Quantum mechanics and quantum information theory
NASA Astrophysics Data System (ADS)
van Camp, Wesley William
The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main question with which this dissertation will be concerned is whether or not an information-theoretic interpretation can serve as a conceptually acceptable interpretation of quantum mechanics. It will be argued that some of the more obvious approaches -- that quantum information theory shows us that ultimately the world is made of information, and quantum Bayesianism -- fail as philosophical interpretations of quantum mechanics. However, the information-theoretic approach of Clifton, Bub, and Halvorson introduces Einstein's distinction between principle theories and constructive theories, arguing that quantum mechanics is best understood as an information-theoretic principle theory. While I argue that this particular approach fails, it does offer a viable new philosophical role for information theory. Specifically, an investigation of interpretationally successful principle theories such as Newtonian mechanics, special relativity, and general relativity, shows that the particular principles employed are necessary as constitutive elements of a framework which partially defines the basic explanatory concepts of space, time, and motion. Without such constitutive principles as preconditions for empirical meaning, scientific progress is hampered. It is argued that the philosophical issues in quantum mechanics stem from an analogous conceptual crisis. On the basis of this comparison, the best strategy for resolving these problems is to apply a similar sort of conceptual analysis to quantum mechanics so as to provide an appropriate set of constitutive principles clarifying the conceptual issues at stake. It is further argued that quantum information theory is ideally placed as a novel
Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Holism, physical theories and quantum mechanics
NASA Astrophysics Data System (ADS)
Seevinck, M. P.
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.
Quantum mechanics of 4-derivative theories.
Salvio, Alberto; Strumia, Alessandro
2016-01-01
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.
Econophysics: from Game Theory and Information Theory to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Jimenez, Edward; Moya, Douglas
2005-03-01
Rationality is the universal invariant among human behavior, universe physical laws and ordered and complex biological systems. Econophysics isboth the use of physical concepts in Finance and Economics, and the use of Information Economics in Physics. In special, we will show that it is possible to obtain the Quantum Mechanics principles using Information and Game Theory.
Exponential complexity and ontological theories of quantum mechanics
Montina, A.
2008-02-15
Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We consider the general class of ontological theories describing a quantum system by a set of variables with Markovian (either deterministic or stochastic) evolution. We provide proof that the number of continuous variables cannot be smaller than 2N-2, N being the Hilbert-space dimension. Thus, any ontological Markovian theory of quantum mechanics requires a number of variables which grows exponentially with the physical size. This result is relevant also in the framework of quantum Monte Carlo methods.
From scalar field theories to supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Bazeia, D.; Bemfica, F. S.
2017-04-01
In this work, we report a new result that appears when one investigates the route that starts from a scalar field theory and ends on a supersymmetric quantum mechanics. The subject has been studied before in several distinct ways and here, we unveil an interesting novelty, showing that the same scalar field model may describe distinct quantum mechanical problems.
Relativistic Quantum Mechanics and Introduction to Field Theory
NASA Astrophysics Data System (ADS)
Yndurain, Francisco J.
This is an advanced textbook meant as a primer in quantum theory for graduate students. A full relativistic treatment of particle dynamics needs to be based on quantum field theory. However, there exists a variety of processes that can be discussed with concepts like potentials, classical current distributions, prescribed external fields dealt with in the framework of relativistic quantum mechanics. Then, in an introduction to field theory the author emphasizes the deduction of the said potentials or currents. The unique feature of this book is the modern presentation of the subject together with many exercises and furthermore the underlying concept to combine a reference book on relativistic quantum mechanics with an introduction into quantum field theory.
Quantum mechanical generalization of the balistic electron wind theory
NASA Astrophysics Data System (ADS)
Lacina, A.
1980-06-01
The Fiks' quasiclassical theory of the electron wind force is quantum mechanically generalized. Within the framework of this generalization the space dependence of the electron wind force is calculated in the vicinity of an interface between two media. It is found that quantum corrections may be comparable with or even greater than corresponding quasiclassical values.
A modified Lax-Phillips scattering theory for quantum mechanics
NASA Astrophysics Data System (ADS)
Strauss, Y.
2015-07-01
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 the 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.
A modified Lax-Phillips scattering theory for quantum mechanics
Strauss, Y.
2015-07-15
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 the 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.
Neutrino oscillations: quantum mechanics vs. quantum field theory
NASA Astrophysics Data System (ADS)
Akhmedov, Evgeny Kh.; Kopp, Joachim
2010-04-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino’s interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Akhmedov, Evgeny Kh.; Kopp, Joachim
2010-01-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Quantum-mechanical theory of optomechanical Brillouin cooling
Tomes, Matthew; Bahl, Gaurav; Carmon, Tal; Marquardt, Florian
2011-12-15
We analyze how to exploit Brillouin scattering of light from sound for the purpose of cooling optomechanical devices and present a quantum-mechanical theory for Brillouin cooling. Our analysis shows that significant cooling ratios can be obtained with standard experimental parameters. A further improvement of cooling efficiency is possible by increasing the dissipation of the optical anti-Stokes resonance.
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
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.
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.
Functional methods underlying classical mechanics, relativity and quantum theory
NASA Astrophysics Data System (ADS)
Kryukov, A.
2013-04-01
The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is "made" of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.
"Spring theory of relativity" originating from quantum mechanics
NASA Astrophysics Data System (ADS)
Yefremov, Alexander P.
Compact derivation of mathematical equations similar to those of quantum and classical mechanics is given on the base of fractal decomposition of a three-dimensional space. In physical units the equations become Shrödinger and Hamilton-Jacobi equations, the wave function of a free particle associated with a virtual ring. Locally uniform motion of the ring in the physical space provides an original helix (or regular cylindrical spring) model of a relativistic theory equivalent in results with special relativity, the free particle's relativistic Lagrangian emerging automatically. Irregular spring model generates theory similar to general relativity.
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.
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2017-02-01
The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations.
The quantum coherent mechanism for singlet fission: experiment and theory.
Chan, Wai-Lun; Berkelbach, Timothy C; Provorse, Makenzie R; Monahan, Nicholas R; Tritsch, John R; Hybertsen, Mark S; Reichman, David R; Gao, Jiali; Zhu, X-Y
2013-06-18
The absorption of one photon by a semiconductor material usually creates one electron-hole pair. However, this general rule breaks down in a few organic semiconductors, such as pentacene and tetracene, where one photon absorption may result in two electron-hole pairs. This process, where a singlet exciton transforms to two triplet excitons, can have quantum yields as high as 200%. Singlet fission may be useful to solar cell technologies to increase the power conversion efficiency beyond the so-called Shockley-Queisser limit. Through time-resolved two-photon photoemission (TR-2PPE) spectroscopy in crystalline pentacene and tetracene, our lab has recently provided the first spectroscopic signatures in singlet fission of a critical intermediate known as the multiexciton state (also called a correlated triplet pair). More importantly, we found that population of the multiexciton state rises at the same time as the singlet state on the ultrafast time scale upon photoexcitation. This observation does not fit with the traditional view of singlet fission involving the incoherent conversion of a singlet to a triplet pair. However, it provides an experimental foundation for a quantum coherent mechanism in which the electronic coupling creates a quantum superposition of the singlet and the multiexciton state immediately after optical excitation. In this Account, we review key experimental findings from TR-2PPE experiments and present a theoretical analysis of the quantum coherent mechanism based on electronic structural and density matrix calculations for crystalline tetracene lattices. Using multistate density functional theory, we find that the direct electronic coupling between singlet and multiexciton states is too weak to explain the experimental observation. Instead, indirect coupling via charge transfer intermediate states is two orders of magnitude stronger, and dominates the dynamics for ultrafast multiexciton formation. Density matrix calculation for the crystalline
NASA Astrophysics Data System (ADS)
Commins, Eugene D.
2014-10-01
Preface; 1. Introduction; 2. Mathematical preliminaries; 3. The rules of quantum mechanics; 4. The connection between the fundamental rules and wave mechanics; 5. Further illustrations of the rules of quantum mechanics; 6. Further developments in one-dimensional wave mechanics; 7. The theory of angular momentum; 8. Wave mechanics in three dimensions: hydrogenic atoms; 9. Time-independent approximations for bound state problems; 10. Applications of static perturbation theory; 11. Identical particles; 12. Atomic structure; 13. Molecules; 14. The stability of matter; 15. Photons; 16. Interaction of non-relativistic charged particles and radiation; 17. Further topics in perturbation theory; 18. Scattering; 19. Special relativity and quantum mechanics: the Klein-Gordon equation; 20. The Dirac equation; 21. Interaction of a relativistic spin 1/2 particle with an external electromagnetic field; 22. The Dirac field; 23. Interaction between relativistic electrons, positrons, and photons; 24. The quantum mechanics of weak interactions; 25. The quantum measurement problem; Appendix A: useful inequalities for quantum mechanics; Appendix B: Bell's inequality; Appendix C: spin of the photon: vector spherical waves; Works cited; Bibliography; Index.
Quantum and statistical mechanics in open systems: theory and examples
NASA Astrophysics Data System (ADS)
Zueco, David
2009-08-01
Using the system-bath model Hamiltonian this thesis covers the equilibrium and out of equilibrium properties of quantum open systems. Topics included are the calculation of thermodynamical quantities of open systems, derivation of quantum master equations, phase space and numerical methods and Linear and non Linear Response Theory. Applications are the transport in periodic potentials and the dynamics of spins.
M-theory Calabi-Yau Quantum Mechanics
NASA Astrophysics Data System (ADS)
Haupt, Alexander S.
2009-11-01
This thesis explores an exotic class of M-theory compactifications in which the compact manifold is taken to be a Calabi-Yau five-fold. The resulting effective theory is a one-dimensional N=2 super-mechanics model that exhibits peculiar features of one-dimensional supersymmetry, such as the appearance of fermion-only super-multiplets. The latter necessitates reducing also the fermionic sector of M-theory, which is not normally included in the compactification literature and is thus presented, together with the required technology, in detail. The one-dimensional effective theory is most elegantly described in superspace and therefore, a detailed account of one-dimensional flat and curved N=2 superspace is provided. This includes developing the theory of fermionic multiplets and the study of cross-couplings between 2a and 2b multiplets. Another important aspect is the inclusion of flux. We study its consistency conditions, its relation to supersymmetry and the way it gives rise to a potential in the one-dimensional effective action. It is also explained how the supersymmetry-preserving part of the potential can be obtained from a Gukov-type superpotential. The main motivation of this compactification scenario is rooted in the realm of cosmology. Its virtue is a democratic treatment of spatial dimensions. As opposed to the artificial 3+7 split in most string compactifications, the early universe starts out with all spatial dimensions compact and small in our approach. One then seeks for dynamical ways in which three dimensions grow large at late times. Possible realisations of this idea are discussed both at the classical and at the quantum level. Finally, preliminary work on Calabi-Yau five-fold compactifications of F-theory and the resulting two-dimensional string-like actions is presented.
Non-exponential decay in Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Giacosa, Francesco
2014-10-01
We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by using relativistic Lagrangians. In particular, the case in which two decay channels are present is analyzed: the ratio of decay probability densities, which is a constant equal to the ratio of decay widths in the exponential limit, shows in general sizable fluctuations which persist also at long times.
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.
A deformation quantization theory for noncommutative quantum mechanics
Costa Dias, Nuno; Prata, Joao Nuno; Gosson, Maurice de; Luef, Franz
2010-07-15
We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].
Extended theory of harmonic maps connects general relativity to chaos and quantum mechanism
NASA Astrophysics Data System (ADS)
Ren, Gang; Duan, Yi-Shi
2017-10-01
General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the line between classical and quantum physics by connecting chaos and entanglement. Here, we showed the early reported extended HM theory that included the general relativity can also be used to recover the classic chaos equations and even the Schrodinger equation in quantum physics, suggesting the extended theory of harmonic maps may act as a universal theory of physics.
Studies on Quantum Field Theory and Statistical Mechanics
NASA Astrophysics Data System (ADS)
Zhang, Shoucheng
This dissertation is a summary of research in various areas of theoretical physics and is divided into three parts. In the first part, quantum fluctuations of the recently proposed superconducting cosmic strings are studied. It is found that vortices on the string world sheet represent an important class of fluctuation modes which tend to disorder the system. Both heuristic arguments and detailed renormalization group analysis reveal that these vortices do not appear in bound pairs but rather form a gas of free vortices. Based on this observation we argue that this fluctuation mode violates the topological conservation law on which superconductivity is based. Anomalies and topological aspects of supersymmetric quantum field theories are studied in the second part of this dissertation. Using the superspace formulation of the N = 1 spinning string, we obtain a path integral measure which is free from the world-sheet general coordinate as well as the supersymmetry anomalies and therefore determine the conformal anomaly and critical dimension of the spinning string. We also apply Fujikawa's formalism to computer the chiral anomaly in conformal as well as ordinary supergravity. Finally, we given a Noether-method construction of the supersymmetrized Chern-Simons term in five dimensional supergravity. In the last part of this dissertation, the soliton excitations in the quarter-filled Peierls-Hubbard model are investigated in both the large and the small U limit. For a strictly one dimensional system at zero temperature, we find that solitons in both limits are in one-to-one correspondence, while in the presence of weak three dimensional couplings or at finite temperature, the large U systems differ qualitatively from the small U systems in that the spin associated with the solitons ceases to be a sharp quantum observable.
Fluctuations in quantum mechanics and field theories from a new version of semiclassical theory. II.
NASA Astrophysics Data System (ADS)
Escobar-Ruiz, M. A.; Shuryak, E.; Turbiner, A. V.
