A. M. Cetto. Inertia and the vacuum-view on the emergence of the inertia reaction force / A. Rueda and H. Sunahata -- pt. F. Models for the electron. Rotating Hopf-Kinks: oscillators in the sense of de Broglie / U. Enz. Kerr-Newman particles: symmetries and other properties / H.I. Arcos and J.G. Pereira. Kerr geometry beyond the quantum theory / Th. M. Nieuwenhuizen -- pt. G. Philosophical considerations. Probability in non-collapse interpretations of a quantum mechanics / D. Dieks. The Schrödinger-Park paradox about the concept of "State" in quantum statistical mechanics and quantum information theory is still open: one more reason to go beyond? / G.P. Beretta. The conjecture that local realism is possible / E. Santos -- pt. H. The round table. Round table discussion / A.M. Cetto ... [et al.].

Insights into teaching quantum mechanics in secondary and lower undergraduate education

NASA Astrophysics Data System (ADS)

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 quantum mechanics in secondary and lower undergraduate education. A conceptual approach to quantum mechanics is being implemented in more and more introductory physics courses around the world. Because of the differences between the conceptual nature of quantum mechanics and classical physics, research on misconceptions, testing, and teaching strategies for introductory quantum mechanics 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 quantum mechanics. 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 quantum mechanics 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 quantum mechanics.

A Framework for Understanding the Patterns of Student Difficulties in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Singh, Chandralekha

2015-04-01

Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. We describe a theoretical framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that the challenges many students face in developing expertise in quantum mechanics 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 quantum mechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantum mechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantum mechanics 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 quantum mechanics. Support from the National Science Foundation is gratefully acknowledged.

Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics

NASA Astrophysics Data System (ADS)

Ohzeki, Masayuki

2013-09-01

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 quantum annealing. The most typical instance is quantum adiabatic computation based on the adiabatic theorem. The quantum adiabatic computation as discussed in the other chapter, unfortunately, has a crucial bottleneck for a part of the optimization problems. We here introduce several recent trials to overcome such a weakpoint by use of developments in statistical mechanics. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.

Emergent mechanics, quantum and un-quantum

NASA Astrophysics Data System (ADS)

Ralston, John P.

2013-10-01

There is great interest in quantum mechanics 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 quantum mechanics 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 quantum mechanics 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

Quantum Interactive Learning Tutorial on the Double-Slit Experiment to Improve Student Understanding of Quantum Mechanics

ERIC Educational Resources Information Center

Sayer, Ryan; Maries, Alexandru; Singh, Chandralekha

2017-01-01

Learning quantum mechanics 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 quantum mechanics pertaining to the double-slit experiment in…

What's the Matter with Waves?; An introduction to techniques and applications of quantum mechanics

NASA Astrophysics Data System (ADS)

Parkinson, William

2017-12-01

Like rocket science or brain surgery, quantum mechanics 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; quantum mechanics 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 quantum mechanics, 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 quantum mechanical 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 quantum mechanics, 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

Quantum Social Science

NASA Astrophysics Data System (ADS)

Haven, Emmanuel; Khrennikov, Andrei

2013-01-01

Preface; Part I. Physics Concepts in Social Science? A Discussion: 1. Classical, statistical and quantum mechanics: all in one; 2. Econophysics: statistical physics and social science; 3. Quantum social science: a non-mathematical motivation; Part II. Mathematics and Physics Preliminaries: 4. Vector calculus and other mathematical preliminaries; 5. Basic elements of quantum mechanics; 6. Basic elements of Bohmian mechanics; Part III. Quantum Probabilistic Effects in Psychology: Basic Questions and Answers: 7. A brief overview; 8. Interference effects in psychology - an introduction; 9. A quantum-like model of decision making; Part IV. Other Quantum Probabilistic Effects in Economics, Finance and Brain Sciences: 10. Financial/economic theory in crisis; 11. Bohmian mechanics in finance and economics; 12. The Bohm-Vigier Model and path simulation; 13. Other applications to economic/financial theory; 14. The neurophysiological sources of quantum-like processing in the brain; Conclusion; Glossary; Index.

Holographic description of a quantum black hole on a computer.

PubMed

Hanada, Masanori; Hyakutake, Yoshifumi; Ishiki, Goro; Nishimura, Jun

2014-05-23

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 quantum mechanics 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 quantum mechanical systems, as conjectured from the theory. Here, we test this conjecture by calculating the mass of a black hole in the corresponding quantum mechanical 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 quantum mechanics. Copyright © 2014, American Association for the Advancement of Science.

Lorentz quantum mechanics

NASA Astrophysics Data System (ADS)

Zhang, Qi; Wu, Biao

2018-01-01

We present a theoretical framework for the dynamics of bosonic Bogoliubov quasiparticles. We call it Lorentz quantum mechanics because the dynamics is a continuous complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantum mechanics, the dynamics is the unitary transformation in Hilbert space. In our Lorentz quantum mechanics, three types of state exist: space-like, light-like and time-like. Fundamental aspects are explored in parallel to the usual quantum mechanics, 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.

Quantum Field Theory in (0 + 1) Dimensions

ERIC Educational Resources Information Center

Boozer, A. D.

2007-01-01

We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…

Relativity, Symmetry, and the Structure of Quantum Theory, Volume 2; Point form relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Klink, William H.; Schweiger, Wolfgang

2018-03-01

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 quantum mechanics, 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 quantum mechanics to nuclear physics.

Anharmonic quantum mechanical systems do not feature phase space trajectories

NASA Astrophysics Data System (ADS)

Oliva, Maxime; Kakofengitis, Dimitris; Steuernagel, Ole

2018-07-01

Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical 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 quantum mechanical 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.

Investigating and improving student understanding of quantum mechanics in the context of single photon interference

NASA Astrophysics Data System (ADS)

Marshman, Emily; Singh, Chandralekha

2017-06-01

Single photon experiments involving a Mach-Zehnder interferometer can illustrate the fundamental principles of quantum mechanics, 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 quantum mechanics. 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 quantum mechanics concepts using the concrete quantum optics context. It strives to help students learn the basics of quantum mechanics in the context of single photon experiment, develop the ability to apply fundamental quantum 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.

Effective equations for the quantum pendulum from momentous quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 quantum mechanics. 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.

Framework for understanding the patterns of student difficulties in quantum mechanics

NASA Astrophysics Data System (ADS)

Marshman, Emily; Singh, Chandralekha

2015-12-01

[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 quantum mechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that the challenges many students face in developing expertise in quantum mechanics 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 quantum mechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantum mechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantum mechanics 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 quantum mechanics.

Bell's theorem and quantum mechanics

NASA Astrophysics Data System (ADS)

Rosen, Nathan

1994-02-01

Bell showed that assuming locality leads to a disagreement with quantum mechanics. Here the nature of the nonlocality that follows from quantum mechanics 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

Calendar effects in quantum mechanics in view of interactive holography

NASA Astrophysics Data System (ADS)

Berkovich, Simon

2013-04-01

Quantum mechanics 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, Quantum Mechanics (February) Quantum Mechanics (August). [1] S. Berkovich, ``A comprehensive explanation of quantum mechanics,'' www.cs.gwu.edu/research/technical-report/170 .

Cylindrical dust acoustic solitary waves with transverse perturbations in quantum dusty plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mushtaq, A.

2007-11-15

The nonlinear quantum dust acoustic waves with effects of nonplanar cylindrical geometry, quantum corrections, and transverse perturbations are studied. By using the perturbation method, a cylindrical Kadomtsev-Petviashvili equation for dust acoustic waves is derived by incorporating quantum-mechanical effects. The quantum-mechanical effects via quantum diffraction and quantum statistics, and the role of transverse perturbations in cylindrical geometry on the dynamics of this wave, are studied both analytically and numerically.

On the hypothesis that quantum mechanism manifests classical mechanics: Numerical approach to the correspondence in search of quantum chaos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Sang-Bong

1993-09-01

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 quantum mechanics 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 quantum mechanics 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

JOURNAL SCOPE GUIDELINES: Paper classification scheme

NASA Astrophysics Data System (ADS)

2005-06-01

This scheme is used to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work. For each of the sections listed in the scope statement we suggest some more detailed subject areas which help define that subject area. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org). 1. Statistical physics numerical and computational methods statistical mechanics, phase transitions and critical phenomena quantum condensed matter theory Bose-Einstein condensation strongly correlated electron systems exactly solvable models in statistical mechanics lattice models, random walks and combinatorics field-theoretical models in statistical mechanics disordered systems, spin glasses and neural networks nonequilibrium systems network theory 2. Chaotic and complex systems nonlinear dynamics and classical chaos fractals and multifractals quantum chaos classical and quantum transport cellular automata granular systems and self-organization pattern formation biophysical models 3. Mathematical physics combinatorics algebraic structures and number theory matrix theory classical and quantum groups, symmetry and representation theory Lie algebras, special functions and orthogonal polynomials ordinary and partial differential equations difference and functional equations integrable systems soliton theory functional analysis and operator theory inverse problems geometry, differential geometry and topology numerical approximation and analysis geometric integration computational methods 4. Quantum mechanics and quantum information theory coherent states eigenvalue problems supersymmetric quantum mechanics scattering theory relativistic quantum mechanics semiclassical approximations foundations of quantum mechanics and measurement theory entanglement and quantum nonlocality geometric phases and quantum tomography quantum tunnelling decoherence and open systems quantum cryptography, communication and computation theoretical quantum optics 5. Classical and quantum field theory quantum field theory gauge and conformal field theory quantum electrodynamics and quantum chromodynamics Casimir effect integrable field theory random matrix theory applications in field theory string theory and its developments classical field theory and electromagnetism metamaterials 6. Fluid and plasma theory turbulence fundamental plasma physics kinetic theory magnetohydrodynamics and multifluid descriptions strongly coupled plasmas one-component plasmas non-neutral plasmas astrophysical and dusty plasmas

The New Quantum Logic

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2014-06-01

It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or decoherent histories interpretation of quantum mechanics by using a modified form of quantum logic to discuss quantum properties (subspaces of the quantum Hilbert space), and treating quantum time development as a stochastic process. The histories approach in turn gives rise to some conceptual difficulties, in particular the correct choice of a framework (probabilistic sample space) or family of histories, and these are discussed. The central issue is that the principle of unicity, the idea that there is a unique single true description of the world, is incompatible with our current understanding of quantum mechanics.

Quantum mechanics and reality: An interpretation of Everett's theory

NASA Astrophysics Data System (ADS)

Lehner, Christoph Albert

The central part of Everett's formulation of quantum mechanics is a quantum mechanical 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 quantum mechanical systems; an assumption of supervenience of mental states (qualities) over quantum mechanical properties; and an assumption about the interpretation of quantum mechanical states in general: quantum mechanical 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 quantum mechanical 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 quantum mechanical state of an observer. Rather, the introspective qualities of a quantum mechanical 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 quantum mechanical state is impossible in principle. Empirical reality for a conscious observer is not described by the objective state, but by a Everettian relative state conditional on the subjective state, and no theoretical 'mark of reality' is necessary for this concept of reality. I compare the resulting concept of reality to Kant's distinction between empirical and transcendental reality.

Making Sense of Bell's Theorem and Quantum Nonlocality

NASA Astrophysics Data System (ADS)

Boughn, Stephen

2017-05-01

Bell's theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell's theorem and its many extensions have led to the claim that quantum mechanics and by inference nature herself are nonlocal in the sense that a measurement on a system by an observer at one location has an immediate effect on a distant entangled system (one with which the original system has previously interacted). Einstein was repulsed by such "spooky action at a distance" and was led to question whether quantum mechanics could provide a complete description of physical reality. In this paper I argue that quantum mechanics does not require spooky action at a distance of any kind and yet it is entirely reasonable to question the assumption that quantum mechanics can provide a complete description of physical reality. The magic of entangled quantum states has little to do with entanglement and everything to do with superposition, a property of all quantum systems and a foundational tenet of quantum mechanics.

Introduction

NASA Astrophysics Data System (ADS)

Bub, Jeffrey; Fuchs, Christopher A.

The great debate between Einstein and Bohr on the interpretation of quantum mechanics culminated with the Einstein-Podolsky-Rosen (EPR) paper in 1935, "Can quantum-mechanical description of physical reality be considered complete?" (Einstein, Podolsky, & Rosen, 1935, and Bohr's reply, 1935). EPR showed that composite quantum systems, consisting of widely separated subsystems, could exist in certain quantum states that they thought spelled trouble for the Copenhagen interpretation. Specifically, they argued that for such states, the correlations between the outcomes of measurements on the subsystems were incompatible with the assumption that the quantum state was a complete description of the system. They concluded that quantum mechanics was an incomplete theory-that the quantum state could not be the whole story about a system.

Quantum enhanced feedback cooling of a mechanical oscillator using nonclassical light.

PubMed

Schäfermeier, Clemens; Kerdoncuff, Hugo; Hoff, Ulrich B; Fu, Hao; Huck, Alexander; Bilek, Jan; Harris, Glen I; Bowen, Warwick P; Gehring, Tobias; Andersen, Ulrik L

2016-11-29

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 quantum mechanics.

Albert Einstein and the Quantum Riddle

ERIC Educational Resources Information Center

Lande, Alfred

1974-01-01

Derives a systematic structure contributing to the solution of the quantum riddle in Einstein's sense by deducing quantum mechanics from the postulates of symmetry, correspondence, and covariance. Indicates that the systematic presentation is in agreement with quantum mechanics established by Schroedinger, Born, and Heisenberg. (CC)

Locality and quantum mechanics.

PubMed

Unruh, W G

2018-07-13

It is argued that it is best not to think of quantum mechanics as non-local, but rather that it is non-realistic.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Heisenberg and the Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Camilleri, Kristian

2011-09-01

Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics 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 Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.

Heisenberg and the Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Camilleri, Kristian

2009-02-01

Preface; 1. Introduction; Part I. The Emergence of Quantum Mechanics: 2. Quantum mechanics 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 Quantum Mechanics: 7. The transformation of Kantian philosophy; 8. The linguistic turn in Heisenberg's thought; Conclusion; References; Index.

Contact geometry and quantum mechanics

NASA Astrophysics Data System (ADS)

Herczeg, Gabriel; Waldron, Andrew

2018-06-01

We present a generally covariant approach to quantum mechanics 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 quantum mechanics 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 quantum mechanics.

Thermodynamic integration from classical to quantum mechanics.

PubMed

Habershon, Scott; Manolopoulos, David E

2011-12-14

We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable. © 2011 American Institute of Physics

Emergent quantum mechanics without wavefunctions

NASA Astrophysics Data System (ADS)

Mesa Pascasio, J.; Fussy, S.; Schwabl, H.; Grössing, G.

2016-03-01

We present our model of an Emergent Quantum Mechanics 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 quantum mechanical 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 quantum mechanics 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.

Fritz London and the scale of quantum mechanisms

NASA Astrophysics Data System (ADS)

Monaldi, Daniela

2017-11-01

Fritz London's seminal idea of ;quantum mechanisms 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 quantum mechanism 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 quantum mechanics was not, as it was commonly assumed, relevant exclusively as a micromechanics.

An adaptive quantum mechanics/molecular mechanics method for the infrared spectrum of water: incorporation of the quantum effect between solute and solvent.

PubMed

Watanabe, Hiroshi C; Banno, Misa; Sakurai, Minoru

2016-03-14

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 quantum mechanical method. However, conventional quantum mechanics/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.

Continuous quantum measurement and the quantum to classical transition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhattacharya, Tanmoy; Habib, Salman; Jacobs, Kurt

2003-04-01

While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the trajectories of the correct classical motion must emerge from quantum mechanics, a process referred to as the quantum to classical transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys. Rev. Lett. 85, 4852 (2000)], here we elucidate this transition in some detail, showing that once the measurement processes that affect all macroscopic systems are taken into account, quantum mechanics indeed predicts the emergence of classical motion. We derive inequalities thatmore » describe the parameter regime in which classical motion is obtained, and provide numerical examples. We also demonstrate two further important properties of the classical limit: first, that multiple observers all agree on the motion of an object, and second, that classical statistical inference may be used to correctly track the classical motion.« less

Gate-controlled electromechanical backaction induced by a quantum dot

NASA Astrophysics Data System (ADS)

Okazaki, Yuma; Mahboob, Imran; Onomitsu, Koji; Sasaki, Satoshi; Yamaguchi, Hiroshi

2016-04-01

Semiconductor-based quantum structures integrated into mechanical resonators have emerged as a unique platform for generating entanglement between macroscopic phononic and mesocopic electronic degrees of freedom. A key challenge to realizing this is the ability to create and control the coupling between two vastly dissimilar systems. Here, such coupling is demonstrated in a hybrid device composed of a gate-defined quantum dot integrated into a piezoelectricity-based mechanical resonator enabling milli-Kelvin phonon states to be detected via charge fluctuations in the quantum dot. Conversely, the single electron transport in the quantum dot can induce a backaction onto the mechanics where appropriate bias of the quantum dot can enable damping and even current-driven amplification of the mechanical motion. Such electron transport induced control of the mechanical resonator dynamics paves the way towards a new class of hybrid semiconductor devices including a current injected phonon laser and an on-demand single phonon emitter.

Macro-mechanics controls quantum mechanics: mechanically controllable quantum conductance switching of an electrochemically fabricated atomic-scale point contact.

PubMed

Staiger, Torben; Wertz, Florian; Xie, Fangqing; Heinze, Marcel; Schmieder, Philipp; Lutzweiler, Christian; Schimmel, Thomas

2018-01-12

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.

Coherent Dynamics of a Hybrid Quantum Spin-Mechanical Oscillator System

NASA Astrophysics Data System (ADS)

Lee, Kenneth William, III

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 previous demonstrations of a strain-mediated spin-mechanical interface and hence the system is largely uncharacterized. Second, fabricating high quality diamond mechanical oscillators is difficult due to the robust and chemically inert nature of diamond. Finally, engineering highly coherent NV centers with a coherent optical interface in nanostructured diamond remains an outstanding challenge. In this thesis, we theoretically and experimentally address each of these challenges, and show that with future improvements, this device is suitable for future quantum-enabled applications. First, we theoretically and experimentally demonstrate a dynamic, strain-mediated coupling between the spin and orbital degrees of freedom of the NV center and the driven mechanical motion of a single-crystal diamond cantilever. We employ Ramsey interferometry to demonstrate coherent, mechanical driving of the NV spin evolution. Using this interferometry technique, we present the first demonstration of nanoscale strain imaging, and quantitatively characterize the previously unknown spin-strain coupling constants. Next, we use the driven motion of the cantilever to perform deterministic control of the frequency and polarization dependence of the optical transitions of the NV center. Importantly, this experiment constitutes the first demonstration of on-chip control of both the frequency and polarization state of a single photon produced by a quantum emitter. In the final experiment, we use mechanical driving to engineer a series of spin ``clock" states and demonstrate a significant increase in the spin coherence time of the NV center. We conclude this thesis with a theoretical discussion of prospective applications for this device, including generation of non-classical mechanical states and spin-spin entanglement, as well as an evaluation of the current limitations of our devices, including a possible avenues for improvement to reach the regime of strong spin-phonon coupling.

Many-Body Localization and Thermalization in Quantum Statistical Mechanics

NASA Astrophysics Data System (ADS)

Nandkishore, Rahul; Huse, David A.

2015-03-01

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.

Nonlinear Riccati equations as a unifying link between linear quantum mechanics and other fields of physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-04-01

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 quantum mechanics, 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 quantum mechanics is not as essential as it apparently seems since quantum mechanics 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 quantum mechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantum mechanics. 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.

Measurements of entanglement over a kilometric distance to test superluminal models of Quantum Mechanics: preliminary results.

NASA Astrophysics Data System (ADS)

Cocciaro, B.; Faetti, S.; Fronzoni, L.

2017-08-01

As shown in the EPR paper (Einstein, Podolsky e Rosen, 1935), Quantum Mechanics 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, Quantum Mechanics and superluminal models lead to different predictions. So far, no deviations from the predictions of Quantum Mechanics 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.

Is a description deeper than the quantum one possible?

NASA Astrophysics Data System (ADS)

Ghirardi, GianCarlo; Romano, Raffaele

2014-12-01

Recently, it has been argued that quantum mechanics is a complete theory, and that different quantum states do necessarily correspond to different elements of reality, under the assumptions that quantum mechanics is correct and that measurement settings can be freely chosen. In this work, we prove that this result is a consequence of an unnecessarily strong mathematical expression of the free choice assumption, which embodies more conditions than explicitly stated. The issues of the completeness of quantum mechanics, and of the interpretation of the state vector, are by no means resolved. Taking this perspective, we describe how the recently introduced class of crypto-nonlocal hidden variables theories can be used to characterize the maximal possible departure from quantum mechanics, when the system consists of a pair of qubits.

"A dedicated missionary". Charles Galton Darwin and the new quantum mechanics in Britain

NASA Astrophysics Data System (ADS)

Navarro, Jaume

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 quantum mechanics.

Prediction and Repetition in Quantum Mechanics: The EPR Experiment and Quantum Probability

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2007-02-01

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 quantum mechanics 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 quantum mechanics.

Quantum biological channel modeling and capacity calculation.

PubMed

Djordjevic, Ivan B

2012-12-10

Quantum mechanics has an important role in photosynthesis, magnetoreception, and evolution. There were many attempts in an effort to explain the structure of genetic code and transfer of information from DNA to protein by using the concepts of quantum mechanics. The existing biological quantum channel models are not sufficiently general to incorporate all relevant contributions responsible for imperfect protein synthesis. Moreover, the problem of determination of quantum biological channel capacity is still an open problem. To solve these problems, we construct the operator-sum representation of biological channel based on codon basekets (basis vectors), and determine the quantum channel model suitable for study of the quantum biological channel capacity and beyond. The transcription process, DNA point mutations, insertions, deletions, and translation are interpreted as the quantum noise processes. The various types of quantum errors are classified into several broad categories: (i) storage errors that occur in DNA itself as it represents an imperfect storage of genetic information, (ii) replication errors introduced during DNA replication process, (iii) transcription errors introduced during DNA to mRNA transcription, and (iv) translation errors introduced during the translation process. By using this model, we determine the biological quantum channel capacity and compare it against corresponding classical biological channel capacity. We demonstrate that the quantum biological channel capacity is higher than the classical one, for a coherent quantum channel model, suggesting that quantum effects have an important role in biological systems. The proposed model is of crucial importance towards future study of quantum DNA error correction, developing quantum mechanical model of aging, developing the quantum mechanical models for tumors/cancer, and study of intracellular dynamics in general.

The Nature of the Chemical Bond--1990.

ERIC Educational Resources Information Center

Ogilvie, J. F.

1990-01-01

Three aspects of quantum mechanics in modern chemistry are stressed: the fundamental structure of quantum mechanics as a basis of chemical applications, the relationship of quantum mechanics to atomic and molecular structure, and the consequent implications for chemical education. A list of 64 references is included. (CW)

Quantum Mechanics for Everyone: Hands-On Activities Integrated with Technology.

ERIC Educational Resources Information Center

Zollman, Dean A.; Rebello, N. Sanjay; Hogg, Kirsten

2002-01-01

Explains a hands-on approach to teaching quantum mechanics that challenges the belief shared by many physics instructors that quantum mechanics is a very abstract subject that cannot be understood until students have learned much of the classical physics. (Contains 23 references.) (Author/YDS)

Some foundational aspects of quantum computers and quantum robots.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benioff, P.; Physics

1998-01-01

This paper addresses foundational issues related to quantum computing. The need for a universally valid theory such as quantum mechanics to describe to some extent its own validation is noted. This includes quantum mechanical descriptions of systems that do theoretical calculations (i.e. quantum computers) and systems that perform experiments. Quantum robots interacting with an environment are a small first step in this direction. Quantum robots are described here as mobile quantum systems with on-board quantum computers that interact with environments. Included are discussions on the carrying out of tasks and the division of tasks into computation and action phases. Specificmore » models based on quantum Turing machines are described. Differences and similarities between quantum robots plus environments and quantum computers are discussed.« less

Elucidating reaction mechanisms on quantum computers.

PubMed

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M; Wecker, Dave; Troyer, Matthias

2017-07-18

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.

Elucidating reaction mechanisms on quantum computers

PubMed Central

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, Matthias

2017-01-01

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

Elucidating reaction mechanisms on quantum computers

NASA Astrophysics Data System (ADS)

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, Matthias

2017-07-01

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.

Single and two-mode mechanical squeezing of an optically levitated nanodiamond via dressed-state coherence

NASA Astrophysics Data System (ADS)

Ge, Wenchao; Bhattacharya, M.

2016-10-01

Nonclassical states of macroscopic objects are promising for ultrasensitive metrology as well as testing quantum mechanics. In this work, we investigate dissipative mechanical quantum state engineering in an optically levitated nanodiamond. First, we study single-mode mechanical squeezed states by magnetically coupling the mechanical motion to a dressed three-level system provided by a nitrogen-vacancy center in the nanoparticle. Quantum coherence between the dressed levels is created via microwave fields to induce a two-phonon transition, which results in mechanical squeezing. Remarkably, we find that in ultrahigh vacuum quantum squeezing is achievable at room temperature with feedback cooling. For moderate vacuum, quantum squeezing is possible with cryogenic temperature. Second, we present a setup for two mechanical modes coupled to the dressed three levels, which results in two-mode squeezing analogous to the mechanism of the single-mode case. In contrast to previous works, our study provides a deterministic method for engineering macroscopic squeezed states without the requirement for a cavity.

Pseudospectra in non-Hermitian quantum mechanics

NASA Astrophysics Data System (ADS)

Krejčiřík, D.; Siegl, P.; Tater, M.; Viola, J.

2015-10-01

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics 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 quantum mechanics.

Categorization of Quantum Mechanics Problems by Professors and Students

ERIC Educational Resources Information Center

Lin, Shih-Yin; Singh, Chandralekha

2010-01-01

We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics 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…

Developing and Evaluating Animations for Teaching Quantum Mechanics Concepts

ERIC Educational Resources Information Center

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 quantum mechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantum mechanics concepts. They focus on known areas of student difficulty and misconceptions by…

Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems

ERIC Educational Resources Information Center

Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih

2009-01-01

In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…

In Defense of a Heuristic Interpretation of Quantum Mechanics

ERIC Educational Resources Information Center

Healy, Eamonn F.

2010-01-01

Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…

Questioning quantum mechanics

NASA Astrophysics Data System (ADS)

Frappier, Mélanie

2018-03-01

A century after its inception, quantum mechanics 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 quantum mechanics's true meaning.

Students' Epistemological Framing in Quantum Mechanics Problem Solving

ERIC Educational Resources Information Center

Modir, Bahar; Thompson, John D.; Sayre, Eleanor C.

2017-01-01

Students' difficulties in quantum mechanics 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 quantum mechanics problems in an upper-division physics course. Using the lens of epistemological framing, we investigated four…

Exploring the boundaries of quantum mechanics: advances in satellite quantum communications.

PubMed

Agnesi, Costantino; Vedovato, Francesco; Schiavon, Matteo; Dequal, Daniele; Calderaro, Luca; Tomasin, Marco; Marangon, Davide G; Stanco, Andrea; Luceri, Vincenza; Bianco, Giuseppe; Vallone, Giuseppe; Villoresi, Paolo

2018-07-13

Recent interest in quantum communications has stimulated great technological progress in satellite quantum technologies. These advances have rendered the aforesaid technologies mature enough to support the realization of experiments that test the foundations of quantum theory at unprecedented scales and in the unexplored space environment. Such experiments, in fact, could explore the boundaries of quantum theory and may provide new insights to investigate phenomena where gravity affects quantum objects. Here, we review recent results in satellite quantum communications and discuss possible phenomena that could be observable with current technologies. Furthermore, stressing the fact that space represents an incredible resource to realize new experiments aimed at highlighting some physical effects, we challenge the community to propose new experiments that unveil the interplay between quantum mechanics and gravity that could be realizable in the near future.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

The actual content of quantum theoretical kinematics and mechanics

NASA Technical Reports Server (NTRS)

Heisenberg, W.

1983-01-01

First, exact definitions are supplied for the terms: position, velocity, energy, etc. (of the electron, for instance), such that they are valid also in quantum mechanics. Canonically conjugated variables are determined simultaneously only with a characteristic uncertainty. This uncertainty is the intrinsic reason for the occurrence of statistical relations in quantum mechanics. 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 quantum mechanics. Several imaginary experiments are discussed to elucidate the theory.

A General No-Cloning Theorem for an infinite Multiverse

NASA Astrophysics Data System (ADS)

Gauthier, Yvon

2013-10-01

In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.

Philosophical Concepts in Physics

NASA Astrophysics Data System (ADS)

Cushing, James T.

1998-01-01

Preface; Part I. The Scientific Enterprise: 1. Ways of knowing; 2. Aristotle and Francis Bacon; 3. Science and metaphysics; Part II. Ancient and Modern Models of the Universe: 4. Observational astronomy and the Ptolemaic model; 5. The Copernican model and Kepler's laws; 6. Galileo on motion; Part III. The Newtonian Universe: 7. Newton's Principia; 8. Newton's law of universal gravitation; 9. Some old questions revisited; Part IV. A Perspective: 10. Galileo's Letter to the Grand Duchess; 11. An overarching Newtonian framework; 12. A view of the world based on science: determinism; Part V. Mechanical Versus Electrodynamical World Views: 13. Models of the aether; 14. Maxwell's theory; 15. The Kaufmann experiments; Part VI. The Theory of Relativity: 16. The background to and essentials of special relativity; 17. Further logical consequences of Einstein's postulates; 18. General relativity and the expanding universe; Part VII. The Quantum World and the Completeness of Quantum Mechanics: 19. The road to quantum mechanics; 20. 'Copenhage' quantum mechanics; 21. Is quantum mechanics complete?; Part VIII. Some Philosophical Lessons from Quantum Mechanics: 22. The EPR paper and Bell's theorem; 23. An alternative version of quantum mechanics; 24. An essential role for historical contingency?; Part IX. A Retrospective: 25. The goals of science and the status of its knowledge; Notes; General references; Bibliography; Author index; Subject index.

Macro-mechanics controls quantum mechanics: mechanically controllable quantum conductance switching of an electrochemically fabricated atomic-scale point contact

NASA Astrophysics Data System (ADS)

Staiger, Torben; Wertz, Florian; Xie, Fangqing; Heinze, Marcel; Schmieder, Philipp; Lutzweiler, Christian; Schimmel, Thomas

2018-01-01

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.

Hybrid quantum and classical methods for computing kinetic isotope effects of chemical reactions in solutions and in enzymes.

PubMed

Gao, Jiali; Major, Dan T; Fan, Yao; Lin, Yen-Lin; Ma, Shuhua; Wong, Kin-Yiu

2008-01-01

A method for incorporating quantum mechanics into enzyme kinetics modeling is presented. Three aspects are emphasized: 1) combined quantum mechanical and molecular mechanical methods are used to represent the potential energy surface for modeling bond forming and breaking processes, 2) instantaneous normal mode analyses are used to incorporate quantum vibrational free energies to the classical potential of mean force, and 3) multidimensional tunneling methods are used to estimate quantum effects on the reaction coordinate motion. Centroid path integral simulations are described to make quantum corrections to the classical potential of mean force. In this method, the nuclear quantum vibrational and tunneling contributions are not separable. An integrated centroid path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method along with a bisection sampling procedure was summarized, which provides an accurate, easily convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. In the ensemble-averaged variational transition state theory with multidimensional tunneling (EA-VTST/MT), these three aspects of quantum mechanical effects can be individually treated, providing useful insights into the mechanism of enzymatic reactions. These methods are illustrated by applications to a model process in the gas phase, the decarboxylation reaction of N-methyl picolinate in water, and the proton abstraction and reprotonation process catalyzed by alanine racemase. These examples show that the incorporation of quantum mechanical effects is essential for enzyme kinetics simulations.

The geometrical structure of quantum theory as a natural generalization of information geometry

NASA Astrophysics Data System (ADS)

Reginatto, Marcel

2015-01-01

Quantum mechanics 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 quantum mechanics 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 quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.

Developing and assessing research-based tools for teaching quantum mechanics and thermodynamics

NASA Astrophysics Data System (ADS)

Brown, Benjamin R.

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 quantum mechanics and thermodynamics courses. Student difficulties in learning quantum mechanics 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 quantum mechanics 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 quantum mechanics. Preliminary evaluations suggest that the QuILT, which strives to help students build a robust knowledge structure of time-dependence of expectation values in quantum mechanics using a guided approach, is successful in helping students learn these topics in the junior-senior level quantum mechanics courses. The technique to help upper-level students in quantum mechanics 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 quantum mechanics 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 of Thermodynamic Processes and the First and Second Laws (STPFaSL) is developed and validated with the purpose of evaluating the effectiveness of these topics in a thermodynamics curriculum. The validity and reliability of this survey are discussed and the student difficulties with these topics among various groups from introductory students to physics graduate students are cataloged.

Student Understanding of Time Dependence in Quantum Mechanics

ERIC Educational Resources Information Center

Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.

2015-01-01

The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. 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…

Bohm's Quantum Potential and the Visualization of Molecular Structure

NASA Technical Reports Server (NTRS)

Levit, Creon; Chancellor, Marisa K. (Technical Monitor)

1997-01-01

David Bohm's ontological interpretation of quantum theory can shed light on otherwise counter-intuitive quantum mechanical phenomena including chemical bonding. In the field of quantum chemistry, Richard Bader has shown that the topology of the Laplacian of the electronic charge density characterizes many features of molecular structure and reactivity. Visual and computational examination suggests that the Laplacian of Bader and the quantum potential of Bohm are morphologically equivalent. It appears that Bohmian mechanics and the quantum potential can make chemistry as clear as they makes physics.

The transactional interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

Cramer, John G.

2001-06-01

The transactional interpretation of quantum mechanics [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 quantum mechanics, (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."

Interactive Simulations to Support Quantum Mechanics Instruction for Chemistry Students

ERIC Educational Resources Information Center

Kohnle, Antje; Benfield, Cory; Hahner, Georg; Paetkau, Mark

2017-01-01

The QuVis Quantum Mechanics Visualization Project provides freely available research-based interactive simulations with accompanying activities for the teaching and learning of quantum mechanics 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…

Teaching the Common Aspects in Mechanical, Electromagnetic and Quantum Waves at Interfaces and Waveguides

ERIC Educational Resources Information Center

Rojas, R.; Robles, P.