2017-08-01
This is the second paper on the semiclassical approach based on the density matrix given by the Euclidean time path integral with fixed coinciding end points. The classical path, interpolating between this point and the classical vacuum (called a "flucton"), as well as systematic one- and two-loop corrections were calculated in the first paper [M. A. Escobar-Ruiz, E. Shuryak, and A. V. Turbiner, Phys. Rev. D 93, 105039 (2016)], 10.1103/PhysRevD.93.105039 for a double-well potential. Here, we extend them for a number of quantum-mechanical problems, such as an anharmonic oscillator and the sine-Gordon potential. The method is based on a systematic expansion in Feynman diagrams and thus can be extended to quantum field theories (QFTs). We show that the loop expansion in quantum mechanics resembles the leading-log approximations in QFT. In this sequel, we present a complete set of results obtained using this method in a unified way. Alternatively, starting from the Schrödinger equation we derive a generalized Bloch equation whose semiclassical-like, iterative solution generates the loop expansion. We rederive the two-loop expansions for all three of the above potentials and extend them to three loops, which has not yet been done via Feynman diagrams. All results for both methods are fully consistent with each other. An asymmetric (tilted) double-well potential (nondegenerate minima) is also studied using the second method.
Chapter 10 Quantum Mechanics and the Special and General Theory of Relativity
NASA Astrophysics Data System (ADS)
Brändas, Erkki J.
The old dilemma of quantum mechanics versus the theory of relativity is reconsidered. A first principles relativistically invariant theory will be provided through a model, which is basically quantum mechanical. Moreover, by analytically extending quantum mechanics into the complex plane, it is possible to include dynamical features such as time-, length-, and temperature-scales into the theory. The flexibility of including complex symmetric interactions will in the same way support a transition from firmly quantum mechanical non-local behaviour to a decidedly classical-local appearance. Furthermore, the extended formulation gives rise to so-called Jordan blocks. They will be shown to appear logically in the present generalized dynamical picture and a compelling interpretation is microscopic self-organization (MSO). Not only have the manifestation of quantum-thermal correlations, and the emergence of generic time scales been established, but the present viewpoint also appears to throw new light on the age-old problem of quantum mechanics versus relativity. To bring all these ideas together, we will demonstrate that our model (i) displays the simple occurrence of such a degenerate unit, (ii) demonstrates the link with the Klein-Gordon-Dirac relativistic theory and (iii) provides dynamical features of both special and general relativity theory.
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Miller, W.H.
1995-07-01
A quantum mechanical theory of collisional recombination (within the Lindemann mechanism, A + B {leftrightarrow} AB*, AB* + M {yields} AB + M) is presented which provides a proper quantum description of the A + B collision dynamics and treats the M + AB* inelastic scattering within the impact approximation (the quantum analog of a classical master equation treatment). The most rigorous version of the theory is similar in structure to the impact theory of spectral line broadening and involves generalized (4-index) rate constants for describing M + AB* collisions. A simplified version is also presented which involves only the normal (2-index) inelastic rate constants for M + AB* scattering but which also retains a proper quantum description of the A + B dynamics.
Unification of Classical and Quantum Mechanics & Theory of Relative Motion
NASA Astrophysics Data System (ADS)
Zheng-Johansson, J. X.
2003-03-01
A systematic survey of relevant pivotal experiments leads us to arrive at (I) vacuum comprises substantial entities called aethers and (II) the velocities of light as measured in vacuum c and by a moving observer c', and the observer's velocity v obey the law of vector addition. (I)-(II) facilitate a General Scheme, which leads to (A) from Newton Mechanics solution for vacuum the fundamental formation of basic material particles having a mass, size, charge, etc. and being a de Broglie wave obeying Quantum Mechanics (B) augmentation in the mass, de Broglie wavevector, etc of a moving particle by a factor γ = 1/[1-(v/c)^2]^1/2 (C) length and time contractions of a moving body as measured in the frame in which the body resides (D) coordinate transformation between an inertial frame at rest and one relatively moving, called Galileo-Lorentz transformation (GLT) (E) using the GLT the prediction of null-fringe shift of the Michelson-Morley experiment and the Doppler effect of electromagnetic waves etc (F) inference of various contemporary empirical rules, incl Uncertainty Relation; etc.
Unification of Classical and Quantum Mechanics & Theory of Relative Motion
NASA Astrophysics Data System (ADS)
Zheng-Johansson, J. X.
2003-03-01
A systematic survey of relevant pivotal experiments leads us to arrive at (I) vacuum comprises substantial entities called aethers and (II) the velocities of light as measured in vacuum c and by a moving observer c', and the observer's velocity v obey the law of vector addition. (I)-(II) facilitate a General Scheme, which lead to (A) the fundamental formation of a basic material particle having a mass, size, charge, etc. and is a de Broglie wave obeying Quantum Mechanics as a result of Newton Mechanics solution (B) augmentation in the mass, de Broglie wavevector, etc of a moving particle by a factor γ =3D 1/[1-(v/c)^2]^1/2 (C) length and time contractions of a moving body as measured in the frame in which the body resides (D) a set of coordinate transformation equations between a inertial frame at rest and one relatively moving, called Galileo-Lorentz transformation (GLT) (E) using the GLT the prediction of null-fringe shift of the Michelson-Morley experiment and the Doppler effect of electromagnetic waves etc (F) inference of various contemporary empirical rules, relations; etc.
Quantum mechanical theory of dynamic nuclear polarization in solid dielectrics
Hu, Kan-Nian; Debelouchina, Galia T.; Smith, Albert A.; Griffin, Robert G.
2011-01-01
Microwave driven dynamic nuclear polarization (DNP) is a process in which the large polarization present in an electron spin reservoir is transferred to nuclei, thereby enhancing NMR signal intensities. In solid dielectrics there are three mechanisms that mediate this transfer—the solid effect (SE), the cross effect (CE), and thermal mixing (TM). Historically these mechanisms have been discussed theoretically using thermodynamic parameters and average spin interactions. However, the SE and the CE can also be modeled quantum mechanically with a system consisting of a small number of spins and the results provide a foundation for the calculations involving TM. In the case of the SE, a single electron–nuclear spin pair is sufficient to explain the polarization mechanism, while the CE requires participation of two electrons and a nuclear spin, and can be used to understand the improved DNP enhancements observed using biradical polarizing agents. Calculations establish the relations among the electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) frequencies and the microwave irradiation frequency that must be satisfied for polarization transfer via the SE or the CE. In particular, if δ, Δ < ω0I, where δ and Δ are the homogeneous linewidth and inhomogeneous breadth of the EPR spectrum, respectively, we verify that the SE occurs when ωM = ω0S ± ω0I, where ωM, ω0S and ω0I are, respectively, the microwave, and the EPR and NMR frequencies. Alternatively, when Δ > ω0I > δ, the CE dominates the polarization transfer. This two-electron process is optimized when ω0S1−ω0S2=ω0I and ωM∼ω0S1 orω0S2, where ω0S1 and ω0S2 are the EPR Larmor frequencies of the two electrons. Using these matching conditions, we calculate the evolution of the density operator from electron Zeeman order to nuclear Zeeman order for both the SE and the CE. The results provide insights into the influence of the microwave irradiation field, the
Quantum mechanical theory of dynamic nuclear polarization in solid dielectrics.
Hu, Kan-Nian; Debelouchina, Galia T; Smith, Albert A; Griffin, Robert G
2011-03-28
Microwave driven dynamic nuclear polarization (DNP) is a process in which the large polarization present in an electron spin reservoir is transferred to nuclei, thereby enhancing NMR signal intensities. In solid dielectrics there are three mechanisms that mediate this transfer--the solid effect (SE), the cross effect (CE), and thermal mixing (TM). Historically these mechanisms have been discussed theoretically using thermodynamic parameters and average spin interactions. However, the SE and the CE can also be modeled quantum mechanically with a system consisting of a small number of spins and the results provide a foundation for the calculations involving TM. In the case of the SE, a single electron-nuclear spin pair is sufficient to explain the polarization mechanism, while the CE requires participation of two electrons and a nuclear spin, and can be used to understand the improved DNP enhancements observed using biradical polarizing agents. Calculations establish the relations among the electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) frequencies and the microwave irradiation frequency that must be satisfied for polarization transfer via the SE or the CE. In particular, if δ, Δ < ω(0I), where δ and Δ are the homogeneous linewidth and inhomogeneous breadth of the EPR spectrum, respectively, we verify that the SE occurs when ω(M) = ω(0S) ± ω(0I), where ω(M), ω(0S) and ω(0I) are, respectively, the microwave, and the EPR and NMR frequencies. Alternatively, when Δ > ω(0I) > δ, the CE dominates the polarization transfer. This two-electron process is optimized when ω(0S(1))-ω(0S(2)) = ω(0I) and ω(M)~ω(0S(1)) or ω(0S(2)), where ω(0S(1)) and ω(0S(2)) are the EPR Larmor frequencies of the two electrons. Using these matching conditions, we calculate the evolution of the density operator from electron Zeeman order to nuclear Zeeman order for both the SE and the CE. The results provide insights into the influence of the
NASA Astrophysics Data System (ADS)
Bastin, Ted
2009-07-01
List of participants; Preface; Part I. Introduction: 1. The function of the colloquium - editorial; 2. The conceptual problem of quantum theory from the experimentalist's point of view O. R. Frisch; Part II. Niels Bohr and Complementarity: The Place of the Classical Language: 3. The Copenhagen interpretation C. F. von Weizsäcker; 4. On Bohr's views concerning the quantum theory D. Bohm; Part III. The Measurement Problem: 5. Quantal observation in statistical interpretation H. J. Groenewold; 6. Macroscopic physics, quantum mechanics and quantum theory of measurement G. M. Prosperi; 7. Comment on the Daneri-Loinger-Prosperi quantum theory of measurement Jeffrey Bub; 8. The phenomenology of observation and explanation in quantum theory J. H. M. Whiteman; 9. Measurement theory and complex systems M. A. Garstens; Part IV. New Directions within Quantum Theory: What does the Quantum Theoretical Formalism Really Tell Us?: 10. On the role of hidden variables in the fundamental structure of physics D. Bohm; 11. Beyond what? Discussion: space-time order within existing quantum theory C. W. Kilmister; 12. Definability and measurability in quantum theory Yakir Aharonov and Aage Petersen; 13. The bootstrap idea and the foundations of quantum theory Geoffrey F. Chew; Part V. A Fresh Start?: 14. Angular momentum: an approach to combinatorial space-time Roger Penrose; 15. A note on discreteness, phase space and cohomology theory B. J. Hiley; 16. Cohomology of observations R. H. Atkin; 17. The origin of half-integral spin in a discrete physical space Ted Bastin; Part VI. Philosophical Papers: 18. The unity of physics C. F. von Weizsäcker; 19. A philosophical obstacle to the rise of new theories in microphysics Mario Bunge; 20. The incompleteness of quantum mechanics or the emperor's missing clothes H. R. Post; 21. How does a particle get from A to B?; Ted Bastin; 22. Informational generalization of entropy in physics Jerome Rothstein; 23. Can life explain quantum mechanics? H. H
NASA Astrophysics Data System (ADS)
Aidas, Kestutis; Kongsted, Jacob; Nielsen, Christian B.; Mikkelsen, Kurt V.; Christiansen, Ove; Ruud, Kenneth
2007-07-01
The theory of a hybrid quantum mechanics/molecular mechanics (QM/MM) approach for gauge-origin independent calculations of the molecular magnetizability using Hartree-Fock or Density Functional Theory is presented. The method is applied to liquid water using configurations generated from classical Molecular Dynamics simulation to calculate the statistical averaged magnetizability. Based on a comparison with experimental data, treating only one water molecule quantum mechanically appears to be insufficient, while a quantum mechanical treatment of also the first solvation shell leads to good agreement between theory and experiment. This indicates that the gas-to-liquid phase shift for the molecular magnetizability is to a large extent of non-electrostatic nature.
Relativity and Quantum Mechanics
NASA Astrophysics Data System (ADS)
Brändas, Erkki J.
2007-12-01
The old dilemma of quantum mechanics versus the theory of relativity is reconsidered via a first principles relativistically invariant theory. By analytic extension of quantum mechanics into the complex plane one may (i) include dynamical features such as time- and length-scales and (ii) examine the possibility and flexibility of so-called general Jordan block formations. The present viewpoint asks for a new perspective on the age-old problem of quantum mechanics versus the theory of relativity. To bring these ideas together, we will establish the relation with the Klein-Gordon-Dirac relativistic theory and confirm some dynamical features of both the special and the general relativity theory.
Suppressing Chaos of Warship Power System Based on the Quantum Mechanics Theory
NASA Astrophysics Data System (ADS)
Cong, Xinrong; Li, Longsuo
2014-08-01
Chaos control of marine power system is investigated by adding the Gaussian white noise to the system. The top Lyapunov exponent is computed to detect whether the classical system chaos or not, also the phase portraits are plotted to further verify the obtained results. The classical control of chaos and its quantum counterpart of the marine power system are investigated. The Hamiltonian of the controlled system is given to analyze the quantum counterpart of the classical system, which is based on the quantum mechanics theory.
Yilmazer, Nusret Duygu; Korth, Martin
2013-07-11
Correctly ranking protein-ligand interactions with respect to overall free energy of binding is a grand challenge for virtual drug design. Here we compare the performance of various quantum chemical approaches for tackling this so-called "scoring" problem. Relying on systematically generated benchmark sets of large protein/ligand model complexes based on the PDBbind database, we show that the performance depends first of all on the general level of theory. Comparing classical molecular mechanics (MM), semiempirical quantum mechanical (SQM), and density functional theory (DFT) based methods, we find that enhanced SQM approaches perform very similar to DFT methods and substantially different from MM potentials.
Sine-Gordon quantum mechanics on the complex plane and N=2 gauge theory
He Wei
2010-05-15
We study the relation between the N=2 gauge theory in the {Omega} background and the quantized integral system recently proposed by Nekrasov and Shatashvili. We focus on the simplest case, the pure Yang-Mills theory with the SU(2) gauge group and the corresponding sine-Gordon integral model on the complex plane. We analyze the periodic wave function and the corresponding energy spectrum of the sine-Gordon quantum mechanics, and find this model contains information of the low energy effective theory of the gauge theory.
Kapustin, Anton
2013-06-15
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
Spin Matrix theory: a quantum mechanical model of the AdS/CFT correspondence
NASA Astrophysics Data System (ADS)
Harmark, Troels; Orselli, Marta
2014-11-01
We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U( N). We show that SMT describes super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the g → ∞ limit of SMT can be mapped to the supersymmetric sector of string theory on AdS5 × S 5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite- N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g = 0 it is a theory of N 2 + 1 harmonic oscillators while for large g it becomes 2 N harmonic oscillators.
NASA Astrophysics Data System (ADS)
Zeh, H. D.
1999-04-01
This is a brief reply to S. Goldstein's article "Quantum theory without observers" in Physics Today. It is pointed out that Bohm's pilot wave theory is successful only because it keeps Schrödinger's (exact) wave mechanics unchanged, while the rest of it is observationally meaningless and solely based on classical prejudice.
Facing quantum mechanical reality.
Rohrlich, F
1983-09-23
Two recent precision experiments provide conclusive evidence against any local hidden variables theory and in favor of standard quantum mechanics. Therefore the epistemology and the ontology of quantum mechanics must now be taken more seriously than ever before. The consequences of the standard interpretation of quantum mechanics are summarized in nontechnical language. The implications of the finiteness of Planck's constant (h > 0) for the quantum world are as strange as the implications of the finiteness of the speed of light (c < infinity for space and time in relativity theory. Both lead to realities beyond our common experience that cannot be rejected.
Quantum algorithms for quantum field theories.
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.
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…
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…
NASA Astrophysics Data System (ADS)
Khots, Boris; Khots, Dmitriy
2014-12-01
Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.
Khots, Boris; Khots, Dmitriy
2014-12-10
Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.
NASA Astrophysics Data System (ADS)
Murdin, P.
2000-11-01
A development of quantum theory that was initiated in the 1920s by Werner Heisenberg (1901-76) and Erwin Schrödinger (1887-1961). The theory drew on a proposal made in 1925 Prince Louis de Broglie (1892-1987), that particles have wavelike properties (the wave-particle duality) and that an electron, for example, could in some respects be regarded as a wave with a wavelength that depended on its mo...
A geometrical theory of energy trajectories in quantum mechanics
NASA Astrophysics Data System (ADS)
Hall, Richard L.
1983-02-01
Suppose f(r) is an attractive central potential of the form f(r)=∑ki=1 g(i)( f(i)(r)), where {f(i)} is a set of basis potentials (powers, log, Hulthén, sech2) and {g(i)} is a set of smooth increasing transformations which, for a given f, are either all convex or all concave. Formulas are derived for bounds on the energy trajectories Enl =Fnl(v) of the Hamiltonian H=-Δ+vf(r), where v is a coupling constant. The transform Λ( f)=F is carried out in two steps: f→f¯→F, where f¯(s) is called the kinetic potential of f and is defined by f¯(s)=inf(ψ,f,ψ) subject to ψ∈D⊆L2(R3), where D is the domain of H, ∥ψ∥=1, and (ψ,-Δψ)=s. A table is presented of the basis kinetic potentials { f¯(i)(s)}; the general trajectory bounds F*(v) are then shown to be given by a Legendre transformation of the form (s, f¯*(s)) →(v, F*(v)), where f¯*(s) =∑ki=1g(i)× ( f¯(i)(s)) and F*(v) =mins>0{s+v f¯*(s)}. With the aid of this potential construction set (a kind of Schrödinger Lego), ground-state trajectory bounds are derived for a variety of translation-invariant N-boson and N-fermion problems together with some excited-state trajectory bounds in the special case N=2. This article combines into a single simplified and more general theory the earlier ``potential envelope method'' and the ``method for linear combinations of elementary potentials.''
Quantum-mechanical diffraction theory of light from a small hole: Extinction-theorem approach
NASA Astrophysics Data System (ADS)
Jung, Jesper; Keller, Ole
2015-07-01
In a recent paper [Phys. Rev. A 90, 043830 (2014), 10.1103/PhysRevA.90.043830] it was shown that the so-called aperture response tensor is the central concept in the microscopic quantum theory of light diffraction from a small hole in a flat screen. It was further shown that the quantum mechanical theory of diffraction only requires a preknowledge of the incident field plus the electronic properties of identical screens with and without a hole. Starting from the quantum mechanical expression for the linear conductivity tensor, we study the related causal conductivity tensor paying particular attention to diamagnetic electron dynamics. Using a nonlocal-potential separation assumption, we present a calculation of the diamagnetic causal surface conductivity for a jellium quantum-well screen using a two-dimensional Hartree-Fock model. In the diamagnetic case the difference between the light-unperturbed electron densities for screens with (n0) and without (n∞0) holes are the primary quantities for the diffraction theory. In a central part (Sec. IV) of this article we determine n0 via a quantum-mechanical two-dimensional extinction-theorem approach related to elastic electron scattering from a hole with an electronic selvedge. For heuristic purposes we illustrate aspects of the extinction-theorem theory by applying the approach for an infinitely high potential barrier to the vacuum hole. Finally, we calculate and discuss the aperture response tensor in the small hole limit and in the zeroth-order Born approximation. Our final result for the aperture response tensor establishes the bridge to the anisotropic electric dipole polarizability tensor of the hole. It turns out that the effective optical aperture (hole) size relates closely to the extension of the relevant electronic wave functions scattered from the hole.
Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory.
Schmidt, Steffen; Klevansky, S P
2013-04-28
This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H=p(2)+x(2)(ix)(ε), H=p(2)+(x(2))(δ) and H=p(2)-(x(2))(μ). In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display PT symmetry. To do so, simple arguments that use the Wentzel-Kramers-Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and PT-symmetric 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
NASA Astrophysics Data System (ADS)
Friedberg, R.; Hohenberg, P. C.
2014-09-01
Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call ‘compatible quantum theory (CQT)’, consists of a ‘microscopic’ part (MIQM), which applies to a closed quantum system of any size, and a ‘macroscopic’ part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths (‘c-truths’), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The
Friedberg, R; Hohenberg, P C
2014-09-01
Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call 'compatible quantum theory (CQT)', consists of a 'microscopic' part (MIQM), which applies to a closed quantum system of any size, and a 'macroscopic' part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths ('c-truths'), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The completion of the theory
Introduction to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Griffiths, David J.
2016-09-01
Part I. Theory: 1. The wave function; 2. Time-independent Schrödinger equation; 3. Formalism; 4. Quantum mechanics in three dimensions; 5. Identical particles; Part II. Applications: 6. Time-independent perturbation theory; 7. The variational principle; 8. The WKB approximation; 9. Time-dependent perturbation theory; 10. The adiabatic approximation; 11. Scattering; 12. Afterword; Appendix. Linear algebra.
The quantum mechanics of cosmology.
NASA Astrophysics Data System (ADS)
Hartle, James B.
The following sections are included: * INTRODUCTION * POST-EVERETT QUANTUM MECHANICS * Probability * Probabilities in general * Probabilities in Quantum Mechanics * Decoherent Histories * Fine and Coarse Grained Histories * Decohering Sets of Coarse Grained Histories * No Moment by Moment Definition of Decoherence * Prediction, Retrodiction, and History * Prediction and Retrodiction * The Reconstruction of History * Branches (Illustrated by a Pure ρ) * Sets of Histories with the Same Probabilities * The Origins of Decoherence in Our Universe * On What Does Decoherence Depend? * Two Slit Model * The Caldeira-Leggett Oscillator Model * The Evolution of Reduced Density Matrices * Towards a Classical Domain * The Branch Dependence of Decoherence * Measurement * The Ideal Measurement Model and the Copenhagen Approximation to Quantum Mechanics * Approximate Probabilities Again * Complex Adaptive Systems * Open Questions * GENERALIZED QUANTUM MECHANICS * General Features * Hamiltonian Quantum Mechanics * Sum-Over-Histories Quantum Mechanics for Theories with a Time * Differences and Equivalences between Hamiltonian and Sum-Over-Histories Quantum Mechanics for Theories with a Time * Classical Physics and the Classical Limit of Quantum Mechanics * Generalizations of Hamiltonian Quantum Mechanics * TIME IN QUANTUM MECHANICS * Observables on Spacetime Regions * The Arrow of Time in Quantum Mechanics * Topology in Time * The Generality of Sum Over Histories Quantum Mechanics * THE QUANTUM MECHANICS OF SPACETIME * The Problem of Time * General Covariance and Time in Hamiltonian Quantum Mechanics * The "Marvelous Moment" * A Quantum Mechanics for Spacetime * What we Need * Sum-Over-Histories Quantum Mechanics for Theories Without a Time * Sum-Over-Spacetime-Histories Quantum Mechanics * Extensions and Contractions * The Construction of Sums Over Spacetime Histories * Some Open Questions * PRACTICAL QUANTUM COSMOLOGY * The Semiclassical Regime * The Semiclassical Approximation
NASA Astrophysics Data System (ADS)
Robbin, J. M.
2007-07-01
he hallmark of a good book of problems is that it allows you to become acquainted with an unfamiliar topic quickly and efficiently. The Quantum Mechanics Solver fits this description admirably. The book contains 27 problems based mainly on recent experimental developments, including neutrino oscillations, tests of Bell's inequality, Bose Einstein condensates, and laser cooling and trapping of atoms, to name a few. Unlike many collections, in which problems are designed around a particular mathematical method, here each problem is devoted to a small group of phenomena or experiments. Most problems contain experimental data from the literature, and readers are asked to estimate parameters from the data, or compare theory to experiment, or both. Standard techniques (e.g., degenerate perturbation theory, addition of angular momentum, asymptotics of special functions) are introduced only as they are needed. The style is closer to a non-specialist seminar rather than an undergraduate lecture. The physical models are kept simple; the emphasis is on cultivating conceptual and qualitative understanding (although in many of the problems, the simple models fit the data quite well). Some less familiar theoretical techniques are introduced, e.g. a variational method for lower (not upper) bounds on ground-state energies for many-body systems with two-body interactions, which is then used to derive a surprisingly accurate relation between baryon and meson masses. The exposition is succinct but clear; the solutions can be read as worked examples if you don't want to do the problems yourself. Many problems have additional discussion on limitations and extensions of the theory, or further applications outside physics (e.g., the accuracy of GPS positioning in connection with atomic clocks; proton and ion tumor therapies in connection with the Bethe Bloch formula for charged particles in solids). The problems use mainly non-relativistic quantum mechanics and are organised into three
The Possibility of a New Metaphysics for Quantum Mechanics from Meinong's Theory of Objects
NASA Astrophysics Data System (ADS)
Graffigna, Matías
According to de Ronde it was Bohr's interpretation of Quantum Mechanics (QM) which closed the possibility of understanding physical reality beyond the realm of the actual, so establishing the Orthodox Line of Research. In this sense, it is not the task of any physical theory to look beyond the language and metaphysics supposed by classical physics, in order to account for what QM describes. If one wishes to maintain a realist position (though not nave) regarding physical theories, one seems then to be trapped by an array of concepts that do not allow to understand the main principles involved in the most successful physical theory thus far, mainly: the quantum postulate, the principle of indetermination and the superposition principle. If de Ronde is right in proposing QM can only be completed as a physical theory by the introduction of `new concepts' that admit as real a domain beyond actuality, then a new ontology that goes beyond Aristotelian and Newtonian actualism is needed. It was already in the early 20th century that misunderstood philosopher Alexius von Meinong proposed a Theory of Objects that admits a domain of being beyond existence-actuality. Member of the so called `School of Brentano', Meinong's concerns were oriented to provide an ontology of everything that can be thought of, and at the same time an intentionality theory of how objects are thought of. I wish to argue that in Meinong's theory of objects we find the rudiments of the ontology and the intentionality theory we need to account for QM's basic principles: mainly the possibility of predicating properties of non-entities, or in other words, the possibility of objectively describing a domain of what is, that is different from the domain of actual existence.
A NEW QUANTUM MECHANICAL THEORY OF EVOLUTION OF UNIVERSE AND LIFE
Nigam, M C
1990-01-01
Based upon the principles of ancient science of Life, which admits both consciousness and matter, a new Quantum Mechanical theory of evolution of universe and life is propounded. The theory advocates: Right from the time, the evolution of universe takes place, life also starts evolving energies and ethereal – consciousness (subtler and real) in anti-electrons, as the complimentary partners. The material body acquires electrons for cordoning of atomic nuclei and displaying its manifestation, in the three spatial dimensions in scale of time. The ethereal consciousness acquires anti electrons for gaining necessary energy for superimposing itself over any of the manifested bodies of equivalent electronic energy and deriving the bliss of materialization. The theory is based upon the solid foundation of the ancient science (ethereal consciousness) laid down by the ancient seekers of knowledge like Kapila and Caraka who interpret many of the riddles of modern science on the frontiers of various disciplines of knowledge. PMID:22556513
A new quantum mechanical theory of evolution of universe and life.