2011-01-01

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 quantum mechanics, massive photons in wave guides and…

Design and Validation of the Quantum Mechanics Conceptual Survey

ERIC Educational Resources Information Center

McKagan, S. B.; Perkins, K. K.; Wieman, C. E.

2010-01-01

The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. 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…

Framework for Understanding the Patterns of Student Difficulties in Quantum Mechanics

ERIC Educational Resources Information Center

Marshman, Emily; Singh, Chandralekha

2015-01-01

Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that…

The criterion for time symmetry of probabilistic theories and the reversibility of quantum mechanics

NASA Astrophysics Data System (ADS)

Holster, A. T.

2003-10-01

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 quantum mechanics 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 quantum mechanics 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 quantum mechanics 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 quantum mechanics. The laws of quantum mechanics would be incompatible with a time-reversed version of our universe.

Topical review: spins and mechanics in diamond

NASA Astrophysics Data System (ADS)

Lee, Donghun; Lee, Kenneth W.; Cady, Jeffrey V.; Ovartchaiyapong, Preeti; Bleszynski Jayich, Ania C.

2017-03-01

There has been rapidly growing interest in hybrid quantum devices involving a solid-state spin and a macroscopic mechanical oscillator. Such hybrid devices create exciting opportunities to mediate interactions between disparate quantum bits (qubits) and to explore the quantum regime of macroscopic mechanical objects. In particular, a system consisting of the nitrogen-vacancy defect center (NV center) in diamond coupled to a high-quality-factor mechanical oscillator is an appealing candidate for such a hybrid quantum device, as it utilizes the highly coherent and versatile spin properties of the defect center. In this paper, we will review recent experimental progress on diamond-based hybrid quantum devices in which the spin and orbital dynamics of single defects are driven by the motion of a mechanical oscillator. In addition, we discuss prospective applications for this device, including long-range, phonon-mediated spin-spin interactions, and phonon cooling in the quantum regime. We conclude the review by evaluating the experimental limitations of current devices and identifying alternative device architectures that may reach the strong coupling regime.

Tampering detection system using quantum-mechanical systems

DOEpatents

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.

A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 quantum mechanical 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

A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.

PubMed

Sinitskiy, Anton V; Voth, Gregory A

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 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 quantum mechanical 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.

Experimental metaphysics2 : The double standard in the quantum-information approach to the foundations of quantum theory

NASA Astrophysics Data System (ADS)

Hagar, Amit

Among the alternatives of non-relativistic quantum mechanics (NRQM) there are those that give different predictions than quantum mechanics in yet-untested circumstances, while remaining compatible with current empirical findings. In order to test these predictions, one must isolate one's system from environmental induced decoherence, which, on the standard view of NRQM, is the dynamical mechanism that is responsible for the 'apparent' collapse in open quantum systems. But while recent advances in condensed-matter physics may lead in the near future to experimental setups that will allow one to test the two hypotheses, namely genuine collapse vs. decoherence, hence make progress toward a solution to the quantum measurement problem, those philosophers and physicists who are advocating an information-theoretic approach to the foundations of quantum mechanics are still unwilling to acknowledge the empirical character of the issue at stake. Here I argue that in doing so they are displaying an unwarranted double standard.

Generalized Weyl-Wigner map and Vey quantum mechanics

NASA Astrophysics Data System (ADS)

Dias, Nuno Costa; Prata, João Nuno

2001-12-01

The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantum mechanics, was presented in the literature many years ago. However, a derivation of the formalism directly from standard operator quantum mechanics, 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 quantum mechanics 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.

Quantum mechanical streamlines. I - Square potential barrier

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.

1974-01-01

Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical 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 quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

ON THE DYNAMICAL DERIVATION OF EQUILIBRIUM STATISTICAL MECHANICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prigogine, I.; Balescu, R.; Henin, F.

1960-12-01

Work on nonequilibrium statistical mechanics, which allows an extension of the kinetic proof to all results of equilibrium statistical mechanics involving a finite number of degrees of freedom, is summarized. As an introduction to the general N-body problem, the scattering theory in classical mechanics is considered. The general N-body problem is considered for the case of classical mechanics, quantum mechanics with Boltzmann statistics, and quantum mechanics including quantum statistics. Six basic diagrams, which describe the elementary processes of the dynamics of correlations, were obtained. (M.C.G.)

Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tanizaki, Yuya, E-mail: yuya.tanizaki@riken.jp; Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198; Koike, Takayuki, E-mail: tkoike@ms.u-tokyo.ac.jp

Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integralsmore » on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem. - Highlights: • Real-time path integral is studied based on Picard–Lefschetz theory. • Lucid demonstration is given through simple examples of quantum mechanics. • This technique is applied to quantum mechanics of the double-well potential. • Difficulty for practical applications is revealed, and we discuss its generality. • Quantum tunneling is shown to be closely related to complex classical solutions.« less

Undergraduate computational physics projects on quantum computing

NASA Astrophysics Data System (ADS)

Candela, D.

2015-08-01

Computational projects on quantum computing suitable for students in a junior-level quantum mechanics course are described. In these projects students write their own programs to simulate quantum computers. Knowledge is assumed of introductory quantum mechanics through the properties of spin 1/2. Initial, more easily programmed projects treat the basics of quantum computation, quantum gates, and Grover's quantum search algorithm. These are followed by more advanced projects to increase the number of qubits and implement Shor's quantum factoring algorithm. The projects can be run on a typical laptop or desktop computer, using most programming languages. Supplementing resources available elsewhere, the projects are presented here in a self-contained format especially suitable for a short computational module for physics students.

Quantum versus classical dynamics in the optical centrifuge

NASA Astrophysics Data System (ADS)

Armon, Tsafrir; Friedland, Lazar

2017-09-01

The interplay between classical and quantum-mechanical evolution in the optical centrifuge (OC) is discussed. The analysis is based on the quantum-mechanical formalism starting from either the ground state or a thermal ensemble. Two resonant mechanisms are identified, i.e., the classical autoresonance and the quantum-mechanical ladder climbing, yielding different dynamics and rotational excitation efficiencies. The rotating-wave approximation is used to analyze the two resonant regimes in the associated dimensionless two-parameter space and calculate the OC excitation efficiency. The results show good agreement between numerical simulations and theory and are relevant to existing experimental setups.

A full quantum analysis of the Stern-Gerlach experiment using the evolution operator method: analyzing current issues in teaching quantum mechanics

NASA Astrophysics Data System (ADS)

Benítez Rodríguez, E.; Arévalo Aguilar, L. M.; Piceno Martínez, E.

2017-03-01

To the quantum mechanics 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 quantum mechanics 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 quantum mechanical 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 quantum mechanics 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 quantum mechanics are heavily intermingled, we analyze some features and drawbacks in the current teaching of quantum mechanics. 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.

Quantum probabilistic logic programming

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan

2015-05-01

We describe a quantum mechanics based logic programming language that supports Horn clauses, random variables, and covariance matrices to express and solve problems in probabilistic logic. The Horn clauses of the language wrap random variables, including infinite valued, to express probability distributions and statistical correlations, a powerful feature to capture relationship between distributions that are not independent. The expressive power of the language is based on a mechanism to implement statistical ensembles and to solve the underlying SAT instances using quantum mechanical machinery. We exploit the fact that classical random variables have quantum decompositions to build the Horn clauses. We establish the semantics of the language in a rigorous fashion by considering an existing probabilistic logic language called PRISM with classical probability measures defined on the Herbrand base and extending it to the quantum context. In the classical case H-interpretations form the sample space and probability measures defined on them lead to consistent definition of probabilities for well formed formulae. In the quantum counterpart, we define probability amplitudes on Hinterpretations facilitating the model generations and verifications via quantum mechanical superpositions and entanglements. We cast the well formed formulae of the language as quantum mechanical observables thus providing an elegant interpretation for their probabilities. We discuss several examples to combine statistical ensembles and predicates of first order logic to reason with situations involving uncertainty.

Optical studies of current-induced magnetization switching and photonic quantum states

NASA Astrophysics Data System (ADS)

Lorenz, Virginia

2017-04-01

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 quantum mechanics 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 fundamental mechanisms 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 quantum mechanics 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 quantum mechanical 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.

Proliferation of Observables and Measurement in Quantum-Classical Hybrids

NASA Astrophysics Data System (ADS)

Elze, Hans-Thomas

2012-01-01

Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they were separable). Hybrids consist in coupled classical (CL) and quantum mechanical (QM) objects. Numerous consistency requirements for their description have been discussed and are fulfilled here. We summarize a representation of quantum mechanics in terms of classical analytical mechanics which is naturally extended to QM-CL hybrids. This framework allows for superposition, separable, and entangled states originating in the QM sector, admits experimenter's "Free Will", and is local and nonsignaling. Presently, we study the set of hybrid observables, which is larger than the Cartesian product of QM and CL observables of its components; yet it is smaller than a corresponding product of all-classical observables. Thus, quantumness and classicality infect each other.

Extracontextuality and extravalence in quantum mechanics.

PubMed

Auffèves, Alexia; Grangier, Philippe

2018-07-13

We develop the point of view where quantum mechanics results from the interplay between the quantized number of 'modalities' accessible to a quantum system, and the continuum of 'contexts' that are required to define these modalities. We point out the specific roles of 'extracontextuality' and 'extravalence' of modalities, and relate them to the Kochen-Specker and Gleason theorems.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Einstein's equivalence principle in quantum mechanics revisited

NASA Astrophysics Data System (ADS)

Nauenberg, Michael

2016-11-01

The gravitational equivalence principle in quantum mechanics 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 quantum mechanics.

Material Phase Causality or a Dynamics-Statistical Interpretation of Quantum Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koprinkov, I. G.

2010-11-25

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 quantum mechanics is introduced.

The geometrical structure of quantum theory as a natural generalization of information geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reginatto, Marcel

2015-01-13

Quantum mechanics 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 quantum mechanics 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 quantum mechanics is constructed usingmore » geometrical quantities. This suggests that quantum theory has its roots in information geometry.« less

Much Polyphony but Little Harmony: Otto Sackur's Groping for a Quantum Theory of Gases

NASA Astrophysics Data System (ADS)

Badino, Massimiliano; Friedrich, Bretislav

2013-09-01

The endeavor of Otto Sackur (1880-1914) was driven, on the one hand, by his interest in Nernst's heat theorem, statistical mechanics, and the problem of chemical equilibrium and, on the other hand, by his goal to shed light on classical mechanics from the quantum vantage point. Inspired by the interplay between classical physics and quantum theory, Sackur chanced to expound his personal take on the role of the quantum in the changing landscape of physics in the turbulent 1910s. We tell the story of this enthusiastic practitioner of the old quantum theory and early contributor to quantum statistical mechanics, whose scientific ontogenesis provides a telling clue about the phylogeny of his contemporaries.

Uncertain for a century: quantum mechanics and the dilemma of interpretation.

PubMed

Frank, Adam

2015-12-01

Quantum mechanics, the physical theory describing the microworld, is one of science's greatest triumphs. Remarkably, however, after more than 100 years it is still unclear what quantum mechanics means in terms of basic philosophical questions about the nature of reality. While there are many interpretations of the mathematical machinery of quantum physics, there remain no experimental means to distinguish between most of them. In this contribution, I wish to consider the ways in which the enduring lack of an agreed-upon interpretation of quantum physics influences a number of critical philosophical debates about physics and reality. I briefly review two problems affected by quantum interpretations: the meaning of the term universe and the nature of consciousness. © 2015 New York Academy of Sciences.

Individuation in Quantum Mechanics and Space-Time

NASA Astrophysics Data System (ADS)

Jaeger, Gregg

2010-10-01

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 quantum mechanical 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 quantum mechanical 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.

The physics of quantum materials

NASA Astrophysics Data System (ADS)

Keimer, B.; Moore, J. E.

2017-11-01

The physical description of all materials is rooted in quantum mechanics, 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 quantum mechanics, such as ferromagnetism.

Circuit quantum acoustodynamics with surface acoustic waves.

PubMed

Manenti, Riccardo; Kockum, Anton F; Patterson, Andrew; Behrle, Tanja; Rahamim, Joseph; Tancredi, Giovanna; Nori, Franco; Leek, Peter J

2017-10-17

The experimental investigation of quantum devices incorporating mechanical resonators has opened up new frontiers in the study of quantum mechanics at a macroscopic level. It has recently been shown that surface acoustic waves (SAWs) can be piezoelectrically coupled to superconducting qubits, and confined in high-quality Fabry-Perot cavities in the quantum regime. Here we present measurements of a device in which a superconducting qubit is coupled to a SAW cavity, realising a surface acoustic version of cavity quantum electrodynamics. We use measurements of the AC Stark shift between the two systems to determine the coupling strength, which is in agreement with a theoretical model. This quantum acoustodynamics architecture may be used to develop new quantum acoustic devices in which quantum information is stored in trapped on-chip acoustic wavepackets, and manipulated in ways that are impossible with purely electromagnetic signals, due to the 10 5 times slower mechanical waves.In this work, Manenti et al. present measurements of a device in which a tuneable transmon qubit is piezoelectrically coupled to a surface acoustic wave cavity, realising circuit quantum acoustodynamic architecture. This may be used to develop new quantum acoustic devices.

Student Ability to Distinguish between Superposition States and Mixed States in Quantum Mechanics

ERIC Educational Resources Information Center

Passante, Gina; Emigh, Paul J.; Shaffer, Peter S.

2015-01-01

Superposition gives rise to the probabilistic nature of quantum mechanics and is therefore one of the concepts at the heart of quantum mechanics. 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…

Phonon counting and intensity interferometry of a nanomechanical resonator

NASA Astrophysics Data System (ADS)

Cohen, Justin D.; Meenehan, Seán M.; Maccabe, Gregory S.; Gröblacher, Simon; Safavi-Naeini, Amir H.; Marsili, Francesco; Shaw, Matthew D.; Painter, Oskar

2015-04-01

In optics, the ability to measure individual quanta of light (photons) enables a great many applications, ranging from dynamic imaging within living organisms to secure quantum communication. Pioneering photon counting experiments, such as the intensity interferometry performed by Hanbury Brown and Twiss to measure the angular width of visible stars, have played a critical role in our understanding of the full quantum nature of light. As with matter at the atomic scale, the laws of quantum mechanics also govern the properties of macroscopic mechanical objects, providing fundamental quantum limits to the sensitivity of mechanical sensors and transducers. Current research in cavity optomechanics seeks to use light to explore the quantum properties of mechanical systems ranging in size from kilogram-mass mirrors to nanoscale membranes, as well as to develop technologies for precision sensing and quantum information processing. Here we use an optical probe and single-photon detection to study the acoustic emission and absorption processes in a silicon nanomechanical resonator, and perform a measurement similar to that used by Hanbury Brown and Twiss to measure correlations in the emitted phonons as the resonator undergoes a parametric instability formally equivalent to that of a laser. Owing to the cavity-enhanced coupling of light with mechanical motion, this effective phonon counting technique has a noise equivalent phonon sensitivity of 0.89 +/- 0.05. With straightforward improvements to this method, a variety of quantum state engineering tasks using mesoscopic mechanical resonators would be enabled, including the generation and heralding of single-phonon Fock states and the quantum entanglement of remote mechanical elements.

Quantum chemical study of the mechanism of action of vitamin K epoxide reductase (VKOR)

NASA Astrophysics Data System (ADS)

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 quantum mechanical 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 quantum mechanical/molecular mechanical method (QM/MM) studies of the enzymatic pathway once three-dimensional structural data are determined and available for VKOR.

A universal test for gravitational decoherence

PubMed Central

Pfister, C.; Kaniewski, J.; Tomamichel, M.; Mantri, A.; Schmucker, R.; McMahon, N.; Milburn, G.; Wehner, S.

2016-01-01

Quantum mechanics and the theory of gravity are presently not compatible. A particular question is whether gravity causes decoherence. Several models for gravitational decoherence have been proposed, not all of which can be described quantum mechanically. Since quantum mechanics may need to be modified, one may question the use of quantum mechanics as a calculational tool to draw conclusions from the data of experiments concerning gravity. Here we propose a general method to estimate gravitational decoherence in an experiment that allows us to draw conclusions in any physical theory where the no-signalling principle holds, even if quantum mechanics needs to be modified. As an example, we propose a concrete experiment using optomechanics. Our work raises the interesting question whether other properties of nature could similarly be established from experimental observations alone—that is, without already having a rather well-formed theory of nature to make sense of experimental data. PMID:27694976

Quantum Teleportation and Grover's Algorithm Without the Wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2017-02-01

In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover's search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead of Hilbert spaces and wavefunctions.

Exponential energy growth due to slow parameter oscillations in quantum mechanical systems.

PubMed

Turaev, Dmitry

2016-05-01

It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical 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.

Quantum acoustics with superconducting qubits

NASA Astrophysics Data System (ADS)

Chu, Yiwen

2017-04-01

The ability to engineer and manipulate different types of quantum mechanical objects allows us to take advantage of their unique properties and create useful hybrid technologies. Thus far, complex quantum states and exquisite quantum control have been demonstrated in systems ranging from trapped ions to superconducting resonators. Recently, there have been many efforts to extend these demonstrations to the motion of complex, macroscopic objects. These mechanical objects have important applications as quantum memories or transducers for measuring and connecting different types of quantum systems. In particular, there have been a few experiments that couple motion to nonlinear quantum objects such as superconducting qubits. This opens up the possibility of creating, storing, and manipulating non-Gaussian quantum states in mechanical degrees of freedom. However, before sophisticated quantum control of mechanical motion can be achieved, we must realize systems with long coherence times while maintaining a sufficient interaction strength. These systems should be implemented in a simple and robust manner that allows for increasing complexity and scalability in the future. In this talk, I will describe our recent experiments demonstrating a high frequency bulk acoustic wave resonator that is strongly coupled to a superconducting qubit using piezoelectric transduction. In contrast to previous experiments with qubit-mechanical systems, our device requires only simple fabrication methods, extends coherence times to many microseconds, and provides controllable access to a multitude of phonon modes. We use this system to demonstrate basic quantum operations on the coupled qubit-phonon system. Straightforward improvements to the current device will allow for advanced protocols analogous to what has been shown in optical and microwave resonators, resulting in a novel resource for implementing hybrid quantum technologies.

Virtual Learning Environment for Interactive Engagement with Advanced Quantum Mechanics

NASA Astrophysics Data System (ADS)

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 quantum mechanics 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 quantum mechanics. The first test of this new virtual learning environment was a 2014 course in advanced quantum mechanics 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.

Resonant electronic excitation energy transfer by Dexter mechanism in the quantum dot system

NASA Astrophysics Data System (ADS)

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.

Transfer of non-Gaussian quantum states of mechanical oscillator to light

NASA Astrophysics Data System (ADS)

Filip, Radim; Rakhubovsky, Andrey A.

2015-11-01

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.

Progress in post-quantum mechanics

NASA Astrophysics Data System (ADS)

Sarfatti, Jack

2017-05-01

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 quantum mechanics 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 quantum mechanics 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 quantum mechanics 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-quantum mechanics 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.

Quantum Mechanics for Everybody: An autonomous MOOC on EdX for nonscientists

NASA Astrophysics Data System (ADS)

Freericks, James; Cutler, Dylan; Vieira-Barbosa, Lucas

2017-01-01

We have launched a MOOC for nonscientists that teaches quantum mechanics 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 quantum mechanics 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 quantum mechanics 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.

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

ERIC Educational Resources Information Center

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

Phase space quantum mechanics - Direct

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nasiri, S.; Sobouti, Y.; Taati, F.

2006-09-15

Conventional approach to quantum mechanics in phase space (q,p), is to take the operator based quantum mechanics 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 quantum mechanics, 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

Teaching Quantum Mechanics with qCraft: Outreach and Video Games

NASA Astrophysics Data System (ADS)

Kubica, Aleksander; Chatwin-Davies, Aidan; Michalakis, Spyridon

Why is quantum mechanics 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 quantum mechanics, 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 quantum mechanics into the game.

Quantum Control of Graphene Plasmon Excitation and Propagation at Heaviside Potential Steps.

PubMed

Wang, Dongli; Fan, Xiaodong; Li, Xiaoguang; Dai, Siyuan; Wei, Laiming; Qin, Wei; Wu, Fei; Zhang, Huayang; Qi, Zeming; Zeng, Changgan; Zhang, Zhenyu; Hou, Jianguo

2018-02-14

Quantum mechanical effects of single particles can affect the collective plasmon behaviors substantially. In this work, the quantum control of plasmon excitation and propagation in graphene is demonstrated by adopting the variable quantum transmission of carriers at Heaviside potential steps as a tuning knob. First, the plasmon reflection is revealed to be tunable within a broad range by varying the ratio γ between the carrier energy and potential height, which originates from the quantum mechanical effect of carrier propagation at potential steps. Moreover, the plasmon excitation by free-space photos can be regulated from fully suppressed to fully launched in graphene potential wells also through adjusting γ, which defines the degrees of the carrier confinement in the potential wells. These discovered quantum plasmon effects offer a unified quantum-mechanical solution toward ultimate control of both plasmon launching and propagating, which are indispensable processes in building plasmon circuitry.

Consistent Quantum Theory

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2001-11-01

Quantum mechanics 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 fundamental quantum 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 quantum mechanics. Comprehensive account Written by one of the main figures in the field Paperback edition of successful work on philosophy of quantum mechanics

Thermal Quantum Correlations in Photosynthetic Light-Harvesting Complexes

NASA Astrophysics Data System (ADS)

Mahdian, M.; Kouhestani, H.

2015-08-01

Photosynthesis is one of the ancient biological processes, playing crucial role converting solar energy to cellular usable currency. Environmental factors and external perturbations has forced nature to choose systems with the highest efficiency and performance. Recent theoretical and experimental studies have proved the presence of quantum properties in biological systems. Energy transfer systems like Fenna-Matthews-Olson (FMO) complex shows quantum entanglement between sites of Bacteriophylla molecules in protein environment and presence of decoherence. Complex biological systems implement more truthful mechanisms beside chemical-quantum correlations to assure system's efficiency. In this study we investigate thermal quantum correlations in FMO protein of the photosynthetic apparatus of green sulfur bacteria by quantum discord measure. The results confirmed existence of remarkable quantum correlations of of BChla pigments in room temperature. This results approve involvement of quantum correlation mechanisms for information storage and retention in living organisms that could be useful for further evolutionary studies. Inspired idea of this study is potentially interesting to practice by the same procedure in genetic data transfer mechanisms.

Probability in the Many-Worlds Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Vaidman, Lev

It is argued that, although in the Many-Worlds Interpretation of quantum mechanics 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 quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing probability measure are discussed.

Nonplanar KdV and KP equations for quantum electron-positron-ion plasma

NASA Astrophysics Data System (ADS)

Dutta, Debjit

2015-12-01

Nonlinear quantum ion-acoustic waves with the effects of nonplanar cylindrical geometry, quantum corrections, and transverse perturbations are studied. By using the standard reductive perturbation technique, a cylindrical Kadomtsev-Petviashvili equation for ion-acoustic waves is derived by incorporating quantum-mechanical effects. The quantum-mechanical effects via quantum diffraction and quantum statistics and the role of transverse perturbations in cylindrical geometry on the dynamics of this wave are studied analytically. It is found that the dynamics of ion-acoustic solitary waves (IASWs) is governed by a three-dimensional cylindrical Kadomtsev-Petviashvili equation (CKPE). The results could help in a theoretical analysis of astrophysical and laser produced plasmas.

Quorum sensing: a quantum perspective.

PubMed

Majumdar, Sarangam; Pal, Sukla

2016-09-01

Quorum sensing is the efficient mode of communication in the bacterial world. After a lot of advancements in the classical theory of quorum sensing few basic questions of quorum sensing still remain unanswered. The sufficient progresses in quantum biology demands to explain these questions from the quantum perspective as non trivial quantum effects already have manifested in various biological processes like photosynthesis, magneto-reception etc. Therefore, it's the time to review the bacterial communications from the quantum view point. In this article we carefully accumulate the latest results and arguments to strengthen quantum biology through the addition of quorum sensing mechanism in the light of quantum mechanics.

Experimental test of state-independent quantum contextuality of an indivisible quantum system

NASA Astrophysics Data System (ADS)

Li, Meng; Huang, Yun-Feng; Cao, Dong-Yang; Zhang, Chao; Zhang, Yong-Sheng; Liu, Bi-Heng; Li, Chuan-Feng; Guo, Guang-Can

2014-05-01

Since the quantum mechanics was born, quantum mechanics was argued among scientists because the differences between quantum mechanics and the classical physics. Because of this, some people give hidden variable theory. One of the hidden variable theory is non-contextual hidden variable theory, and KS inequalities are famous in non-contextual hidden variable theory. But the original KS inequalities have 117 directions to measure, so it is almost impossible to test the KS inequalities in experiment. However bout two years ago, Sixia Yu and C.H. Oh point out that for a single qutrit, we only need to measure 13 directions, then we can test the KS inequalities. This makes it possible to test the KS inequalities in experiment. We use the polarization and the path of single photon to construct a qutrit, and we use the half-wave plates, the beam displacers and polar beam splitters to prepare the quantum state and finish the measurement. And the result prove that quantum mechanics is right and non-contextual hidden variable theory is wrong.

Quantum Hamilton equations of motion for bound states of one-dimensional quantum systems

NASA Astrophysics Data System (ADS)

Köppe, J.; Patzold, M.; Grecksch, W.; Paul, W.

2018-06-01

On the basis of Nelson's stochastic mechanics derivation of the Schrödinger equation, a formal mathematical structure of non-relativistic quantum mechanics equivalent to the one in classical analytical mechanics has been established in the literature. We recently were able to augment this structure by deriving quantum Hamilton equations of motion by finding the Nash equilibrium of a stochastic optimal control problem, which is the generalization of Hamilton's principle of classical mechanics to quantum systems. We showed that these equations allow a description and numerical determination of the ground state of quantum problems without using the Schrödinger equation. We extend this approach here to deliver the complete discrete energy spectrum and related eigenfunctions for bound states of one-dimensional stationary quantum systems. We exemplify this analytically for the one-dimensional harmonic oscillator and numerically by analyzing a quartic double-well potential, a model of broad importance in many areas of physics. We furthermore point out a relation between the tunnel splitting of such models and mean first passage time concepts applied to Nelson's diffusion paths in the ground state.

Molecular recognition of the environment and mechanisms of the origin of species in quantum-like modeling of evolution.

PubMed

Melkikh, Alexey V; Khrennikov, Andrei

2017-11-01

A review of the mechanisms of speciation is performed. The mechanisms of the evolution of species, taking into account the feedback of the state of the environment and mechanisms of the emergence of complexity, are considered. It is shown that these mechanisms, at the molecular level, cannot work steadily in terms of classical mechanics. Quantum mechanisms of changes in the genome, based on the long-range interaction potential between biologically important molecules, are proposed as one of possible explanation. Different variants of interactions of the organism and environment based on molecular recognition and leading to new species origins are considered. Experiments to verify the model are proposed. This bio-physical study is completed by the general operational model of based on quantum information theory. The latter is applied to model of epigenetic evolution. We briefly present the basics of the quantum-like approach to modeling of bio-informational processes. This approach is illustrated by the quantum-like model of epigenetic evolution. Copyright © 2017 Elsevier Ltd. All rights reserved.

Solvable Quantum Macroscopic Motions and Decoherence Mechanisms in Quantum Mechanics on Nonstandard Space

NASA Technical Reports Server (NTRS)

Kobayashi, Tsunehiro

1996-01-01

Quantum macroscopic motions are investigated in the scheme consisting of N-number of harmonic oscillators in terms of ultra-power representations of nonstandard analysis. Decoherence is derived from the large internal degrees of freedom of macroscopic matters.

Study of optimum methods of optical communication. [accounting for the effects of the turbulent atmosphere and quantum mechanics

NASA Technical Reports Server (NTRS)

Harger, R. O.

1974-01-01

Abstracts are reported relating to the techniques used in the research concerning optical transmission of information. Communication through the turbulent atmosphere, quantum mechanics, and quantum communication theory are discussed along with the results.

Typical Local Measurements in Generalized Probabilistic Theories: Emergence of Quantum Bipartite Correlations

NASA Astrophysics Data System (ADS)

Kleinmann, Matthias; Osborne, Tobias J.; Scholz, Volkher B.; Werner, Albert H.

2013-01-01

What singles out quantum mechanics 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 quantum mechanics. Our result makes use of a generalization of Dvoretzky’s theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantum mechanics, however.

Foundations of Quantum Mechanics and Quantum Computation

NASA Astrophysics Data System (ADS)

Aspect, Alain; Leggett, Anthony; Preskill, John; Durt, Thomas; Pironio, Stefano

2013-03-01

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 quantum mechanics (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 quantum mechanics, 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.

A Gleason-Type Theorem for Any Dimension Based on a Gambling Formulation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco

2017-07-01

Based on a gambling formulation of quantum mechanics, we derive a Gleason-type theorem that holds for any dimension n of a quantum system, and in particular for n=2. The theorem states that the only logically consistent probability assignments are exactly the ones that are definable as the trace of the product of a projector and a density matrix operator. In addition, we detail the reason why dispersion-free probabilities are actually not valid, or rational, probabilities for quantum mechanics, and hence should be excluded from consideration.

Reality, Causality, and Probability, from Quantum Mechanics to Quantum Field Theory

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2015-10-01

These three lectures consider the questions of reality, causality, and probability in quantum theory, from quantum mechanics 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 quantum mechanics. I close by briefly addressing some of the implications of the argument presented here for the current state of fundamental physics.

Quantum Physics for Beginners.

ERIC Educational Resources Information Center

Strand, J.

1981-01-01

Suggests a new approach for teaching secondary school quantum physics. Reviews traditional approaches and presents some characteristics of the three-part "Quantum Physics for Beginners" project, including: quantum physics, quantum mechanics, and a short historical survey. (SK)

Noncommutativity and Humanity — Julius Wess and his Legacy

NASA Astrophysics Data System (ADS)

Djordjevic, Goran S.

2012-03-01

A personal view on Julius Wess's human and scientific legacy in Serbia and the Balkan region is given. Motivation for using noncommutative and nonarchimedean geometry on very short distances is presented. In addition to some mathematical preliminaries, we present a short introduction in adelic quantum mechanics in a way suitable for its noncommutative generalization. We also review the basic ideas and tools embedded in q-deformed and noncommutative quantum mechanics. A rather fundamental approach, called deformation quantization, is noted. A few relations between noncommutativity and nonarchimedean spaces, as well as similarities between corresponding quantum theories, in particular, quantum cosmology are pointed out. An extended Moyal product in a frame of an adelic noncommutative quantum mechanics is also considered.

What is Quantum Information?

NASA Astrophysics Data System (ADS)

Lombardi, Olimpia; Fortin, Sebastian; Holik, Federico; López, Cristian

2017-04-01

Preface; Introduction; Part I. About the Concept of Information: 1. About the concept of information Sebastian Fortin and Olimpia Lombardi; 2. Representation, information, and theories of information Armond Duwell; 3. Information, communication, and manipulability Olimpia Lombardi and Cristian López; Part II. Information and quantum mechanics: 4. Quantum versus classical information Jeffrey Bub; 5. Quantum information and locality Dennis Dieks; 6. Pragmatic information in quantum mechanics Juan Roederer; 7. Interpretations of quantum theory: a map of madness Adán Cabello; Part III. Probability, Correlations, and Information: 8. On the tension between ontology and epistemology in quantum probabilities Amit Hagar; 9. Inferential versus dynamical conceptions of physics David Wallace; 10. Classical models for quantum information Federico Holik and Gustavo Martin Bosyk; 11. On the relative character of quantum correlations Guido Bellomo and Ángel Ricardo Plastino; Index.

From correspondence to complementarity: The emergence of Bohr's Copenhagen interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

Tanona, Scott Daniel

I develop a new analysis of Niels Bohr's Copenhagen interpretation of quantum mechanics 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 quantum mechanics. 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 quantum mechanics 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 quantum mechanical 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 quantum mechanics incorporates the correspondence approach in the way in which it represents quantum properties with matrices of transition probabilities, the empirical meaning of which depend on the situation but in general are tied to the correspondence connection to the spectra. For Bohr, it is then the commutation relations, which arise from the formalism, which inform us of the complementary nature of this approximate representation of quantum properties via the classical equations through which we connect them to experiments.

Information transmission in microbial and fungal communication: from classical to quantum.

PubMed

Majumdar, Sarangam; Pal, Sukla

2018-06-01

Microbes have their own communication systems. Secretion and reception of chemical signaling molecules and ion-channels mediated electrical signaling mechanism are yet observed two special ways of information transmission in microbial community. In this article, we address the aspects of various crucial machineries which set the backbone of microbial cell-to-cell communication process such as quorum sensing mechanism (bacterial and fungal), quorum sensing regulated biofilm formation, gene expression, virulence, swarming, quorum quenching, role of noise in quorum sensing, mathematical models (therapy model, evolutionary model, molecular mechanism model and many more), synthetic bacterial communication, bacterial ion-channels, bacterial nanowires and electrical communication. In particular, we highlight bacterial collective behavior with classical and quantum mechanical approaches (including quantum information). Moreover, we shed a new light to introduce the concept of quantum synthetic biology and possible cellular quantum Turing test.

Multimode optomechanical system in the quantum regime.

PubMed

Nielsen, William Hvidtfelt Padkær; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S; Schliesser, Albert

2017-01-03

We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 10 7 ) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.

Supersymmetric symplectic quantum mechanics

NASA Astrophysics Data System (ADS)

de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.

2018-02-01

Symplectic Quantum Mechanics 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 quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical 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.

Plasmonic resonances of nanoparticles from large-scale quantum mechanical simulations

NASA Astrophysics Data System (ADS)

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, quantum mechanical 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 quantum mechanical simulations of plasmonic responses of metallic nanostructures. Using TD-OFDFT, we have performed quantum mechanical 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.

Multimode optomechanical system in the quantum regime

NASA Astrophysics Data System (ADS)

Hvidtfelt Padkær Nielsen, William; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S.; Schliesser, Albert

2017-01-01

We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 107) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes’ motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.