Nigam, M C
1990-10-01
Based upon the principles of ancient science of Life, which admits both consciousness and matter, a new Quantum Mechanical theory of evolution of universe and life is propounded. The theory advocates: Right from the time, the evolution of universe takes place, life also starts evolving energies and ethereal - consciousness (subtler and real) in anti-electrons, as the complimentary partners. The material body acquires electrons for cordoning of atomic nuclei and displaying its manifestation, in the three spatial dimensions in scale of time. The ethereal consciousness acquires anti electrons for gaining necessary energy for superimposing itself over any of the manifested bodies of equivalent electronic energy and deriving the bliss of materialization. The theory is based upon the solid foundation of the ancient science (ethereal consciousness) laid down by the ancient seekers of knowledge like Kapila and Caraka who interpret many of the riddles of modern science on the frontiers of various disciplines of knowledge.
Quantum Theory at the Crossroads
NASA Astrophysics Data System (ADS)
Bacciagaluppi, Guido; Valentini, Antony
2013-11-01
Part I. Perspectives on the 1927 Solvay Conference: 1. Historical introduction; 2. De Broglie's pilot-wave theory; 3. From matrix mechanics to quantum mechanics; 4. Schrödinger's wave mechanics; Part II. Quantum Foundations and the 1927 Solvay Conference: 5. Quantum theory and the measurement problem; 6. Interference, superposition, and wave packet collapse; 7. Locality and incompleteness; 8. Time, determinism, and the spacetime framework; 9. Guiding fields in 3-space; 10. Scattering and measurement in de Broglie's pilot-wave theory; 11. Pilot-wave theory in retrospect; 12. Beyond the Bohr-Einstein debate; Part III. The Proceedings of the 1927 Solvay Conference: The intensity of X-ray reflection; Disagreements between experiment and the electromagnetic theory of radiation; The new dynamics of quanta; Quantum mechanics; Wave mechanics; General discussion; Appendix; References; Index.
Quantum Theory at the Crossroads
NASA Astrophysics Data System (ADS)
Bacciagaluppi, Guido; Valentini, Antony
2009-10-01
Part I. Perspectives on the 1927 Solvay Conference: 1. Historical introduction; 2. De Broglie's pilot-wave theory; 3. From matrix mechanics to quantum mechanics; 4. Schrödinger's wave mechanics; Part II. Quantum Foundations and the 1927 Solvay Conference: 5. Quantum theory and the measurement problem; 6. Interference, superposition, and wave packet collapse; 7. Locality and incompleteness; 8. Time, determinism, and the spacetime framework; 9. Guiding fields in 3-space; 10. Scattering and measurement in de Broglie's pilot-wave theory; 11. Pilot-wave theory in retrospect; 12. Beyond the Bohr-Einstein debate; Part III. The Proceedings of the 1927 Solvay Conference: The intensity of X-ray reflection; Disagreements between experiment and the electromagnetic theory of radiation; The new dynamics of quanta; Quantum mechanics; Wave mechanics; General discussion; Appendix; References; Index.
General quantum-mechanical setting for field-antifield formalism as a hyper-gauge theory
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.
2016-09-01
A general quantum-mechanical setting is proposed for the field-antifield formalism as a unique hyper-gauge theory in the field-antifield space. We formulate a Schr\\"odinger-type equation to describe the quantum evolution in a "current time" purely formal in its nature. The corresponding Hamiltonian is defined in the form of a supercommutator of the delta-operator with a hyper-gauge Fermion. The initial wave function is restricted to be annihilated with the delta-operator. The Schr\\"odinger's equation is resolved in a closed form of the path integral, whose action contains the symmetric Weyl's symbol of the Hamiltonian. We take the path integral explicitly in the case of being a hyper-gauge Fermion an arbitrary function rather than an operator.
A quantum-mechanical perspective on linear response theory within polarizable embedding
NASA Astrophysics Data System (ADS)
List, Nanna Holmgaard; Norman, Patrick; Kongsted, Jacob; Jensen, Hans Jørgen Aagaard
2017-06-01
We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole structures as well as residues of the individual terms are discussed. In addition to providing a thorough justification for the descriptions used in polarizable embedding models, this theoretical analysis clarifies which form of the response function to use and highlights complications in separating out subsystem contributions to molecular properties. The basic features of the presented expressions and various approximate forms are illustrated by their application to a composite model system.
NASA Astrophysics Data System (ADS)
Banks, Tom
2008-09-01
1. Introduction; 2. Quantum theory of free scalar fields; 3. Interacting field theory; 4. Particles of spin one, and gauge invariance; 5. Spin 1/2 particles and Fermi statistics; 6. Massive quantum electrodynamics; 7. Symmetries, Ward identities and Nambu Goldstone bosons; 8. Non-abelian gauge theory; 9. Renormalization and effective field theory; 10. Instantons and solitons; 11. Concluding remarks; Appendices; References; Index.
Quantum Field Theory Tools:. a Mechanism of Mass Generation of Gauge Fields
NASA Astrophysics Data System (ADS)
Flores-Baez, F. V.; Godina-Nava, J. J.; Ordaz-Hernandez, G.
We present a simple mechanism for mass generation of gauge fields for the Yang-Mills theory, where two gauge SU(N)-connections are introduced to incorporate the mass term. Variations of these two sets of gauge fields compensate each other under local gauge transformations with the local gauge transformations of the matter fields, preserving gauge invariance. In this way the mass term of gauge fields is introduced without violating the local gauge symmetry of the Lagrangian. Because the Lagrangian has strict local gauge symmetry, the model is a renormalizable quantum model. This model, in the appropriate limit, comes from a class of universal Lagrangians which define a new massive Yang-Mills theories without Higgs bosons.
ERIC Educational Resources Information Center
Velentzas, Athanasios; Halkia, Krystallia; Skordoulis, Constantine
2007-01-01
This work investigates the presence of Thought Experiments (TEs) which refer to the theory of relativity and to quantum mechanics in physics textbooks and in books popularizing physics theories. A further point of investigation is whether TEs--as presented in popular physics books--can be used as an introduction to familiarize secondary school…
ERIC Educational Resources Information Center
Velentzas, Athanasios; Halkia, Krystallia; Skordoulis, Constantine
2007-01-01
This work investigates the presence of Thought Experiments (TEs) which refer to the theory of relativity and to quantum mechanics in physics textbooks and in books popularizing physics theories. A further point of investigation is whether TEs--as presented in popular physics books--can be used as an introduction to familiarize secondary school…
Quantum Transition State Theory
NASA Astrophysics Data System (ADS)
Waalkens, Holger
2009-03-01
The main idea of Wigner's transition state theory (TST) is to compute reaction rates from the flux through a dividing surface placed between reactants and products. In order not to overestimate the rate the dividing surface needs to have the no- recrossing property, i.e. reactive trajectories cross the dividing surface exactly once, and nonreactive trajectories do not cross it at all. The long standing problem of how to construct such a diving surface for multi-degree-of-freedom systems was solved only recently using ideas from dynamical systems theory. Here a normal form allows for a local decoupling of the classical dynamics which leads to the explicit construction of the phase space structures that govern the reaction dynamics through transition states. The dividing surface is spanned by a normally hyperbolic manifold which is the mathematical manifestation of the transition state as an unstable invariant subsystem of one degree of freedom less than the full system. The mere existence of a quantum version of TST is discussed controversially in the literature. The key isssue is the presence of quantum mechanical tunneling which prohibits the existence of a local theory analogous to the classical case. Various approaches have been devloped to overcome this problem by propagating quantum wavefunctions through the transition state region. These approaches have in common that they are computationally very expensive which seriously limits their applicability. In contrast the approach by Roman Schubert, Stephen Wiggins and myself is local in nature. A quantum normal form allows us to locally decouple the quantum dynamics to any desired order in Planck's constant. This yields not only the location of the scattering and resonance wavefunctions relative to the classical phase space structures, but also leads to very efficient algorithms to compute cumulative reaction probabilities and Gamov-Siegert resonances which are the quantum imprints of the transition state.
NASA Astrophysics Data System (ADS)
Mouloudakis, K.; Kominis, I. K.
2017-02-01
Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We show here that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures, and quantum retrodiction, thus exemplifying the paradigm of quantum biology, satisfies the Ozawa bound as well as the Lanford-Robinson bound on information extraction. By considering Groenewold's information, the quantum information extracted during the reaction, we reproduce the known and unravel other magnetic-field effects not conveyed by reaction yields.
Mouloudakis, K; Kominis, I K
2017-02-01
Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We show here that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures, and quantum retrodiction, thus exemplifying the paradigm of quantum biology, satisfies the Ozawa bound as well as the Lanford-Robinson bound on information extraction. By considering Groenewold's information, the quantum information extracted during the reaction, we reproduce the known and unravel other magnetic-field effects not conveyed by reaction yields.
Time, Chance and Quantum Theory
NASA Astrophysics Data System (ADS)
Sudbery, Anthony
I propose an understanding of Everett and Wheeler's relative-state interpretation of quantum mechanics, which restores the feature of indeterminism to the theory. This incorporates a theory of probability as truth values in a many-valued logic for future statements, and a contextual theory of truth which gives objective and subjective perspectives equal validity.
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.
Application of Quantum Mechanical Interpretation of Kohn-Sham Theory to the Hooke's Atom.
NASA Astrophysics Data System (ADS)
Qian, Z.; Sahni, V.
1997-03-01
The quantum-mechanical interpretation of Kohn-Sham theory is in terms of two fields. The first E_ee(r), representative of Pauli and Coulomb correlations, is determined by Coulomb's law from the pair-correlation density. The second Z_t_c(r) is representative of the correlation contribution to the kinetic energy, and is proportional to the difference in fields obtained as the derivative of the noninteracting and interacting system kinetic-energy-density tensors. The potential (functional derivative) v_ee^KS(r)=δE_ee^KS[ρ]/δρ (r) where E_ee^KS[ ρ] is the Kohn-Sham electron-interaction energy functional, is the work done to move an electron in the sum of the fields. The quantum-mechanical electron-interaction E_ee[ρ] and correlation-kinetic T_c[ρ] energy components of E_ee^KS[ρ] can also be expressed in virial form in terms of the fields E_ee(r) and Z_t_c(r) , respectively. In this paper we consider the ground state of the Hooke's atom from this physical perspective, and present an entirely analytical solution of the kinetic-energy-density tensors, the Hartree, Pauli, Coulomb, and correlation-kinetic components of the fields, potentials, their asymptotic structure, and energies.
Bohmian quantum mechanics with quantum trajectories
NASA Astrophysics Data System (ADS)
Jeong, Yeuncheol
The quantum trajectory method in the hydrodynamical formulation of Madelung-Bohm-Takabayasi quantum mechanics is an example of showing the cognitive importance of scientific illustrations and metaphors, especially, in this case, in computational quantum chemistry and electrical engineering. The method involves several numerical schemes of solving a set of hydrodynamical equations of motion for probability density fluids, based on the propagation of those probability density trajectories. The quantum trajectory method gives rise to, for example, an authentic quantum electron transport theory of motion to, among others, classically-minded applied scientists who probably have less of a commitment to traditional quantum mechanics. They were not the usual audience of quantum mechanics and simply choose to use a non-Copenhagen type interpretation to their advantage. Thus, the metaphysical issues physicists had a trouble with are not the main concern of the scientists. With the advantages of a visual and illustrative trajectory, the quantum theory of motion by Bohm effectively bridges quantum and classical physics, especially, in the mesoscale domain. Without having an abrupt shift in actions and beliefs from the classical to the quantum world, scientists and engineers are able to enjoy human cognitive capacities extended into the quantum mechanical domain.
Resonances of quantum mechanical scattering systems and Lax-Phillips scattering theory
NASA Astrophysics Data System (ADS)
Baumgärtel, Hellmut
2010-11-01
For selected classes of quantum mechanical scattering systems a canonical association of a decay semigroup is presented. The spectrum of the generator of this semigroup is a pure eigenvalue spectrum and it coincides with the set of all resonances. The essential condition for the results is the meromorphic continuability of the scattering matrix onto {C}setminus (-infty,0] and the rims {R}-± i0. Further finite multiplicity is assumed. The approach is based on an adaption of the Lax-Phillips scattering theory to semibounded Hamiltonians. It is applied to trace class perturbations with analyticity conditions. A further example is the potential scattering for central-symmetric potentials with compact support and angular momentum 0.
Hawking temperature: an elementary approach based on Newtonian mechanics and quantum theory
NASA Astrophysics Data System (ADS)
Pinochet, Jorge
2016-01-01
In 1974, the British physicist Stephen Hawking discovered that black holes have a characteristic temperature and are therefore capable of emitting radiation. Given the scientific importance of this discovery, there is a profuse literature on the subject. Nevertheless, the available literature ends up being either too simple, which does not convey the true physical significance of the issue, or too technical, which excludes an ample segment of the audience interested in science, such as physics teachers and their students. The present article seeks to remedy this shortcoming. It develops a simple and plausible argument that provides insight into the fundamental aspects of Hawking’s discovery, which leads to an approximate equation for the so-called Hawking temperature. The exposition is mainly intended for physics teachers and their students, and it only requires elementary algebra, as well as basic notions of Newtonian mechanics and quantum theory.
Analysis of fission-fragment mass distribution within the quantum-mechanical fragmentation theory
NASA Astrophysics Data System (ADS)
Singh, Pardeep; Kaur, Harjeet
2016-11-01
The fission-fragment mass distribution is analysed for the 208Pb(18O, f) reaction within the quantum-mechanical fragmentation theory (QMFT). The reaction potential has been calculated by taking the binding energies, Coulomb potential and proximity potential of all possible decay channels and a stationary Schrödinger equation has been solved numerically to calculate the fission-fragment yield. The overall results for mass distribution are compared with those obtained in experiment. Fine structure dips in yield, corresponding to fragment shell closures at Z = 50 and N=82, which are observed by Bogachev et al., are reproduced successfully in the present calculations. These calculations will help to estimate the formation probabilities of fission fragments and to understand many related phenomena occurring in the fission process.
NASA Astrophysics Data System (ADS)
Blencowe, Miles
The emergence of the macroscopic classical world from the microscopic quantum world is commonly understood to be a consequence of the fact that any given quantum system is open, unavoidably interacting with unobserved environmental degrees of freedom that will cause initial quantum superposition states of the system to decohere, resulting in classical mixtures of either-or alternatives. A fundamental question concerns how large a macroscopic object can be placed in a manifest quantum state, such as a center of mass quantum superposition state, under conditions where the effects of the interacting environmental degrees of freedom are reduced (i.e. in ultrahigh vacuum and at ultralow temperatures). Recent experiments have in fact demonstrated manifest quantum behavior in nano-to-micron-scale mechanical systems. Gravity has been invoked in various ways as playing a possible fundamental role in enforcing classicality of matter systems beyond a certain scale. Adopting the viewpoint that the standard perturbative quantization of general relativity provides an effective description of quantum gravity that is valid at ordinary energies, we show that it is possible to describe quantitatively how gravity as an environment can induce the decoherence of matter superposition states. The justification for such an approach follows from the fact that we are considering laboratory scale systems, where the matter is localized to regions of small curvature. As with other low energy effects, such as the quantum gravity correction to the Newtonian potential between two ordinary masses, it should be possible to quantitatively evaluate gravitationally induced decoherence rates by employing standard perturbative quantum gravity as an effective field theory; whatever the final form the eventual correct quantum theory of gravity takes, it must converge in its predictions with the effective field theory description at low energies. Research supported by the National Science Foundation (NSF
Thellamurege, Nandun M.; Si, Dejun; Cui, Fengchao; Li, Hui
2014-05-07
A combined quantum mechanical/molecular mechanical/continuum (QM/MM/C) style second order Møller-Plesset perturbation theory (MP2) method that incorporates induced dipole polarizable force field and induced surface charge continuum solvation model is established. The Z-vector method is modified to include induced dipoles and induced surface charges to determine the MP2 response density matrix, which can be used to evaluate MP2 properties. In particular, analytic nuclear gradient is derived and implemented for this method. Using the Assisted Model Building with Energy Refinement induced dipole polarizable protein force field, the QM/MM/C style MP2 method is used to study the hydrogen bonding distances and strengths of the photoactive yellow protein chromopore in the wild type and the Glu46Gln mutant.
Quantum theory and gravitation
Not Available
1986-01-01
This journal presents information on the following subjects: some problems of the natural sciences; quantum theory of fields and origin of gravity: gauge group of gravity, spinors, and anomalies; scalar manifolds and Jordan pairs in supergravity; quantum de Sitter fiber bundle interpretation of hadron extension; why the universe is so large; symplectic manifolds; coadjoint orbits, and mean field theory; and quantum theoretical orgin of spacetime structure.
Reverse engineering quantum field theory
NASA Astrophysics Data System (ADS)
Oeckl, Robert
2012-12-01
An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.
From Classical to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Esposito, Giampiero; Marmo, Giuseppe; Sudarshan, George
2010-06-01
Preface; Acknowledgements; Part I. From Classical to Wave Mechanics: 1. Experimental foundations of quantum theory; 2. Classical dynamics; 3. Wave equations; 4. Wave mechanics; 5. Applications of wave mechanics; 6. Introduction to spin; 7. Perturbation theory; 8. Scattering theory; Part II. Weyl Quantization and Algebraic Methods: 9. Weyl quantization; 10. Harmonic oscillators and quantum optics; 11. Angular momentum operators; 12. Algebraic methods for eigenvalue problems; 13. From density matrix to geometric phases; Part III. Selected Topics: 14. From classical to quantum statistical mechanics; 15. Lagrangian and phase-space formulations; 16. Dirac equation and no-interaction theorem; References; Index.
From Classical to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Esposito, Giampiero; Marmo, Giuseppe; Sudarshan, George
2004-03-01
Preface; Acknowledgements; Part I. From Classical to Wave Mechanics: 1. Experimental foundations of quantum theory; 2. Classical dynamics; 3. Wave equations; 4. Wave mechanics; 5. Applications of wave mechanics; 6. Introduction to spin; 7. Perturbation theory; 8. Scattering theory; Part II. Weyl Quantization and Algebraic Methods: 9. Weyl quantization; 10. Harmonic oscillators and quantum optics; 11. Angular momentum operators; 12. Algebraic methods for eigenvalue problems; 13. From density matrix to geometric phases; Part III. Selected Topics: 14. From classical to quantum statistical mechanics; 15. Lagrangian and phase-space formulations; 16. Dirac equation and no-interaction theorem; References; Index.
Grassmann matrix quantum mechanics
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
Grassmann matrix quantum mechanics
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. In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.
NASA Astrophysics Data System (ADS)
Wang, Hao; Yang, Weitao
2016-06-01
We developed a new method to calculate the atomic polarizabilities by fitting to the electrostatic potentials (ESPs) obtained from quantum mechanical (QM) calculations within the linear response theory. This parallels the conventional approach of fitting atomic charges based on electrostatic potentials from the electron density. Our ESP fitting is combined with the induced dipole model under the perturbation of uniform external electric fields of all orientations. QM calculations for the linear response to the external electric fields are used as input, fully consistent with the induced dipole model, which itself is a linear response model. The orientation of the uniform external electric fields is integrated in all directions. The integration of orientation and QM linear response calculations together makes the fitting results independent of the orientations and magnitudes of the uniform external electric fields applied. Another advantage of our method is that QM calculation is only needed once, in contrast to the conventional approach, where many QM calculations are needed for many different applied electric fields. The molecular polarizabilities obtained from our method show comparable accuracy with those from fitting directly to the experimental or theoretical molecular polarizabilities. Since ESP is directly fitted, atomic polarizabilities obtained from our method are expected to reproduce the electrostatic interactions better. Our method was used to calculate both transferable atomic polarizabilities for polarizable molecular mechanics' force fields and nontransferable molecule-specific atomic polarizabilities.
Wang, Hao; Yang, Weitao
2016-06-14
We developed a new method to calculate the atomic polarizabilities by fitting to the electrostatic potentials (ESPs) obtained from quantum mechanical (QM) calculations within the linear response theory. This parallels the conventional approach of fitting atomic charges based on electrostatic potentials from the electron density. Our ESP fitting is combined with the induced dipole model under the perturbation of uniform external electric fields of all orientations. QM calculations for the linear response to the external electric fields are used as input, fully consistent with the induced dipole model, which itself is a linear response model. The orientation of the uniform external electric fields is integrated in all directions. The integration of orientation and QM linear response calculations together makes the fitting results independent of the orientations and magnitudes of the uniform external electric fields applied. Another advantage of our method is that QM calculation is only needed once, in contrast to the conventional approach, where many QM calculations are needed for many different applied electric fields. The molecular polarizabilities obtained from our method show comparable accuracy with those from fitting directly to the experimental or theoretical molecular polarizabilities. Since ESP is directly fitted, atomic polarizabilities obtained from our method are expected to reproduce the electrostatic interactions better. Our method was used to calculate both transferable atomic polarizabilities for polarizable molecular mechanics' force fields and nontransferable molecule-specific atomic polarizabilities.
NASA Astrophysics Data System (ADS)
Gulden, Tobias
Increased interest in non-Hermitian quantum systems calls for the development of efficient methods to treat these. This interest was sparked by the introduction of PT-symmetry and the study of mathematical mappings which map conventional statistical or quantum mechanics onto non-Hermitian quantum operators. One of the most common methods in quantum mechanics is the semiclassial approximation which requires integration along trajectories that solve classical equations of motion. However in non-Hermitian systems these solutions are rarely attainable. We borrow concepts from algebraic topology to develop methods to avoid solving the equations of motion and avoid straightforward integration altogether. We apply these methods to solve the semiclassical problem for three largely dierent systems and demonstrate their usefulness for Hermitian and non-Hermitian systems alike.
Liu, Peng; Li, Chen; Wang, Dunyou
2017-09-25
The Cl(-) + CH3I → CH3Cl + I(-) reaction in water was studied using combined multi-level quantum mechanism theories and molecular mechanics with an explicit water solvent model. The study shows a significant influence of aqueous solution on the structures of the stationary points along the reaction pathway. A detailed, atomic-level evolution of the reaction mechanism shows a concerted one-bond-broken and one-bond-formed mechanism, as well as a synchronized charge-transfer process. The potentials of mean force calculations with the CCSD(T) and DFT treatments of the solute produce a free activation barrier at 24.5 kcal/mol and 19.0 kcal/mol respectively, which agrees with the experimental one at 22.0 kcal/mol. The solvent effects have also been quantitatively analyzed: in total, the solvent effects raise the activation energy by 20.2 kcal/mol, which shows a significant impact on this reaction in water.
Theory of self-resonance after inflation. II. Quantum mechanics and particle-antiparticle asymmetry
NASA Astrophysics Data System (ADS)
Hertzberg, Mark P.; Karouby, Johanna; Spitzer, William G.; Becerra, Juana C.; Li, Lanqing
2014-12-01
We further develop a theory of self-resonance after inflation in a large class of models involving multiple scalar fields. We concentrate on inflaton potentials that carry an internal symmetry, but also analyze weak breaking of this symmetry. This is the second part of a two-part series of papers. Here in Part 2 we develop an understanding of the resonance structure from the underlying many-particle quantum mechanics. We begin with a small-amplitude analysis, which obtains the central resonant wave numbers, and relate it to perturbative processes. We show that the dominant resonance structure is determined by (i) the nonrelativistic scattering of many quantum particles and (ii) the application of Bose-Einstein statistics to the adiabatic and isocurvature modes, as introduced in Part 1 [M. P. Hertzberg et al., Phys. Rev. D 90, 123528 (2014)]. Other resonance structures are understood in terms of annihilations and decays. We set up Bunch-Davies vacuum initial conditions during inflation and track the evolution of modes including Hubble expansion. In the case of a complex inflaton carrying an internal U(1) symmetry, we show that when the isocurvature instability is active, the inflaton fragments into separate regions of ϕ -particles and anti-ϕ -particles. We then introduce a weak breaking of the U(1) symmetry; this can lead to baryogenesis, as shown by some of us recently [M. P. Hertzberg and J. Karouby, Phys. Lett. B 737, 34 (2014); Phys. Rev. D 89, 063523 (2014)]. Then using our results, we compute corrections to the particle-antiparticle asymmetry from this preheating era.
Quantum Electrodynamics: Theory
Lincoln, Don
2016-03-30
The Standard Model of particle physics is composed of several theories that are added together. The most precise component theory is the theory of quantum electrodynamics or QED. In this video, Fermilab’s Dr. Don Lincoln explains how theoretical QED calculations can be done. This video links to other videos, giving the viewer a deep understanding of the process.
Quantum Electrodynamics: Theory
Lincoln, Don
2016-07-12
The Standard Model of particle physics is composed of several theories that are added together. The most precise component theory is the theory of quantum electrodynamics or QED. In this video, Fermilabâs Dr. Don Lincoln explains how theoretical QED calculations can be done. This video links to other videos, giving the viewer a deep understanding of the process.
QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES
G. GEIGER; ET AL
2000-11-01
The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory.
NASA Astrophysics Data System (ADS)
De Visser, Sam; Quesne, Matthew; Ward, Richard
2013-12-01
Cysteine protease enzymes are important for human physiology and catalyze key protein degradation pathways. These enzymes react via a nucleophilic reaction mechanism that involves a cysteine residue and the proton of a proximal histidine. Particularly efficient inhibitors of these enzymes are nitrile-based, however, the details of the catalytic reaction mechanism currently are poorly understood. To gain further insight into the inhibition of these molecules, we have performed a combined density functional theory and quantum mechanics/molecular mechanics study on the reaction of a nitrile-based inhibitor with the enzyme active site amino acids. We show here that small perturbations to the inhibitor structure can have dramatic effects on the catalysis and inhibition processes. Thus, we investigated a range of inhibitor templates and show that specific structural changes reduce the inhibitory efficiency by several orders of magnitude. Moreover, as the reaction takes place on a polar surface, we find strong differences between the DFT and QM/MM calculated energetics. In particular, the DFT model led to dramatic distortions from the starting structure and the convergence to a structure that would not fit the enzyme active site. In the subsequent QM/MM study we investigated the use of mechanical versus electronic embedding on the kinetics, thermodynamics and geometries along the reaction mechanism. We find minor effects on the kinetics of the reaction but large geometric and thermodynamics differences as a result of inclusion of electronic embedding corrections. The work here highlights the importance of model choice in the investigation of this biochemical reaction mechanism.
Sindelka, Milan; Moiseyev, Nimrod
2006-04-27
We study a general problem of the translational/rotational/vibrational/electronic dynamics of a diatomic molecule exposed to an interaction with an arbitrary external electromagnetic field. The theory developed in this paper is relevant to a variety of specific applications, such as alignment or orientation of molecules by lasers, trapping of ultracold molecules in optical traps, molecular optics and interferometry, rovibrational spectroscopy of molecules in the presence of intense laser light, or generation of high order harmonics from molecules. Starting from the first quantum mechanical principles, we derive an appropriate molecular Hamiltonian suitable for description of the center of mass, rotational, vibrational, and electronic molecular motions driven by the field within the electric dipole approximation. Consequently, the concept of the Born-Oppenheimer separation between the electronic and the nuclear degrees of freedom in the presence of an electromagnetic field is introduced. Special cases of the dc/ac-field limits are then discussed separately. Finally, we consider a perturbative regime of a weak dc/ac field, and obtain simple analytic formulas for the associated Born-Oppenheimer translational/rotational/vibrational molecular Hamiltonian.