EDITORIAL: Focus on Mechanical Systems at the Quantum Limit FOCUS ON MECHANICAL SYSTEMS AT THE QUANTUM LIMIT

NASA Astrophysics Data System (ADS)

Aspelmeyer, Markus; Schwab, Keith

2008-09-01

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 diverse backgrounds and approaches of the researchers. As diverse as the approaches are the manifold of goals and perspectives for operating mechanical systems close to or within the quantum regime. Already now, nanomechanical sensors achieve single-molecule mass detection and magnetic resonance force detection from single-electron spins although they are operated far from quantum. Quantum-limited mechanical devices promise a new technology with hitherto unachieved performance for high-resolution sensing. This is also of high relevance for macroscopic mechanical resonators used in gravitational wave detectors. Furthermore, the increasing capability to couple mechanical modes to individual quantum systems raises the interesting question of whether mechanics can serve as a quantum bus in hybrid implementations of quantum information processing. Finally, the possibility of generating quantum superposition states that involve displacements of a massive macroscopic object (such as the center of mass of a mechanical beam) provides a completely new parameter regime for testing quantum theory over the amazing range from nanomechanical objects of several picograms up to gram-scale mirrors used in gravitational wave interferometers. We are looking forward to these fascinating developments! This Focus Issue is intended to highlight the present status of the field and to provide both introduction and motivation for students and researchers who want to get familiar with this exciting area or even want to join it. It also complements the conference activities of our community during the last year, where a series of dedicated invited sessions at several international conferences (APS March Meeting 2008, CLEO/QELS 2008, OSA Frontiers in Optics 2008, PQE 2008/2009 etc) culminated in the first Gordon Conference on 'Mechanical Systems at the Quantum Limit'. Given the fast development of the field it was not surprising to see that during the collection of the following contributions new progress was reported almost on a monthly basis and new groups entered the field. We intend to keep submission to this Focus Issue open for some time and invite everyone to share their latest results with us. And finally, a note to our fellow colleagues: keep up the good work! We would like to call the next Focus Issue 'Mechanical Systems IN the Quantum Regime'. Focus on Mechanical Systems at the Quantum Limit Contents Parametric coupling between macroscopic quantum resonators L Tian, M S Allman and R W Simmonds Quantum noise in a nanomechanical Duffing resonator E Babourina-Brooks, A Doherty and G J Milburn Creating and verifying a quantum superposition in a micro-optomechanical system Dustin Kleckner, Igor Pikovski, Evan Jeffrey, Luuk Ament, Eric Eliel, Jeroen van den Brink and Dirk Bouwmeester Ground-state cooling of a nanomechanical resonator via a Cooper-pair box qubit Konstanze Jaehne, Klemens Hammerer and Margareta Wallquist Dissipation in circuit quantum electrodynamics: lasing and cooling of a low-frequency oscillator Julian Hauss, Arkady Fedorov, Stephan André, Valentina Brosco, Carsten Hutter, Robin Kothari, Sunil Yeshwanth, Alexander Shnirman and Gerd Schön Route to ponderomotive entanglement of light via optically trapped mirrors Christopher Wipf, Thomas Corbitt, Yanbei Chen and Nergis Mavalvala Nanomechanical-resonator-assisted induced transparency in a Cooper-pair box system Xiao-Zhong Yuan, Hsi-Sheng Goan, Chien-Hung Lin, Ka-Di Zhu and Yi-Wen Jiang High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators A Schliesser, G Anetsberger, R Rivière, O Arcizet and T J Kippenberg Optomechanical to mechanical entanglement transformation Giovanni Vacanti, Mauro Paternostro, G Massimo Palma and Vlatko Vedral The optomechanical instability in the quantum regime Max Ludwig, Björn Kubala and Florian Marquardt Quantum limits of photothermal and radiation pressure cooling of a movable mirror M Pinard and A Dantan Mechanical feedback in the high-frequency limit R El Boubsi, O Usmani and Ya M Blanter Back-action evasion and squeezing of a mechanical resonator using a cavity detector A A Clerk, F Marquardt and K Jacobs Simultaneous cooling and entanglement of mechanical modes of a micromirror in an optical cavity Claudiu Genes, David Vitali and Paolo Tombesi Dispersive optomechanics: a membrane inside a cavity A M Jayich, J C Sankey, B M Zwickl, C Yang, J D Thompson, S M Girvin, A A Clerk, F Marquardt and J G E Harris Cavity-assisted backaction cooling of mechanical resonators I Wilson-Rae, N Nooshi, J Dobrindt, T J Kippenberg and W Zwerger Cavity cooling of a nanomechanical resonator by light scattering I Favero and K Karrai Probing the quantum coherence of a nanomechanical resonator using a superconducting qubit: II. Implementation M P Blencowe and A D Armour Probing the quantum coherence of a nanomechanical resonator using a superconducting qubit: I. Echo scheme A D Armour and M P Blencowe Nanoelectromechanics of suspended carbon nanotubes A K Hüttel, M Poot, B Witkamp and H S J van der Zant Prospects for cooling nanomechanical motion by coupling to a superconducting microwave resonator J D Teufel, C A Regal and K W Lehnert

An Overview of the Transactional Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Cramer, John G.

1988-02-01

The transactional interpretation of quantum mechanics (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 quantum mechanical interpretations to experimental tests and results are discussed.

An overview of the transactional interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

Cramer, J. G.

We summarize the transactional interpretation (TI) of quantum mechanics (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 quantum mechanical interpretations to experimental tests and results are discussed.

Quantum work statistics of charged Dirac particles in time-dependent fields

DOE PAGES

Deffner, Sebastian; Saxena, Avadh

2015-09-28

The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Thus, special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.

Physics at the FMQT’08 conference

NASA Astrophysics Data System (ADS)

Špička, V.; Nieuwenhuizen, Th. M.; Keefe, P. D.

2010-01-01

This paper summarizes the recent state of the art of the following topics presented at the FQMT’08 conference: Foundations of quantum physics, Quantum measurement; Quantum noise, decoherence and dephasing; Cold atoms and Bose-Einstein condensation; Physics of quantum computing and information; Nonequilibrium quantum statistical mechanics; Quantum, mesoscopic and partly classical thermodynamics; Mesoscopic, nano-electro-mechanical systems and optomechanical systems; Spins systems and their dynamics, Brownian motion and molecular motors; Physics of biological systems, and Relevant experiments from the nanoscale to the macroscale. To all these subjects an introduction is given and the recent literature is overviewed. The paper contains some 680 references in total.

Philosophical perspectives on quantum chaos: Models and interpretations

NASA Astrophysics Data System (ADS)

Bokulich, Alisa Nicole

2001-09-01

The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and theoretical pluralism, are inadequate. The fruitful ways in which models have been used in quantum chaos research point to the need for a new framework for addressing intertheoretic relations that focuses on models rather than laws.

Characterizing and engineering tunable spin functionality inside indium arsenide/gallium arsenide quantum dot molecules

NASA Astrophysics Data System (ADS)

Liu, Weiwen

The continual downsizing of the basic functional units used in the electronics industry has motivated the study of the quantum computation and related topics. To overcome the limitations of classical physics and engineering, some unique quantum mechanical features, especially entanglement and superpositions have begun to be considered as important properties for future bits. Including these quantum mechanical features is attractive because the ability to utilize quantum mechanics can dramatically enhance computational power. Among the various ways of constructing the basic building blocks for quantum computation, we are particularly interested in using spins inside epitaxially grown InAs/GaAs quantum dot molecules as quantum bits (qubits). The ability to design and engineer nanostructures with tailored quantum properties is critical to engineering quantum computers and other novel electro-optical devices and is one of the key challenges for scaling up new ideas for device application. In this thesis, we will focus on how the structure and composition of quantum dot molecules can be used to control spin properties and charge interactions. Tunable spin and charge properties can enable new, more scalable, methods of initializing and manipulating quantum information. In this thesis, we demonstrate one method to enable electric-field tunability of Zeeman splitting for a single electron spin inside a quantum dot molecules by using heterostructure engineering techniques to modify the barrier that separates quantum dots. We describe how these structural changes to the quantum dot molecules also change charge interactions and propose ways to use this effect to enable accurate measurement of coulomb interactions and possibly charge occupancy inside these complicated quantum dot molecules.

Quantum origins of objectivity

NASA Astrophysics Data System (ADS)

Horodecki, R.; Korbicz, J. K.; Horodecki, P.

2015-03-01

In spite of all of its successes, quantum mechanics leaves us with a central problem: How does nature create a bridge from fragile quanta to the objective world of everyday experience? Here we find that a basic structure within quantum mechanics that leads to the perceived objectivity is a so-called spectrum broadcast structure. We uncover this based on minimal assumptions, without referring to any dynamical details or a concrete model. More specifically, working formally within the decoherence theory setting with multiple environments (called quantum Darwinism), we show how a crucial for quantum mechanics notion of nondisturbance due to Bohr [N. Bohr, Phys. Rev. 48, 696 (1935), 10.1103/PhysRev.48.696] and a natural definition of objectivity lead to a canonical structure of a quantum system-environment state, reflecting objective information records about the system stored in the environment.

On the geometrization of quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tavernelli, Ivano, E-mail: ita@zurich.ibm.com

Nonrelativistic quantum mechanics 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 quantum mechanics 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

A discussion on the origin of quantum probabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Holik, Federico, E-mail: olentiev2@gmail.com; Departamento de Matemática - Ciclo Básico Común, Universidad de Buenos Aires - Pabellón III, Ciudad Universitaria, Buenos Aires; Sáenz, Manuel

We study the origin of quantum probabilities as arising from non-Boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorovian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case). -- Highlights: •Several recent works use a derivation similar to that of R.T. Cox to obtain quantum probabilities. •We apply Cox’s method to the lattice of subspaces of the Hilbert space. •We obtain a derivationmore » of quantum probabilities which includes mixed states. •The method presented in this work is susceptible to generalization. •It includes quantum mechanics and classical mechanics as particular cases.« less

From First Principles: The Application of Quantum Mechanics to Complex Molecules and Solvated Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freitag, Mark A.

2001-12-31

The major title of this dissertation, 'From first principles,' is a phase often heard in the study of thermodynamics and quantum mechanics. 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 quantum mechanics-specifically, non-relativistic quantum mechanics, which is appropriate formore » most systems of chemical interest.« less

Tales from the prehistory of Quantum Gravity. Léon Rosenfeld's earliest contributions

NASA Astrophysics Data System (ADS)

Peruzzi, Giulio; Rocci, Alessio

2018-05-01

The main purpose of this paper is to analyse the earliest work of Léon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld tried to face this problem in 1927, analysing the role of his mentors: Oskar Klein, Louis de Broglie and Théophile De Donder. Rosenfeld asked himself how quantum mechanics should concretely modify general relativity. In the context of a five-dimensional theory, Rosenfeld tried to construct a unifying framework for the gravitational and electromagnetic interaction and wave mechanics. Using a sort of "general relativistic quantum mechanics" Rosenfeld introduced a wave equation on a curved background. He investigated the metric created by what he called `quantum phenomena', represented by wave functions. Rosenfeld integrated Einstein equations in the weak field limit, with wave functions as source of the gravitational field. The author performed a sort of semi-classical approximation obtaining at the first order the Reissner-Nordström metric. We analyse how Rosenfeld's work is part of the history of Quantum Mechanics, because in his investigation Rosenfeld was guided by Bohr's correspondence principle. Finally we briefly discuss how his contribution is connected with the task of finding out which metric can be generated by a quantum field, a problem that quantum field theory on curved backgrounds will start to address 35 years later.

Tales from the prehistory of Quantum Gravity - Léon Rosenfeld's earliest contributions

NASA Astrophysics Data System (ADS)

Peruzzi, Giulio; Rocci, Alessio

2018-04-01

The main purpose of this paper is to analyse the earliest work of Léon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld tried to face this problem in 1927, analysing the role of his mentors: Oskar Klein, Louis de Broglie and Théophile De Donder. Rosenfeld asked himself how quantum mechanics should concretely modify general relativity. In the context of a five-dimensional theory, Rosenfeld tried to construct a unifying framework for the gravitational and electromagnetic interaction and wave mechanics. Using a sort of "general relativistic quantum mechanics" Rosenfeld introduced a wave equation on a curved background. He investigated the metric created by what he called `quantum phenomena', represented by wave functions. Rosenfeld integrated Einstein equations in the weak field limit, with wave functions as source of the gravitational field. The author performed a sort of semi-classical approximation obtaining at the first order the Reissner-Nordström metric. We analyse how Rosenfeld's work is part of the history of Quantum Mechanics, because in his investigation Rosenfeld was guided by Bohr's correspondence principle. Finally we briefly discuss how his contribution is connected with the task of finding out which metric can be generated by a quantum field, a problem that quantum field theory on curved backgrounds will start to address 35 years later.

Stochastic mechanics of reciprocal diffusions

NASA Astrophysics Data System (ADS)

Levy, Bernard C.; Krener, Arthur J.

1996-02-01

The dynamics and kinematics of reciprocal diffusions were examined in a previous paper [J. Math. Phys. 34, 1846 (1993)], where it was shown that reciprocal diffusions admit a chain of conservation laws, which close after the first two laws for two disjoint subclasses of reciprocal diffusions, the Markov and quantum diffusions. For the case of quantum diffusions, the conservation laws are equivalent to Schrödinger's equation. The Markov diffusions were employed by Schrödinger [Sitzungsber. Preuss. Akad. Wiss. Phys. Math Kl. 144 (1931); Ann. Inst. H. Poincaré 2, 269 (1932)], Nelson [Dynamical Theories of Brownian Motion (Princeton University, Princeton, NJ, 1967); Quantum Fluctuations (Princeton University, Princeton, NJ, 1985)], and other researchers to develop stochastic formulations of quantum mechanics, called stochastic mechanics. We propose here an alternative version of stochastic mechanics based on quantum diffusions. A procedure is presented for constructing the quantum diffusion associated to a given wave function. It is shown that quantum diffusions satisfy the uncertainty principle, and have a locality property, whereby given two dynamically uncoupled but statistically correlated particles, the marginal statistics of each particle depend only on the local fields to which the particle is subjected. However, like Wigner's joint probability distribution for the position and momentum of a particle, the finite joint probability densities of quantum diffusions may take negative values.

Quantum enigma cipher as a generalization of the quantum stream cipher

NASA Astrophysics Data System (ADS)

Kato, Kentaro

2016-09-01

Various types of randomizations for the quantum stream cipher by Y00 protocol have been developed so far. In particular, it must be noted that the analysis of immunity against correlation attacks with a new type of randomization by Hirota and Kurosawa prompted a new look at the quantum stream cipher by Y00 protocol (Quant. Inform. Process. 6(2) 2007). From the preceding study on the quantum stream cipher, we recognized that the quantum stream cipher by Y00 protocol would be able to be generalized to a new type of physical cipher that has potential to exceed the Shannon limit by installing additional randomization mechanisms, in accordance with the law of quantum mechanics. We call this new type of physical random cipher the quantum enigma cipher. In this article, we introduce the recent developments for the quantum stream cipher by Y00 protocol and future plans toward the quantum enigma cipher.

Extending Bell's beables to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories

NASA Astrophysics Data System (ADS)

Lorenzen, F.; de Ponte, M. A.; Moussa, M. H. Y.

2009-09-01

In this paper, employing the Itô stochastic Schrödinger equation, we extend Bell’s beable interpretation of quantum mechanics to encompass dissipation, decoherence, and the quantum-to-classical transition through quantum trajectories. For a particular choice of the source of stochasticity, the one leading to a dissipative Lindblad-type correction to the Hamiltonian dynamics, we find that the diffusive terms in Nelsons stochastic trajectories are naturally incorporated into Bohm’s causal dynamics, yielding a unified Bohm-Nelson theory. In particular, by analyzing the interference between quantum trajectories, we clearly identify the decoherence time, as estimated from the quantum formalism. We also observe the quantum-to-classical transition in the convergence of the infinite ensemble of quantum trajectories to their classical counterparts. Finally, we show that our extended beables circumvent the problems in Bohm’s causal dynamics regarding stationary states in quantum mechanics.

Investigation of spin-zero bosons in q-deformed relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Sobhani, H.; Chung, W. S.; Hassanabadi, H.

2018-04-01

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 quantum mechanics have been derived. At first, we discussed how q-deformed formalism can be constructed and used. Postulates of this q-deformed quantum mechanics are noted. Then scattering problems for spin-zero bosons are studied.

Mathematical sense-making in quantum mechanics: An initial peek

NASA Astrophysics Data System (ADS)

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 quantum mechanics question to illustrate what mathematical sense-making can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, 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.

An Introduction to Dispersive Interactions

ERIC Educational Resources Information Center

Taddei, M. M.; Mendes, T. N. C.; Farina, C.

2010-01-01

Dispersive forces are a kind of van der Waals intermolecular force which could only be fully understood with the establishment of quantum mechanics and, in particular, of quantum electrodynamics. In this pedagogical paper, we introduce the subject in a more elementary approach, aiming at students with basic knowledge of quantum mechanics. We…

Learning and Retention of Quantum Concepts with Different Teaching Methods

ERIC Educational Resources Information Center

Deslauriers, Louis; Wieman, Carl

2011-01-01

We measured mastery and retention of conceptual understanding of quantum mechanics in a modern physics course. This was studied for two equivalent cohorts of students taught with different pedagogical approaches using the Quantum Mechanics Conceptual Survey. We measured the impact of pedagogical approach both on the original conceptual learning…

Improving Student Understanding of Addition of Angular Momentum in Quantum Mechanics

ERIC Educational Resources Information Center

Zhu, Guangtian; Singh, Chandralekha

2013-01-01

We describe the difficulties advanced undergraduate and graduate students have with concepts related to addition of angular momentum in quantum mechanics. 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…

Response to ``Comment on `Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics' '' [J. Chem. Phys. 127, 197101 (2007)

NASA Astrophysics Data System (ADS)

Goldfarb, Yair; Degani, Ilan; Tannor, David J.

2007-11-01

In their comment, Sanz and Miret-Artés (SMA) describe previous trajectory-based formalisms based on the quantum Hamilton-Jacobi (QHJ) formalism. In this reply, we highlight our unique contributions: the identification of the smallness of the quantum force in the complex QHJ and its solution using complex trajectories. SMA also raise the question of how the term locality should be used in quantum mechanics. We suggest that at least certain aspects of nonlocality can depend on the method used to solve the problem.

Double-slit experiment with single wave-driven particles and its relation to quantum mechanics.

PubMed

Andersen, Anders; Madsen, Jacob; Reichelt, Christian; Rosenlund Ahl, Sonja; Lautrup, Benny; Ellegaard, Clive; Levinsen, Mogens T; Bohr, Tomas

2015-07-01

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 quantum mechanics. Quantum mechanical 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 quantum mechanics, 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 quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics 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 quantum mechanics.

Multimode optomechanical system in the quantum regime

PubMed Central

Nielsen, William Hvidtfelt Padkær; Tsaturyan, Yeghishe; Møller, Christoffer Bo; Polzik, Eugene S.; Schliesser, Albert

2017-01-01

We realize a simple and robust optomechanical system with a multitude of long-lived (Q > 107) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry–Perot resonator detects these modes’ motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to −2.4 dB (−3.6 dB if corrected for detection losses) and bandwidths ≲90 kHz. The multimode nature of the membrane and Fabry–Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom. PMID:27999182

Quantum electromechanics on silicon nitride nanomembranes

PubMed Central

Fink, J. M.; Kalaee, M.; Pitanti, A.; Norte, R.; Heinzle, L.; Davanço, M.; Srinivasan, K.; Painter, O.

2016-01-01

Radiation pressure has recently been used to effectively couple the quantum motion of mechanical elements to the fields of optical or microwave light. Integration of all three degrees of freedom—mechanical, optical and microwave—would enable a quantum interconnect between microwave and optical quantum systems. We present a platform based on silicon nitride nanomembranes for integrating superconducting microwave circuits with planar acoustic and optical devices such as phononic and photonic crystals. Using planar capacitors with vacuum gaps of 60 nm and spiral inductor coils of micron pitch we realize microwave resonant circuits with large electromechanical coupling to planar acoustic structures of nanoscale dimensions and femtoFarad motional capacitance. Using this enhanced coupling, we demonstrate microwave backaction cooling of the 4.48 MHz mechanical resonance of a nanobeam to an occupancy as low as 0.32. These results indicate the viability of silicon nitride nanomembranes as an all-in-one substrate for quantum electro-opto-mechanical experiments. PMID:27484751

QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.

PubMed

Wollman, E E; Lei, C U; Weinstein, A J; Suh, J; Kronwald, A; Marquardt, F; Clerk, A A; Schwab, K C

2015-08-28

According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion. Copyright © 2015, American Association for the Advancement of Science.

Quantum Mechanics predicts evolutionary biology.

PubMed

Torday, J S

2018-07-01

Nowhere are the shortcomings of conventional descriptive biology more evident than in the literature on Quantum Biology. In the on-going effort to apply Quantum Mechanics to evolutionary biology, merging Quantum Mechanics with the fundamentals of evolution as the First Principles of Physiology-namely negentropy, chemiosmosis and homeostasis-offers an authentic opportunity to understand how and why physics constitutes the basic principles of biology. Negentropy and chemiosmosis confer determinism on the unicell, whereas homeostasis constitutes Free Will because it offers a probabilistic range of physiologic set points. Similarly, on this basis several principles of Quantum Mechanics also apply directly to biology. The Pauli Exclusion Principle is both deterministic and probabilistic, whereas non-localization and the Heisenberg Uncertainty Principle are both probabilistic, providing the long-sought after ontologic and causal continuum from physics to biology and evolution as the holistic integration recognized as consciousness for the first time. Copyright © 2018 Elsevier Ltd. All rights reserved.

Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

PubMed

Chou, Chia-Chun; Kouri, Donald J

2013-04-25

We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics 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 quantum mechanics, 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.

Physics of Electronic Materials

NASA Astrophysics Data System (ADS)

Rammer, Jørgen

2017-03-01

1. Quantum mechanics; 2. Quantum tunneling; 3. Standard metal model; 4. Standard conductor model; 5. Electric circuit theory; 6. Quantum wells; 7. Particle in a periodic potential; 8. Bloch currents; 9. Crystalline solids; 10. Semiconductor doping; 11. Transistors; 12. Heterostructures; 13. Mesoscopic physics; 14. Arithmetic, logic and machines; Appendix A. Principles of quantum mechanics; Appendix B. Dirac's delta function; Appendix C. Fourier analysis; Appendix D. Classical mechanics; Appendix E. Wave function properties; Appendix F. Transfer matrix properties; Appendix G. Momentum; Appendix H. Confined particles; Appendix I. Spin and quantum statistics; Appendix J. Statistical mechanics; Appendix K. The Fermi-Dirac distribution; Appendix L. Thermal current fluctuations; Appendix M. Gaussian wave packets; Appendix N. Wave packet dynamics; Appendix O. Screening by symmetry method; Appendix P. Commutation and common eigenfunctions; Appendix Q. Interband coupling; Appendix R. Common crystal structures; Appendix S. Effective mass approximation; Appendix T. Integral doubling formula; Bibliography; Index.

Quantum electromechanics on silicon nitride nanomembranes.

PubMed

Fink, J M; Kalaee, M; Pitanti, A; Norte, R; Heinzle, L; Davanço, M; Srinivasan, K; Painter, O

2016-08-03

Radiation pressure has recently been used to effectively couple the quantum motion of mechanical elements to the fields of optical or microwave light. Integration of all three degrees of freedom-mechanical, optical and microwave-would enable a quantum interconnect between microwave and optical quantum systems. We present a platform based on silicon nitride nanomembranes for integrating superconducting microwave circuits with planar acoustic and optical devices such as phononic and photonic crystals. Using planar capacitors with vacuum gaps of 60 nm and spiral inductor coils of micron pitch we realize microwave resonant circuits with large electromechanical coupling to planar acoustic structures of nanoscale dimensions and femtoFarad motional capacitance. Using this enhanced coupling, we demonstrate microwave backaction cooling of the 4.48 MHz mechanical resonance of a nanobeam to an occupancy as low as 0.32. These results indicate the viability of silicon nitride nanomembranes as an all-in-one substrate for quantum electro-opto-mechanical experiments.

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems

NASA Astrophysics Data System (ADS)

Gogolin, Christian; Eisert, Jens

2016-05-01

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.

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.

PubMed

Gogolin, Christian; Eisert, Jens

2016-05-01

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.

Testing the development of student conceptual and visualization understanding in quantum mechanics through the undergraduate career

NASA Astrophysics Data System (ADS)

Robinett, Richard

2003-04-01

In order to probe various aspects of student understanding of some of the core ideas of quantum mechanics, and especially how they develop over the undergraduate curriculum, we have developed an assessment instrument designed to test conceptual and visualization understanding in quantum theory. We report data obtained from students ranging from sophomore-level modern physics courses, through junior-senior level quantum theory classes, to first year graduate quantum mechanics courses in what may be the first such study of the development of student understanding in this important core subject of physics through the undergraduate career. We discuss the results and their possible relevance to the standard curriculum as well as to the development of new curricular materials.

Cation solvation with quantum chemical effects modeled by a size-consistent multi-partitioning quantum mechanics/molecular mechanics method.

PubMed

Watanabe, Hiroshi C; Kubillus, Maximilian; Kubař, Tomáš; Stach, Robert; Mizaikoff, Boris; Ishikita, Hiroshi

2017-07-21

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 quantum mechanical (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) quantum mechanics/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.

Efficient experimental design of high-fidelity three-qubit quantum gates via genetic programming

NASA Astrophysics Data System (ADS)

Devra, Amit; Prabhu, Prithviraj; Singh, Harpreet; Arvind; Dorai, Kavita

2018-03-01

We have designed efficient quantum circuits for the three-qubit Toffoli (controlled-controlled-NOT) and the Fredkin (controlled-SWAP) gate, optimized via genetic programming methods. The gates thus obtained were experimentally implemented on a three-qubit NMR quantum information processor, with a high fidelity. Toffoli and Fredkin gates in conjunction with the single-qubit Hadamard gates form a universal gate set for quantum computing and are an essential component of several quantum algorithms. Genetic algorithms are stochastic search algorithms based on the logic of natural selection and biological genetics and have been widely used for quantum information processing applications. We devised a new selection mechanism within the genetic algorithm framework to select individuals from a population. We call this mechanism the "Luck-Choose" mechanism and were able to achieve faster convergence to a solution using this mechanism, as compared to existing selection mechanisms. The optimization was performed under the constraint that the experimentally implemented pulses are of short duration and can be implemented with high fidelity. We demonstrate the advantage of our pulse sequences by comparing our results with existing experimental schemes and other numerical optimization methods.

A note on the roles of quantum and mechanical models in social biophysics.

PubMed

Takahashi, Taiki; Kim, Song-Ju; Naruse, Makoto

2017-11-01

Recent advances in the applications of quantum models into various disciplines such as cognitive science, social sciences, economics, and biology witnessed enormous achievements and possible future progress. In this paper, we propose one of the most promising directions in the applications of quantum models: the combination of quantum and mechanical models in social biophysics. The possible resulting discipline may be called as experimental quantum social biophysics and could foster our understandings of the relationships between the society and individuals. Copyright © 2017 Elsevier Ltd. All rights reserved.

Comment on "Peres experiment using photons: No test for hypercomplex (quaternionic) quantum theories"

NASA Astrophysics Data System (ADS)

Procopio, Lorenzo M.; Rozema, Lee A.; Dakić, Borivoje; Walther, Philip

2017-09-01

In his recent article [Phys. Rev. A 95, 060101(R) (2017), 10.1103/PhysRevA.95.060101], Adler questions the usefulness of the bound found in our experimental search for genuine effects of hypercomplex quantum mechanics [Nat. Commun. 8, 15044 (2017), 10.1038/ncomms15044]. Our experiment was performed using a black-box (instrumentalist) approach to generalized probabilistic theories; therefore, it does not assume a priori any particular underlying mechanism. From that point of view our experimental results do indeed place meaningful bounds on the possible effects of "postquantum theories," including quaternionic quantum mechanics. In his article, Adler compares our experiment to nonrelativistic and Möller formal scattering theories within quaternionic quantum mechanics. With a particular set of assumptions, he finds that quaternionic effects would likely not manifest themselves in general. Although these assumptions are justified in the nonrelativistic case, a proper calculation for relativistic particles is still missing. Here, we provide a concrete relativistic example of Klein-Gordon scattering wherein the quaternionic effects persist. We note that when the Klein-Gordon equation is formulated using a Hamiltonian formalism it displays a so-called "indefinite metric," a characteristic feature of relativistic quantum wave equations. In Adler's example this is directly forbidden by his assumptions, and therefore our present example is not in contradiction to his work. In complex quantum mechanics this problem of an indefinite metric is solved in a second quantization. Unfortunately, there is no known algorithm for canonical field quantization in quaternionic quantum mechanics.

Interpreting Quantum Logic as a Pragmatic Structure

NASA Astrophysics Data System (ADS)

Garola, Claudio

2017-12-01

Many scholars maintain that the language of quantum mechanics introduces a quantum notion of truth which is formalized by (standard, sharp) quantum logic and is incompatible with the classical (Tarskian) notion of truth. We show that quantum logic can be identified (up to an equivalence relation) with a fragment of a pragmatic language LGP of assertive formulas, that are justified or unjustified rather than trueor false. Quantum logic can then be interpreted as an algebraic structure that formalizes properties of the notion of empirical justification according to quantum mechanics rather than properties of a quantum notion of truth. This conclusion agrees with a general integrationist perspective that interprets nonstandard logics as theories of metalinguistic notions different from truth, thus avoiding incompatibility with classical notions and preserving the globality of logic.

Energy spectra of quantum rings.

PubMed

Fuhrer, A; Lüscher, S; Ihn, T; Heinzel, T; Ensslin, K; Wegscheider, W; Bichler, M

2001-10-25

Quantum mechanical experiments in ring geometries have long fascinated physicists. Open rings connected to leads, for example, allow the observation of the Aharonov-Bohm effect, one of the best examples of quantum mechanical phase coherence. The phase coherence of electrons travelling through a quantum dot embedded in one arm of an open ring has also been demonstrated. The energy spectra of closed rings have only recently been studied by optical spectroscopy. The prediction that they allow persistent current has been explored in various experiments. Here we report magnetotransport experiments on closed rings in the Coulomb blockade regime. Our experiments show that a microscopic understanding of energy levels, so far limited to few-electron quantum dots, can be extended to a many-electron system. A semiclassical interpretation of our results indicates that electron motion in the rings is governed by regular rather than chaotic motion, an unexplored regime in many-electron quantum dots. This opens a way to experiments where even more complex structures can be investigated at a quantum mechanical level.

A cellular automaton for the signed particle formulation of quantum mechanics

NASA Astrophysics Data System (ADS)

Sellier, J. M.; Kapanova, K. G.; Dimov, I.

2017-02-01

Recently, a new formulation of quantum mechanics, 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 quantum mechanical 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 Misapplication of Probability Theory in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Racicot, Ronald

2014-03-01

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 Quantum Mechanics 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 quantum mechanics and quantum information theory.

Statistical mechanics based on fractional classical and quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 quantum mechanics. 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 quantum mechanics, 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.

Decoherence in quantum mechanics and quantum cosmology

NASA Technical Reports Server (NTRS)

Hartle, James B.

1992-01-01

A sketch of the quantum mechanics 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.

Quantum plasmonics: optical properties of a nanomatryushka.

PubMed

Kulkarni, Vikram; Prodan, Emil; Nordlander, Peter

2013-01-01

Quantum mechanical effects can significantly reduce the plasmon-induced field enhancements around nanoparticles. Here we present a quantum mechanical investigation of the plasmon resonances in a nanomatryushka, which is a concentric core-shell nanoparticle consisting of a solid metallic core encapsulated in a thin metallic shell. We compute the optical response using the time-dependent density functional theory and compare the results with predictions based on the classical electromagnetic theory. We find strong quantum mechanical effects for core-shell spacings below 5 Å, a regime where both the absorption cross section and the local field enhancements differ significantly from the classical predictions. We also show that the workfunction of the metal is a crucial parameter determining the onset and magnitude of quantum effects. For metals with lower workfunctions such as aluminum, the quantum effects are found to be significantly more pronounced than for a noble metal such as gold.

Uncertainty in quantum mechanics: faith or fantasy?

PubMed

Penrose, Roger

2011-12-13

The word 'uncertainty', in the context of quantum mechanics, 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 quantum mechanics 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.

A Generalized Quantum Theory

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2014-09-01

In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space quantum mechanics, but it is not. The same triple role occurs for the elements of a certain ordered Banach space in a much more general theory based upon quantum logics and a conditional probability calculus (which is a quantum logical model of the Lueders-von Neumann measurement process). It is shown how positive groups, automorphism groups, Lie algebras and statistical operators emerge from one major postulate - the non-existence of third-order interference (third-order interference and its impossibility in quantum mechanics were discovered by R. Sorkin in 1994). This again underlines the power of the combination of the conditional probability calculus with the postulate that there is no third-order interference. In two earlier papers, its impact on contextuality and nonlocality had already been revealed.

Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory

NASA Astrophysics Data System (ADS)

Bley, Gonzalo A.; Thomas, Lawrence E.

2017-01-01

We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics 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 quantum mechanical 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.

Quantum crystallography: A perspective.

PubMed

Massa, Lou; Matta, Chérif F

2018-06-30

Extraction of the complete quantum mechanics from X-ray scattering data is the ultimate goal of quantum crystallography. This article delivers a perspective for that possibility. It is desirable to have a method for the conversion of X-ray diffraction data into an electron density that reflects the antisymmetry of an N-electron wave function. A formalism for this was developed early on for the determination of a constrained idempotent one-body density matrix. The formalism ensures pure-state N-representability in the single determinant sense. Applications to crystals show that quantum mechanical density matrices of large molecules can be extracted from X-ray scattering data by implementing a fragmentation method termed the kernel energy method (KEM). It is shown how KEM can be used within the context of quantum crystallography to derive quantum mechanical properties of biological molecules (with low data-to-parameters ratio). © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Entropic uncertainty and measurement reversibility

NASA Astrophysics Data System (ADS)

Berta, Mario; Wehner, Stephanie; Wilde, Mark M.

2016-07-01

The entropic uncertainty relation with quantum side information (EUR-QSI) from (Berta et al 2010 Nat. Phys. 6 659) is a unifying principle relating two distinctive features of quantum mechanics: quantum uncertainty due to measurement incompatibility, and entanglement. In these relations, quantum uncertainty takes the form of preparation uncertainty where one of two incompatible measurements is applied. In particular, the ‘uncertainty witness’ lower bound in the EUR-QSI is not a function of a post-measurement state. An insightful proof of the EUR-QSI from (Coles et al 2012 Phys. Rev. Lett. 108 210405) makes use of a fundamental mathematical consequence of the postulates of quantum mechanics known as the non-increase of quantum relative entropy under quantum channels. Here, we exploit this perspective to establish a tightening of the EUR-QSI which adds a new state-dependent term in the lower bound, related to how well one can reverse the action of a quantum measurement. As such, this new term is a direct function of the post-measurement state and can be thought of as quantifying how much disturbance a given measurement causes. Our result thus quantitatively unifies this feature of quantum mechanics with the others mentioned above. We have experimentally tested our theoretical predictions on the IBM quantum experience and find reasonable agreement between our predictions and experimental outcomes.