Yang, Weitao
2016-01-01
We developed a new method to calculate the atomic polarizabilities by fitting to the electrostatic potentials (ESPs) obtained from quantum mechanical (QM) calculations within the linear response theory. This parallels the conventional approach of fitting atomic charges based on electrostatic potentials from the electron density. Our ESP fitting is combined with the induced dipole model under the perturbation of uniform external electric fields of all orientations. QM calculations for the linear response to the external electric fields are used as input, fully consistent with the induced dipole model, which itself is a linear response model. The orientation of the uniform external electric fields is integrated in all directions. The integration of orientation and QM linear response calculations together makes the fitting results independent of the orientations and magnitudes of the uniform external electric fields applied. Another advantage of our method is that QM calculation is only needed once, in contrast to the conventional approach, where many QM calculations are needed for many different applied electric fields. The molecular polarizabilities obtained from our method show comparable accuracy with those from fitting directly to the experimental or theoretical molecular polarizabilities. Since ESP is directly fitted, atomic polarizabilities obtained from our method are expected to reproduce the electrostatic interactions better. Our method was used to calculate both transferable atomic polarizabilities for polarizable molecular mechanics’ force fields and nontransferable molecule-specific atomic polarizabilities. PMID:27305996
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.
NASA Astrophysics Data System (ADS)
Hollowood, Timothy J.
2016-07-01
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists' laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr's quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.
Epigenetics: Biology's Quantum Mechanics.
Jorgensen, Richard A
2011-01-01
The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider.
Tang, Jau
1996-02-01
As an alternative to better physical explanations of the mechanisms of quantum interference and the origins of uncertainty broadening, a linear hopping model is proposed with ``color-varying`` dynamics to reflect fast exchange between time-reversed states. Intricate relations between this model, particle-wave dualism, and relativity are discussed. The wave function is shown to possess dual characteristics of a stable, localized ``soliton-like`` de Broglie wavelet and a delocalized, interfering Schroedinger carrier wave function.
Yuan, Jie; Liu, Yun
This paper relates the quantum-mechanical equilibrium isotopic fractionation correction to the radiocarbon dating method by Eq. 9, and also shows the significant influence of temperature on the method. It is suggested that the correction is a function of the frequencies and temperature of a specific sample and these two variables can be evaluated theoretically by the ab initio quantum calculations and experimentally by analyzing the clumped-isotope ratios in it, respectively. This paper also suggests that the (14)C/(12)C ratio in the atmosphere in geological time can be calculated by Eq. 10.
Jang, Seogjoo
2007-11-07
The Forster resonance energy transfer theory is generalized for inelastic situations with quantum mechanical modulation of the donor-acceptor coupling. Under the assumption that the modulations are independent of the electronic excitation of the donor and the acceptor, a general rate expression is derived, which involves two dimensional frequency-domain convolution of the donor emission line shape, the acceptor absorption line shape, and the spectral density of the modulation of the donor-acceptor coupling. For two models of modulation, detailed rate expressions are derived. The first model is the fluctuation of the donor-acceptor distance, approximated as a quantum harmonic oscillator coupled to a bath of other quantum harmonic oscillators. The distance fluctuation results in additional terms in the rate, which in the small fluctuation limit depend on the inverse eighth power of the donor-acceptor distance. The second model is the fluctuation of the torsional angle between the two transition dipoles, which is modeled as a quantum harmonic oscillator coupled to a bath of quantum harmonic oscillators and causes sinusoidal modulation of the donor-acceptor coupling. The rate expression has new elastic and inelastic terms, depending sensitively on the value of the minimum energy torsional angle. Experimental implications of the present theory and some of the open theoretical issues are discussed.
Propensity, Probability, and Quantum Theory
NASA Astrophysics Data System (ADS)
Ballentine, Leslie E.
2016-08-01
Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.
Communication: Quantum mechanics without wavefunctions
Schiff, Jeremy; Poirier, Bill
2012-01-21
We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.
NASA Astrophysics Data System (ADS)
Griffiths, Robert B.
2003-11-01
1. Introduction; 2. Wave functions; 3. Linear algebra in Dirac notation; 4. Physical properties; 5. Probabilities and physical variables; 6. Composite systems and tensor products; 7. Unitary dynamics; 8. Stochastic histories; 9. The Born rule; 10. Consistent histories; 11. Checking consistency; 12. Examples of consistent families; 13. Quantum interference; 14. Dependent (contextual) events; 15. Density matrices; 16. Quantum reasoning; 17. Measurements I; 18. Measurements II; 19. Coins and counterfactuals; 20. Delayed choice paradox; 21. Indirect measurement paradox; 22. Incompatibility paradoxes; 23. Singlet state correlations; 24. EPR paradox and Bell inequalities; 25. Hardy's paradox; 26. Decoherence and the classical limit; 27. Quantum theory and reality; Bibliography.
Testing Nonassociative Quantum Mechanics.
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.
Nuclear Quantum Gravitation - The Correct Theory
NASA Astrophysics Data System (ADS)
Kotas, Ronald
2016-03-01
Nuclear Quantum Gravitation provides a clear, definitive Scientific explanation of Gravity and Gravitation. It is harmonious with Newtonian and Quantum Mechanics, and with distinct Scientific Logic. Nuclear Quantum Gravitation has 10 certain, Scientific proofs and 21 more good indications. With this theory the Physical Forces are obviously Unified. See: OBSCURANTISM ON EINSTEIN GRAVITATION? http://www.santilli- Foundation.org/inconsistencies-gravitation.php and Einstein's Theory of Relativity versus Classical Mechanics http://www.newtonphysics.on.ca/einstein/
Scale relativity theory and integrative systems biology: 2. Macroscopic quantum-type mechanics.
Nottale, Laurent; Auffray, Charles
2008-05-01
In these two companion papers, we provide an overview and a brief history of the multiple roots, current developments and recent advances of integrative systems biology and identify multiscale integration as its grand challenge. Then we introduce the fundamental principles and the successive steps that have been followed in the construction of the scale relativity theory, which aims at describing the effects of a non-differentiable and fractal (i.e., explicitly scale dependent) geometry of space-time. The first paper of this series was devoted, in this new framework, to the construction from first principles of scale laws of increasing complexity, and to the discussion of some tentative applications of these laws to biological systems. In this second review and perspective paper, we describe the effects induced by the internal fractal structures of trajectories on motion in standard space. Their main consequence is the transformation of classical dynamics into a generalized, quantum-like self-organized dynamics. A Schrödinger-type equation is derived as an integral of the geodesic equation in a fractal space. We then indicate how gauge fields can be constructed from a geometric re-interpretation of gauge transformations as scale transformations in fractal space-time. Finally, we introduce a new tentative development of the theory, in which quantum laws would hold also in scale space, introducing complexergy as a measure of organizational complexity. Initial possible applications of this extended framework to the processes of morphogenesis and the emergence of prokaryotic and eukaryotic cellular structures are discussed. Having founded elements of the evolutionary, developmental, biochemical and cellular theories on the first principles of scale relativity theory, we introduce proposals for the construction of an integrative theory of life and for the design and implementation of novel macroscopic quantum-type experiments and devices, and discuss their potential
Liu, Peng; Zhang, Jingxue; Wang, Dunyou
2017-06-07
A double-inversion mechanism of the F(-) + CH3I reaction was discovered in aqueous solution using combined multi-level quantum mechanics theories and molecular mechanics. The stationary points along the reaction path show very different structures to the ones in the gas phase due to the interactions between the solvent and solute, especially strong hydrogen bonds. An intermediate complex, a minimum on the potential of mean force, was found to serve as a connecting-link between the abstraction-induced inversion transition state and the Walden-inversion transition state. The potentials of mean force were calculated with both the DFT/MM and CCSD(T)/MM levels of theory. Our calculated free energy barrier of the abstraction-induced inversion is 69.5 kcal mol(-1) at the CCSD(T)/MM level of theory, which agrees with the one at 72.9 kcal mol(-1) calculated using the Born solvation model and gas-phase data; and our calculated free energy barrier of the Walden inversion is 24.2 kcal mol(-1), which agrees very well with the experimental value at 25.2 kcal mol(-1) in aqueous solution. The calculations show that the aqueous solution makes significant contributions to the potentials of mean force and exerts a big impact on the molecular-level evolution along the reaction pathway.
NASA Astrophysics Data System (ADS)
Höhn, Philipp Andres; Wever, Christopher S. P.
2017-01-01
We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and define S 's state as O 's "catalog of knowledge" about S . From the rules we derive the state spaces for N elementary systems and show that (a) they coincide with the set of density matrices over an N -qubit Hilbert space C2N; (b) states evolve unitarily under the group PSU (2N) according to the von Neumann evolution equation; and (c) O 's binary questions correspond to projective Pauli operator measurements with outcome probabilities given by the Born rule. As a by-product, this results in a propositional formulation of quantum theory. Aside from offering an informational explanation for the theory's architecture, the reconstruction also unravels previously unnoticed structural insights. We show that, in a derived quadratic information measure, (d) qubits satisfy inequalities which bound the information content in any set of mutually complementary questions to 1 bit; and (e) maximal sets of mutually complementary questions for one and two qubits must carry precisely 1 bit of information in pure states. The latter relations constitute conserved informational charges which define the unitary groups and, together with their conservation conditions, the sets of pure quantum states. These results highlight information as a "charge of quantum theory" and the benefits of this informational approach. This work emphasizes the sufficiency of restricting to an observer's information to reconstruct the theory and completes the quantum reconstruction initiated in a companion paper (P. Höhn, arXiv:1412.8323).
Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory
NASA Technical Reports Server (NTRS)
Sun, Yan; Kouri, Donald J.; Truhlar, Donald G.; Schwenke, David W.
1990-01-01
New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.
Computational quantum field theory
NASA Astrophysics Data System (ADS)
Grobe, Rainer
2006-05-01
I will give an overview on recent attempts to solve the time-dependent Dirac equation for the electron-positron field operator. These numerical solutions permit a first temporally and spatially resolved insight into the mechanisms of how an electron-positron pair can be created from vacuum in a very strong force field. This approach has helped to illuminate a wide range of controversial questions. Some of these questions arise for complicated physical situations such as how an electron scatters off a supercritical potential barrier (Klein paradox). This requires the application of quantum field theory to study the combined effect of the pair-production due to the supercriticality of the potential together with the scattering at the barrier involving the Pauli-principle. Other phenomena include Schr"odinger's Zitterbewegung and the localization problem for a relativistic particle. This work has been supported by the NSF and Research Corporation. P. Krekora, K. Cooley, Q. Su and R. Grobe, Phys. Rev. Lett. 95, 070403 (2005). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 93, 043004 (2004). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 92, 040406 (2004).
Non-Hermitian quantum mechanics
NASA Astrophysics Data System (ADS)
Jones-Smith, Katherine
The basic structure of quantum mechanics was delineated in the early days of the theory and has not been modified since. One of the fundamental assumptions used in formulating the theory is that operators are represented by Hermitian matrices. In recent years it has been shown that quantum mechanics can be formulated consistently without making this assumption, using instead a combination of the parity (P) and time-reversal (T) operators and a number of other requirements related to P and T. Only the case of even T has been analyzed in the literature; here we generalize the principles to include odd time-reversal. We use this generalization to construct a non-Hermitian version of the Dirac equation, and in doing so discover a new type of particle not allowed within the (Hermitian) Standard Model. Finally we present a potential application of the ideas of non-Hermitian quantum mechanics to the unsolved problems of quantum magnetism and high temperature superconductivity.
Revisiting Bohr's semiclassical quantum theory.
Ben-Amotz, Dor
2006-10-12
Bohr's atomic theory is widely viewed as remarkable, both for its accuracy in predicting the observed optical transitions of one-electron atoms and for its failure to fully correspond with current electronic structure theory. What is not generally appreciated is that Bohr's original semiclassical conception differed significantly from the Bohr-Sommerfeld theory and offers an alternative semiclassical approximation scheme with remarkable attributes. More specifically, Bohr's original method did not impose action quantization constraints but rather obtained these as predictions by simply matching photon and classical orbital frequencies. In other words, the hydrogen atom was treated entirely classically and orbital quantized emerged directly from the Planck-Einstein photon quantization condition, E = h nu. Here, we revisit this early history of quantum theory and demonstrate the application of Bohr's original strategy to the three quintessential quantum systems: an electron in a box, an electron in a ring, and a dipolar harmonic oscillator. The usual energy-level spectra, and optical selection rules, emerge by solving an algebraic (quadratic) equation, rather than a Bohr-Sommerfeld integral (or Schroedinger) equation. However, the new predictions include a frozen (zero-kinetic-energy) state which in some (but not all) cases lies below the usual zero-point energy. In addition to raising provocative questions concerning the origin of quantum-chemical phenomena, the results may prove to be of pedagogical value in introducing students to quantum mechanics.
Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces
Gulden, T.; Janas, M.; Koroteev, P.; Kamenev, A.
2013-09-15
Statistical mechanics of a 1D multivalent Coulomb gas can be mapped onto non-Hermitian quantum mechanics. We use this example to develop the instanton calculus on Riemann surfaces. Borrowing from the formalism developed in the context of the Seiberg-Witten duality, we treat momentum and coordinate as complex variables. Constant-energy manifolds are given by Riemann surfaces of genus g {>=} 1. The actions along principal cycles on these surfaces obey the ordinary differential equation in the moduli space of the Riemann surface known as the Picard-Fuchs equation. We derive and solve the Picard-Fuchs equations for Coulomb gases of various charge content. Analysis of monodromies of these solutions around their singular points yields semiclassical spectra as well as instanton effects such as the Bloch bandwidth. Both are shown to be in perfect agreement with numerical simulations.