Quantum Computer Games: Quantum Minesweeper

ERIC Educational Resources Information Center

Gordon, Michal; Gordon, Goren

2010-01-01

The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…

Simulation Of Wave Function And Probability Density Of Modified Poschl Teller Potential Derived Using Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Angraini, Lily Maysari; Suparmi, Variani, Viska Inda

2010-12-01

SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.

Grassmann matrix quantum mechanics

DOE PAGES

Anninos, Dionysios; Denef, Frederik; Monten, Ruben

2016-04-21

We explore quantum mechanical 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 quantum mechanics. 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 quantum mechanics 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

Quantum acoustics with superconducting qubits

NASA Astrophysics Data System (ADS)

Chu, Yiwen; Kharel, Prashanta; Renninger, William H.; Burkhart, Luke D.; Frunzio, Luigi; Rakich, Peter T.; Schoelkopf, Robert J.

2017-10-01

Mechanical objects have important practical applications in the fields of quantum information and metrology as quantum memories or transducers for measuring and connecting different types of quantum systems. The field of electromechanics is in pursuit of a robust and highly coherent device that couples motion to nonlinear quantum objects such as superconducting qubits. Here, we experimentally demonstrate a high-frequency bulk acoustic wave resonator that is strongly coupled to a superconducting qubit using piezoelectric transduction with a cooperativity of 260. We measure qubit and mechanical coherence times on the order of 10 microseconds. Our device requires only simple fabrication methods and provides controllable access to a multitude of phonon modes. We demonstrate quantum control and measurement on gigahertz phonons at the single-quantum level.

Superconducting Qubits as Mechanical Quantum Engines

NASA Astrophysics Data System (ADS)

Sachtleben, Kewin; Mazon, Kahio T.; Rego, Luis G. C.

2017-09-01

We propose the equivalence of superconducting qubits with a pistonlike mechanical quantum 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.

Musical Example to Visualize Abstract Quantum Mechanical Ideas

ERIC Educational Resources Information Center

Eagle, Forrest W.; Seaney, Kyser D.; Grubb, Michael P.

2017-01-01

Quantum mechanics 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…

Infinite-mode squeezed coherent states and non-equilibrium statistical mechanics (phase-space-picture approach)

NASA Technical Reports Server (NTRS)

Yeh, Leehwa

1993-01-01

The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite-mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena.

New Potentials for Old: The Darboux Transformation in Quantum Mechanics

ERIC Educational Resources Information Center

Williams, Brian Wesley; Celius, Tevye C.

2008-01-01

The Darboux transformation in quantum mechanics 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…

Investigating and Improving Student Understanding of Quantum Mechanics in the Context of Single Photon Interference

ERIC Educational Resources Information Center

Marshman, Emily; Singh, Chandralekha

2017-01-01

Single photon experiments involving a Mach-Zehnder interferometer can illustrate the fundamental principles of quantum mechanics, 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…

Book Review:

NASA Astrophysics Data System (ADS)

Giannetto, E.

2005-08-01

This book is a sort of tribute to Rob Clifton (1964 2002), Associate Professor of Philosophy and Associate Director of the Center for Philosophy of Science at the University of Pittsburgh, philosopher of physics and editor of the journal Studies in the History and Philosophy of Modern Physics, who tragically died of cancer. It contains fourteen papers by Clifton, for the most part written in collaboration with other authors (Jeffrey Bub (2), Sheldon Goldstein, Michael Dickson, Hans Halvorson (6), Adrian Kent (2)), published between 1995 and 2002. The choice of papers made by the editors is very impressive. They concern the foundations of quantum mechanics and quantum field theory. Among the issues discussed are the modal interpretations of quantum mechanics, the problems of hidden variables theories, non-locality, Bell's inequality, the Einstein Podolsky Rosen paradox, Lorentz invariance, de-coherence, non-contextuality, complementarity, entanglement and quantum information. A consequence of such investigations is that non-separability is a more complex issue than violation of Bell's inequality. Apart from the perspective one can follow—whether one agrees or not with Clifton—these papers are effective contributions to an understanding of the problems involved in the foundations of quantum mechanics. The most interesting parts, in my opinion, are related to the extension of the discussion of foundational problems to quantum field theory: on the algebraic approach, and on the twin concepts of particle and vacuum. Non-locality appears to be `worse' in relativistic quantum field theory than in non-relativistic quantum mechanics. All the papers deal with relevant epistemological and even historical aspects of quantum mechanics interpretations, but all the issues are discussed from a technical, logical and mathematical approach. A complete bibliography of Clifton's papers is given at the end of the volume.

What is Quantum Mechanics? A Minimal Formulation

NASA Astrophysics Data System (ADS)

Friedberg, R.; Hohenberg, P. C.

2018-03-01

This paper presents a minimal formulation of nonrelativistic quantum mechanics, 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 quantum mechanics, 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.

Confinement control mechanism for two-electron Hulthen quantum dots in plasmas

NASA Astrophysics Data System (ADS)

Bahar, M. K.; Soylu, A.

2018-05-01

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 quantum mechanical 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.

Non Locality Proofs in Quantum Mechanics Analyzed by Ordinary Mathematical Logic

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2014-10-01

The so-called non-locality theorems aim to show that Quantum Mechanics 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 Quantum Mechanics 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.

Quantum Chemistry via the Periodic Law.

ERIC Educational Resources Information Center

Blinder, S. M.

1981-01-01

Describes an approach to quantum mechanics exploiting the periodic structure of the elements as a foundation for the quantum theory of matter. Indicates that a quantum chemistry course can be developed using this approach. (SK)

Relativistic quantum chaos-An emergent interdisciplinary field.

PubMed

Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

2018-05-01

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Relativistic quantum chaos—An emergent interdisciplinary field

NASA Astrophysics Data System (ADS)

Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

2018-05-01

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics—all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Quantum probability and Hilbert's sixth problem

NASA Astrophysics Data System (ADS)

Accardi, Luigi

2018-04-01

With the birth of quantum mechanics, the two disciplines that Hilbert proposed to axiomatize, probability and mechanics, became entangled and a new probabilistic model arose in addition to the classical one. Thus, to meet Hilbert's challenge, an axiomatization should account deductively for the basic features of all three disciplines. This goal was achieved within the framework of quantum probability. The present paper surveys the quantum probabilistic axiomatization. This article is part of the themed issue `Hilbert's sixth problem'.

Against the empirical viability of the Deutsch-Wallace-Everett approach to quantum mechanics

NASA Astrophysics Data System (ADS)

Dawid, Richard; Thébault, Karim P. Y.

2014-08-01

The subjective Everettian approach to quantum mechanics 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 quantum mechanics 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.

Quantum mechanics and hidden superconformal symmetry

NASA Astrophysics Data System (ADS)

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 quantum mechanical 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 quantum mechanical 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 ).

Quantum mechanics without the projection postulate and its realistic interpretation

NASA Astrophysics Data System (ADS)

Dieks, D.

1989-11-01

It is widely held that quantum mechanics 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 quantum mechanics 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 quantum mechanics. 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.

Review of the inverse scattering problem at fixed energy in quantum mechanics

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics 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 quantum mechanical 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.

Resolution of quantum singularities

NASA Astrophysics Data System (ADS)

Konkowski, Deborah; Helliwell, Thomas

2017-01-01

A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.

Quantum Mechanics, Path Integrals and Option Pricing:. Reducing the Complexity of Finance

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.; Corianò, Claudio; Srikant, Marakani

2003-04-01

Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics 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.

Quantum probe of Hořava-Lifshitz gravity

NASA Astrophysics Data System (ADS)

Gurtug, O.; Mangut, M.

2018-04-01

Particle probe analysis of the Kehagias-Sfetsos black hole spacetime of Hořava-Lifshitz gravity is extended to wave probe analysis within the framework of quantum mechanics. The time-like naked singularity that develops when ωM2 < 1/2 is probed with quantum fields obeying Klein-Gordon and Chandrasekhar-Dirac equations. The quantum field probe of the naked singularity has revealed that both the spatial part of the wave and the Hamiltonian operators of Klein-Gordon and Chandrasekhar-Dirac equations are essentially self-adjoint, and thus, the naked singularity in the Kehagias-Sfetsos spacetime becomes quantum mechanically non-singular.

Elucidating Reaction Mechanisms on Quantum Computers

NASA Astrophysics Data System (ADS)

Wiebe, Nathan; Reiher, Markus; Svore, Krysta; Wecker, Dave; Troyer, Matthias

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.

Relativistic quantum cryptography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Molotkov, S. N., E-mail: molotkov@issp.ac.ru

2011-03-15

A new protocol of quantum key distribution is proposed to transmit keys through free space. Along with quantum-mechanical restrictions on the discernibility of nonorthogonal quantum states, the protocol uses additional restrictions imposed by special relativity theory. Unlike all existing quantum key distribution protocols, this protocol ensures key secrecy for a not strictly one-photon source of quantum states and an arbitrary length of a quantum communication channel.

What is quantum in quantum randomness?

PubMed

Grangier, P; Auffèves, A

2018-07-13

It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of 'What is quantum in quantum randomness?', i.e. what is the impact of quantization and discreteness on the nature of randomness, remains to be answered. In a first part, we make explicit the differences between quantum and classical randomness within a recently proposed ontology for quantum mechanics based on contextual objectivity. In this view, quantum randomness is the result of contextuality and quantization. We show that this approach strongly impacts the purposes of quantum theory as well as its areas of application. In particular, it challenges current programmes inspired by classical reductionism, aiming at the emergence of the classical world from a large number of quantum systems. In a second part, we analyse quantum physics and thermodynamics as theories of randomness, unveiling their mutual influences. We finally consider new technological applications of quantum randomness that have opened up in the emerging field of quantum thermodynamics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Unitary cocycle representations of the Galilean line group: Quantum mechanical principle of equivalence

DOE Office of Scientific and Technical Information (OSTI.GOV)

MacGregor, B.R.; McCoy, A.E.; Wickramasekara, S., E-mail: wickrama@grinnell.edu

2012-09-15

We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics 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 quantum mechanics 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 quantum mechanics. - Highlights: Black-Right-Pointing-Pointer A formulation of Galilean quantum mechanics 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

Interfacing planar superconducting qubits with high overtone bulk acoustic phonons

NASA Astrophysics Data System (ADS)

Kervinen, Mikael; Rissanen, Ilkka; Sillanpää, Mika

2018-05-01

Mechanical resonators are a promising way for interfacing qubits in order to realize hybrid quantum systems that offer great possibilities for applications. Mechanical systems can have very long energy lifetimes, and they can be further interfaced to other systems. Moreover, integration of a mechanical oscillator with qubits creates a potential platform for the exploration of quantum physics in macroscopic mechanical degrees of freedom. The utilization of high overtone bulk acoustic resonators coupled to superconducting qubits is an intriguing platform towards these goals. These resonators exhibit a combination of high-frequency and high-quality factors. They can reach their quantum ground state at dilution refrigeration temperatures and they can be strongly coupled to superconducting qubits via their piezoelectric effect. In this paper, we demonstrate our system where bulk acoustic phonons of a high overtone resonator are coupled to a transmon qubit in a planar circuit architecture. We show that the bulk acoustic phonons are interacting with the qubit in a simple design architecture at the quantum level, representing further progress towards the quantum control of mechanical motion.

Quantum mechanics: why complex Hilbert space?

NASA Astrophysics Data System (ADS)

Cassinelli, G.; Lahti, P.

2017-10-01

We outline a programme for an axiomatic reconstruction of quantum mechanics 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'.

The Double-Well Potential in Quantum Mechanics: A Simple, Numerically Exact Formulation

ERIC Educational Resources Information Center

Jelic, V.; Marsiglio, F.

2012-01-01

The double-well potential is arguably one of the most important potentials in quantum mechanics, 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…

On the Use of a Virtual Mach-Zehnder Interferometer in the Teaching of Quantum Mechanics

ERIC Educational Resources Information Center

Pereira, Alexsandro; Ostermann, Fernanda; Cavalcanti, Claudio

2009-01-01

For many students, the conceptual learning of quantum mechanics can be rather painful owing to the counter-intuitive nature of quantum phenomena. In order to enhance students' understanding of the odd behaviour of photons and electrons, we introduce a computational simulation of the Mach-Zehnder interferometer, developed by our research group. An…

Board Games and Board Game Design as Learning Tools for Complex Scientific Concepts: Some Experiences

ERIC Educational Resources Information Center

Chiarello, Fabio; Castellano, Maria Gabriella

2016-01-01

In this paper the authors report different experiences in the use of board games as learning tools for complex and abstract scientific concepts such as Quantum Mechanics, Relativity or nano-biotechnologies. In particular we describe "Quantum Race," designed for the introduction of Quantum Mechanical principles, "Lab on a chip,"…

Lectures on Quantum Mechanics

NASA Astrophysics Data System (ADS)

Weinberg, Steven

2015-09-01

Preface; Notation; 1. Historical introduction; 2. Particle states in a central potential; 3. General principles of quantum mechanics; 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.

Visualization of the Invisible: The Qubit as Key to Quantum Physics

ERIC Educational Resources Information Center

Dür, Wolfgang; Heusler, Stefan

2014-01-01

Quantum mechanics is one of the pillars of modern physics, however rather difficult to teach at the introductory level due to the conceptual difficulties and the required advanced mathematics. Nevertheless, attempts to identify relevant features of quantum mechanics and to put forward concepts of how to teach it have been proposed. Here we present…

Quantum mechanics from Newton's second law and the canonical commutation relation [X, P] = i

NASA Astrophysics Data System (ADS)

Palenik, Mark C.

2014-07-01

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 quantum mechanics 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 quantum mechanics 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 quantum mechanics and help solidify the equivalence of the Hamiltonian, Lagrangian, and Newtonian pictures of physics in their minds.

Non-commutative methods in quantum mechanics

NASA Astrophysics Data System (ADS)

Millard, Andrew Clive

1997-09-01

Non-commutativity appears in physics almost hand in hand with quantum mechanics. Non-commuting operators corresponding to observables lead to Heisenberg's Uncertainty Principle, which is often used as a prime example of how quantum mechanics 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 quantum mechanics, 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 quantum mechanics. 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.

Particles, Waves, and the Interpretation of Quantum Mechanics

ERIC Educational Resources Information Center

Christoudouleas, N. D.

1975-01-01

Presents an explanation, without mathematical equations, of the basic principles of quantum mechanics. Includes wave-particle duality, the probability character of the wavefunction, and the uncertainty relations. (MLH)

Quantum-mechanical transport equation for atomic systems.

NASA Technical Reports Server (NTRS)

Berman, P. R.

1972-01-01

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 quantum mechanical 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 mechanical modeling the emission pattern and polarization of nanoscale light emitting diodes.

PubMed

Wang, Rulin; Zhang, Yu; Bi, Fuzhen; Frauenheim, Thomas; Chen, GuanHua; Yam, ChiYung

2016-07-21

Understanding of the electroluminescence (EL) mechanism in optoelectronic devices is imperative for further optimization of their efficiency and effectiveness. Here, a quantum mechanical 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 quantum mechanical modeling of the electrically induced optical response in nanoscale systems.

Squeezed cooling of mechanical motion beyond the resolved-sideband limit

NASA Astrophysics Data System (ADS)

Yang, Cheng; Zhang, Lin; Zhang, Weiping

2018-04-01

Cavity optomechanics provides a unique platform for controlling micromechanical systems by means of optical fields that cross the classical-quantum boundary to achieve solid foundations for quantum technologies. Currently, optomechanical resonators have become promising candidates for the development of precisely controlled nano-motors, ultrasensitive sensors and robust quantum information processors. For all these applications, a crucial requirement is to cool the mechanical resonators down to their quantum ground states. In this paper, we present a novel cooling scheme to further cool a micromechanical resonator via the noise squeezing effect. One quadrature in such a resonator can be squeezed to induce enhanced fluctuations in the other, “heated” quadrature, which can then be used to cool the mechanical motion via conventional optomechanical coupling. Our theoretical analysis and numerical calculations demonstrate that this squeeze-and-cool mechanism offers a quick technique for deeply cooling a macroscopic mechanical resonator to an unprecedented temperature region below the zero-point fluctuations.

The Physics of Semiconductors

NASA Astrophysics Data System (ADS)

Brennan, Kevin F.

1999-02-01

Modern fabrication techniques have made it possible to produce semiconductor devices whose dimensions are so small that quantum mechanical effects dominate their behavior. This book describes the key elements of quantum mechanics, statistical mechanics, and solid-state physics that are necessary in understanding these modern semiconductor devices. The author begins with a review of elementary quantum mechanics, and then describes more advanced topics, such as multiple quantum wells. He then disusses equilibrium and nonequilibrium statistical mechanics. Following this introduction, he provides a thorough treatment of solid-state physics, covering electron motion in periodic potentials, electron-phonon interaction, and recombination processes. The final four chapters deal exclusively with real devices, such as semiconductor lasers, photodiodes, flat panel displays, and MOSFETs. The book contains many homework exercises and is suitable as a textbook for electrical engineering, materials science, or physics students taking courses in solid-state device physics. It will also be a valuable reference for practicing engineers in optoelectronics and related areas.

Tests of alternative quantum theories with neutrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sponar, S.; Durstberger-Rennhofer, K.; Badurek, G.

2014-12-04

According to Bell’s theorem, every theory based on local realism is at variance with certain predictions of quantum mechanics. A theory that maintains realism but abandons reliance on locality, which has been proposed by Leggett, is incompatible with experimentally observable quantum correlations. In our experiment correlation measurements of spin-energy entangled single-neutrons violate a Leggett-type inequality by more than 7.6 standard deviations. The experimental data falsify the contextual realistic model and are fully in favor of quantum mechanics.

Strange Bedfellows: Quantum Mechanics and Data Mining

NASA Astrophysics Data System (ADS)

Weinstein, Marvin

2010-02-01

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 quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.

Playing with Quantum Toys: Julian Schwinger's Measurement Algebra and the Material Culture of Quantum Mechanics Pedagogy at Harvard in the 1960s

NASA Astrophysics Data System (ADS)

Gauvin, Jean-François

2018-03-01

In the early 1960s, a PhD student in physics, Costas Papaliolios, designed a simple—and playful—system of Polaroid polarizer filters with a specific goal in mind: explaining the core principles behind Julian Schwinger's quantum mechanical measurement algebra, developed at Harvard in the late 1940s and based on the Stern-Gerlach experiment confirming the quantization of electron spin. Papaliolios dubbed his invention "quantum toys." This article looks at the origins and function of this amusing pedagogical device, which landed half a century later in the Collection of Historical Scientific Instruments at Harvard University. Rendering the abstract tangible was one of Papaliolios's demonstration tactics in reforming basic teaching of quantum mechanics. This article contends that Papaliolios's motivation in creating the quantum toys came from a renowned endeavor aimed, inter alia, at reforming high-school physics training in the United States: Harvard Project Physics. The pedagogical study of these quantum toys, finally, compels us to revisit the central role playful discovery performs in pedagogy, at all levels of training and in all fields of knowledge.

Increase in the Random Dopant Induced Threshold Fluctuations and Lowering in Sub 100 nm MOSFETs Due to Quantum Effects: A 3-D Density-Gradient Simulation Study

NASA Technical Reports Server (NTRS)

Asenov, Asen; Slavcheva, G.; Brown, A. R.; Davies, J. H.; Saini, S.

2000-01-01

In this paper we present a detailed simulation study of the influence of quantum mechanical effects in the inversion layer on random dopant induced threshold voltage fluctuations and lowering in sub 100 nm MOSFETs. The simulations have been performed using a 3-D implementation of the density gradient (DG) formalism incorporated in our established 3-D atomistic simulation approach. This results in a self-consistent 3-D quantum mechanical picture, which implies not only the vertical inversion layer quantisation but also the lateral confinement effects related to current filamentation in the 'valleys' of the random potential fluctuations. We have shown that the net result of including quantum mechanical effects, while considering statistical dopant fluctuations, is an increase in both threshold voltage fluctuations and lowering. At the same time, the random dopant induced threshold voltage lowering partially compensates for the quantum mechanical threshold voltage shift in aggressively scaled MOSFETs with ultrathin gate oxides.

Thermalization and its mechanism for generic quantum isolated systems

NASA Astrophysics Data System (ADS)

Olshanii, Maxim; Dunjko, Vanja; Rigol, Marcos

2008-05-01

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).

Symmetry aspects in emergent quantum mechanics

NASA Astrophysics Data System (ADS)

Elze, Hans-Thomas

2009-06-01

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 quantum mechanics, 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 quantum mechanical level, but the relation to the underlying classical degrees of freedom is nonlocal.

Quantum inertia stops superposition: Scan Quantum Mechanics

NASA Astrophysics Data System (ADS)

Gato-Rivera, Beatriz

2017-08-01

Scan Quantum Mechanics is a novel interpretation of some aspects of quantum mechanics 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.

Electron Tunneling, a Quantum Probe for the Quantum World of Nanotechnology

ERIC Educational Resources Information Center

Hipps, K. W.; Scudiero, L.

2005-01-01

A quantum-mechanical probe is essential to study the quantum world, which is provided by electron tunneling. A spectroscopic mapping to image the electron-transport pathways on a sub-molecular scale is used.

Free energies of binding from large-scale first-principles quantum mechanical calculations: application to ligand hydration energies.

PubMed

Fox, Stephen J; Pittock, Chris; Tautermann, Christofer S; Fox, Thomas; Christ, Clara; Malcolm, N O J; Essex, Jonathan W; Skylaris, Chris-Kriton

2013-08-15

Schemes of increasing sophistication for obtaining free energies of binding have been developed over the years, where configurational sampling is used to include the all-important entropic contributions to the free energies. However, the quality of the results will also depend on the accuracy with which the intermolecular interactions are computed at each molecular configuration. In this context, the energy change associated with the rearrangement of electrons (electronic polarization and charge transfer) upon binding is a very important effect. Classical molecular mechanics force fields do not take this effect into account explicitly, and polarizable force fields and semiempirical quantum or hybrid quantum-classical (QM/MM) calculations are increasingly employed (at higher computational cost) to compute intermolecular interactions in free-energy schemes. In this work, we investigate the use of large-scale quantum mechanical calculations from first-principles as a way of fully taking into account electronic effects in free-energy calculations. We employ a one-step free-energy perturbation (FEP) scheme from a molecular mechanical (MM) potential to a quantum mechanical (QM) potential as a correction to thermodynamic integration calculations within the MM potential. We use this approach to calculate relative free energies of hydration of small aromatic molecules. Our quantum calculations are performed on multiple configurations from classical molecular dynamics simulations. The quantum energy of each configuration is obtained from density functional theory calculations with a near-complete psinc basis set on over 600 atoms using the ONETEP program.

Two-Photon Quantum Entanglement from Type-II Spontaneous Parametric Down-Conversion

NASA Astrophysics Data System (ADS)

Pittman, Todd Butler

The concept of two (or more) particle entanglement lies at the heart of many fascinating questions concerning the foundations of quantum mechanics. The counterintuitive nonlocal behavior of entangled states led Einstein, Podolsky, and Rosen (EPR) to ask their famous 1935 question, "Can quantum mechanical description of reality be considered complete?". Although the debate has been raging on for more than 60 years, there is still no absolutely conclusive answer to this question. For if entangled states exist and can be observed, then accepting quantum mechanics as a complete theory requires a drastic overhaul of one's physical intuition with regards to the common sense notions of locality and reality put forth by EPR. Contained herein are the results of research investigating various non-classical features of the two-photon entangled states produced in Type-II Spontaneous Parametric Down -Conversion (SPDC). Through a series of experiments we have manifest the nonlocal nature of the quantum mechanical "two-photon effective wavefunction" (or Biphoton) realized by certain photon-counting coincidence measurements performed on these states. In particular, we examine a special double entanglement, in which the states are seen to be simultaneously entangled in both spin and space-time variables. The observed phenomena based on this double entanglement lead to many interesting results which defy classical explanation, but are well described within the framework of quantum mechanics. The implications provide a unique perspective concerning the nature of the photon, and the concept of quantum entanglement.

On the Meaning of Element in the Science of Italic Tradition, the Question of Physical Objectivity (and/or Physical Meaning) and Quantum Mechanics

NASA Astrophysics Data System (ADS)

Boscarino, Giuseppe

2006-06-01

It is questioned: Is quantum mechanics a new science or a new (or rather old) philosophy of physical science? It is shown that Einstein's attempt in his article of 1935 to bring the concept of "element" from the classical (we call it Italic) philosophical-epistemological tradition, which goes under the names of Pythagoras Parmenides, Democritus, and Newton, into quantum mechanical theory is unclear, inadequate and contradictory.

Combined quantum and molecular mechanics (QM/MM).

PubMed

Friesner, Richard A

2004-12-01

We describe the current state of the art of mixed quantum mechanics/molecular mechanics (QM/MM) methodology, with a particular focus on modeling of enzymatic reactions. Over the past decade, the effectiveness of these methods has increased dramatically, based on improved quantum chemical methods, advances in the description of the QM/MM interface, and reductions in the cost/performance of computing hardware. Two examples of pharmaceutically relevant applications, cytochrome P450 and class C β-lactamase, are presented.: © 2004 Elsevier Ltd . All rights reserved.

Probing finite coarse-grained virtual Feynman histories with sequential weak values

NASA Astrophysics Data System (ADS)

Georgiev, Danko; Cohen, Eliahu

2018-05-01

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete set of orthogonal quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories.

No extension of quantum theory can have improved predictive power.

PubMed

Colbeck, Roger; Renner, Renato

2011-08-02

According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory that removes this indeterminism, as suspected by Einstein, Podolsky and Rosen. Although this has been shown to be impossible, existing results do not imply that the current theory is maximally informative. Here we ask the more general question of whether any improved predictions can be achieved by any extension of quantum theory. Under the assumption that measurements can be chosen freely, we answer this question in the negative: no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself. Our result has significance for the foundations of quantum mechanics, as well as applications to tasks that exploit the inherent randomness in quantum theory, such as quantum cryptography.

Quantum Brownian motion model for the stock market

NASA Astrophysics Data System (ADS)

Meng, Xiangyi; Zhang, Jian-Wei; Guo, Hong

2016-06-01

It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system-a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.

No extension of quantum theory can have improved predictive power

PubMed Central

Colbeck, Roger; Renner, Renato

2011-01-01

According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory that removes this indeterminism, as suspected by Einstein, Podolsky and Rosen. Although this has been shown to be impossible, existing results do not imply that the current theory is maximally informative. Here we ask the more general question of whether any improved predictions can be achieved by any extension of quantum theory. Under the assumption that measurements can be chosen freely, we answer this question in the negative: no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself. Our result has significance for the foundations of quantum mechanics, as well as applications to tasks that exploit the inherent randomness in quantum theory, such as quantum cryptography. PMID:21811240

Quantum Foundations of Quantum Information

NASA Astrophysics Data System (ADS)

Griffiths, Robert

2009-03-01

The main foundational issue for quantum information is: What is quantum information about? What does it refer to? Classical information typically refers to physical properties, and since classical is a subset of quantum information (assuming the world is quantum mechanical), quantum information should--and, it will be argued, does--refer to quantum physical properties represented by projectors on appropriate subspaces of a quantum Hilbert space. All sorts of microscopic and macroscopic properties, not just measurement outcomes, can be represented in this way, and are thus a proper subject of quantum information. The Stern-Gerlach experiment illustrates this. When properties are compatible, which is to say their projectors commute, Shannon's classical information theory based on statistical correlations extends without difficulty or change to the quantum case. When projectors do not commute, giving rise to characteristic quantum effects, a foundation for the subject can still be constructed by replacing the ``measurement and wave-function collapse'' found in textbooks--an efficient calculational tool, but one giving rise to numerous conceptual difficulties--with a fully consistent and paradox free stochastic formulation of standard quantum mechanics. This formulation is particularly helpful in that it contains no nonlocal superluminal influences; the reason the latter carry no information is that they do not exist.

Quantum market games: implementing tactics via measurements

NASA Astrophysics Data System (ADS)

Pakula, I.; Piotrowski, E. W.; Sladkowski, J.

2006-02-01

A major development in applying quantum mechanical formalism to various fields has been made during the last few years. Quantum counterparts of Game Theory, Economy, as well as diverse approaches to Quantum Information Theory have been found and currently are being explored. Using connections between Quantum Game Theory and Quantum Computations, an application of the universality of a measurement based computation in Quantum Market Theory is presented.

Measurements and mathematical formalism of quantum mechanics

NASA Astrophysics Data System (ADS)

Slavnov, D. A.

2007-03-01

A scheme for constructing quantum mechanics 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 quantum mechanics, 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.

Cavity Optomechanics at Millikelvin Temperatures

NASA Astrophysics Data System (ADS)

Meenehan, Sean Michael

The field of cavity optomechanics, which concerns the coupling of a mechanical object's motion to the electromagnetic field of a high finesse cavity, allows for exquisitely sensitive measurements of mechanical motion, from large-scale gravitational wave detection to microscale accelerometers. Moreover, it provides a potential means to control and engineer the state of a macroscopic mechanical object at the quantum level, provided one can realize sufficiently strong interaction strengths relative to the ambient thermal noise. Recent experiments utilizing the optomechanical interaction to cool mechanical resonators to their motional quantum ground state allow for a variety of quantum engineering applications, including preparation of non-classical mechanical states and coherent optical to microwave conversion. Optomechanical crystals (OMCs), in which bandgaps for both optical and mechanical waves can be introduced through patterning of a material, provide one particularly attractive means for realizing strong interactions between high-frequency mechanical resonators and near-infrared light. Beyond the usual paradigm of cavity optomechanics involving isolated single mechanical elements, OMCs can also be fashioned into planar circuits for photons and phonons, and arrays of optomechanical elements can be interconnected via optical and acoustic waveguides. Such coupled OMC arrays have been proposed as a way to realize quantum optomechanical memories, nanomechanical circuits for continuous variable quantum information processing and phononic quantum networks, and as a platform for engineering and studying quantum many-body physics of optomechanical meta-materials. However, while ground state occupancies (that is, average phonon occupancies less than one) have been achieved in OMC cavities utilizing laser cooling techniques, parasitic absorption and the concomitant degradation of the mechanical quality factor fundamentally limit this approach. On the other hand, the high mechanical frequency of these systems allows for the possibility of using a dilution refrigerator to simultaneously achieve low thermal occupancy and long mechanical coherence time by passively cooling the device to the millikelvin regime. This thesis describes efforts to realize the measurement of OMC cavities inside a dilution refrigerator, including the development of fridge-compatible optical coupling schemes and the characterization of the heating dynamics of the mechanical resonator at sub-kelvin temperatures. We will begin by summarizing the theoretical framework used to describe cavity optomechanical systems, as well as a handful of the quantum applications envisioned for such devices. Then, we will present background on the design of the nanobeam OMC cavities used for this work, along with details of the design and characterization of tapered fiber couplers for optical coupling inside the fridge. Finally, we will present measurements of the devices at fridge base temperatures of Tf = 10 mK, using both heterodyne spectroscopy and time-resolved sideband photon counting, as well as detailed analysis of the prospects for future quantum applications based on the observed optically-induced heating.

Quantum Statistical Mechanics on a Quantum Computer

NASA Astrophysics Data System (ADS)

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.

Resolving the vacuum fluctuations of an optomechanical system using an artificial atom

NASA Astrophysics Data System (ADS)

Lecocq, F.; Teufel, J. D.; Aumentado, J.; Simmonds, R. W.

2015-08-01

Heisenberg’s uncertainty principle results in one of the strangest quantum behaviours: a mechanical oscillator can never truly be at rest. Even at a temperature of absolute zero, its position and momentum are still subject to quantum fluctuations. However, direct energy detection of the oscillator in its ground state makes it seem motionless, and in linear position measurements detector noise can masquerade as mechanical fluctuations. Thus, how can we resolve quantum fluctuations? Here, we parametrically couple a micromechanical oscillator to a microwave cavity to prepare the system in its quantum ground state and then amplify the remaining vacuum fluctuations into real energy quanta. We monitor the photon/phonon-number distributions using a superconducting qubit, allowing us to resolve the quantum vacuum fluctuations of the macroscopic oscillator’s motion. Our results further demonstrate the ability to control a long-lived mechanical oscillator using a non-Gaussian resource, directly enabling applications in quantum information processing and enhanced detection of displacement and forces.

Investigations of a voltage-biased microwave cavity for quantum measurements of nanomechanical resonators

NASA Astrophysics Data System (ADS)

Rouxinol, Francisco; Hao, Hugo; Lahaye, Matt

2015-03-01

Quantum electromechanical systems incorporating superconducting qubits have received extensive interest in recent years due to their promising prospects for studying fundamental topics of quantum mechanics 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.

Dynamic strain-mediated coupling of a single diamond spin to a mechanical resonator

NASA Astrophysics Data System (ADS)

Ovartchaiyapong, Preeti; Lee, Kenneth W.; Myers, Bryan A.; Jayich, Ania C. Bleszynski

2014-07-01

The development of hybrid quantum systems is central to the advancement of emerging quantum technologies, including quantum information science and quantum-assisted sensing. The recent demonstration of high-quality single-crystal diamond resonators has led to significant interest in a hybrid system consisting of nitrogen-vacancy centre spins that interact with the resonant phonon modes of a macroscopic mechanical resonator through crystal strain. However, the nitrogen-vacancy spin-strain interaction has not been well characterized. Here, we demonstrate dynamic, strain-mediated coupling of the mechanical motion of a diamond cantilever to the spin of an embedded nitrogen-vacancy centre. Via quantum control of the spin, we quantitatively characterize the axial and transverse strain sensitivities of the nitrogen-vacancy ground-state spin. The nitrogen-vacancy centre is an atomic scale sensor and we demonstrate spin-based strain imaging with a strain sensitivity of 3 × 10-6 strain Hz-1/2. Finally, we show how this spin-resonator system could enable coherent spin-phonon interactions in the quantum regime.