NASA Astrophysics Data System (ADS)
Jones, Robert
2011-03-01
I do not agree with mind-body dualism. Today the consensus view is that thought and mind is a combination of processes like memory, generalization, comparison, deduction, organization, induction, classification, feature detection, analogy, etc. performed by computational machinery. (R. Jones, Trans. of the Kansas Acad. Sci., vol. 109, # 3/4, 2006 and www.robert-w-jones.com, philosopher, theory of thought) But I believe that quantum mechanics is a more plausible dualist theory of reality. The quantum mechanical wave function is nonphysical, it exists in a 3N space (for an N body system) not in (x,y,z,t) 4-space, and does not possess physical properties. But real physical things like energy (which do exist in our 4-space world) influence the wave function and the wave function, in its turn, influences real physical things, like where a particle can be found in 4-space. The coupling between the spirit-like wave function and things found in the real (4-space) world (like energy) is via mathematical equations like the Schrodinger equation and Born normalization.
Quantum cellular automata and free quantum field theory
NASA Astrophysics Data System (ADS)
D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-02-01
In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.
Quantum mechanical theory of collisional ionization in the presence of intense laser radiation
NASA Technical Reports Server (NTRS)
Bellum, J. C.; George, T. F.
1978-01-01
The paper presents a quantum mechanical formalism for treating ionizing collisions occurring in the presence of an intense laser field. Both the intense laser radiation and the internal electronic continuum states associated with the emitted electrons are rigorously taken into account by combining discretization techniques with expansions in terms of electronic-field representations for the quasi-molecule-plus-photon system. The procedure leads to a coupled-channel description of the heavy-particle dynamics which involves effective electronic-field potential surfaces and continua. It is suggested that laser-influenced ionizing collisions can be studied to verify the effects of intense laser radiation on inelastic collisional processes. Calculation procedures for electronic transition dipole matrix elements between discrete and continuum electronic states are outlined.
Exact integrability in quantum field theory
Thacker, H.B.
1980-08-01
The treatment of exactly integrable systems in various branches of two-dimensional classical and quantum physics has recently been placed in a unified framework by the development of the quantum inverse method. This method consolidates a broad range of developments in classical nonlinear wave (soliton) physics, statistical mechanics, and quantum field theory. The essential technique for analyzing exactly integrable quantum systems was invested by Bethe in 1931. The quantum-mechanical extension of the inverse scattering method and its relationship to the methods associated with Bethe's ansatz are examined here. (RWR)
NASA Astrophysics Data System (ADS)
Berkovitz, Joseph
Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the theorems of probability and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that degrees of belief be coherent, and he argued that the whole of probability theory could be derived from these coherence conditions. De Finetti's interpretation of probability has been highly influential in science. This paper focuses on the application of this interpretation to quantum mechanics. We argue that de Finetti held that the coherence conditions of degrees of belief in events depend on their verifiability. Accordingly, the standard coherence conditions of degrees of belief that are familiar from the literature on subjective probability only apply to degrees of belief in events which could (in principle) be jointly verified; and the coherence conditions of degrees of belief in events that cannot be jointly verified are weaker. While the most obvious explanation of de Finetti's verificationism is the influence of positivism, we argue that it could be motivated by the radical subjectivist and instrumental nature of probability in his interpretation; for as it turns out, in this interpretation it is difficult to make sense of the idea of coherent degrees of belief in, and accordingly probabilities of unverifiable events. We then consider the application of this interpretation to quantum mechanics, concentrating on the Einstein-Podolsky-Rosen experiment and Bell's theorem.
Quantum probability from decision theory?
NASA Astrophysics Data System (ADS)
Barnum, H.; Caves, C. M.; Finkelstein, J.; Fuchs, C. A.; Schack, R.
2000-05-01
In a recent paper (quant-ph/9906015), Deutsch claims to derive the "probabilistic predictions of quantum theory" from the "non-probabilistic axioms of quantum theory" and the "non-probabilistic part of classical decision theory." We show that his derivation fails because it includes hidden probabilistic assumptions.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics.
Mishima, K; Yamashita, K
2009-01-21
We have constructed free-time and fixed end-point optimal control theory for quantum systems and applied it to entanglement generation between rotational modes of two polar molecules coupled by dipole-dipole interaction. The motivation of the present work is to solve optimal control problems more flexibly by extending the popular fixed time and fixed end-point optimal control theory for quantum systems to free-time and fixed end-point optimal control theory. As a demonstration, the theory that we have constructed in this paper will be applied to entanglement generation in rotational modes of NaCl-NaBr polar molecular systems that are sensitive to the strength of entangling interactions. Our method will significantly be useful for the quantum control of nonlocal interaction such as entangling interaction, which depends crucially on the strength of the interaction or the distance between the two molecules, and other general quantum dynamics, chemical reactions, and so on.
NASA Astrophysics Data System (ADS)
Mishima, K.; Yamashita, K.
2009-01-01
We have constructed free-time and fixed end-point optimal control theory for quantum systems and applied it to entanglement generation between rotational modes of two polar molecules coupled by dipole-dipole interaction. The motivation of the present work is to solve optimal control problems more flexibly by extending the popular fixed time and fixed end-point optimal control theory for quantum systems to free-time and fixed end-point optimal control theory. As a demonstration, the theory that we have constructed in this paper will be applied to entanglement generation in rotational modes of NaCl-NaBr polar molecular systems that are sensitive to the strength of entangling interactions. Our method will significantly be useful for the quantum control of nonlocal interaction such as entangling interaction, which depends crucially on the strength of the interaction or the distance between the two molecules, and other general quantum dynamics, chemical reactions, and so on.
Free Quantum Field Theory from Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Principles of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Landé, Alfred
2013-10-01
ödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.
Polymer quantum mechanics and its continuum limit
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.
2007-08-15
A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.
NASA Technical Reports Server (NTRS)
Shen, Y.; Shen, Z. J.; Shen, G. T.; Yang, B. C.
1996-01-01
By the measurement theory of quantum mechanics and the method of Fourier transform,we proved that the wave function psi(x,y,z,t)= (8/((2(pi)(2L(exp (1/2)))(exp 3))(Phi(L,t,x)Phi(L,t,y)Phi(L,t,z)). According to the theory that the velocity of any particle can not be larger than the velocity of light and the Born interpretation, when absolute value of delta greater than (ct+ L),Phi(L,t,delta) = 0. But according to the calculation, we proved that for some delta, even if absolute value of delta is greater than (ct+L), Phi(L,t,delta) is not equal to 0.
Tests of alternative quantum theories with neutrons
Sponar, S.; Durstberger-Rennhofer, K.; Badurek, G.; Hasegawa, Y.; Klepp, J.; Schmitzer, C.; Bartosik, H.
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.
NASA Astrophysics Data System (ADS)
Son, Hyeonho; Choi, Honggu; Oh, Kyunghwan
2017-01-01
In this paper, a free-space light propagation analysis between 3-dimensional (3-D) volumetric spaces is proposed. In contrast to conventional scalar diffraction, the proposed theory is based on quantum mechanical scattering providing a general volumetric analysis for the free-space light propagation. Assuming a plane wave light incidence, we obtained a new analytic formula for 3-D volumetric convolution, which provided a transfer function in a closed form used for caculating the electric fields at the observation points. The proposed method was consistent with the conventional numerical methods for a 2-dimensional aperture and can be further applied to exact calculation of diffraction fields from 3-D surfaces, providing a compact reconstruction algorithm for 3-D images in a computer generated hologram.
NASA Astrophysics Data System (ADS)
Habegger, Eric John
2005-02-01
It is theorized that the quantum vacuum is a random electromagnetic field that permeates the universe. It will be shown that acceleration between a quark and a random electromagnetic energy field is an analog of the reaction between a charge moving at constant velocity with respect to an organized electromagnetic field. The difference is that with a quark any natural perpendicular deflection during that motion, as predicted by Lorentz, is contained by the strong force, which results in a change in the angular momentum of the spin of a quark. The first derivative of the equations of motion of charges in an organized electromagnetic field may be used when applied to a random electromagnetic field to invoke the same fields modeled by Maxwell's equations. Mass is intimately bound up with a quark's spin angular momentum and the energy for that increase comes directly from the local field. The underlying randomness of the local field normally remains intact through these energy exchanges but it is speculated that in a quantum entanglement, an absolute level of order is imposed on the field along a path between two particles. This causes the non local effects seen in quantum entanglement. The mechanism that may cause this effect is discussed and a simple experiment is proposed that can test the hypothesis. Also discussed are new theoretical constructs for electromagnetic radiation, mass, the skin effect, self-inductance, superposition, and gravity. The emphasis will be on an intuitive and logical approach more than a mathematical approach.
[Boltzmann's principle and Einstein's first quantum theories].
Navarro Veguillas, Luis; Pérez Canals, Enric
2002-01-01
The crucial role played by statistical mechanics in Einstein's work on quantum theory has been repeatedly stressed. Nevertheless, in this paper we argue that Einstein's attitude to Boltzmann's principle was more complex than is usually understood. In fact, there are significant differences and nuances that in our opinion have yet to be sufficiently considered, in the various interpretations and uses Einstein made of this principle in his work on quantum theory, more specifically between 1905 and the First Solvay Conference, in 1911.
Graduate quantum mechanics reform
NASA Astrophysics Data System (ADS)
Carr, L. D.; McKagan, S. B.
2009-04-01
We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field of quantum mechanics over the last 50years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We also find that students' ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. In contrast, we find that students' understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.
NASA Astrophysics Data System (ADS)
Cunningham, Bruce
2009-11-01
The Initial Condition (that which existed prior to the universe) is compared as an infinite thermodynamic system (reservoir and system) to a two-component blackbody system, where one component, composed of unbound bosons, contained a symmetry breaking potential. Symmetry breaking resulted in the moment of inflation in a subsystem (small part) of one component, which in turn ignited an unloading wave. The ensuing Big Bang Unloading Wave created a continuously expanding cavity in that component. The cavity is the universe. Within the expanding unloading wave, the first energy cascade has continuously produced intense plasma effects, superelectric fields, and supermagnetic effects. The intense plasma produces violent pinch effects propelling superelectric-magnetic particles to the speed of light c impacting them within the other component (bound boson Fermi-Dirac particles) as original energy particles representing the apex of the spectral ladder and the beginning of the second energy cascade. Here quench factors freeze persistent superconducting current vibrations into place prior to application of the algorithmic ladder of the quantum field theory time line. Energies evolve to include the formation of std model physics (QM,QED,QCD) general theory of relativity (GRT), special theory (SRT), linear momentum, and angular momentum, etc.
Treating time travel quantum mechanically
NASA Astrophysics Data System (ADS)
Allen, John-Mark A.
2014-10-01
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilizing the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their nonlinearity and time-travel paradoxes. In particular, the "equivalent circuit model"—which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory—is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of alternate theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features—such as time-travel paradoxes, the ability to distinguish nonorthogonal states with certainty, and the ability to clone or delete arbitrary pure states—that are present with D-CTCs and P-CTCs. The problems with nonlinear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
Quantum mechanical theory of positron production in heavy ion collisions with nuclear contact
Heinz, U.
1986-01-01
The interplay between atomic and nuclear interactions in heavy ion collisions with nuclear contact is studied. The general theoretical description is outlined and analyzed in a number of different limits (semiclassical approximation, DWBA, fully quantal description). The two most important physical mechanisms for generating atomic-nuclear interference, i.e., energy conservation and the introduction of additional phase shifts by nuclear reactions, are extracted. The resulting typical coupling matrix elements are analyzed for their relative importance in atomic and nuclear excitations. The description of nuclear influence on atomic excitations in terms of a classical time delay caused by nuclear reactions is reviewed, and its relationship to the underlying quantal character of the nuclear reaction is discussed. The theory is applied to spontaneous positron emission in supercritical heavy-ion collisions (Z/sub tot/ greater than or equal to 173). It is shown that nuclear contact can lead to line structures in the positron energy spectra if the probability distribution for nuclear delay times caused by the contact has contributions for T greater than or equal to 10/sup -19/ sec. We explicitly evaluate a model where a pocket in the internuclear potential near the touching configuration leads to formation of nuclear molecules, and predict a resonance-like excitation function for the positron peak. 25 refs., 7 figs.
Mullin, Jonathan; Valley, Nicholas; Blaber, Martin G; Schatz, George C
2012-09-27
Multiscale models that combine quantum mechanics and classical electrodynamics are presented, which allow for the evaluation of surface-enhanced Raman (SERS) and hyper-Raman scattering spectra (SEHRS) for both chemical (CHEM) and electrodynamic (EM) enhancement mechanisms. In these models, time-dependent density functional theory (TDDFT) for a system consisting of the adsorbed molecule and a metal cluster fragment of the metal particle is coupled to Mie theory for the metal particle, with the surface of the cluster being overlaid with the surface of the metal particle. In model A, the electromagnetic enhancement from plasmon-excitation of the metal particle is combined with the chemical enhancement associated with a static treatment of the molecule-metal structure to determine overall spectra. In model B, the frequency dependence of the Raman spectrum of the isolated molecule is combined with the enhancements determined in model A to refine the enhancement estimate. An equivalent theory at the level of model A is developed for hyper-Raman spectra calculations. Application to pyridine interacting with a 20 nm diameter silver sphere is presented, including comparisons with an earlier model (denoted G), which combines plasmon enhanced fields with gas-phase Raman (or hyper-Raman) spectra. The EM enhancement factor for spherical particles at 357 nm is found to be 10(4) and 10(6) for SERS and SEHRS, respectively. Including both chemical and electromagnetic mechanisms at the level of model A leads to enhancements on the order of 10(4) and 10(9) for SERS and SEHRS.