Potential Functions and the Characterization of Economics-Based Information

NASA Astrophysics Data System (ADS)

Haven, Emmanuel

2015-10-01

The formulation of quantum mechanics as a diffusion process by Nelson (Phys Rev 150:1079-1085, 1966) provides for an interesting approach on how we may transit from classical mechanics into quantum mechanics. Besides the presence of the real potential function, another type of potential function (often denoted as `quantum potential') forms an intrinsic part of this theory. In this paper we attempt to show how both types of potential functions can have a use in a resolutely macroscopic context like financial asset pricing. We are particularly interested in uncovering how the `quantum potential' can add to the economics-based relevant information which is already supplied by the real potential function.

Monogamy equalities for qubit entanglement from Lorentz invariance.

PubMed

Eltschka, Christopher; Siewert, Jens

2015-04-10

A striking result from nonrelativistic quantum mechanics is the monogamy of entanglement, which states that a particle can be maximally entangled only with one other party, not with several ones. While there is the exact quantitative relation for three qubits and also several inequalities describing monogamy properties, it is not clear to what extent exact monogamy relations are a general feature of quantum mechanics. We prove that in all many-qubit systems there exist strict monogamy laws for quantum correlations. They come about through the curious relationship between the nonrelativistic quantum mechanics of qubits and Minkowski space. We elucidate the origin of entanglement monogamy from this symmetry perspective and provide recipes to construct new families of such equalities.

A Nanotechnology Enhancement to Moore’s Law

DTIC Science & Technology

2013-01-01

suggested that quantummechanics may be playing a role in consciousness , if a quantum mechanical model of mind and consciousness was developed, this would...necessary enhancement by an increasingly maturing nanotechnology and facing the inevitable quantum -mechanical atomic and nuclei limits. Since we cannot...important. (ii) Quantum computing: The other types of transistor material are rapidly developed in laboratories worldwide, for example, Spintronics

Quantum mechanics: why complex Hilbert space?

PubMed

Cassinelli, G; Lahti, P

2017-11-13

We outline a programme for an axiomatic reconstruction of quantum mechanics 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'. © 2017 The Author(s).

Quantum approach to classical statistical mechanics.

PubMed

Somma, R D; Batista, C D; Ortiz, G

2007-07-20

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 quantum mechanics. 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.

Quantum dice rolling: a multi-outcome generalization of quantum coin flipping

NASA Astrophysics Data System (ADS)

Aharon, N.; Silman, J.

2010-03-01

The problem of quantum dice rolling (DR)—a generalization of the problem of quantum coin flipping (CF) to more than two outcomes and parties—is studied in both its weak and strong variants. We prove by construction that quantum mechanics allows for (i) weak N-sided DR admitting arbitrarily small bias for any N and (ii) two-party strong N-sided DR saturating Kitaev's bound for any N. To derive (ii) we also prove by construction that quantum mechanics allows for (iii) strong imbalanced CF saturating Kitaev's bound for any degree of imbalance. Furthermore, as a corollary of (ii) we introduce a family of optimal 2m-party strong nm-sided DR protocols for any pair m and n.

Superposing pure quantum states with partial prior information

NASA Astrophysics Data System (ADS)

Dogra, Shruti; Thomas, George; Ghosh, Sibasish; Suter, Dieter

2018-05-01

The principle of superposition is an intriguing feature of quantum mechanics, 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 quantum mechanics 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.

Photosynthetic Energy Transfer at the Quantum/Classical Border.

PubMed

Keren, Nir; Paltiel, Yossi

2018-06-01

Quantum mechanics diverges from the classical description of our world when very small scales or very fast processes are involved. Unlike classical mechanics, quantum effects cannot be easily related to our everyday experience and are often counterintuitive to us. Nevertheless, the dimensions and time scales of the photosynthetic energy transfer processes puts them close to the quantum/classical border, bringing them into the range of measurable quantum effects. Here we review recent advances in the field and suggest that photosynthetic processes can take advantage of the sensitivity of quantum effects to the environmental 'noise' as means of tuning exciton energy transfer efficiency. If true, this design principle could be a base for 'nontrivial' coherent wave property nano-devices. Copyright © 2018 Elsevier Ltd. All rights reserved.

Quantum Information Biology: From Information Interpretation of Quantum Mechanics to Applications in Molecular Biology and Cognitive Psychology

NASA Astrophysics Data System (ADS)

Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro

2015-10-01

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 quantum mechanics (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.

Investigating and improving student understanding of quantum mechanical observables and their corresponding operators in Dirac notation

NASA Astrophysics Data System (ADS)

Marshman, Emily; Singh, Chandralekha

2018-01-01

In quantum mechanics, for every physical observable, there is a corresponding Hermitian operator. According to the most common interpretation of quantum mechanics, measurement of an observable collapses the quantum state into one of the possible eigenstates of the operator and the corresponding eigenvalue is measured. Since Dirac notation is an elegant notation that is commonly used in upper-level quantum mechanics, it is important that students learn to express quantum operators corresponding to observables in Dirac notation in order to apply the quantum formalism effectively in diverse situations. Here we focus on an investigation that suggests that, even though Dirac notation is used extensively, many advanced undergraduate and PhD students in physics have difficulty expressing the identity operator and other Hermitian operators corresponding to physical observables in Dirac notation. We first describe the difficulties students have with expressing the identity operator and a generic Hermitian operator corresponding to an observable in Dirac notation. We then discuss how the difficulties found via written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of these concepts. The QuILT strives to help students become proficient in expressing the identity operator and a generic Hermitian operator corresponding to an observable in Dirac notation. We also discuss the effectiveness of the QuILT based on in-class evaluations.

Quantum back-action-evading measurement of motion in a negative mass reference frame

NASA Astrophysics Data System (ADS)

Møller, Christoffer B.; Thomas, Rodrigo A.; Vasilakis, Georgios; Zeuthen, Emil; Tsaturyan, Yeghishe; Balabas, Mikhail; Jensen, Kasper; Schliesser, Albert; Hammerer, Klemens; Polzik, Eugene S.

2017-07-01

Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random quantum back-action (QBA) perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty on the measurement of motion. As a consequence of this randomness, and in accordance with the Heisenberg uncertainty principle, the QBA puts a limitation—the so-called standard quantum limit—on the precision of sensing of position, velocity and acceleration. Here we show that QBA on a macroscopic mechanical oscillator can be evaded if the measurement of motion is conducted in the reference frame of an atomic spin oscillator. The collective quantum measurement on this hybrid system of two distant and disparate oscillators is performed with light. The mechanical oscillator is a vibrational ‘drum’ mode of a millimetre-sized dielectric membrane, and the spin oscillator is an atomic ensemble in a magnetic field. The spin oriented along the field corresponds to an energetically inverted spin population and realizes a negative-effective-mass oscillator, while the opposite orientation corresponds to an oscillator with positive effective mass. The QBA is suppressed by -1.8 decibels in the negative-mass setting and enhanced by 2.4 decibels in the positive-mass case. This hybrid quantum system paves the way to entanglement generation and distant quantum communication between mechanical and spin systems and to sensing of force, motion and gravity beyond the standard quantum limit.

A rational explanation of wave-particle duality of light

NASA Astrophysics Data System (ADS)

Rashkovskiy, S. A.

2013-10-01

The wave-particle duality is a fundamental property of the nature. At the same time, it is one of the greatest mysteries of modern physics. This gave rise to a whole direction in quantum physics - the interpretation of quantum mechanics. The Wiener experiments demonstrating the wave-particle duality of light are discussed. It is shown that almost all interpretations of quantum mechanics allow explaining the double-slit experiments, but are powerless to explain the Wiener experiments. The reason of the paradox, associated with the wave-particle duality is analyzed. The quantum theory consists of two independent parts: (i) the dynamic equations describing the behavior of a quantum object (for example, the Schrodinger or Maxwell equations), and (ii) the Born's rule, the relation between the wave function and the probability of finding the particle at a given point. It is shown that precisely the Born's rule results in paradox in explaining the wave-particle duality. In order to eliminate this paradox, we propose a new rational interpretation of the wave-particle duality and associated new rule, connecting the corpuscular and wave properties of quantum objects. It is shown that this new rational interpretation of the wave-particle duality allows using the classic images of particle and wave in explaining the quantum mechanical and optical phenomena, does not result in paradox in explaining the doubleslit experiments and Wiener experiments, and does not contradict to the modern quantum mechanical concepts. It is shown that the Born's rule follows immediately from proposed new rules as an approximation.

Spekkens’ toy model in all dimensions and its relationship with stabiliser quantum mechanics

NASA Astrophysics Data System (ADS)

Catani, Lorenzo; E Browne, Dan

2017-07-01

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 quantum mechanics 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 quantum mechanics (SQM) is a sub-theory of quantum mechanics 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 back-action-evading measurement of motion in a negative mass reference frame.

PubMed

Møller, Christoffer B; Thomas, Rodrigo A; Vasilakis, Georgios; Zeuthen, Emil; Tsaturyan, Yeghishe; Balabas, Mikhail; Jensen, Kasper; Schliesser, Albert; Hammerer, Klemens; Polzik, Eugene S

2017-07-12

Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random quantum back-action (QBA) perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty on the measurement of motion. As a consequence of this randomness, and in accordance with the Heisenberg uncertainty principle, the QBA puts a limitation-the so-called standard quantum limit-on the precision of sensing of position, velocity and acceleration. Here we show that QBA on a macroscopic mechanical oscillator can be evaded if the measurement of motion is conducted in the reference frame of an atomic spin oscillator. The collective quantum measurement on this hybrid system of two distant and disparate oscillators is performed with light. The mechanical oscillator is a vibrational 'drum' mode of a millimetre-sized dielectric membrane, and the spin oscillator is an atomic ensemble in a magnetic field. The spin oriented along the field corresponds to an energetically inverted spin population and realizes a negative-effective-mass oscillator, while the opposite orientation corresponds to an oscillator with positive effective mass. The QBA is suppressed by -1.8 decibels in the negative-mass setting and enhanced by 2.4 decibels in the positive-mass case. This hybrid quantum system paves the way to entanglement generation and distant quantum communication between mechanical and spin systems and to sensing of force, motion and gravity beyond the standard quantum limit.

Non-equilibrium mechanisms of light in the microwave region

NASA Astrophysics Data System (ADS)

Mortenson, Juliana H. J.

2011-09-01

Quantum mechanics and quantum chemistry have taught for more than 100 years that "photons" associated with microwaves cannot exert photochemical effects because their "photon energies" are smaller than chemical bond energies. Those quantum theories have been strongly contradicted within the last few decades by physical experiments demonstrating non-equilibrium, photochemical and photomaterial activity by microwaves. Reactions among scientists to these real physical models and proofs have varied from disbelief and denial, to acceptance of the real physical phenomena and demands for revisions to quantum theory. At the previous "Nature of Light" meeting, an advance in the foundations of quantum mechanics was presented. Those discoveries have revealed the source of these conflicts between quantum theory and microwave experiments. Critical variables and constants were missing from quantum theory due to a minor mathematical inadvertence in Planck's original quantum work. As a result, erroneous concepts were formed nearly a century ago regarding the energetics and mechanisms of lower frequency light, such as in the microwave region. The new discoveries have revealed that the traditional concept of "photons" mistakenly attributed elementary particle status to what is actually an arbitrarily time-based collection of sub-photonic, elementary particles. In a mathematical dimensional sense, those time-based energy measurements cannot be mathematically equivalent to bond energies as historically believed. Only an "isolated quantity of energy", as De Broglie referred to it, can be equivalent to bond energy. With the aid of the new variables and constants, the non-equilibrium mechanisms of light in the microwave region can now be described. They include resonant absorption, splitting frequency stimulation leading to electronic excitation, and resonant acoustic transduction. Numerous practical engineering applications can be envisioned for non-equilibrium microwaves.

An inquiry-based approach to the Franck-Hertz experiment

NASA Astrophysics Data System (ADS)

Persano Adorno, Dominique; Pizzolato, Nicola

2016-05-01

The practice of scientists and engineers is today exerted within interdisciplinary contexts, placed at the intersections of different research fields, including nanoscale science. The development of the required competences is based on an effective science and engineering instruction, which should be able to drive the students towards a deeper understanding of quantum mechanics fundamental concepts and, at the same time, strengthen their reasoning skills and transversal abilities. In this study we report the results of an inquiry-driven learning path experienced by a sample of 12 electronic engineering undergraduates engaged to perform the Franck-Hertz experiment. Before being involved in this experimental activity, the students received a traditional lecture-based instruction on the fundamental concepts of quantum mechanics, but their answers to an open-ended questionnaire, administered at the beginning of the inquiry activity, demonstrated that the acquired knowledge was characterized by a strictly theoretical vision of quantum science, basically in terms of an artificial mathematical framework having very poor connections with the real world. The Franck Hertz experiment was introduced to the students by starting from the problem of finding an experimental confirmation of the Bohr's postulates asserting that atoms can absorb energy only in quantum portions. The whole activity has been videotaped and this allowed us to deeply analyse the student perception's change about the main concepts of quantum mechanics. We have found that the active participation to this learning experience favored the building of cognitive links among student theoretical perceptions of quantum mechanics and their vision of quantum phenomena, within an everyday context of knowledge. Furthermore, our findings confirm the benefits of integrating traditional lecture-based instruction on quantum mechanics with learning experiences driven by inquiry-based teaching strategies.

Unified Field Mechanics: A Brief Introduction

NASA Astrophysics Data System (ADS)

Amoroso, Richard L.

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 Quantum Mechanics; 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 Quantum Mechanics. 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.

Mechanical equivalent of quantum heat engines.

PubMed

Arnaud, Jacques; Chusseau, Laurent; Philippe, Fabrice

2008-06-01

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.

Controlled Quantum Packets

NASA Technical Reports Server (NTRS)

DeMartino, Salvatore; DeSiena, Silvio

1996-01-01

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

Application of high level wavefunction methods in quantum mechanics/molecular mechanics hybrid schemes.

PubMed

Mata, Ricardo A

2010-05-21

In this Perspective, several developments in the field of quantum mechanics/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.

Complex Teichmüller Space below the Planck Length for the Interpretation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Winterberg, Friedwardt

2014-03-01

As Newton's mysterious action at a distance law of gravity was explained as a Riemannian geometry by Einstein, it is proposed that the likewise mysterious non-local quantum mechanics is explained by the analytic continuation below the Planck length into a complex Teichmüller space. Newton's theory worked extremely well, as does quantum mechanics, but no satisfactory explanation has been given for quantum mechanics. In one space dimension, sufficient to explain the EPR paradox, the Teichmüller space is reduced to a space of complex Riemann surfaces. Einstein's curved space-time theory of gravity was confirmed by a tiny departure from Newton's theory in the motion of the planet Mercury, and an experiment is proposed to demonstrate the possible existence of a Teichmüller space below the Planck length.

Optimization of metabolite detection by quantum mechanics simulations in magnetic resonance spectroscopy.

PubMed

Gambarota, Giulio

2017-07-15

Magnetic resonance spectroscopy (MRS) is a well established modality for investigating tissue metabolism in vivo. In recent years, many efforts by the scientific community have been directed towards the improvement of metabolite detection and quantitation. Quantum mechanics simulations allow for investigations of the MR signal behaviour of metabolites; thus, they provide an essential tool in the optimization of metabolite detection. In this review, we will examine quantum mechanics simulations based on the density matrix formalism. The density matrix was introduced by von Neumann in 1927 to take into account statistical effects within the theory of quantum mechanics. We will discuss the main steps of the density matrix simulation of an arbitrary spin system and show some examples for the strongly coupled two spin system. Copyright © 2016 Elsevier Inc. All rights reserved.

Wigner functions for noncommutative quantum mechanics: A group representation based construction

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 quantum mechanics, 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 quantum mechanics 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 quantum mechanics, obeying the canonical commutation relations only.« less

Measurements in Quantum Mechanics and von NEUMANN's Model

NASA Astrophysics Data System (ADS)

Mello, Pier A.; Johansen, Lars M.

2010-12-01

Many textbooks on Quantum Mechanics 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 Quantum Mechanics, 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 Quantum Mechanics, 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 with Silicon Nanostructures

NASA Astrophysics Data System (ADS)

Safavi-Naeini, Amir H.

Mechanical resonators are the most basic and ubiquitous physical systems known. In on-chip form, they are used to process high frequency signals in every cell phone, television, and laptop. They have also been in the last few decades in different shapes and forms, a critical part of progress in quantum information sciences with kilogram scale mirrors for gravitational wave detection measuring motion at its quantum limits, and the motion of single ions being used to link qubits for quantum computation. Optomechanics is a field primarily concerned with coupling light to the motion of mechanical structures. This thesis contains descriptions of recent work with mechanical systems in the megahertz to gigahertz frequency range, formed by nanofabricating novel photonic/phononic structures on a silicon chip. These structures are designed to have both optical and mechanical resonances, and laser light is used to address and manipulate their motional degrees of freedom through radiation pressure forces. We laser cool these mechanical resonators to their ground states, and observe for the first time the quantum zero-point motion of a nanomechanical resonator. Conversely, we show that engineered mechanical resonances drastically modify the optical response of our structures, creating large effective optical nonlinearities not present in bulk silicon. We experimentally demonstrate aspects of these nonlinearities by proposing and observing ``electromagnetically induced transparency'' and light slowed down to 6 m/s, as well as wavelength conversion, and generation of nonclassical optical radiation. Finally, the application of optomechanics to longstanding problems in quantum and classical communications are proposed and investigated.

Contrasting grading approaches in introductory physics and quantum mechanics: The case of graduate teaching assistants

NASA Astrophysics Data System (ADS)

Marshman, Emily; Sayer, Ryan; Henderson, Charles; Singh, Chandralekha

2017-06-01

At large research universities, physics graduate teaching assistants (TAs) are often responsible for grading in courses at all levels. However, few studies have focused on TAs' grading practices in introductory and advanced physics courses. This study was designed to investigate whether physics graduate TAs grade students in introductory physics and quantum mechanics using different criteria and if so, why they may be inclined to do so. To investigate possible discrepancies in TAs' grading approaches in courses at different levels, we implemented a sequence of instructional activities in a TA professional development course that asked TAs to grade student solutions of introductory physics and upper-level quantum mechanics problems and explain why, if at all, their grading approaches were different or similar in the two contexts. We analyzed the differences in TAs' grading approaches in the two contexts and discuss the reasons they provided for the differences in their grading approaches in introductory physics and quantum mechanics in individual interviews, class discussions, and written responses. We find that a majority of the TAs graded solutions to quantum mechanics problems differently than solutions to introductory physics problems. In quantum mechanics, the TAs focused more on physics concepts and reasoning and penalized students for not showing evidence of understanding. The findings of the study have implications for TA professional development programs, e.g., the importance of helping TAs think about the difficulty of a problem from an introductory students' perspective and reflecting on the benefits of formative assessment.

Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. II. Application of the local basis equation.

PubMed

Ferenczy, György G

2013-04-05

The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009, 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self-consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree-Fock-Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self-consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave-function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem. Copyright © 2013 Wiley Periodicals, Inc.

QuVis interactive simulations: tools to support quantum mechanics instruction

NASA Astrophysics Data System (ADS)

Kohnle, Antje

2015-04-01

Quantum mechanics holds a fascination for many students, but its mathematical complexity and counterintuitive results can present major barriers. The QuVis Quantum Mechanics 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 quantum mechanics. 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 quantum mechanics 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 quantum mechanics 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.

Quantum mechanical force field for water with explicit electronic polarization.

PubMed

Han, Jaebeom; Mazack, Michael J M; Zhang, Peng; Truhlar, Donald G; Gao, Jiali

2013-08-07

A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical 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 quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical 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 biological ion channels through membranes.

Sampling Molecular Conformers in Solution with Quantum Mechanical Accuracy at a Nearly Molecular-Mechanics Cost.

PubMed

Rosa, Marta; Micciarelli, Marco; Laio, Alessandro; Baroni, Stefano

2016-09-13

We introduce a method to evaluate the relative populations of different conformers of molecular species in solution, aiming at quantum mechanical 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.

Mechanisms of SN2 reactions: insights from a nearside/farside analysis.

PubMed

Hennig, Carsten; Schmatz, Stefan

2015-10-28

A nearside/farside analysis of differential cross sections has been performed for the complex-forming SN2 reaction Cl(-) + CH3Br → ClCH3 + Br(-). It is shown that for low rotational quantum numbers a direct "nearside" reaction mechanism plays an important role and leads to anisotropic differential cross sections. For high rotational quantum numbers, indirect mechanisms via a long-lived intermediate complex are prevalent (independent of a nearside/farside configuration), leading to isotropic cross sections. Quantum mechanical interference can be significant at specific energies or angles. Averaging over energies and angles reveals that the nearside/farside decomposition in a semiclassical interpretation can reasonably account for the analysis of the reaction mechanism.

Quantum Mechanics/Molecular Mechanics Study of the Sialyltransferase Reaction Mechanism.

PubMed

Hamada, Yojiro; Kanematsu, Yusuke; Tachikawa, Masanori

2016-10-11

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 quantum mechanics/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 quantum mechanical interaction with CMP.

Gradual Introduction of Some Aspects of Quantum Mechanics in a High School Curriculum.

ERIC Educational Resources Information Center

Cuppari, A.; Rinaudo, G.; Robutti, O.; Violino, P.

1997-01-01

Suggests that the basic concepts of quantum mechanics can be introduced at the high school level by considering the action of classical mechanics, then introducing Planck's constant as the granularity of that action. Uses the periodic motion of a spring as a practical example. (AIM)

Investigating Learners' Epistemological Framings of Quantum Mechanics

ERIC Educational Resources Information Center

Dini, Vesal

2017-01-01

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 quantum mechanics (QM), students, like physicists, need to adjust this approach, in particular with respect to the roles that…

Quantum mechanics in noninertial reference frames: Violations of the nonrelativistic equivalence principle

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 quantum mechanics 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 quantum mechanics, 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 quantum mechanics 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

OpenFlow arbitrated programmable network channels for managing quantum metadata

DOE PAGES

Dasari, Venkat R.; Humble, Travis S.

2016-10-10

Quantum networks must classically exchange complex metadata between devices in order to carry out information for protocols such as teleportation, super-dense coding, and quantum key distribution. Demonstrating the integration of these new communication methods with existing network protocols, channels, and data forwarding mechanisms remains an open challenge. Software-defined networking (SDN) offers robust and flexible strategies for managing diverse network devices and uses. We adapt the principles of SDN to the deployment of quantum networks, which are composed from unique devices that operate according to the laws of quantum mechanics. We show how quantum metadata can be managed within a software-definedmore » network using the OpenFlow protocol, and we describe how OpenFlow management of classical optical channels is compatible with emerging quantum communication protocols. We next give an example specification of the metadata needed to manage and control quantum physical layer (QPHY) behavior and we extend the OpenFlow interface to accommodate this quantum metadata. Here, we conclude by discussing near-term experimental efforts that can realize SDN’s principles for quantum communication.« less

OpenFlow arbitrated programmable network channels for managing quantum metadata

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dasari, Venkat R.; Humble, Travis S.

Quantum networks must classically exchange complex metadata between devices in order to carry out information for protocols such as teleportation, super-dense coding, and quantum key distribution. Demonstrating the integration of these new communication methods with existing network protocols, channels, and data forwarding mechanisms remains an open challenge. Software-defined networking (SDN) offers robust and flexible strategies for managing diverse network devices and uses. We adapt the principles of SDN to the deployment of quantum networks, which are composed from unique devices that operate according to the laws of quantum mechanics. We show how quantum metadata can be managed within a software-definedmore » network using the OpenFlow protocol, and we describe how OpenFlow management of classical optical channels is compatible with emerging quantum communication protocols. We next give an example specification of the metadata needed to manage and control quantum physical layer (QPHY) behavior and we extend the OpenFlow interface to accommodate this quantum metadata. Here, we conclude by discussing near-term experimental efforts that can realize SDN’s principles for quantum communication.« less

Student understanding of time dependence in quantum mechanics

NASA Astrophysics Data System (ADS)

Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.

2015-12-01

[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 quantum mechanics. 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 quantum mechanics. Evidence is also given that the problems persist throughout undergraduate instruction and into the graduate level.

Devil's staircases, quantum dimer models, and stripe formation in strong coupling models of quantum frustration.

NASA Astrophysics Data System (ADS)

Raman, Kumar; Papanikolaou, Stefanos; Fradkin, Eduardo

2007-03-01

We construct a two-dimensional microscopic model of interacting quantum dimers that displays an infinite number of periodic striped phases in its T=0 phase diagram. The phases form an incomplete devil's staircase and the period becomes arbitrarily large as the staircase is traversed. The Hamiltonian has purely short-range interactions, does not break any symmetries, and is generic in that it does not involve the fine tuning of a large number of parameters. Our model, a quantum mechanical analog of the Pokrovsky-Talapov model of fluctuating domain walls in two dimensional classical statistical mechanics, provides a mechanism by which striped phases with periods large compared to the lattice spacing can, in principle, form in frustrated quantum magnetic systems with only short-ranged interactions and no explicitly broken symmetries. Please see cond-mat/0611390 for more details.

Classical and quantum filaments in the ground state of trapped dipolar Bose gases

NASA Astrophysics Data System (ADS)

Cinti, Fabio; Boninsegni, Massimo

2017-07-01

We study, by quantum Monte Carlo simulations, the ground state of a harmonically confined dipolar Bose gas with aligned dipole moments and with the inclusion of a repulsive two-body potential of varying range. Two different limits can clearly be identified, namely, a classical one in which the attractive part of the dipolar interaction dominates and the system forms an ordered array of parallel filaments and a quantum-mechanical one, wherein filaments are destabilized by zero-point motion, and eventually the ground state becomes a uniform cloud. The physical character of the system smoothly evolves from classical to quantum mechanical as the range of the repulsive two-body potential increases. An intermediate regime is observed in which ordered filaments are still present, albeit forming different structures from the ones predicted classically; quantum-mechanical exchanges of indistinguishable particles across different filaments allow phase coherence to be established, underlying a global superfluid response.

An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions.

PubMed

Liu, Jian; Miller, William H

2011-03-14

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.

A modified Lax-Phillips scattering theory for quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strauss, Y., E-mail: ystrauss@cs.bgu.ac.il

The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical 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 quantum mechanical 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

Nilpotent Quantum Mechanics: Analogues and Applications

NASA Astrophysics Data System (ADS)

Marcer, Peter; Rowlands, Peter

2017-07-01

The most significant characteristic of nilpotent quantum mechanics 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 quantum mechanics, will apply.

A simple quantum mechanical treatment of scattering in nanoscale transistors

NASA Astrophysics Data System (ADS)

Venugopal, R.; Paulsson, M.; Goasguen, S.; Datta, S.; Lundstrom, M. S.

2003-05-01

We present a computationally efficient, two-dimensional quantum mechanical 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 quantum mechanical 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.

Separability and Non-Individuality: Is It Possible to Conciliate (At Least A Form Of) Einstein's Realism with Quantum Mechanics?

NASA Astrophysics Data System (ADS)

Krause, Décio; Arenhart, Jonas R. B.

2014-12-01

In this paper we argue that physical theories, including quantum mechanics, refer to some kind of `objects', even if only implicitly. We raise questions about the logico-mathematical apparatuses commonly employed in such theories, bringing to light some metaphysical presuppositions underlying such apparatuses. We point out to some incongruities in the discourse holding that quantum objects would be entities of some `new kind' while still adhering to the logico-mathematical framework we use to deal with classical objects. The use of such apparatus would hinder us from being in complete agreement with the ontological novelties the theories of quanta seem to advance. Thus, we join those who try to investigate a `logic of quantum mechanics', but from a different point of view: looking for a formal foundation for a supposed new ontology. As a consequence of this move, we can revisit Einstein's ideas on physical reality and propose that, by considering a new kind of object traditionally termed `non-individuals', it is possible to sustain that they still obey some of Einstein's conditions for `physical realities', so that it will be possible to talk of a `principle of separability' in a sense which is not in complete disagreement with quantum mechanics. So, Einstein's departure from quantum mechanics might be softened at least concerning a form of his realism, which sees separated physical objects as distinct `physical realities'.

A quantum renaissance

NASA Astrophysics Data System (ADS)

Aspelmeyer, Markus; Zeilinger, Anton

2008-07-01

Pure curiosity has been the driving force behind many groundbreaking experiments in physics. This is no better illustrated than in quantum mechanics, initially the physics of the extremely small. Since its beginnings in the 1920s and 1930s, researchers have wanted to observe the counterintuitive properties of quantum mechanics directly in the laboratory. However, because experimental technology was not sufficiently developed at the time, people like Niels Bohr, Albert Einstein, Werner Heisenberg and Erwin Schrödinger relied instead on "gedankenexperiments" (thought experiments) to investigate the quantum physics of individual particles, mainly electrons and photons.

Efficiency at Maximum Power Output of a Quantum-Mechanical Brayton Cycle

NASA Astrophysics Data System (ADS)

Yuan, Yuan; He, Ji-Zhou; Gao, Yong; Wang, Jian-Hui

2014-03-01

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.

Single-temperature quantum engine without feedback control.

PubMed

Yi, Juyeon; Talkner, Peter; Kim, Yong Woon

2017-08-01

A cyclically working quantum-mechanical engine that operates at a single temperature is proposed. Its energy input is delivered by a quantum measurement. The functioning of the engine does not require any feedback control. We analyze work, heat, and the efficiency of the engine for the case of a working substance that is governed by the laws of quantum mechanics and that can be adiabatically compressed and expanded. The obtained general expressions are exemplified for a spin in an adiabatically changing magnetic field and a particle moving in a potential with slowly changing shape.

Quantum Kibble-Zurek Mechanism in a Spin-1 Bose-Einstein Condensate

NASA Astrophysics Data System (ADS)

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.

Two types of potential functions and their use in the modeling of information: two applications from the social sciences.

PubMed

Haven, Emmanuel E

2015-01-01

In this paper we consider how two types of potential functions, the real and quantum potential can be shown to be of use in a social science context. The real potential function is a key ingredient in the Hamiltonian framework used in both classical and quantum mechanics. The quantum potential however emerges in a different way in quantum mechanics. In this paper we consider both potentials and we attempt to give them a social science interpretation within the setting of two applications.

Two types of potential functions and their use in the modeling of information: two applications from the social sciences

PubMed Central

Haven, Emmanuel E.

2015-01-01

In this paper we consider how two types of potential functions, the real and quantum potential can be shown to be of use in a social science context. The real potential function is a key ingredient in the Hamiltonian framework used in both classical and quantum mechanics. The quantum potential however emerges in a different way in quantum mechanics. In this paper we consider both potentials and we attempt to give them a social science interpretation within the setting of two applications. PMID:26539130

Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems

PubMed Central

Putz, Mihai V.

2009-01-01

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems. PMID:20087467

Path integrals for electronic densities, reactivity indices, and localization functions in quantum systems.

PubMed

Putz, Mihai V

2009-11-10

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.

Consciousness and values in the quantum universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stapp, H.P.

1985-01-01

Application of quantum mechanical description to neurophysiological processes appears to provide for a natural unification of the physical and humanistic sciences. The categories of thought used to represent physical and psychical processes become united, and the mechanical conception of man created by classical physics is replaced by a profoundly different quantum conception. This revised image of man allows human values to be rooted in contemporary science.

Eigenforms, Discrete Processes and Quantum Processes

NASA Astrophysics Data System (ADS)

Kauffman, Louis H.

2012-05-01

This essay is a discussion of the concept of eigenform, due to Heinz von Foerster, and its relationship with discrete physics and quantum mechanics. We interpret the square root of minus one as a simple oscillatory process - a clock, and as an eigenform. By taking a generalization of this identification of i as a clock and eigenform, we show how quantum mechanics emerges from discrete physics.

The Heisenberg Microscope: A Powerful Instructional Tool for Promoting Meta-Cognitive and Meta-Scientific Thinking on Quantum Mechanics and the "Nature of Science"

ERIC Educational Resources Information Center

Hadzidaki, Pandora

2008-01-01

In this paper, we present a multi-dimensional study concerning Heisenberg's "gamma ray microscope", a thought experiment, which is intimately connected with the historical development of quantum mechanics (QM), and also with the most disputed interpretations of quantum theory. In this study: (a) we investigate how philosophers of science read and…

Nonassociativity, supersymmetry, and hidden variables

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dzhunushaliev, Vladimir

2008-04-15

It is shown that the supersymmetric quantum mechanics has an octonionic generalization. The generalization is based on the inclusion of quaternions into octonions. The elements from the coset octonions/quaternions are unobservables because they cannot be considered as quantum operators as a consequence of their nonassociative properties. The idea that the octonionic generalization of the supersymmetric quantum mechanics describes an observable particle formed with unobservable ''particles'' is presented.

The Least Particle Theory

NASA Astrophysics Data System (ADS)

Hartsock, Robert

2011-10-01

The Least Particle Theory states that the universe was cast as a great sea of energy. MaX Planck declared a quantum of energy to be the least value in the universe. We declare the quantum of energy to be the least particle in the universe. Stephen Hawking declared quantum mechanics to be of no value in todays gross mechanics. That's like saying the number 1 has no place in mathematics.

Perspectives in Quantum Physics: Epistemological, Ontological and Pedagogical--An Investigation into Student and Expert Perspectives on the Physical Interpretation of Quantum Mechanics, with Implications for Modern Physics Instruction

ERIC Educational Resources Information Center

Baily, Charles Raymond

2011-01-01

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 quantum mechanics. Our studies suggest this notoriously difficult task may be frustrated by the intuitively "realist" perspectives of introductory…

Quantum-chemical Calculations in the Study of Antitumour Compounds

NASA Astrophysics Data System (ADS)

Luzhkov, V. B.; Bogdanov, G. N.

1986-01-01

The results of quantum-chemical calculations on antitumour preparations concerning the mechanism of their action at the electronic and molecular levels and structure-activity correlations are discussed in this review. Preparations whose action involves alkylating and free-radial mechanisms, complex-forming agents, and antimetabolites are considered. Modern quantum-chemical methods for calculations on biologically active substances are described. The bibliography includes 106 references.

Sachdev–Ye–Kitaev model as Liouville quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 quantum mechanics.

Quantum Hamiltonian daemons: Unitary analogs of combustion engines

NASA Astrophysics Data System (ADS)

Thesing, Eike P.; Gilz, Lukas; Anglin, James R.

2017-07-01

Hamiltonian daemons have recently been defined classically as small, closed Hamiltonian systems which can exhibit secular energy transfer from high-frequency to low-frequency degrees of freedom (steady downconversion), analogous to the steady transfer of energy in a combustion engine from the high terahertz frequencies of molecular excitations to the low kilohertz frequencies of piston motion [L. Gilz, E. P. Thesing, and J. R. Anglin, Phys. Rev. E 94, 042127 (2016), 10.1103/PhysRevE.94.042127]. Classical daemons achieve downconversion within a small, closed system by exploiting nonlinear resonances; the adiabatic theorem permits their operation but imposes nontrivial limitations on their efficiency. Here we investigate a simple example of a quantum mechanical daemon. In the correspondence regime it obeys similar efficiency limits to its classical counterparts, but in the strongly quantum mechanical regime the daemon operates in an entirely different manner. It maintains an engine-like behavior in a distinctly quantum mechanical form: a weight is lifted at a steady average speed through a long sequence of quantum jumps in momentum, at each of which a quantum of fuel is consumed. The quantum daemon can cease downconversion at any time through nonadiabatic Landau-Zener transitions, and continuing operation of the quantum daemon is associated with steadily growing entanglement between fast and slow degrees of freedom.

Controlling the thermoelectric effect by mechanical manipulation of the electron's quantum phase in atomic junctions.

PubMed

Aiba, Akira; Demir, Firuz; Kaneko, Satoshi; Fujii, Shintaro; Nishino, Tomoaki; Tsukagoshi, Kazuhito; Saffarzadeh, Alireza; Kirczenow, George; Kiguchi, Manabu

2017-08-11

The thermoelectric voltage developed across an atomic metal junction (i.e., a nanostructure in which one or a few atoms connect two metal electrodes) in response to a temperature difference between the electrodes, results from the quantum interference of electrons that pass through the junction multiple times after being scattered by the surrounding defects. Here we report successfully tuning this quantum interference and thus controlling the magnitude and sign of the thermoelectric voltage by applying a mechanical force that deforms the junction. The observed switching of the thermoelectric voltage is reversible and can be cycled many times. Our ab initio and semi-empirical calculations elucidate the detailed mechanism by which the quantum interference is tuned. We show that the applied strain alters the quantum phases of electrons passing through the narrowest part of the junction and hence modifies the electronic quantum interference in the device. Tuning the quantum interference causes the energies of electronic transport resonances to shift, which affects the thermoelectric voltage. These experimental and theoretical studies reveal that Au atomic junctions can be made to exhibit both positive and negative thermoelectric voltages on demand, and demonstrate the importance and tunability of the quantum interference effect in the atomic-scale metal nanostructures.

Analytic structure of the S-matrix for singular quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Camblong, Horacio E.; Epele, Luis N.; Fanchiotti, Huner

2015-06-15

The analytic structure of the S-matrix of singular quantum mechanics 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 quantum mechanics and their determination from the unitary family.

A New Quantum Proxy Multi-signature Scheme Using Maximally Entangled Seven-Qubit States

NASA Astrophysics Data System (ADS)

Cao, Hai-Jing; Zhang, Jia-Fu; Liu, Jian; Li, Zeng-You

2016-02-01

In this paper, we propose a new secure quantum proxy multi-signature scheme using seven-qubit entangled quantum state as quantum channels, which may have applications in e-payment system, e-government, e-business, etc. This scheme is based on controlled quantum teleportation. The scheme uses the physical characteristics of quantum mechanics to guarantee its anonymity, verifiability, traceability, unforgetability and undeniability.

Minimal Length Scale Scenarios for Quantum Gravity.

PubMed

Hossenfelder, Sabine

2013-01-01

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 quantum mechanics 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 quantum mechanics, 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.

Qubit assisted enhancement of quantum correlations in an optomechanical system

NASA Astrophysics Data System (ADS)

Chakraborty, Subhadeep; Sarma, Amarendra K.

2018-05-01

We perform a theoretical study on quantum correlations in an optomechanical system where the mechanical mirror is perturbatively coupled to an auxiliary qubit. In our study, we consider logarithmic negativity to quantify the degree of stationary entanglement between the cavity field and mechanical mirror, and, Gaussian quantum discord as a witness of the quantumness of the correlation beyond entanglement. Utilizing experimentally feasible parameters, we show that both entanglement and quantum discord enhance significantly with increase in mirror-qubit coupling. Moreover, we find that in presence of the mirror-qubit coupling entanglement could be generated at a considerably lower optomechanical coupling strength, which is also extremely robust against the environmental temperature. Overall, our proposed scheme offers some considerable advantages for realizing the continuous-variable quantum information and communication.

Composition in the Quantum World

NASA Astrophysics Data System (ADS)

Hall, Edward Jonathan

This thesis presents a problem for the foundations of quantum mechanics. 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 quantum mechanics. That quantum mechanics 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 quantum mechanics 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 quantum mechanics 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 this sense! In what follows I develop the principles needed to explore this problem, contrast it with the Measurement Problem, and consider, finally, how it should influence our judgments of the relative merits of the many extant interpretations of quantum mechanics.

Exploring the propagation of relativistic quantum wavepackets in the trajectory-based formulation

NASA Astrophysics Data System (ADS)

Tsai, Hung-Ming; Poirier, Bill

2016-03-01

In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schrödinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which both the Klein-Gordon and Dirac wave equations result in strange and counterintuitive wavepacket behaviors, even for free-particle Gaussians. These behaviors include zitterbewegung and other interference effects. As a potential remedy, this paper explores a new trajectory-based formulation of quantum mechanics, in which the wavefunction plays no role [Phys. Rev. X, 4, 040002 (2014)]. Quantum states are represented as ensembles of trajectories, whose mutual interaction is the source of all quantum effects observed in nature—suggesting a “many interacting worlds” interpretation. It is shown that the relativistic generalization of the trajectory-based formulation results in well-behaved free-particle Gaussian wavepacket solutions. In particular, probability density is positive and well-localized everywhere, and its spatial integral is conserved over time—in any inertial frame. Finally, the ensemble-averaged wavepacket motion is along a straight line path through spacetime. In this manner, the pathologies of the wave-based relativistic quantum theory, as applied to wavepacket propagation, are avoided.

Mixing Categories and Modal Logics in the Quantum Setting

NASA Astrophysics Data System (ADS)

Cinà, Giovanni

The study of the foundations of Quantum Mechanics, especially after the advent of Quantum Computation and Information, has benefited from the application of category-theoretic tools and modal logics to the analysis of Quantum processes: we witness a wealth of theoretical frameworks casted in either of the two languages. This paper explores the interplay of the two formalisms in the peculiar context of Quantum Theory. After a review of some influential abstract frameworks, we show how different modal logic frames can be extracted from the category of finite dimensional Hilbert spaces, connecting the Categorical Quantum Mechanics approach to some modal logics that have been proposed for Quantum Computing. We then apply a general version of the same technique to two other categorical frameworks, the `topos approach' of Doering and Isham and the sheaf-theoretic work on contextuality by Abramsky and Brandenburger, suggesting how some key features can be expressed with modal languages.

Generalized uncertainty principle: implications for black hole complementarity

NASA Astrophysics Data System (ADS)

Chen, Pisin; Ong, Yen Chin; Yeom, Dong-han

2014-12-01

At the heart of the black hole information loss paradox and the firewall controversy lies the conflict between quantum mechanics and general relativity. Much has been said about quantum corrections to general relativity, but much less in the opposite direction. It is therefore crucial to examine possible corrections to quantum mechanics due to gravity. Indeed, the Heisenberg Uncertainty Principle is one profound feature of quantum mechanics, which nevertheless may receive correction when gravitational effects become important. Such generalized uncertainty principle [GUP] has been motivated from not only quite general considerations of quantum mechanics and gravity, but also string theoretic arguments. We examine the role of GUP in the context of black hole complementarity. We find that while complementarity can be violated by large N rescaling if one assumes only the Heisenberg's Uncertainty Principle, the application of GUP may save complementarity, but only if certain N -dependence is also assumed. This raises two important questions beyond the scope of this work, i.e., whether GUP really has the proposed form of N -dependence, and whether black hole complementarity is indeed correct.

Another look through Heisenberg’s microscope

NASA Astrophysics Data System (ADS)

Boughn, Stephen; Reginatto, Marcel

2018-05-01

Heisenberg introduced his famous uncertainty relations in a seminal 1927 paper entitled The Physical Content of Quantum Kinematics and Mechanics. He motivated his arguments with a gedanken experiment, a gamma ray microscope to measure the position of a particle. A primary result was that, due to the quantum nature of light, there is an inherent uncertainty in the determinations of the particle’s position and momentum dictated by an indeterminacy relation, δ qδ p∼ h. Heisenberg offered this demonstration as ‘a direct physical interpretation of the [quantum mechanical] equation {{pq}}-{{qp}}=-{{i}}{\\hslash }’ but considered the indeterminacy relation to be much more than this. He also argued that it implies limitations on the very meanings of position and momentum and emphasised that these limitations are the source of the statistical character of quantum mechanics. In addition, Heisenberg hoped but was unable to demonstrate that the laws of quantum mechanics could be derived directly from the uncertainty relation. In this paper, we revisit Heisenberg’s microscope and argue that the Schrödinger equation for a free particle does indeed follow from the indeterminacy relation together with reasonable statistical assumptions.

Fundamental Quantum Mechanics--A Graphic Presentation

ERIC Educational Resources Information Center

Wise, M. N.; Kelley, T. G.

1977-01-01

Describes a presentation of basic quantum mechanics 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)

Teaching Reform and Practice of the Provincial-Level Quality Course: Quantum Mechanics

ERIC Educational Resources Information Center

Wang, Hongmei

2010-01-01

According to the actuality of Dezhou University, some useful reforms in teaching content, teaching method, and teaching measure are introduced, combining with the characteristics of the course of quantum mechanism in this article.

Conversations With Albert Einstein. II

ERIC Educational Resources Information Center

Shankland, R. S.

1973-01-01

Discusses Einstein's views on the role of Michelson-Morley, Fizeau, and Miller experiments in the development of relativity and his attitude toward the theories of new quantum mechanics. Indicates that Einstein's opposition to quantum mechanics is beyond dispute. (CC)

1−1=Counterfactual: on the potency and significance of quantum non-events

PubMed Central

Cohen, E.

2016-01-01

We study the unique role played in quantum mechanics by non-events or ‘counterfactuals’. Our earlier analysis of ‘quantum oblivion’ has revealed some subtle stages in the measurement process, which may end up in self-cancellation. To these findings, we now add two insights derived by two time-symmetric interpretations of quantum mechanics. (i) Like all quantum interactions, the non-event is formed by the conjunction of forward-plus-backward-evolving wave functions. (ii) Then, it is another feature of such dual evolutions, namely the involvement of negative masses and energies, that enables Nature to make some events ‘unhappen’ while leaving causal traces. PMID:27091159

1-1=Counterfactual: on the potency and significance of quantum non-events.

PubMed

Elitzur, A C; Cohen, E

2016-05-28

We study the unique role played in quantum mechanics by non-events or 'counterfactuals'. Our earlier analysis of 'quantum oblivion' has revealed some subtle stages in the measurement process, which may end up in self-cancellation. To these findings, we now add two insights derived by two time-symmetric interpretations of quantum mechanics. (i) Like all quantum interactions, the non-event is formed by the conjunction of forward-plus-backward-evolving wave functions. (ii) Then, it is another feature of such dual evolutions, namely the involvement of negative masses and energies, that enables Nature to make some events 'unhappen' while leaving causal traces. © 2016 The Author(s).

Equivalence principle and quantum mechanics: quantum simulation with entangled photons.

PubMed

Longhi, S

2018-01-15

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 quantum mechanics 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 Corrections to the 'Atomistic' MOSFET Simulations

NASA Technical Reports Server (NTRS)

Asenov, Asen; Slavcheva, G.; Kaya, S.; Balasubramaniam, R.

2000-01-01

We have introduced in a simple and efficient manner quantum mechanical corrections in our 3D 'atomistic' MOSFET simulator using the density gradient formalism. We have studied in comparison with classical simulations the effect of the quantum mechanical corrections on the simulation of random dopant induced threshold voltage fluctuations, the effect of the single charge trapping on interface states and the effect of the oxide thickness fluctuations in decanano MOSFETs with ultrathin gate oxides. The introduction of quantum corrections enhances the threshold voltage fluctuations but does not affect significantly the amplitude of the random telegraph noise associated with single carrier trapping. The importance of the quantum corrections for proper simulation of oxide thickness fluctuation effects has also been demonstrated.

Quantum healing of spacetime singularities: A review

NASA Astrophysics Data System (ADS)

Konkowski, D. A.; Helliwell, T. M.

2018-02-01

Singularities are commonplace in general relativistic spacetimes. It is natural to hope that they might be “healed” (or resolved) by the inclusion of quantum mechanics, either in the theory itself (quantum gravity) or, more modestly, in the description of the spacetime geodesic paths used to define them. We focus here on the latter, mainly using a procedure proposed by Horowitz and Marolf to test whether singularities in broad classes of spacetimes can be resolved by replacing geodesic paths with quantum wave packets. We list the spacetime singularities that various authors have studied in this context, and distinguish those which are healed quantum mechanically (QM) from those which remain singular. Finally, we mention some alternative approaches to healing singularities.

Can Quantum-Mechanical Description of Physical Reality Be Considered Correct?

NASA Astrophysics Data System (ADS)

Brassard, Gilles; Méthot, André Allan

2010-04-01

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 quantum mechanics. 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 quantum mechanics 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 quantum mechanics, or would at least violate Heisenberg’s Uncertainty Principle.

Path integrals, supersymmetric quantum mechanics, and the Atiyah-Singer index theorem for twisted Dirac

NASA Astrophysics Data System (ADS)

Fine, Dana S.; Sawin, Stephen

2017-01-01

Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time approximation to the propagator in a general class of imaginary-time quantum mechanics on a Riemannian manifold which ensure that these products converge. The limit defines a path integral which agrees pointwise with the heat kernel for a generalized Laplacian. The result is a rigorous construction of the propagator for supersymmetric quantum mechanics, with potential, as a path integral. Further, the class of Laplacians includes the square of the twisted Dirac operator, which corresponds to an extension of N = 1/2 supersymmetric quantum mechanics. General results on the rate of convergence of the approximate path integrals suffice in this case to derive the local version of the Atiyah-Singer index theorem.

Multi-dimensional single-spin nano-optomechanics with a levitated nanodiamond

NASA Astrophysics Data System (ADS)

Neukirch, Levi P.; von Haartman, Eva; Rosenholm, Jessica M.; Nick Vamivakas, A.

2015-10-01

Considerable advances made in the development of nanomechanical and nano-optomechanical devices have enabled the observation of quantum effects, improved sensitivity to minute forces, and provided avenues to probe fundamental physics at the nanoscale. Concurrently, solid-state quantum emitters with optically accessible spin degrees of freedom have been pursued in applications ranging from quantum information science to nanoscale sensing. Here, we demonstrate a hybrid nano-optomechanical system composed of a nanodiamond (containing a single nitrogen-vacancy centre) that is levitated in an optical dipole trap. The mechanical state of the diamond is controlled by modulation of the optical trapping potential. We demonstrate the ability to imprint the multi-dimensional mechanical motion of the cavity-free mechanical oscillator into the nitrogen-vacancy centre fluorescence and manipulate the mechanical system's intrinsic spin. This result represents the first step towards a hybrid quantum system based on levitating nanoparticles that simultaneously engages optical, phononic and spin degrees of freedom.

Wigner's quantum phase-space current in weakly-anharmonic weakly-excited two-state systems

NASA Astrophysics Data System (ADS)

Kakofengitis, Dimitris; Steuernagel, Ole

2017-09-01

There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current J . This current reveals fine details of quantum dynamics —finer than is ordinarily thought accessible according to quantum folklore invoking Heisenberg's uncertainty principle. Here, we focus on the simplest, most intuitive, and analytically accessible aspects of J. We investigate features of J for bound states of time-reversible, weakly-anharmonic one-dimensional quantum-mechanical systems which are weakly-excited. We establish that weakly-anharmonic potentials can be grouped into three distinct classes: hard, soft, and odd potentials. We stress connections between each other and the harmonic case. We show that their Wigner current fieldline patterns can be characterised by J's discrete stagnation points, how these arise and how a quantum system's dynamics is constrained by the stagnation points' topological charge conservation. We additionally show that quantum dynamics in phase space, in the case of vanishing Planck constant ℏ or vanishing anharmonicity, does not pointwise converge to classical dynamics.

Atomistic insight into the catalytic mechanism of glycosyltransferases by combined quantum mechanics/molecular mechanics (QM/MM) methods.

PubMed

Tvaroška, Igor

2015-02-11

Glycosyltransferases catalyze the formation of glycosidic bonds by assisting the transfer of a sugar residue from donors to specific acceptor molecules. Although structural and kinetic data have provided insight into mechanistic strategies employed by these enzymes, molecular modeling studies are essential for the understanding of glycosyltransferase catalyzed reactions at the atomistic level. For such modeling, combined quantum mechanics/molecular mechanics (QM/MM) methods have emerged as crucial. These methods allow the modeling of enzymatic reactions by using quantum mechanical methods for the calculation of the electronic structure of the active site models and treating the remaining enzyme environment by faster molecular mechanics methods. Herein, the application of QM/MM methods to glycosyltransferase catalyzed reactions is reviewed, and the insight from modeling of glycosyl transfer into the mechanisms and transition states structures of both inverting and retaining glycosyltransferases are discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.

Wave-Mechanical Properties of Stationary States.

ERIC Educational Resources Information Center

Holden, Alan

This monograph is a review of the quantum mechanical concepts presented in two other monographs, "The Nature of Atoms" and "Bonds Between Atoms," by the same author. It is assumed the reader is familiar with these ideas. The monograph sketches only those aspects of quantum mechanics that are of most direct use in picturing and calculating the…

Estimation of the Young’s modulus of cellulose Iß by MM3 and quantum mechanics

USDA-ARS?s Scientific Manuscript database

Young’s modulus provides a measure of the resistance to deformation of an elastic material. In this study, modulus estimations for models of cellulose Iß relied on calculations performed with molecular mechanics (MM) and quantum mechanics (QM) programs. MM computations used the second generation emp...

Young’s modulus calculations for cellulose Iß by MM3 and quantum mechanics

USDA-ARS?s Scientific Manuscript database

Quantum mechanics (QM) and molecular mechanics (MM) calculations were performed to elucidate Young’s moduli for a series of cellulose Iß models. Computations using the second generation empirical force field MM3 with a disaccharide cellulose model, 1,4'-O-dimethyl-ß-cellobioside (DMCB), and an analo...

Observables, measurements and phase operators from a Bohmian perspective

NASA Technical Reports Server (NTRS)

Daumer, Martin; Goldstein, Sheldon

1993-01-01

Bohmian mechanics is a deterministic theory of point particles in motion. While avoiding all the paradoxes of nonrelativistic quantum mechanics, it yields the quantum formalism itself--especially the role of self-adjoint operators--as a macroscopic measurement formalism. As an 'application' it is shown that much of the confusion connected with the phase operator for the electromagnetic field arises from a misunderstanding of the role of operators in quantum theory.

Zero-point angular momentum of supersymmetric Penning trap

NASA Astrophysics Data System (ADS)

Zhang, Jian-zu; Xu, Qiang

2000-10-01

The quantum behavior of supersymmetric Penning trap, specially the superpartner of its angular momentum, is investigated in the formulation of multi-dimensional semiunitary transformation of supersymmetric quantum mechanics. In the limit case of vanishing kinetic energy it is found that its lowest angular momentum is 3ℏ/2, which provides a possibility of directly checking the idea of supersymmetric quantum mechanics and thus suggests a possible experimental verification about this prediction.

Time Asymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

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 quantum mechanical 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 quantum mechanical 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 quantum mechanics.

Locality, reflection, and wave-particle duality

NASA Astrophysics Data System (ADS)

Mugur-Schächter, Mioara

1987-08-01

Bell's theorem is believed to establish that the quantum mechanical predictions do not generally admit a causal representation compatible with Einsten's principle of separability, thereby proving incompatibility between quantum mechanics and relativity. This interpretation is contested via two convergent approaches which lead to a sharp distinction between quantum nonseparability and violation of Einstein's theory of relativity. In a first approach we explicate from the quantum mechanical formalism a concept of “reflected dependence.” Founded on this concept, we produce a causal representation of the quantum mechanical probability measure involved in Bell's proof, which is clearly separable in Einstein's sense, i.e., it does not involve supraluminal velocities, and nevertheless is “nonlocal” in Bell's sense. So Bell locality and Einstein separability are distinct qualifications, and Bell nonlocality (or Bell nonseparability) and Einstein separability are not incompatible. It is then proved explicitly that with respect to the mentioned representation Bell's derivation does not hold. So Bell's derivation does not establish that any Einstein-separable representation is incompatible with quantum mechanics. This first—negative—conclusion is a syntactic fact. The characteristics of the representation and of the reasoning involved in the mentioned counterexample to the usual interpretation of Bell's theorem suggest that the representation used—notwithstanding its ability to bring forth the specified syntactic fact—is not factually true. Factual truth and syntactic properties also have to be radically distinguished in their turn. So, in a second approach, starting from de Broglie's initial relativistic model of a microsystem, a deeper, factually acceptable representation is constructed. The analyses leading to this second representation show that quantum mechanics does indeed involve basically a certain sort of nonseparability, called here de Broglie-Bohr quantum nonseparability. But the de Broglie-Bohr quantum nonseparability is shown to stem directly from the relativistic character of the considerations which led Louis de Broglie to the fundamental relation p = h/λ, thereby being essentially consistent with relativity. As to Einstein separability, it appears to be a still insufficiently specified concept of which a future, improved specification, will probably be explicitly harmonizable with the de Broglie-Bohr quantum nonseparability. The ensemble of the conclusions obtained here brings forth a new concept of causality, a concept of folded, zigzag, reflexive causality, with respect to which the type of causality conceived of up to now appears as a particular case of outstretched, one-way causality. The reflexive causality is found compatible with the results of Aspect's experiment, and it suggests new experiments. Considered globally, the conclusions obtained in the present work might convert the conceptual situation created by Bell's proof into a process of unification of quantum mechanics and relativity.

Computational applications of the many-interacting-worlds interpretation of quantum mechanics.

PubMed

Sturniolo, Simone

2018-05-01

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 quantum mechanics. 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.

Quantum Proxy Multi-Signature Scheme Using Genuinely Entangled Six Qubits State

NASA Astrophysics Data System (ADS)

Cao, Hai-Jing; Wang, Huai-Sheng; Li, Peng-Fei

2013-04-01

A quantum proxy multi-signature scheme is presented based on controlled teleportation. Genuinely entangled six qubits quantum state functions as quantum channel. The scheme uses the physical characteristics of quantum mechanics to implement delegation, signature and verification. Quantum key distribution and one-time pad are adopted in our scheme, which could guarantee not only the unconditional security of the scheme but also the anonymity of the messages owner.

Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment

NASA Astrophysics Data System (ADS)

Yao, Xi-Wei; Wang, Hengyan; Liao, Zeyang; Chen, Ming-Cheng; Pan, Jian; Li, Jun; Zhang, Kechao; Lin, Xingcheng; Wang, Zhehui; Luo, Zhihuang; Zheng, Wenqiang; Li, Jianzhong; Zhao, Meisheng; Peng, Xinhua; Suter, Dieter

2017-07-01

Processing of digital images is continuously gaining in volume and relevance, with concomitant demands on data storage, transmission, and processing power. Encoding the image information in quantum-mechanical systems instead of classical ones and replacing classical with quantum information processing may alleviate some of these challenges. By encoding and processing the image information in quantum-mechanical systems, we here demonstrate the framework of quantum image processing, where a pure quantum state encodes the image information: we encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states. Our quantum image representation reduces the required number of qubits compared to existing implementations, and we present image processing algorithms that provide exponential speed-up over their classical counterparts. For the commonly used task of detecting the edge of an image, we propose and implement a quantum algorithm that completes the task with only one single-qubit operation, independent of the size of the image. This demonstrates the potential of quantum image processing for highly efficient image and video processing in the big data era.

Does an Emphasis on the Concept of Quantum States Enhance Students' Understanding of Quantum Mechanics?

NASA Astrophysics Data System (ADS)

Greca, Ileana Maria; Freire, Olival

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 quantum mechanics (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.

Quantum indistinguishability in chemical reactions.

PubMed

Fisher, Matthew P A; Radzihovsky, Leo

2018-05-15

Quantum indistinguishability plays a crucial role in many low-energy physical phenomena, from quantum fluids to molecular spectroscopy. It is, however, typically ignored in most high-temperature processes, particularly for ionic coordinates, implicitly assumed to be distinguishable, incoherent, and thus well approximated classically. We explore enzymatic chemical reactions involving small symmetric molecules and argue that in many situations a full quantum treatment of collective nuclear degrees of freedom is essential. Supported by several physical arguments, we conjecture a "quantum dynamical selection" (QDS) rule for small symmetric molecules that precludes chemical processes that involve direct transitions from orbitally nonsymmetric molecular states. As we propose and discuss, the implications of the QDS rule include ( i ) a differential chemical reactivity of para- and orthohydrogen, ( ii ) a mechanism for inducing intermolecular quantum entanglement of nuclear spins, ( iii ) a mass-independent isotope fractionation mechanism, ( iv ) an explanation of the enhanced chemical activity of "reactive oxygen species", ( v ) illuminating the importance of ortho-water molecules in modulating the quantum dynamics of liquid water, and ( vi ) providing the critical quantum-to-biochemical linkage in the nuclear spin model of the (putative) quantum brain, among others.

Nuclear rotations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bertsch, G.F.; Janssens, R.V.

1997-07-01

An analysis of the gamma-ray spectra produced using the quantum mechanical rotational energy formula is presented for nuclei with large angular momentum. This analysis is suitable for quantum mechanics, modern physics, or nuclear physics courses. (AIP) {copyright}{ital 1997 American Institute of Physics}

Loss of coherence and memory effects in quantum dynamics Loss of coherence and memory effects in quantum dynamics

NASA Astrophysics Data System (ADS)

Benatti, Fabio; Floreanini, Roberto; Scholes, Greg

2012-08-01

The last years have witnessed fast growing developments in the use of quantum mechanics in technology-oriented and information-related fields, especially in metrology, in the developments of nano-devices and in understanding highly efficient transport processes. The consequent theoretical and experimental outcomes are now driving new experimental tests of quantum mechanical effects with unprecedented accuracies that carry with themselves the concrete possibility of novel technological spin-offs. Indeed, the manifold advances in quantum optics, atom and ion manipulations, spintronics and nano-technologies are allowing direct experimental verifications of new ideas and their applications to a large variety of fields. All of these activities have revitalized interest in quantum mechanics and created a unique framework in which theoretical and experimental physics have become fruitfully tangled with information theory, computer, material and life sciences. This special issue aims to provide an overview of what is currently being pursued in the field and of what kind of theoretical reference frame is being developed together with the experimental and theoretical results. It consists of three sections: 1. Memory effects in quantum dynamics and quantum channels 2. Driven open quantum systems 3. Experiments concerning quantum coherence and/or decoherence The first two sections are theoretical and concerned with open quantum systems. In all of the above mentioned topics, the presence of an external environment needs to be taken into account, possibly in the presence of external controls and/or forcing, leading to driven open quantum systems. The open system paradigm has proven to be central in the analysis and understanding of many basic issues of quantum mechanics, such as the measurement problem, quantum communication and coherence, as well as for an ever growing number of applications. The theory is, however, well-settled only when the so-called Markovian or memoryless, approximation applies. When strong coupling or long environmental relaxation times make memory effects important for a realistic description of the dynamics, new strategies are asked for and the assessment of the general structure of non-Markovian dynamical equations for realistic systems is a crucial issue. The impact of quantum phenomena such as coherence and entanglement in biology has recently started to be considered as a possible source of the high efficiency of certain biological mechanisms, including e.g. light harvesting in photosynthesis and enzyme catalysis. In this effort, the relatively unknown territory of driven open quantum systems is being explored from various directions, with special attention to the creation and stability of coherent structures away from thermal equilibrium. These investigations are likely to advance our understanding of the scope and role of quantum mechanics in living systems; at the same time they provide new ideas for the developments of next generations of devices implementing highly efficient energy harvesting and conversion. The third section concerns experimental studies that are currently being pursued. Multidimensional nonlinear spectroscopy, in particular, has played an important role in enabling experimental detection of the signatures of coherence. Recent remarkable results suggest that coherence—both electronic and vibrational—survive for substantial timescales even in complex biological systems. The papers reported in this issue describe work at the forefront of this field, where researchers are seeking a detailed understanding of the experimental signatures of coherence and its implications for light-induced processes in biology and chemistry.

"Electronium": A Quantum Atomic Teaching Model.

ERIC Educational Resources Information Center

Budde, Marion; Niedderer, Hans; Scott, Philip; Leach, John

2002-01-01

Outlines an alternative atomic model to the probability model, the descriptive quantum atomic model Electronium. Discusses the way in which it is intended to support students in learning quantum-mechanical concepts. (Author/MM)

EDITORIAL: Squeezed states and uncertainty relations

NASA Astrophysics Data System (ADS)

Jauregue-Renaud, Rocio; Kim, Young S.; Man'ko, Margarita A.; Moya-Cessa, Hector

2004-06-01

This special issue of Journal of Optics B: Quantum and Semiclassical Optics is composed mainly of extended versions of talks and papers presented at the Eighth International Conference on Squeezed States and Uncertainty Relations held in Puebla, Mexico on 9-13 June 2003. The Conference was hosted by Instituto de Astrofísica, Óptica y Electrónica, and the Universidad Nacional Autónoma de México. This series of meetings began at the University of Maryland, College Park, USA, in March 1991. The second and third workshops were organized by the Lebedev Physical Institute in Moscow, Russia, in 1992 and by the University of Maryland Baltimore County, USA, in 1993, respectively. Afterwards, it was decided that the workshop series should be held every two years. Thus the fourth meeting took place at the University of Shanxi in China and was supported by the International Union of Pure and Applied Physics (IUPAP). The next three meetings in 1997, 1999 and 2001 were held in Lake Balatonfüred, Hungary, in Naples, Italy, and in Boston, USA, respectively. All of them were sponsored by IUPAP. The ninth workshop will take place in Besançon, France, in 2005. The conference has now become one of the major international meetings on quantum optics and the foundations of quantum mechanics, where most of the active research groups throughout the world present their new results. Accordingly this conference has been able to align itself to the current trend in quantum optics and quantum mechanics. The Puebla meeting covered most extensively the following areas: quantum measurements, quantum computing and information theory, trapped atoms and degenerate gases, and the generation and characterization of quantum states of light. The meeting also covered squeeze-like transformations in areas other than quantum optics, such as atomic physics, nuclear physics, statistical physics and relativity, as well as optical devices. There were many new participants at this meeting, particularly from Latin American countries including, of course, Mexico. There were many talks on the subjects traditionally covered in this conference series, including quantum fluctuations, different forms of squeezing, unlike kinds of nonclassical states of light, and distinct representations of the quantum superposition principle, such as even and odd coherent states. The entanglement phenomenon, frequently in the form of the EPR paradox, is responsible for the main advantages of quantum engineering compared with classical methods. Even though entanglement has been known since the early days of quantum mechanics, its properties, such as the most appropriate entanglement measures, are still under current investigation. The phenomena of dissipations and decoherence of the initial pure states are very important because the fast decoherence can destroy all the advantages of quantum processes in teleportation, quantum computing and image processing. Due to this, methods of controlling the decoherence, such as by the use of different kinds of nonlinearities and deformations, are also under study. From the very beginning of quantum mechanics, the uncertainty relations were basic inequalities distinguishing the classical and quantum worlds. Among the theoretical methods for quantum optics and quantum mechanics, this conference covered phase space and group representations, such as the Wigner and probability distribution functions, which provide an alternative approach to the Schr\\"odinger or Heisenberg picture. Different forms of probability representations of quantum states are important tools to be applied in studying various quantum phenomena, such as quantum interference, decoherence and quantum tomography. They have been established also as a very useful tool in all branches of classical optics. From the mathematical point of view, it is well known that the coherent and squeezed states are representations of the Lorentz group. It was noted throughout the conference that another form of the Lorentz group, namely, the 2 x 2 representation of the SL(2,c) group, is becoming more prominent while providing the mathematical basis for the Poincaré sphere, entanglement, qubits and decoherence, as well as classical ray optics traditionally based on 2 x 2 `ABCD' matrices. The contributions of this special issue cover the most recent trends in all areas of quantum optics and the foundations of quantum mechanics.

Some thoughts about consciousness: from a quantum mechanics perspective.

PubMed

Gargiulo, Gerald J

2013-08-01

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 quantum mechanics 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.

An Introduction to Quantum Theory

NASA Astrophysics Data System (ADS)

Greensite, Jeff

2017-02-01

Written in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica® codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics. Supplementary Mathematica codes available within Book Information

Quantum-mechanical engines working with an ideal gas with a finite number of particles confined in a power-law trap

NASA Astrophysics Data System (ADS)

Wang, Jianhui; Ma, Yongli; He, Jizhou

2015-07-01

Based on quantum thermodynamic processes, we make a quantum-mechanical (QM) extension of the typical heat engine cycles, such as the Carnot, Brayton, Otto, Diesel cycles, etc., with no introduction of the concept of temperature. When these QM engine cycles are implemented by an ideal gas confined in an arbitrary power-law trap, a relation between the quantum adiabatic exponent and trap exponent is found. The differences and similarities between the efficiency of a given QM engine cycle and its classical counterpart are revealed and discussed.

Generalization of uncertainty relation for quantum and stochastic systems

NASA Astrophysics Data System (ADS)

Koide, T.; Kodama, T.

2018-06-01

The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable to the Gross-Pitaevskii equation and the Navier-Stokes-Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantum mechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions.

The path integral on the Poincaré upper half plane and for Liouville quantum mechanics

NASA Astrophysics Data System (ADS)

Grosche, C.; Steiner, F.

1987-08-01

We present a rigorous path integral treatment of free motion on the Poincaré upper half plane. The Poincaré upper half plane, as a riemannian manifold, has recently become important in string theory and in the theory of quantum chaos. The calculation is done by a time-transformation and the use of the canonical method for determining quantum corrections to the classical lagrangian. Furthermore, we shall show that the same method also works for Liouville quantum mechanics. In both cases, the energy spectrum and the normalized wavefunctions are determined.

Determinism, independence, and objectivity are incompatible.

PubMed

Ionicioiu, Radu; Mann, Robert B; Terno, Daniel R

2015-02-13

Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we study the mutual compatibility of apparently reasonable classical assumptions. We analyze a version of the delayed-choice experiment which ostensibly combines determinism, independence of hidden variables on the conducted experiments, and wave-particle objectivity (the assertion that quantum systems are, at any moment, either particles or waves, but not both). These three ideas are incompatible with any theory, not only with quantum mechanics.

Model for quantum effects in stellar collapse

NASA Astrophysics Data System (ADS)

Arderucio-Costa, Bruno; Unruh, William G.

2018-01-01

We present a simple model for stellar collapse and evaluate the quantum mechanical stress-energy tensor to argue that quantum effects do not play an important role for the collapse of astrophysical objects.

Quantum thermalization through entanglement in an isolated many-body system.

PubMed

Kaufman, Adam M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Schittko, Robert; Preiss, Philipp M; Greiner, Markus

2016-08-19

Statistical mechanics relies on the maximization of entropy in a system at thermal equilibrium. However, an isolated quantum many-body system initialized in a pure state remains pure during Schrödinger evolution, and in this sense it has static, zero entropy. We experimentally studied the emergence of statistical mechanics in a quantum state and observed the fundamental role of quantum entanglement in facilitating this emergence. Microscopy of an evolving quantum system indicates that the full quantum state remains pure, whereas thermalization occurs on a local scale. We directly measured entanglement entropy, which assumes the role of the thermal entropy in thermalization. The entanglement creates local entropy that validates the use of statistical physics for local observables. Our measurements are consistent with the eigenstate thermalization hypothesis. Copyright © 2016, American Association for the Advancement of Science.

Quantum Bayesian networks with application to games displaying Parrondo's paradox

NASA Astrophysics Data System (ADS)

Pejic, Michael

Bayesian networks and their accompanying graphical models are widely used for prediction and analysis across many disciplines. We will reformulate these in terms of linear maps. This reformulation will suggest a natural extension, which we will show is equivalent to standard textbook quantum mechanics. Therefore, this extension will be termed quantum. However, the term quantum should not be taken to imply this extension is necessarily only of utility in situations traditionally thought of as in the domain of quantum mechanics. In principle, it may be employed in any modelling situation, say forecasting the weather or the stock market---it is up to experiment to determine if this extension is useful in practice. Even restricting to the domain of quantum mechanics, with this new formulation the advantages of Bayesian networks can be maintained for models incorporating quantum and mixed classical-quantum behavior. The use of these will be illustrated by various basic examples. Parrondo's paradox refers to the situation where two, multi-round games with a fixed winning criteria, both with probability greater than one-half for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probabilitygreater than one-half. Using the extended Bayesian networks, we will formulate and analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox, finding bounds for the discrepancy from naive expectations for the occurrence of the paradox. A quantum paradox inspired by Parrondo's paradox will also be analyzed. We will prove a bound for the discrepancy from naive expectations for this paradox as well. Games involving quantum walks that achieve this bound will be presented.

Lyapounov variable: Entropy and measurement in quantum mechanics

PubMed Central

Misra, B.; Prigogine, I.; Courbage, M.

1979-01-01

We discuss the question of the dynamical meaning of the second law of thermodynamics in the framework of quantum mechanics. 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 quantum mechanics. It is found that no dynamical variable with the characteristic properties of nonequilibrium entropy can be defined in the standard formulation of quantum mechanics. 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 quantum mechanics. PMID:16578757

Geometric reduction of dynamical nonlocality in nanoscale quantum circuits.

PubMed

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.

Quantum Mechanical Enhancement of the Random Dopant Induced Threshold Voltage Fluctuations and Lowering in Sub 0.1 Micron MOSFETs

NASA Technical Reports Server (NTRS)

Asenov, Asen; Slavcheva, G.; Brown, A. R.; Davies, J. H.; Saini, Subhash

1999-01-01

A detailed study of the influence of quantum effects in the inversion layer on the random dopant induced threshold voltage fluctuations and lowering in sub 0.1 micron MOSFETs has been performed. This has been achieved using a full 3D implementation of the density gradient (DG) formalism incorporated in our previously published 3D 'atomistic' simulation approach. This results in a consistent, fully 3D, quantum mechanical picture which implies not only the vertical inversion layer quantisation but also the lateral confinement effects manifested by current filamentation in the 'valleys' of the random potential fluctuations. We have shown that the net result of including quantum mechanical effects, while considering statistical fluctuations, is an increase in both threshold voltage fluctuations and lowering.

Short distance modification of the quantum virial theorem

NASA Astrophysics Data System (ADS)

Zhao, Qin; Faizal, Mir; Zaz, Zaid

2017-07-01

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

Quantum interactive learning tutorial on the double-slit experiment to improve student understanding of quantum mechanics

NASA Astrophysics Data System (ADS)

Sayer, Ryan; Maries, Alexandru; Singh, Chandralekha

2017-06-01

Learning quantum mechanics 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 quantum mechanics 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 quantum mechanics. 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 quantum mechanics 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.

Understanding Quantum Numbers in General Chemistry Textbooks

ERIC Educational Resources Information Center

Niaz, Mansoor; Fernandez, Ramon

2008-01-01

Quantum numbers and electron configurations form an important part of the general chemistry curriculum and textbooks. The objectives of this study are: (1) Elaboration of a framework based on the following aspects: (a) Origin of the quantum hypothesis, (b) Alternative interpretations of quantum mechanics, (c) Differentiation between an orbital and…

Quantum Computer Games: Schrodinger Cat and Hounds

ERIC Educational Resources Information Center

Gordon, Michal; Gordon, Goren

2012-01-01

The quantum computer game "Schrodinger cat and hounds" is the quantum extension of the well-known classical game fox and hounds. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. "Schrodinger cat and hounds" demonstrates the effects of superposition, destructive and constructive interference, measurements and…

Strong quantum squeezing of mechanical resonator via parametric amplification and coherent feedback

NASA Astrophysics Data System (ADS)

You, Xiang; Li, Zongyang; Li, Yongmin

2017-12-01

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.

Charge transport model in nanodielectric composites based on quantum tunneling mechanism and dual-level traps

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Guochang; Chen, George, E-mail: gc@ecs.soton.ac.uk, E-mail: sli@mail.xjtu.edu.cn; School of Electronic and Computer Science, University of Southampton, Southampton SO17 1BJ

Charge transport properties in nanodielectrics present different tendencies for different loading concentrations. The exact mechanisms that are responsible for charge transport in nanodielectrics are not detailed, especially for high loading concentration. A charge transport model in nanodielectrics has been proposed based on quantum tunneling mechanism and dual-level traps. In the model, the thermally assisted hopping (TAH) process for the shallow traps and the tunnelling process for the deep traps are considered. For different loading concentrations, the dominant charge transport mechanisms are different. The quantum tunneling mechanism plays a major role in determining the charge conduction in nanodielectrics with high loadingmore » concentrations. While for low loading concentrations, the thermal hopping mechanism will dominate the charge conduction process. The model can explain the observed conductivity property in nanodielectrics with different loading concentrations.« less

On the Reasonable and Unreasonable Effectiveness of Mathematics in Classical and Quantum Physics

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2011-03-01

The point of departure for this article is Werner Heisenberg's remark, made in 1929: "It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which seems entirely adequate for the treatment of atomic processes." The cost of this discovery, at least in Heisenberg's and related interpretations of quantum mechanics (such as that of Niels Bohr), is that, in contrast to classical mechanics, the mathematical scheme in question no longer offers a description, even an idealized one, of quantum objects and processes. This scheme only enables predictions, in general, probabilistic in character, of the outcomes of quantum experiments. As a result, a new type of the relationships between mathematics and physics is established, which, in the language of Eugene Wigner adopted in my title, indeed makes the effectiveness of mathematics unreasonable in quantum but, as I shall explain, not in classical physics. The article discusses these new relationships between mathematics and physics in quantum theory and their implications for theoretical physics—past, present, and future.

Dynamical Correspondence in a Generalized Quantum Theory

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2015-05-01

In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general classes of abstractly defined Jordan algebras (JB- and JBW-algebras). One particularly important distinguishing property was identified by Alfsen and Shultz and is the existence of a dynamical correspondence. It reproduces the dual role of the selfadjoint operators as observables and generators of dynamical groups in quantum mechanics. In the paper, this concept is extended to another class of nonassociative algebras, arising from recent studies of the quantum logics with a conditional probability calculus and particularly of those that rule out third-order interference. The conditional probability calculus is a mathematical model of the Lüders-von Neumann quantum measurement process, and third-order interference is a property of the conditional probabilities which was discovered by Sorkin (Mod Phys Lett A 9:3119-3127, 1994) and which is ruled out by quantum mechanics. It is shown then that the postulates that a dynamical correspondence exists and that the square of any algebra element is positive still characterize, in the class considered, those algebras that emerge from the selfadjoint parts of C*-algebras equipped with the Jordan product. Within this class, the two postulates thus result in ordinary quantum mechanics using the complex Hilbert space or, vice versa, a genuine generalization of quantum theory must omit at least one of them.

Integrability versus Thermalizability in Isolated Quantum Systems

NASA Astrophysics Data System (ADS)

Olshanii, Maxim

2012-02-01

The purpose of this presentation is to assess the status of our understanding of the transition from integrability to thermalizability in isolated quantum systems. In Classical Mechanics, the boundary stripe between the two is relatively sharp: its integrability edge is marked by the appearance of finite Lyapunov's exponents that further converge to a unique value when the ergodicity edge is reached. Classical ergodicity is a universal property: if a system is ergodic, then every observable attains its microcanonical value in the infinite time average over the trajectory. On the contrary, in Quantum Mechanics, Lyapunov's exponents are always zero. Furthermore, since quantum dynamics necessarily invokes coherent superpositions of eigenstates of different energy, projectors to the eigenstates become more relevant; those in turn never thermalize. All of the above indicates that in quantum many-body systems, (a) the integrability-thermalizability transition is smooth, and (b) the degree of thermalizability is not absolute like in classical mechanics, but it is relative to the class of observables of interest. In accordance with these observations, we propose a concrete measure of the degree of quantum thermalizability, consistent with the expected empirical manifestations of it. As a practical application of this measure, we devise a unified recipe for choosing an optimal set of conserved quantities to govern the after-relaxation values of observables, in both integrable quantum systems and in quantum systems in between integrable and thermalizable.

Quantum formalism for classical statistics

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-06-01

In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schrödinger picture that keeps track of the local probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity.

Consistent resolution of some relativistic quantum paradoxes

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2002-12-01

A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse, Bohm's formulation of the Einstein-Podolsky-Rosen paradox, and Hardy's paradox. It is argued that wave function collapse is not needed for introducing probabilities into relativistic quantum mechanics, and in any case should never be thought of as a physical process. Alternative approaches to stochastic time dependence can be used to construct a physical picture of the measurement process that is less misleading than collapse models. In particular, one can employ a coarse-grained but fully quantum-mechanical description in which particles move along trajectories, with behavior under Lorentz transformations the same as in classical relativistic physics, and detectors are triggered by particles reaching them along such trajectories. States entangled between spacelike separate regions are also legitimate quantum descriptions, and can be consistently handled by the formalism presented here. The paradoxes in question arise because of using modes of reasoning which, while correct for classical physics, are inconsistent with the mathematical structure of quantum theory, and are resolved (or tamed) by using a proper quantum analysis. In particular, there is no need to invoke, nor any evidence for, mysterious long-range superluminal influences, and thus no incompatibility, at least from this source, between relativity theory and quantum mechanics.

Quantum-mechanical treatment of an electron undergoing synchrotron radiation.

NASA Technical Reports Server (NTRS)

White, D.

1972-01-01

The problem of an electron moving perpendicular to an intense magnetic field is approached from the framework of quantum mechanics. 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.

Noncommutative quantum mechanics

NASA Astrophysics Data System (ADS)

Gamboa, J.; Loewe, M.; Rojas, J. C.

2001-09-01

A general noncommutative quantum mechanical 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 quantum mechanical 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.

Variational method for nonconservative field theories: Formulation and two PT-symmetric case examples

NASA Astrophysics Data System (ADS)

Restrepo, Juan; Ciuti, Cristiano; Favero, Ivan

2014-01-01

This Letter investigates a hybrid quantum system combining cavity quantum electrodynamics and optomechanics. The Hamiltonian problem of a photon mode coupled to a two-level atom via a Jaynes-Cummings coupling and to a mechanical mode via radiation pressure coupling is solved analytically. The atom-cavity polariton number operator commutes with the total Hamiltonian leading to an exact description in terms of tripartite atom-cavity-mechanics polarons. We demonstrate the possibility to obtain cooling of mechanical motion at the single-polariton level and describe the peculiar quantum statistics of phonons in such an unconventional regime.

Bond order potential module for LAMMPS

DOE Office of Scientific and Technical Information (OSTI.GOV)

2012-09-11

pair_bop is a module for performing energy calculations using the Bond Order Potential (BOP) for use in the parallel molecular dynamics code LAMMPS. The bop pair style computes BOP based upon quantum mechanical incorporating both sigma and pi bondings. By analytically deriving the BOP pair bop from quantum mechanical theory its transferability to different phases can approach that of quantum mechanical methods. This potential is extremely effective at modeling 111-V and II-VI compounds such as GaAs and CdTe. This potential is similar to the original BOP developed by Pettifor and later updated by Murdock et al. and Ward et al.

A multiscale quantum mechanics/electromagnetics method for device simulations.

PubMed

Yam, ChiYung; Meng, Lingyi; Zhang, Yu; Chen, GuanHua

2015-04-07

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 quantum mechanics into electronic device modeling with the electromagnetic environment included through classical electrodynamics. In the quantum mechanics/electromagnetics (QM/EM) method, the regions of the system where active electron scattering processes take place are treated quantum mechanically, 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 quantum mechanical 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.

Development of Vector Parabolic Equation Technique for Propagation in Urban and Tunnel Environments

DTIC Science & Technology

2010-09-01

relativistic quantum mechanics J. Phys. A: Math. Gen. 16 1869–84 [8] Nottale L 1995 Scale relativity, fractal space- time and quantum mechanics Quantum...proportional to the “ time ” elapsed. By performing various approximations to the transfer function, several approximate absorbing boundary condi- tions...The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing

“Quantumness” versus “classicality” of quantum states and quantum protocols

NASA Astrophysics Data System (ADS)

Brodutch, Aharon; Groisman, Berry; Kenigsberg, Dan; Mor, Tal

Entanglement is one of the pillars of quantum mechanics and quantum information processing, and as a result, the quantumness of nonentangled states has typically been overlooked and unrecognized until the last decade. We give a robust definition for the classicality versus quantumness of a single multipartite quantum state, a set of states, and a protocol using quantum states. We show a variety of nonentangled (separable) states that exhibit interesting quantum properties, and we explore the “zoo” of separable states; several interesting subclasses are defined based on the diagonalizing bases of the states, and their nonclassical behavior is investigated.

Generation of Antibunched Light by Excited Molecules in a Microcavity Trap

NASA Technical Reports Server (NTRS)

DeMartini, F.; DiGiuseppe, G.; Marrocco, M.

1996-01-01

The active microcavity is adopted as an efficient source of non-classical light. By this device, excited by a mode-locked laser at a rate of 100 MHz, single-photons are generated over a single field mode with a nonclassical sub-poissonian distribution. The process of adiabatic recycling within a multi-step Franck-Condon molecular optical-pumping mechanism, characterized in our case by a quantum efficiency very close to one, implies a pump self-regularization process leading to a striking n-squeezing effect. By a replication of the basic single-atom excitation process a beam of quantum photon (Fock states) can be created. The new process represents a significant advance in the modern fields of basic quantum-mechanical investigation, quantum communication and quantum cryptography.

Toward protocols for quantum-ensured privacy and secure voting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonanome, Marianna; Buzek, Vladimir; Ziman, Mario

2011-08-15

We present a number of schemes that use quantum mechanics to preserve privacy, in particular, we show that entangled quantum states can be useful in maintaining privacy. We further develop our original proposal [see M. Hillery, M. Ziman, V. Buzek, and M. Bielikova, Phys. Lett. A 349, 75 (2006)] for protecting privacy in voting, and examine its security under certain types of attacks, in particular dishonest voters and external eavesdroppers. A variation of these quantum-based schemes can be used for multiparty function evaluation. We consider functions corresponding to group multiplication of N group elements, with each element chosen by amore » different party. We show how quantum mechanics can be useful in maintaining the privacy of the choices group elements.« less

Intraband light absorption by holes in InGaAsP/InP quantum wells

NASA Astrophysics Data System (ADS)

Pavlov, N. V.; Zegrya, G. G.

2018-03-01

A microscopic analysis of the mechanism of intraband radiation absorption by holes with their transition to a spin-split band for quantum wells based on InGaAsP/InP solid solutions is performed within the framework of the four-band Kane model. The calculation is made for two polarizations of the incident radiation: along the crystal growth axis and in the plane of the quantum well. It is shown that this process can be the main mechanism of internal radiation losses for quantum well lasers. It is also shown that the dependence of the absorption coefficient on the width of the quantum well has a maximum at a well width from 40 to 60 A.

Interpretations

NASA Astrophysics Data System (ADS)

Bellac, Michel Le

2014-11-01

Although nobody can question the practical efficiency of quantum mechanics, there remains the serious question of its interpretation. As Valerio Scarani puts it, "We do not feel at ease with the indistinguishability principle (that is, the superposition principle) and some of its consequences." Indeed, this principle which pervades the quantum world is in stark contradiction with our everyday experience. From the very beginning of quantum mechanics, a number of physicists--but not the majority of them!--have asked the question of its "interpretation". One may simply deny that there is a problem: according to proponents of the minimalist interpretation, quantum mechanics is self-sufficient and needs no interpretation. The point of view held by a majority of physicists, that of the Copenhagen interpretation, will be examined in Section 10.1. The crux of the problem lies in the status of the state vector introduced in the preceding chapter to describe a quantum system, which is no more than a symbolic representation for the Copenhagen school of thought. Conversely, one may try to attribute some "external reality" to this state vector, that is, a correspondence between the mathematical description and the physical reality. In this latter case, it is the measurement problem which is brought to the fore. In 1932, von Neumann was first to propose a global approach, in an attempt to build a purely quantum theory of measurement examined in Section 10.2. This theory still underlies modern approaches, among them those grounded on decoherence theory, or on the macroscopic character of the measuring apparatus: see Section 10.3. Finally, there are non-standard interpretations such as Everett's many worlds theory or the hidden variables theory of de Broglie and Bohm (Section 10.4). Note, however, that this variety of interpretations has no bearing whatsoever on the practical use of quantum mechanics. There is no controversy on the way we should use quantum mechanics!

Quantum Mechanics/Molecular Mechanics Method Combined with Hybrid All-Atom and Coarse-Grained Model: Theory and Application on Redox Potential Calculations.

PubMed

Shen, Lin; Yang, Weitao

2016-04-12

We developed a new multiresolution method that spans three levels of resolution with quantum mechanical, atomistic molecular mechanical, and coarse-grained models. The resolution-adapted all-atom and coarse-grained water model, in which an all-atom structural description of the entire system is maintained during the simulations, is combined with the ab initio quantum mechanics and molecular mechanics method. We apply this model to calculate the redox potentials of the aqueous ruthenium and iron complexes by using the fractional number of electrons approach and thermodynamic integration simulations. The redox potentials are recovered in excellent accordance with the experimental data. The speed-up of the hybrid all-atom and coarse-grained water model renders it computationally more attractive. The accuracy depends on the hybrid all-atom and coarse-grained water model used in the combined quantum mechanical and molecular mechanical method. We have used another multiresolution model, in which an atomic-level layer of water molecules around redox center is solvated in supramolecular coarse-grained waters for the redox potential calculations. Compared with the experimental data, this alternative multilayer model leads to less accurate results when used with the coarse-grained polarizable MARTINI water or big multipole water model for the coarse-grained layer.

Synchronization of an optomechanical system to an external drive

NASA Astrophysics Data System (ADS)

Amitai, Ehud; Lörch, Niels; Nunnenkamp, Andreas; Walter, Stefan; Bruder, Christoph

2017-05-01

Optomechanical systems driven by an effective blue-detuned laser can exhibit self-sustained oscillations of the mechanical oscillator. These self-oscillations are a prerequisite for the observation of synchronization. Here, we study the synchronization of the mechanical oscillations to an external reference drive. We study two cases of reference drives: (1) an additional laser applied to the optical cavity; (2) a mechanical drive applied directly to the mechanical oscillator. Starting from a master equation description, we derive a microscopic Adler equation for both cases, valid in the classical regime in which the quantum shot noise of the mechanical self-oscillator does not play a role. Furthermore, we numerically show that, in both cases, synchronization arises also in the quantum regime. The optomechanical system is therefore a good candidate for the study of quantum synchronization.

Quantum feedback cooling of a mechanical oscillator using variational measurements: tweaking Heisenberg’s microscope

NASA Astrophysics Data System (ADS)

Habibi, Hojat; Zeuthen, Emil; Ghanaatshoar, Majid; Hammerer, Klemens

2016-08-01

We revisit the problem of preparing a mechanical oscillator in the vicinity of its quantum-mechanical ground state by means of feedback cooling based on continuous optical detection of the oscillator position. In the parameter regime relevant to ground-state cooling, the optical back-action and imprecision noise set the bottleneck of achievable cooling and must be carefully balanced. This can be achieved by adapting the phase of the local oscillator in the homodyne detection realizing a so-called variational measurement. The trade-off between accurate position measurement and minimal disturbance can be understood in terms of Heisenberg’s microscope and becomes particularly relevant when the measurement and feedback processes happen to be fast within the quantum coherence time of the system to be cooled. This corresponds to the regime of large quantum cooperativity {C}{{q}}≳ 1, which was achieved in recent experiments on feedback cooling. Our method provides a simple path to further pushing the limits of current state-of-the-art experiments in quantum optomechanics.

Analysis of decoherence mechanisms in a single-atom quantum memory

NASA Astrophysics Data System (ADS)

Koerber, Matthias; Langenfeld, Stefan; Morin, Olivier; Neuzner, Andreas; Ritter, Stephan; Rempe, Gerhard

2017-04-01

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.

From Einstein's theorem to Bell's theorem: a history of quantum non-locality

NASA Astrophysics Data System (ADS)

Wiseman, H. M.

2006-04-01

In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality locality completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.

Relativistic particle in a box: Klein-Gordon versus Dirac equations

NASA Astrophysics Data System (ADS)

Alberto, Pedro; Das, Saurya; Vagenas, Elias C.

2018-03-01

The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.

The dynamics of stock exchange based on the formalism of weak continuous quantum measurement

NASA Astrophysics Data System (ADS)

Melnyk, S.; Tuluzov, I.

2010-07-01

The problem of measurement in economic models and the possibility of their quantum-mechanical description are considered. It is revealed that the apparent paradox of such a description is associated with a priori requirement of conformity of the model to all the alternatives of free choice of the observer. The measurement of the state of a trader on a stock exchange is formally defined as his responses to the proposals of sale at a fixed price. It is shown that an analogue of Bell's inequalities for this measurement model is violated at the most general assumptions related to the strategy of the trader and requires a quantum-mechanical description of the dynamics of his condition. In the framework of the theory of weak continuous quantum measurements, the equation of stock price dynamics and the quantum-mechanical generalization of the F. Black and M. Scholes model for pricing options are obtained. The fundamental distinctions between the obtained model and the classical one are discussed.

Revealing the Mystery of the Galilean Principle of Relativity. Part I: Basic Assertions

NASA Astrophysics Data System (ADS)

Yarman, Tolga

2009-08-01

As Galileo has formulated, one cannot detect, once embarked in a uniform translational motion, and not receiving any information from the outside, how fast he is moving. Why? No one that we recall of, has worked out the answer of this question, although the Galilean Principle of Relativity ( GPR), constituted a major ingredient of the Special Theory of Relativity (STR). Thus, consider a quantum mechanical object of “ clock mass” M 0 ( which is just a mass), doing a “ clock motion”, such as rotation, vibration, etc., with a total energy E 0, in a space of size ℛ0. Previously we have established that, if the mass M 0 is multiplied by an arbitrary number γ, then through the relativistic or non-relativistic quantum mechanical description of the object ( which ever is appropriate to describe the case in hand), the size ℛ0 of it, shrinks as much, and the total energy E 0, concomitantly, increases as much. This quantum mechanical occurrence yields, at once, the invariance of the quantity E 0 M 0ℛ{0/2} with regards to the mass change in question, the object being overall at rest; this latter quantity is, on the other hand, as induced by the quantum mechanical framework, necessarily strapped to h 2, the square of the Planck Constant. But this constant is already, dimension wise, Lorentz invariant. Thus, any quantity bearing the dimension of h 2, is Lorentz invariant, too. So is then, the quantity E 0 M 0ℛ{0/2} ( no matter how the size of concern lies with respect to the direction of uniform translational motion) that would come into play. Thence, the quantum mechanical invariance of the quantity E 0 M 0ℛ{0/2} with regards to an arbitrary mass change, comes to be identical to the Lorentz invariance of this quantity, were the object brought to a uniform translational motion. It is this prevalence, which displays, amazingly, the underlying mechanism, securing the end results of the STR, and this via quantum mechanics. The Lorentz invariant quantum mechanical architecture, E 0 M 0ℛ{0/2}˜ h 2, more fundamentally, constitutes the answer of the mystery drawn by the GPR. In this article, we frame the basic assertions, which will be used in a subsequent article, to display the quantum mechanical machinery making the GPR, and to draw the bridge between the GPR and the architecture, we disclose.

Epitaxial Zn quantum dots coherently grown on Si(1 1 1): growth mechanism, nonlinear optical and chemical states analyses

NASA Astrophysics Data System (ADS)

Huang, Bo-Jia; Kao, Li-Chi; Brahma, Sanjaya; Jeng, Yu-En; Chiu, Shang-Jui; Ku, Ching-Shun; Lo, Kuang-Yao

2017-05-01

Oxide- and defect-free metal/semiconductor interface is important to improve Ohmic contact for the suppression of electron scattering and the avoidance of an extrinsic surface state in estimating the barrier of the Schottky contact at the nanodevice interface. This study reports the growth mechanism of Zn quantum dots coherently grown on Si(1 1 1) and the physical phenomena of the crystalline, nonlinear optics, and the chemical states of Zn quantum dots. Epitaxial Zn quantum dots were coherently formed on a non-oxide Si(1 1 1) surface through the liquid- to solid-phase transformation as a result of pattern matching between the Zn(0 0 2) and Si(1 1 1) surfaces. The growth mechanism of constrained Zn quantum dots grown through strategic magnetron radio frequency sputtering is complex. Some factors, such as substrate temperature, hydrogen gas flow, and negative DC bias, influence the configuration of epitaxial Zn quantum dots. In particular, hydrogen gas plays an important role in reducing the ZnO+ and native oxide that is bombarded by accelerated ions, thereby enhancing the Zn ion surface diffusion. The reduction reaction can be inspected by distinguishing the chemical states of ZnO/Zn quantum dots from natural oxidation or the states of Zn 3d through the analysis of x-ray absorption near the edge structure spectrum. The complex growth mechanism can be systematically understood by analyzing a noncancelled anisotropic 3 m dipole from reflective second harmonic generation and inspecting the evolution between the Zn(0 0 2) and Zn(1 1 1) peaks of the collective ZnO/Zn quantum dots in synchrotron XRD.

BOOK REVIEW: The Odd Quantum

NASA Astrophysics Data System (ADS)

Reynolds, Helen

2000-03-01

The Odd Quantum is aiming to be odd. Falling between being a quantum mechanics textbook and a `popular' science book, it aims to convey something of the substance of quantum mechanics without being overly technical or professional. It does not shy away from the mathematics of the subject or resort solely to analogy and metaphor, as so often is the case. Books aimed at the lay reader tend to take on a particular aspect of quantum mechanics, for example, wave-particle duality, and can do little more than hint at the complexity of the subject. This book is more than a textbook on quantum mechanics; it gives the reader a comprehensive account of history and an appreciation of the nature of quantum mechanics. The introductory chapters deal with the earlier part of the century and the thinking of that time. The approach is familiar, as are the stories that Treiman tells, but he also manages to convey the speed with which ideas changed and the excitement this brought to the physics community. Classical ideas of force and energy are dealt with succinctly but with sufficient depth to set up the reader for what is to come; Maxwell's equations and a brief glimpse at relativity are included. This is followed by a brief description of what the author terms the `old' quantum mechanics, in effect a highly readable tour around black body radiation and spectroscopy and the models of the atom that emerged from them. The `new' quantum mechanics begins about a third of the way through the book, and in a chapter entitled `Foundations' starts gently but rapidly moves into a detailed mathematical treatment. This section, of necessity, relapses into the style of a textbook and covers a lot of ground quickly. It is at this point that the non-specialist popular science readers for whom Treiman has written this book may become a little bemused. Concepts such as non-degeneracy and operators come thick and fast. It is difficult to imagine an educated non-physicist with little mathematical ability keeping track of the equations and their meaning. However, the text continues to be accessible and moves swiftly from `quantum classics' such as the harmonic oscillator to electrical conductivity and the collapse of stars. Reassuringly, Treiman takes time out to ask `What's going on?' where he considers the question of how probabilities get converted into `facts' when things are measured. His own fascination with the subject comes through as he considers the different interpretations of quantum mechanics. The chapter on `building blocks' starts in 1932 when ` ... it could seem that all the basic building blocks of the whole world were at last in hand'. Swiftly and succinctly it moves through to the standard model, acknowledging that a closer look would ` ... quickly carry us far afield into highly technical thickets'. The final chapter tackles the more difficult subject of quantum field theory. This is a very swift journey through quantum electrodynamics and quantum chromodynamics. It is the final summary that stands out, however. The author reminds us what to marvel about: the miracles of quantum theory that are ` ... outrageous to common sense and intuition'. This is a useful book for any science department. It will be of particular use to those of us who studied the subject some time ago and who need to refresh their memories, for example teachers of A-level physics. The asides about `what is going on' and the history that is included make it a `book' rather than a `textbook'. First-year undergraduates, or just possibly motivated and mathematically able A-level students, would also benefit. Beware, however. The mathematics is not trivial and you would arguably need to have met it before in order to cope. Although the book occasionally relapses into textbook style you are left with a sense of the wonder of the subject and an appreciation of the beauty of the mathematics that underpins it.

Predicted phototoxicities of carbon nano-material by quantum mechanical calculations.

EPA Science Inventory

The basis of this research is obtaining the best quantum mechanical 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...

Teaching the EPR Paradox at High School?

ERIC Educational Resources Information Center

Pospiech, Gesche

1999-01-01

Argues the importance of students at university and in the final years of high school gaining an appreciation of the principles of quantum mechanics. Presents the EPR gedanken experiment (thought experiment) as a method of teaching the principles of quantum mechanics. (Author/CCM)

Hermeneutics, Underdetermination and Quantum Mechanics.

ERIC Educational Resources Information Center

Cushing, James T.

1995-01-01

States that the existence of an essential underdetermination in the interpretation of the formalism of quantum mechanics, 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)

Classical system boundaries cannot be determined within quantum Darwinism

NASA Astrophysics Data System (ADS)

Fields, Chris

Multiple observers who interact with environmental encodings of the states of a macroscopic quantum system S as required by quantum Darwinism cannot demonstrate that they are jointly observing S without a joint a priori assumption of a classical boundary separating S from its environment E. Quantum Darwinism cannot, therefore, be regarded as providing a purely quantum-mechanical explanation of the "emergence" of classicality.

Particle in a box in PT-symmetric quantum mechanics and an electromagnetic analog

NASA Astrophysics Data System (ADS)

Dasarathy, Anirudh; Isaacson, Joshua P.; Jones-Smith, Katherine; Tabachnik, Jason; Mathur, Harsh

2013-06-01

In PT-symmetric quantum mechanics a fundamental principle of quantum mechanics, 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 quantum mechanics 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 quantum mechanics. In the second part of this paper we formulate a variational principle for PT-symmetric quantum mechanics 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.

Quantum mechanics in non-inertial reference frames: Time-dependent rotations and loop prolongations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klink, W.H., E-mail: william-klink@uiowa.edu; Wickramasekara, S., E-mail: wickrama@grinnell.edu; Department of Physics, Grinnell College, Grinnell, IA 50112

2013-09-15

This is the fourth in a series of papers on developing a formulation of quantum mechanics 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 to include transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. In previous work, we have shown that there exist representations of the Galilean line group that uphold the non-relativistic equivalence principle asmore » well as representations that violate the equivalence principle. In these previous studies, the focus was on linear accelerations. In this paper, we undertake an extension of the formulation to include rotational accelerations. We show that the incorporation of rotational accelerations requires a class of loop prolongations of the Galilean line group and their unitary cocycle representations. We recover the centrifugal and Coriolis force effects from these loop representations. Loops are more general than groups in that their multiplication law need not be associative. Hence, our broad theoretical claim is that a Galilean quantum theory that holds in arbitrary non-inertial reference frames requires going beyond groups and group representations, the well-established framework for implementing symmetry transformations in quantum mechanics. -- Highlights: •A formulation of Galilean quantum mechanics in non-inertial reference frames is presented. •The Galilei group is generalized to infinite dimensional Galilean line group. •Loop prolongations of Galilean line group contain central extensions of Galilei group. •Unitary representations of the loops are constructed. •These representations lead to terms in the Hamiltonian corresponding to fictitious forces, including centrifugal and Coriolis forces.« less

Constraints on primordial magnetic fields from inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Green, Daniel; Kobayashi, Takeshi, E-mail: drgreen@cita.utoronto.ca, E-mail: takeshi.kobayashi@sissa.it

2016-03-01

We present generic bounds on magnetic fields produced from cosmic inflation. By investigating field bounds on the vector potential, we constrain both the quantum mechanical production of magnetic fields and their classical growth in a model independent way. For classical growth, we show that only if the reheating temperature is as low as T{sub reh} ∼< 10{sup 2} MeV can magnetic fields of 10{sup −15} G be produced on Mpc scales in the present universe. For purely quantum mechanical scenarios, even stronger constraints are derived. Our bounds on classical and quantum mechanical scenarios apply to generic theories of inflationary magnetogenesis with a two-derivative timemore » kinetic term for the vector potential. In both cases, the magnetic field strength is limited by the gravitational back-reaction of the electric fields that are produced simultaneously. As an example of quantum mechanical scenarios, we construct vector field theories whose time diffeomorphisms are spontaneously broken, and explore magnetic field generation in theories with a variable speed of light. Transitions of quantum vector field fluctuations into classical fluctuations are also analyzed in the examples.« less

Darwinism in quantum systems?

NASA Astrophysics Data System (ADS)

Iqbal, A.; Toor, A. H.

2002-03-01

We investigate the role of quantum mechanical effects in the central stability concept of evolutionary game theory, i.e., an evolutionarily stable strategy (ESS). Using two and three-player symmetric quantum games we show how the presence of quantum phenomenon of entanglement can be crucial to decide the course of evolutionary dynamics in a population of interacting individuals.

Quantum information aspects of noncommutative quantum mechanics

NASA Astrophysics Data System (ADS)

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.

Real quantum cybernetics

NASA Astrophysics Data System (ADS)

Grössing, Gerhard

1987-05-01

It is shown on the basis of quantum cybernetics that one can obtain the usual predictions of quantum theory without ever referring to complex numbered “quantum mechanical amplitudes”. Instead, a very simple formula for transition and certain conditional probabilities is developed that involves real numbers only, thus relating intuitively understandable and in principle directly observable physical quantities.

Enhancing non-local correlations in the bipartite partitions of two qubit-system with non-mutual interaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mohamed, A.-B.A., E-mail: abdelbastm@yahoo.com; Faculty of Science, Assiut University, Assiut; Joshi, A., E-mail: mcbamji@gmail.com

2016-03-15

Several quantum-mechanical correlations, notably, quantum entanglement, measurement-induced nonlocality and Bell nonlocality are studied for a two qubit-system having no mutual interaction. Analytical expressions for the measures of these quantum-mechanical correlations of different bipartite partitions of the system are obtained, for initially two entangled qubits and the two photons are in their vacuum states. It is found that the qubits-fields interaction leads to the loss and gain of the initial quantum correlations. The lost initial quantum correlations transfer from the qubits to the cavity fields. It is found that the maximal violation of Bell’s inequality is occurring when the quantum correlationsmore » of both the logarithmic negativity and measurement-induced nonlocality reach particular values. The maximal violation of Bell’s inequality occurs only for certain bipartite partitions of the system. The frequency detuning leads to quick oscillations of the quantum correlations and inhibits their transfer from the qubits to the cavity modes. It is also found that the dynamical behavior of the quantum correlation clearly depends on the qubit distribution angle.« less

2016 Summer Series - Mark Kasevich: Quantum Mechanics at Macroscopic Scales

NASA Image and Video Library

2016-06-09

The underpinning of the universe is quantum mechanics. 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.

Determination of the Unstable States of the Solid State Plasma in Semiconductor Devices

DTIC Science & Technology

1988-05-01

of the carrier moving through the lattice potentials, which alter the carrier’s response to an external electromag- netic field. so If the average...see quantum mechanical affects from the lattice potentials and a spread in carrier momentums due to the Heisenburg Uncertainty Principle. We can...us to account for the quantum mechanical source of the plasma. That source is the lattice . At values of the quantum compression parameter near unity

2 + 1 dimensional de Sitter universe emerging from the gauge structure of a nonlinear quantum system.

PubMed

Kam, Chon-Fai; Liu, Ren-Bao

2017-08-29

Berry phases and gauge structures are fundamental quantum phenomena. In linear quantum mechanics the gauge field in parameter space presents monopole singularities where the energy levels become degenerate. In nonlinear quantum mechanics, 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.

Quantum chaos: An entropy approach

NASA Astrophysics Data System (ADS)

Sl/omczyński, Wojciech; Życzkowski, Karol

1994-11-01

A new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics. It generalizes other definitions of entropy, in both the classical and quantum cases. The Kolmogorov-Sinai (KS) entropy is obtained for a classical system and the sharp measurement instrument. For a quantum system and a coherent states instrument, a new quantity, coherent states entropy, is defined. It may be used to measure chaos in quantum mechanics. The following correspondence principle is proved: the upper limit of the coherent states entropy of a quantum map as ℏ→0 is less than or equal to the KS-entropy of the corresponding classical map. ``Chaos umpire sits, And by decision more imbroils the fray By which he reigns: next him high arbiter Chance governs all.'' John Milton, Paradise Lost, Book II

Quantum state conversion in opto-electro-mechanical systems via shortcut to adiabaticity

NASA Astrophysics Data System (ADS)

Zhou, Xiao; Liu, Bao-Jie; Shao, L.-B.; Zhang, Xin-Ding; Xue, Zheng-Yuan

2017-09-01

Adiabatic processes have found many important applications in modern physics, the distinct merit of which is that accurate control over process timing is not required. However, such processes are slow, which limits their application in quantum computation, due to the limited coherent times of typical quantum systems. Here, we propose a scheme to implement quantum state conversion in opto-electro-mechanical systems via a shortcut to adiabaticity, where the process can be greatly speeded up while precise timing control is still not necessary. In our scheme, by modifying only the coupling strength, we can achieve fast quantum state conversion with high fidelity, where the adiabatic condition does not need to be met. In addition, the population of the unwanted intermediate state can be further suppressed. Therefore, our protocol presents an important step towards practical state conversion between optical and microwave photons, and thus may find many important applications in hybrid quantum information processing.

Sharp peaks in the conductance of a double quantum dot and a quantum-dot spin valve at high temperatures: A hierarchical quantum master equation approach

NASA Astrophysics Data System (ADS)

Wenderoth, S.; Bätge, J.; Härtle, R.

2016-09-01

We study sharp peaks in the conductance-voltage characteristics of a double quantum dot and a quantum dot spin valve that are located around zero bias. The peaks share similarities with a Kondo peak but can be clearly distinguished, in particular as they occur at high temperatures. The underlying physical mechanism is a strong current suppression that is quenched in bias-voltage dependent ways by exchange interactions. Our theoretical results are based on the quantum master equation methodology, including the Born-Markov approximation and a numerically exact, hierarchical scheme, which we extend here to the spin-valve case. The comparison of exact and approximate results allows us to reveal the underlying physical mechanisms, the role of first-, second- and beyond-second-order processes and the robustness of the effect.

Intermediate-band photosensitive device with quantum dots embedded in energy fence barrier

DOEpatents

Forrest, Stephen R.; Wei, Guodan

2010-07-06

A plurality of layers of a first semiconductor material and a plurality of dots-in-a-fence barriers disposed in a stack between a first electrode and a second electrode. Each dots-in-a-fence barrier consists essentially of a plurality of quantum dots of a second semiconductor material embedded between and in direct contact with two layers of a third semiconductor material. Wave functions of the quantum dots overlap as at least one intermediate band. The layers of the third semiconductor material are arranged as tunneling barriers to require a first electron and/or a first hole in a layer of the first material to perform quantum mechanical tunneling to reach the second material within a respective quantum dot, and to require a second electron and/or a second hole in a layer of the first semiconductor material to perform quantum mechanical tunneling to reach another layer of the first semiconductor material.

Nonrelativistic Quantum Mechanics with Fundamental Environment

NASA Astrophysics Data System (ADS)

Gevorkyan, Ashot S.

2011-03-01

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.

Fermi Blobs and the Symplectic Camel: A Geometric Picture of Quantum States

NASA Astrophysics Data System (ADS)

Gossona, Maurice A. De

We have explained in previous work the correspondence between the standard squeezed coherent states of quantum mechanics, and quantum blobs, which are the smallest phase space units compatible with the uncertainty principle of quantum mechanics and having the symplectic group as a group of symmetries. In this work, we discuss the relation between quantum blobs and a certain level set (which we call "Fermi blob") introduced by Enrico Fermi in 1930. Fermi blobs allows us to extend our previous results not only to the excited states of the generalized harmonic oscillator in n dimensions, but also to arbitrary quadratic Hamiltonians. As is the case for quantum blobs, we can evaluate Fermi blobs using a topological notion, related to the uncertainty principle, the symplectic capacity of a phase space set. The definition of this notion is made possible by Gromov's symplectic non-squeezing theorem, nicknamed the "principle of the symplectic camel".

CGS-MSFSS Project report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harvey-Collard, Patrick

2015-10-27

From January 2015 to July 2015, I was doing research at Sandia National Laboratories in Albuquerque, United States. My work there consisted of performing experimental measurements using Sandia’s unique silicon quantum computing platform. The project is about coupling donor spin quantum bits, or qubits, to quantum dots in a silicon nanostructure based on conventional microchip technology. During the project, I devised a new quantum state readout mechanism that allow better, longer lived measurement signals. The measurement (or readout) mechanism is key to any qubit architecture. Next, I was able to demonstrate a quantum manipulation of the two-electron spin states ofmore » the coupled donor and quantum dot system. This constitutes a breakthrough for donor spin qubits in silicon because it could enable larger systems consisting of many qubits. This project will lead to publications in scientific journals, presentations in international conferences, and generates exciting new opportunities for manipulating nature at the nanoscale.« less

Spin Lifetimes in III-V Semiconductor Heterostructures Originating from Zincblende Symmetry

NASA Astrophysics Data System (ADS)

Lau, Wayne; Olesberg, Jon; Flatté, Michael

2000-03-01

Electron spin relaxation in zincblende type semiconductors at room temperature is dominated by the D'yakonov-Perel' mechanism (DP), which is a direct result of the spin splitting of the conduction band due to the bulk inversion asymmetry (BIA) of zincblende materials. To accurately describe the DP spin relaxation mechanism in quantum wells we employ a heterostructure model based on a fourteen bulk band basis, which accounts for the zincblende symmetry of the heterostructure constituents. Electron spin lifetimes are calculated for 75Å n-doped GaAs/Al_0.4Ga_0.6As quantum wells at room temperature. Excellent agreement between theory and experiments is found. In contrast, the calculated spin lifetimes based on the D'yakonov-Kachorovskii theory are an order magnitude shorter than the experimental values. The spin splitting and spin lifetime in no common atom In_0.53Ga_0.47As/InP quantum wells are also investigated. The contribution to the conduction subband spin splitting is dominated by the native interface asymmetry (NIA) mechanism for thin quantum wells; while the spin splitting is governed by the BIA mechanism for thick quantum wells. We find that BIA provides a satisfactory explanation for the spin lifetime measured in an In_0.53Ga_0.47As/InP quantum well with a 97Å barrier and a 70Å well at room temperature.

On a quantum mechanical system theory of the origin of life: from the Stapp-model to the origin of natural symbols

NASA Astrophysics Data System (ADS)

Balázs, András

2016-01-01

The Heisenberg-James-Stapp (quantum mechanical) 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 quantum mechanical 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 (quantum mechanically 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.

How the wave mechanics of Schrodinger was met in the USSR?

NASA Astrophysics Data System (ADS)

Vizgin, Vl. P.

1990-12-01

The author is giving an almost complete review of the era of quantum mechanics in the USSR during 20-th of XX-th century. The author is making accent on the vision of Soviet physicists visavi the new area of science. The most important European and Soviet physicists with major and notable contributions in quantum mechanics are cited.

Physical and Constructive (Limiting) Criterions of Gear Wheels Wear

NASA Astrophysics Data System (ADS)

Fedorov, S. V.

2018-01-01

We suggest using a generalized model of friction - the model of elastic-plastic deformation of the body element, which is located on the surface of the friction pairs. This model is based on our new engineering approach to the problem of friction-triboergodynamics. Friction is examined as transformative and dissipative process. Structural-energetic interpretation of friction as a process of elasto-plastic deformation and fracture contact volumes is proposed. The model of Hertzian (heavy-loaded) friction contact evolution is considered. The least wear particle principle is formulated. It is mechanical (nano) quantum. Mechanical quantum represents the least structural form of solid material body in conditions of friction. It is dynamic oscillator of dissipative friction structure and it can be examined as the elementary nanostructure of metal’s solid body. At friction in state of most complete evolution of elementary tribosystem (tribocontact) all mechanical quanta (subtribosystems) with the exception of one, elasticity and reversibly transform energy of outer impact (mechanic movement). In these terms only one mechanical quantum is the lost - standard of wear. From this position we can consider the physical criterion of wear and the constructive (limiting) criterion of gear teeth and other practical examples of tribosystems efficiency with new tribology notion - mechanical (nano) quantum.

How far do EPR-Bell experiments constrain physical collapse theories?

NASA Astrophysics Data System (ADS)

Leggett, A. J.

2007-03-01

A class of theories alternative to standard quantum mechanics, including that of Ghirardi et al ('GRWP'), postulates that when a quantum superposition becomes amplified to the point that the superposed states reach some level of 'macroscopic distinctness', then some non-quantum-mechanical principle comes into play and realizes one or other of the two macroscopic outcomes. Without specializing to any particular theory of this class, I ask how far such 'macrorealistic' theories are generically constrained, if one insists that the physical reduction process should respect Einstein locality, by the results of existing EPR-Bell experiments. I conclude that provided one does not demand that the prescription for reduction respects Lorentz invariance, at least some theories of this type, while in principle inevitably making some predictions that conflict with those of standard quantum mechanics, are not refuted by any existing experiment.

Multi-shell spherical GaAs /AlxGa1-x As quantum dot shells-size distribution as a mechanism to generate intermediate band energy levels

NASA Astrophysics Data System (ADS)

Rodríguez-Magdaleno, K. A.; Pérez-Álvarez, R.; Martínez-Orozco, J. C.; Pernas-Salomón, R.

2017-04-01

In this work the generation of an intermediate band of energy levels from multi-shell spherical GaAs /AlxGa1-x As quantum dot shells-size distribution is reported. Within the effective mass approximation the electronic structure of a GaAs spherical quantum-dot surrounded by one, two and three shells is studied in detail using a numerically stable transfer matrix method. We found that a shells-size distribution characterized by continuously wider GaAs domains is a suitable mechanism to generate the intermediate band whose width is also dependent on the Aluminium concentration x. Our results suggest that this effective mechanism can be used for the design of wider intermediate band than reported in other quantum systems with possible solar cells enhanced performance.

Quantum-Limited Directional Amplifiers with Optomechanics

NASA Astrophysics Data System (ADS)

Malz, Daniel; Tóth, László D.; Bernier, Nathan R.; Feofanov, Alexey K.; Kippenberg, Tobias J.; Nunnenkamp, Andreas

2018-01-01

Directional amplifiers are an important resource in quantum-information processing, as they protect sensitive quantum systems from excess noise. Here, we propose an implementation of phase-preserving and phase-sensitive directional amplifiers for microwave signals in an electromechanical setup comprising two microwave cavities and two mechanical resonators. We show that both can reach their respective quantum limits on added noise. In the reverse direction, they emit thermal noise stemming from the mechanical resonators; we discuss how this noise can be suppressed, a crucial aspect for technological applications. The isolation bandwidth in both is of the order of the mechanical linewidth divided by the amplitude gain. We derive the bandwidth and gain-bandwidth product for both and find that the phase-sensitive amplifier has an unlimited gain-bandwidth product. Our study represents an important step toward flexible, on-chip integrated nonreciprocal amplifiers of microwave signals.

Horizon Quantum Mechanics: Spherically Symmetric and Rotating Sources

NASA Astrophysics Data System (ADS)

Casadio, Roberto; Giugno, Andrea; Giusti, Andrea; Micu, Octavian

2018-04-01

The Horizon Quantum Mechanics 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 Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem disfavoured.

Grover Search and the No-Signaling Principle

NASA Astrophysics Data System (ADS)

Bao, Ning; Bouland, Adam; Jordan, Stephen P.

2016-09-01

Two of the key properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply superluminal signaling, and despite a form of exponential parallelism, quantum mechanics does not imply polynomial-time brute force solution of NP-complete problems. Here, we investigate the degree to which these two properties are connected. We examine four classes of deviations from quantum mechanics, for which we draw inspiration from the literature on the black hole information paradox. We show that in these models, the physical resources required to send a superluminal signal scale polynomially with the resources needed to speed up Grover's algorithm. Hence the no-signaling principle is equivalent to the inability to solve NP-hard problems efficiently by brute force within the classes of theories analyzed.

Insights into the mechanism and inhibition of fatty acid amide hydrolase from quantum mechanics/molecular mechanics (QM/MM) modelling.

PubMed

Lodola, Alessio; Mor, Marco; Sirirak, Jitnapa; Mulholland, Adrian J

2009-04-01

FAAH (fatty acid amide hydrolase) is a promising target for the treatment of several central nervous system and peripheral disorders. Combined QM/MM (quantum mechanics/molecular mechanics) calculations have elucidated the role of its unusual catalytic triad in the hydrolysis of oleamide and oleoylmethyl ester substrates, and have identified the productive inhibitor-binding orientation for the carbamoylating compound URB524. These are potentially crucial insights for designing new covalent inhibitors of this drug target.

Predicted phototoxicities of carbon nano-material by quantum mechanical calculations

EPA Science Inventory

The purpose of this research is to develop a predictive model for the phototoxicity potential of carbon nanomaterials (fullerenols and single-walled carbon nanotubes). This model is based on the quantum mechanical (ab initio) calculations on these carbon-based materials and compa...

Comparison of Classical and Quantum Mechanical Uncertainties.

ERIC Educational Resources Information Center

Peslak, John, Jr.

1979-01-01

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)

Integrating Computational Chemistry into a Course in Classical Thermodynamics

ERIC Educational Resources Information Center

Martini, Sheridan R.; Hartzell, Cynthia J.

2015-01-01

Computational chemistry is commonly addressed in the quantum mechanics course of undergraduate physical chemistry curricula. Since quantum mechanics traditionally follows the thermodynamics course, there is a lack of curricula relating computational chemistry to thermodynamics. A method integrating molecular modeling software into a semester long…

Security analysis with improved design of post-confirmation mechanism for quantum sealed-bid auction with single photons

NASA Astrophysics Data System (ADS)

Zhang, Ke-Jia; Kwek, Leong-Chuan; Ma, Chun-Guang; Zhang, Long; Sun, Hong-Wei

2018-02-01

Quantum sealed-bid auction (QSA) has been widely studied in quantum cryptography. For a successful auction, post-confirmation is regarded as an important mechanism to make every bidder verify the identity of the winner after the auctioneer has announced the result. However, since the auctioneer may be dishonest and collude with malicious bidders in practice, some potential loopholes could exist. In this paper, we point out two types of collusion attacks for a particular post-confirmation technique with EPR pairs. And it is not difficult to see that there exists no unconditionally secure post-confirmation mechanism in the existing QSA model, if the dishonest participants have the ability to control multiparticle entanglement. In the view of this, we note that some secure implementation could exist if the participants are supposed to be semi-quantum, i.e., they can only control single photons. Finally, two potential methods to design post-confirmation mechanism are presented in this restricted scenario.

Benchmarking Quantum Mechanics/Molecular Mechanics (QM/MM) Methods on the Thymidylate Synthase-Catalyzed Hydride Transfer.

PubMed

Świderek, Katarzyna; Arafet, Kemel; Kohen, Amnon; Moliner, Vicent

2017-03-14

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 quantum mechanics/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.

Proposal for quantum many-body simulation and torsional matter-wave interferometry with a levitated nanodiamond

NASA Astrophysics Data System (ADS)

Ma, Yue; Hoang, Thai M.; Gong, Ming; Li, Tongcang; Yin, Zhang-qi

2017-08-01

Hybrid spin-mechanical systems have great potential in sensing, macroscopic quantum mechanics, and quantum information science. In order to induce strong coupling between an electron spin and the center-of-mass motion of a mechanical oscillator, a large magnetic gradient usually is required, which is difficult to achieve. Here we show that strong coupling between the electron spin of a nitrogen-vacancy (NV) center and the torsional vibration of an optically levitated nanodiamond can be achieved in a uniform magnetic field. Thanks to the uniform magnetic field, multiple spins can strongly couple to the torsional vibration at the same time. We propose utilizing this coupling mechanism to realize the Lipkin-Meshkov-Glick (LMG) model by an ensemble of NV centers in a levitated nanodiamond. The quantum phase transition in the LMG model and finite number effects can be observed with this system. We also propose generating torsional superposition states and realizing torsional matter-wave interferometry with spin-torsional coupling.

Challenges in large scale quantum mechanical calculations: Challenges in large scale quantum mechanical calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ratcliff, Laura E.; Mohr, Stephan; Huhs, Georg

2016-11-07

During the past decades, quantum mechanical 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

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

NASA Astrophysics Data System (ADS)

Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer

2016-06-01

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman’s idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments—the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.

Photodissociation of ultracold diatomic strontium molecules with quantum state control.

PubMed

McDonald, M; McGuyer, B H; Apfelbeck, F; Lee, C-H; Majewska, I; Moszynski, R; Zelevinsky, T

2016-07-07

Chemical reactions at ultracold temperatures are expected to be dominated by quantum mechanical effects. Although progress towards ultracold chemistry has been made through atomic photoassociation, Feshbach resonances and bimolecular collisions, these approaches have been limited by imperfect quantum state selectivity. In particular, attaining complete control of the ground or excited continuum quantum states has remained a challenge. Here we achieve this control using photodissociation, an approach that encodes a wealth of information in the angular distribution of outgoing fragments. By photodissociating ultracold (88)Sr2 molecules with full control of the low-energy continuum, we access the quantum regime of ultracold chemistry, observing resonant and nonresonant barrier tunnelling, matter-wave interference of reaction products and forbidden reaction pathways. Our results illustrate the failure of the traditional quasiclassical model of photodissociation and instead are accurately described by a quantum mechanical model. The experimental ability to produce well-defined quantum continuum states at low energies will enable high-precision studies of long-range molecular potentials for which accurate quantum chemistry models are unavailable, and may serve as a source of entangled states and coherent matter waves for a wide range of experiments in quantum optics.

Investigation of trypsin-CdSe quantum dot interactions via spectroscopic methods and effects on enzymatic activity.

PubMed

Kaur, Gurvir; Tripathi, S K

2015-01-05

The paper presents the interactions between trypsin and water soluble cadmium selenide (CdSe) quantum dots investigated by spectrophotometric methods. CdSe quantum dots have strong ability to quench the intrinsic fluorescence of trypsin by a static quenching mechanism. The quenching has been studied at three different temperatures where the results revealed that electrostatic interactions exist between CdSe quantum dots and trypsin and are responsible to stabilize the complex. The Scatchard plot from quenching revealed 1 binding site for quantum dots by trypsin, the same has been confirmed by making isothermal titrations of quantum dots against trypsin. The distance between donor and acceptor for trypsin-CdSe quantum dot complexes is calculated to be 2.8 nm by energy transfer mechanisms. The intrinsic fluorescence of CdSe quantum dots has also been enhanced by the trypsin, and is linear for concentration of trypsin ranging 1-80 μl. All the observations evidence the formation of trypsin-CdSe quantum dot conjugates, where trypsin retains the enzymatic activity which in turn is temperature and pH dependent. Copyright © 2014 Elsevier B.V. All rights reserved.

Entanglement between exciton and mechanical modes via dissipation-induced coupling

NASA Astrophysics Data System (ADS)

Sete, Eyob A.; Eleuch, H.; Ooi, C. H. Raymond

2015-09-01

We analyze the entanglement between two matter modes in a hybrid quantum system consisting of a microcavity, a quantum well, and a mechanical oscillator. Although the exciton mode in the quantum well and the mechanical oscillator are initially uncoupled, their interaction through the microcavity field results in an indirect exciton-mode-mechanical-mode coupling. We show that this coupling is a Fano-Agarwal-type coupling induced by the decay of the exciton and the mechanical modes caused by the leakage of photons through the microcavity to the environment. Using experimental parameters and for slowly varying microcavity field, we show that the generated coupling leads to an exciton-mode-mechanical-mode entanglement. The maximum entanglement is achieved at the avoided level crossing frequency, where the hybridization of the two modes is maximum. The entanglement is also robust against the phonon thermal bath temperature.

Solvation of fluoro-acetonitrile in water by 2D-IR spectroscopy: A combined experimental-computational study

NASA Astrophysics Data System (ADS)

Cazade, Pierre-André; Tran, Halina; Bereau, Tristan; Das, Akshaya K.; Kläsi, Felix; Hamm, Peter; Meuwly, Markus

2015-06-01

The solvent dynamics around fluorinated acetonitrile is characterized by 2-dimensional infrared spectroscopy and atomistic simulations. The lineshape of the linear infrared spectrum is better captured by semiempirical (density functional tight binding) mixed quantum mechanical/molecular mechanics simulations, whereas force field simulations with multipolar interactions yield lineshapes that are significantly too narrow. For the solvent dynamics, a relatively slow time scale of 2 ps is found from the experiments and supported by the mixed quantum mechanical/molecular mechanics simulations. With multipolar force fields fitted to the available thermodynamical data, the time scale is considerably faster—on the 0.5 ps time scale. The simulations provide evidence for a well established CF-HOH hydrogen bond (population of 25%) which is found from the radial distribution function g(r) from both, force field and quantum mechanics/molecular mechanics simulations.

Vacuum-induced quantum memory in an opto-electromechanical system

NASA Astrophysics Data System (ADS)

Qin, Li-Guo; Wang, Zhong-Yang; Wu, Shi-Chao; Gong, Shang-Qing; Ma, Hong-Yang; Jing, Jun

2018-03-01

We propose a scheme to implement electrically controlled quantum memory based on vacuum-induced transparency (VIT) in a high-Q tunable cavity, which is capacitively coupled to a mechanically variable capacitor by a charged mechanical cavity mirror as an interface. We analyze the changes of the cavity photons arising from vacuum-induced-Raman process and discuss VIT in an atomic ensemble trapped in the cavity. By slowly adjusting the voltage on the capacitor, the VIT can be adiabatically switched on or off, meanwhile, the transfer between the probe photon state and the atomic spin state can be electrically and adiabatically modulated. Therefore, we demonstrate a vacuum-induced quantum memory by electrically manipulating the mechanical mirror of the cavity based on electromagnetically induced transparency mechanism.

Experimental Trapped-ion Quantum Simulation of the Kibble-Zurek dynamics in momentum space

PubMed Central

Cui, Jin-Ming; Huang, Yun-Feng; Wang, Zhao; Cao, Dong-Yang; Wang, Jian; Lv, Wei-Min; Luo, Le; del Campo, Adolfo; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can

2016-01-01

The Kibble-Zurek mechanism is the paradigm to account for the nonadiabatic dynamics of a system across a continuous phase transition. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of Landau-Zener crossings in pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. We test the Kibble-Zurek mechanism in the quantum regime in the momentum space and find the measured scaling of excitations is in accordance with the theoretical prediction. PMID:27633087

Quantum synchronization of a driven self-sustained oscillator.

PubMed

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.

Quantum cybernetics and its test in “late choice” experiments

NASA Astrophysics Data System (ADS)

Grössing, Gerhard

1986-11-01

A relativistically invariant wave equation for the propagation of wave fronts S = const ( S being the action function) is derived on the basis of a cybernetic model of quantum systems involving “hidden variables”. This equation can be considered both as an expression of Huygens' principle and as a general continuity equation providing a close link between classical and quantum mechanics. Although the theory reproduces ordinary quantum mechanics, there are particular situations providing experimental predictions differing from those existing theories. Such predictions are made for so-called “late choice” experiments, which are modified versions of the familiar “delayed choice” experiments.

Perturbatively deformed defects in Pöschl-Teller-driven scenarios for quantum mechanics

NASA Astrophysics Data System (ADS)

Bernardini, Alex E.; da Rocha, Roldão

2016-07-01

Pöschl-Teller-driven solutions for quantum mechanical 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 quantum mechanics 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.

Karl Popper's Quantum Ghost

NASA Astrophysics Data System (ADS)

Shields, William

2004-05-01

Karl Popper, though not trained as a physicist and embarrassed early in his career by a physics error pointed out by Einstein and Bohr, ultimately made substantial contributions to the interpretation of quantum mechanics. As was often the case, Popper initially formulated his position by criticizing the views of others - in this case Niels Bohr and Werner Heisenberg. Underlying Popper's criticism was his belief that, first, the "standard interpretation" of quantum mechanics, sometimes called the Copenhagen interpretation, abandoned scientific realism and second, the assertion that quantum theory was "complete" (an assertion rejected by Einstein among others) amounted to an unfalsifiable claim. Popper insisted that the most basic predictions of quantum mechanics should continue to be tested, with an eye towards falsification rather than mere adding of decimal places to confirmatory experiments. His persistent attacks on the Copenhagen interpretation were aimed not at the uncertainty principle itself and the formalism from which it was derived, but at the acceptance by physicists of an unclear epistemology and ontology that left critical questions unanswered. In 1999, physicists at the University of Maryland conducted a version of Popper's Experiment, re-igniting the debate over quantum predictions and the role of locality in physics.

QUANTUM: The Exhibition - quantum at the museum

NASA Astrophysics Data System (ADS)

Laforest, Martin; Olano, Angela; Day-Hamilton, Tobi

Distilling the essence of quantum phenomena, and how they are being harnessed to develop powerful quantum technologies, into a series of bite-sized, elementary-school-level pieces is what the scientific outreach team at the University of Waterloo's Institute for Quantum Computing was tasked with. QUANTUM: The Exhibition uses a series of informational panels, multimedia and interactive displays to introduce visitors to quantum phenomena and how they will revolutionize computing, information security and sensing. We'll discuss some of the approaches we took to convey the essence and impact of quantum mechanics and technologies to a lay audience while ensuring scientific accuracy.

Quantum theory of multiscale coarse-graining.

PubMed

Han, Yining; Jin, Jaehyeok; Wagner, Jacob W; Voth, Gregory A

2018-03-14

Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.

(Never) Mind your p's and q's: Von Neumann versus Jordan on the foundations of quantum theory

NASA Astrophysics Data System (ADS)

Duncan, A.; Janssen, M.

2013-03-01

In 1927, in two papers entitled "On a new foundation [Neue Begründung] of quantum mechanics," Pascual Jordan presented his version of what came to be known as the Dirac-Jordan statistical transformation theory. Jordan and Paul Dirac arrived at essentially the same theory independently of one another at around the same time. Later in 1927, partly in response to Jordan and Dirac and avoiding the mathematical difficulties facing their approach, John von Neumann developed the modern Hilbert space formalism of quantum mechanics. We focus on Jordan and von Neumann. Central to the formalisms of both are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in quantum mechanics. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identification of sets of canonically conjugate variables, i.e., p's and q's. For von Neumann, not constrained by the analogy to classical mechanics, it required only the identification of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p's and q's. Jordan and von Neumann also stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan and Dirac were the first to state those rules in full generality. Von Neumann rephrased them and, in a paper published a few months later, sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by Hilbert, von Neumann, and Nordheim. We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics. This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin.

Quantum algorithms for quantum field theories.

PubMed

Jordan, Stephen P; Lee, Keith S M; Preskill, John

2012-06-01

Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.

Quantization and Quantum-Like Phenomena: A Number Amplitude Approach

NASA Astrophysics Data System (ADS)

Robinson, T. R.; Haven, E.

2015-12-01

Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.

Quantum mechanics of excitation transport in photosynthetic complexes: a key issues review.

PubMed

Levi, Federico; Mostarda, Stefano; Rao, Francesco; Mintert, Florian

2015-07-01

For a long time microscopic physical descriptions of biological processes have been based on quantum mechanical 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 quantum mechanical 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.

Quantum Mechanics for Everyone: Can it be done with Technology?

NASA Astrophysics Data System (ADS)

Zollman, Dean

2004-10-01

The Visual Quantum Mechanics 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 quantum mechanics. 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 Quantum Mechanics 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/.

On classical and quantum dynamics of tachyon-like fields and their cosmological implications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimitrijević, Dragoljub D., E-mail: ddrag@pmf.ni.ac.rs; Djordjević, Goran S., E-mail: ddrag@pmf.ni.ac.rs; Milošević, Milan, E-mail: ddrag@pmf.ni.ac.rs

2014-11-24

We consider a class of tachyon-like potentials, motivated by string theory, D-brane dynamics and inflation theory in the context of classical and quantum mechanics. A formalism for describing dynamics of tachyon fields in spatially homogenous and one-dimensional - classical and quantum mechanical limit is proposed. A few models with concrete potentials are considered. Additionally, possibilities for p-adic and adelic generalization of these models are discussed. Classical actions and corresponding quantum propagators, in the Feynman path integral approach, are calculated in a form invariant on a change of the background number fields, i.e. on both archimedean and nonarchimedean spaces. Looking formore » a quantum origin of inflation, relevance of p-adic and adelic generalizations are briefly discussed.« less

Effects of Noise-Induced Coherence on the Performance of Quantum Absorption Refrigerators

NASA Astrophysics Data System (ADS)

Holubec, Viktor; Novotný, Tomáš

2018-05-01

We study two models of quantum absorption refrigerators with the main focus on discerning the role of noise-induced coherence on their thermodynamic performance. Analogously to the previous studies on quantum heat engines, we find the increase in the cooling power due to the mechanism of noise-induced coherence. We formulate conditions imposed on the microscopic parameters of the models under which they can be equivalently described by classical stochastic processes and compare the performance of the two classes of fridges (effectively classical vs. truly quantum). We find that the enhanced performance is observed already for the effectively classical systems, with no significant qualitative change in the quantum cases, which suggests that the noise-induced-coherence-enhancement mechanism is caused by static interference phenomena.

Quantum Effects at a Proton Relaxation at Low Temperatures

NASA Astrophysics Data System (ADS)

Kalytka, V. A.; Korovkin, M. V.

2016-11-01

Quantum effects during migratory polarization in multi-well crystals (including multi-well silicates and crystalline hydrates) are investigated in a variable electric field at low temperatures by direct quantum-mechanical calculations. Based on analytical solution of the quantum Liouville kinetic equation in the linear approximation for the polarizing field, the non-stationary density matrix is calculated for an ensemble of non-interacting protons moving in the field of one-dimensional multi-well crystal potential relief of rectangular shape. An expression for the complex dielectric constant convenient for a comparison with experiment and calculation of relaxer parameters is derived using the nonequilibrium polarization density matrix. The density matrix apparatus can be used for analytical investigation of the quantum mechanism of spontaneous polarization of a ferroelectric material (KDP and DKDP).

The Nanoelectric Modeling Tool (NEMO) and Its Expansion to High Performance Parallel Computing

NASA Technical Reports Server (NTRS)

Klimeck, G.; Bowen, C.; Boykin, T.; Oyafuso, F.; Salazar-Lazaro, C.; Stoica, A.; Cwik, T.

1998-01-01

Material variations on an atomic scale enable the quantum mechanical functionality of devices such as resonant tunneling diodes (RTDs), quantum well infrared photodetectors (QWIPs), quantum well lasers, and heterostructure field effect transistors (HFETs).

Scheme for teleportation of quantum states onto a mechanical resonator.

PubMed

Mancini, Stefano; Vitali, David; Tombesi, Paolo

2003-04-04

We propose an experimentally feasible scheme to teleport an unkown quantum state onto the vibrational degree of freedom of a macroscopic mirror. The quantum channel between the two parties is established by exploiting radiation pressure effects.