NASA Astrophysics Data System (ADS)
Mishima, Kenji; Yamashita, Koichi
2009-03-01
We have constructed free-time and fixed end-point optimal control theory for quantum systems and applied it to entanglement generation between rotational modes of two polar molecules coupled by dipole-dipole interaction. The motivation of the present work is to solve optimal control problems more flexibly by extending the popular fixed-time and fixed end-point optimal control theory for quantum systems to free-time and fixed end-point optimal control theory. Our theory can not only achieve high transition probabilities but also determine exact temporal duration of the laser pulses. As a demonstration, our theory is applied to entanglement generation in rotational modes of NaCl-NaBr polar molecular systems that are sensitive to the strength of entangling interactions. Using the tailored laser pulses, we discuss the fidelity of entanglement distillation and quantum teleportation. Our method will significantly be useful for the quantum control of non-local interaction such as entangling interaction, and other time-sensitive general quantum dynamics, chemical reactions.
Speakable and Unspeakable in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Bell, J. S.; Aspect, Introduction by Alain
2004-06-01
List of papers on quantum philosophy by J. S. Bell; Preface; Acknowledgements; Introduction by Alain Aspect; 1. On the problem of hidden variables in quantum mechanics; 2. On the Einstein-Rosen-Podolsky paradox; 3. The moral aspects of quantum mechanics; 4. Introduction to the hidden-variable question; 5. Subject and object; 6. On wave packet reduction in the Coleman-Hepp model; 7. The theory of local beables; 8. Locality in quantum mechanics: reply to critics; 9. How to teach special relativity; 10. Einstein-Podolsky-Rosen experiments; 11. The measurement theory of Everett and de Broglie's pilot wave; 12. Free variables and local causality; 13. Atomic-cascade photons and quantum-mechanical nonlocality; 14. de Broglie-Bohm delayed choice double-slit experiments and density matrix; 15. Quantum mechanics for cosmologists; 16. Bertlmann's socks and the nature of reality; 17. On the impossible pilot wave; 18. Speakable and unspeakable in quantum mechanics; 19. Beables for quantum field theory; 20. Six possible worlds of quantum mechanics; 21. EPR correlations and EPR distributions; 22. Are there quantum jumps?; 23. Against 'measurement'; 24. La Nouvelle cuisine.
The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory
NASA Astrophysics Data System (ADS)
Frey, Kimberly
The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum
Hybrid theory and calculation of e-N2 scattering. [quantum mechanics - nuclei (nuclear physics)
NASA Technical Reports Server (NTRS)
Chandra, N.; Temkin, A.
1975-01-01
A theory of electron-molecule scattering was developed which was a synthesis of close coupling and adiabatic-nuclei theories. The theory is shown to be a close coupling theory with respect to vibrational degrees of freedom but is a adiabatic-nuclei theory with respect to rotation. It can be applied to any number of partial waves required, and the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential and total) to be calculated. Explicit formulae for all the cross sections are presented.
Sun, Qiming; Chan, Garnet Kin-Lic
2016-12-20
parallel as closely as possible the density functional embedding equations, with the hybridization playing the role of the embedding potential. Embedding a high-level self-energy within a low-level self-energy is treated analogously to wave function in density functional embedding. The numerical computation of the high-level self-energy allows us to briefly introduce the bath representation in the quantum impurity problem. We then consider translationally invariant systems to bring in the important dynamical mean-field theory. Recent developments to incorporate screening and long-range interactions are discussed. The third section concerns density matrix embedding. Here, we first highlight some mathematical complications associated with a simple Euler equation derivation, arising from the open nature of fragments. This motivates the density matrix embedding theory, where we use the Schmidt decomposition to represent the entanglement through bath orbitals. The resulting impurity plus bath formulation resembles that of dynamical mean-field theory. We discuss the numerical self-consistency associated with using a high-level correlated wave function with a mean-field low-level treatment, and connect the resulting numerical inversion to that used in density functional embedding. We finish with perspectives on the future of all three methods.
Quantum theory of measurements as quantum decision theory
NASA Astrophysics Data System (ADS)
Yukalov, V. I.; Sornette, D.
2015-03-01
Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is essentially more complicated in the case of composite events. The most difficult point is the relation between decisions under uncertainty and measurements under uncertainty. We suggest a unified language for describing the processes of quantum decision making and quantum measurements. The notion of quantum measurements under uncertainty is introduced. We show that the correct mathematical foundation for the theory of measurements under uncertainty, as well as for quantum decision theory dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of projection-valued measure. The latter is appropriate for operationally testable events, while the former is necessary for characterizing operationally uncertain events. In both decision making and quantum measurements, one has to distinguish composite nonentangled events from composite entangled events. Quantum probability can be essentially different from classical probability only for entangled events. The necessary condition for the appearance of an interference term in the quantum probability is the occurrence of entangled prospects and the existence of an entangled strategic state of a decision maker or of an entangled statistical state of a measuring device.
Quantum Mechanics From the Cradle?
ERIC Educational Resources Information Center
Martin, John L.
1974-01-01
States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)
Quantum Mechanics From the Cradle?
ERIC Educational Resources Information Center
Martin, John L.
1974-01-01
States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)
NASA Astrophysics Data System (ADS)
Salam, Abdus; Wigner, E. P.
2010-03-01
Preface; List of contributors; Bibliography of P. A. M. Dirac; 1. Dirac in Cambridge R. J. Eden and J. C. Polkinghorne; 2. Travels with Dirac in the Rockies J. H. Van Vleck; 3. 'The golden age of theoretical physics': P. A. M. Dirac's scientific work from 1924 to 1933 Jagdish Mehra; 4. Foundation of quantum field theory Res Jost; 5. The early history of the theory of electron: 1897-1947 A. Pais; 6. The Dirac equation A. S. Wightman; 7. Fermi-Dirac statistics Rudolph Peierls; 8. Indefinite metric in state space W. Heisenberg; 9. On bras and kets J. M. Jauch; 10. The Poisson bracket C. Lanczos; 11. La 'fonction' et les noyaux L. Schwartz; 12. On the Dirac magnetic poles Edoardo Amadli and Nicola Cabibbo; 13. The fundamental constants and their time variation Freeman J. Dyson; 14. On the time-energy uncertainty relation Eugene P. Wigner; 15. The path-integral quantisation of gravity Abdus Salam and J. Strathdee; Index; Plates.
ERIC Educational Resources Information Center
DeWitt, Bryce S.
1970-01-01
Discusses the quantum theory of measurement and von Neumann's catastrophe of infinite regression." Examines three ways of escapint the von Neumann catastrophe, and suggests that the solution to the dilemma of inteterminism is a universe in which all possible outcomes of an experiment actually occur. Bibliography. (LC)
Chuev, Gennady N.; Valiev, Marat; Fedotova, Marina V.
2012-04-10
We have developed a hybrid approach based on a combination of integral equation theory of molecular liquids and QM/MM methodology in NorthWest computational Chemistry (NWChem) software package. We have split the evaluations into conse- quent QM/MM and statistical mechanics calculations based on the one-dimensional reference interaction site model, which allows us to reduce signicantly the time of computation. The method complements QM/MM capabilities existing in the NWChem package. The accuracy of the presented method was tested through com- putation of water structure around several organic solutes and their hydration free energies. We have also evaluated the solvent effect on the conformational equilibria. The applicability and limitations of the developed approach are discussed.
Quantum theory of electroabsorption in semiconductor nanocrystals.
Tepliakov, Nikita V; Leonov, Mikhail Yu; Baranov, Alexander V; Fedorov, Anatoly V; Rukhlenko, Ivan D
2016-01-25
We develop a simple quantum-mechanical theory of interband absorption by semiconductor nanocrystals exposed to a dc electric field. The theory is based on the model of noninteracting electrons and holes in an infinitely deep quantum well and describes all the major features of electroabsorption, including the Stark effect, the Franz-Keldysh effect, and the field-induced spectral broadening. It is applicable to nanocrystals of different shapes and dimensions (quantum dots, nanorods, and nanoplatelets), and will prove useful in modeling and design of electrooptical devices based on ensembles of semiconductor nanocrystals.
Arrival time in quantum field theory
NASA Astrophysics Data System (ADS)
Wang, Zhi-Yong; Xiong, Cai-Dong; He, Bing
2008-09-01
Via the proper-time eigenstates (event states) instead of the proper-mass eigenstates (particle states), free-motion time-of-arrival theory for massive spin-1/2 particles is developed at the level of quantum field theory. The approach is based on a position-momentum dual formalism. Within the framework of field quantization, the total time-of-arrival is the sum of the single event-of-arrival contributions, and contains zero-point quantum fluctuations because the clocks under consideration follow the laws of quantum mechanics.
Towards a theory of intention: An application of quantum mechanics within psychotherapy
NASA Astrophysics Data System (ADS)
Van Wyck, Jennifer
This study incorporated grounded research methodology to analyze and code three fields of research: psychoneuroimmunology, psychokinesis, and guided imagery. The works of Tiller (2001, 2007) and Dyer (2004) were used as a validity check for the grounded theory results and provided further input into a final theory of intention. It was found that intention requires three elements to be most successful in producing targeted outcomes. These include consciousness, thought, and emotion. The emotional aspect of intention had previously been mentioned but never incorporated into earlier theories of intention and appears to be a new finding that has potentially strong implications. The paper concludes with a discussion of how the theory of intention can inform practice in the field of psychotherapy.
Quantum Mechanics: Myths and Facts
NASA Astrophysics Data System (ADS)
Nikolić, Hrvoje
2007-11-01
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
Studies in quantum information theory
NASA Astrophysics Data System (ADS)
Menicucci, Nicolas C.
Quantum information theory started as the backdrop for quantum computing and is often considered only in relation to this technology, which is still in its infancy. But quantum information theory is only partly about quantum computing. While much of the interest in this field is spurred by the possible use of quantum computers for code breaking using fast factoring algorithms, to a physicist interested in deeper issues, it presents an entirely new set of questions based on an entirely different way of looking at the quantum world. This thesis is an exploration of several topics in quantum information theory. But it is also more than this. This thesis explores the new paradigm brought about by quantum information theory---that of physics as the flow of information. The thesis consists of three main parts. The first part describes my work on continuous-variable cluster states, a new platform for quantum computation. This begins with background material discussing classical and quantum computation and emphasizing the physical underpinnings of each, followed by a discussion of two recent unorthodox models of quantum computation. These models are combined into an original proposal for quantum computation using continuous-variable cluster states, including a proposed optical implementation. These are followed by a mathematical result radically simplifying the optical construction. Subsequent work simplifies this connection even further and provides a constructive proposal for scalable generation of large-scale cluster states---necessary if there is to be any hope of using this method in practical quantum computation. Experimental implementation is currently underway by my collaborators at The University of Virginia. The second part describes my work related to the physics of trapped ions, starting with an overview of the basic theory of linear ion traps. Although ion traps are often discussed in terms of their potential use for quantum computation, my work looks at their
Unification of quantum information theory
NASA Astrophysics Data System (ADS)
Abeyesinghe, Anura
We present the unification of many previously disparate results in noisy quantum Shannon theory and the unification of all of noiseless quantum Shannon theory. More specifically we deal here with bipartite, unidirectional, and memoryless quantum Shannon theory. We find all the optimal protocols and quantify the relationship between the resources used, both for the one-shot and for the ensemble case, for what is arguably the most fundamental task in quantum information theory: sharing entangled states between a sender and a receiver. We find that all of these protocols are derived from our one-shot superdense coding protocol and relate nicely to each other. We then move on to noisy quantum information theory and give a simple, direct proof of the "mother" protocol, or rather her generalization to the Fully Quantum Slepian-Wolf protocol (FQSW). FQSW simultaneously accomplishes two goals: quantum communication-assisted entanglement distillation, and state transfer from the sender to the receiver. As a result, in addition to her other "children," the mother protocol generates the state merging primitive of Horodecki, Oppenheim, and Winter as well as a new class of distributed compression protocols for correlated quantum sources, which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the so-called "father" protocol, demonstrating that the division of single-sender/single-receiver protocols into two families was unnecessary: all protocols in the family are children of the mother.
NASA Astrophysics Data System (ADS)
Weinberg, Steven
1996-08-01
In this second volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly expoistion of quantum theory. Volume 2 provides an up-to-date and self-contained account of the methods of quantum field theory, and how they have led to an understanding of the weak, strong, and electromagnetic interactions of the elementary particles. The presentation of modern mathematical methods is throughout interwoven with accounts of the problems of elementary particle physics and condensed matter physics to which they have been applied. Exercises are included at the end of each chapter.
Comments on quantum probability theory.
Sloman, Steven
2014-01-01
Quantum probability theory (QP) is the best formal representation available of the most common form of judgment involving attribute comparison (inside judgment). People are capable, however, of judgments that involve proportions over sets of instances (outside judgment). Here, the theory does not do so well. I discuss the theory both in terms of descriptive adequacy and normative appropriateness.
NASA Astrophysics Data System (ADS)
Hassan, Sergio A.; Mehler, Ernest L.
Biological macromolecules and other polymers belong to the class of mesoscopic systems, with characteristic length scale of the order of a nanometer. Although microscopic models would be the preferred choice in theoretical calculations, their use in computer simulations becomes prohibitive for large systems or long simulation times. On the other hand, the use of purely macroscopic models in the mesoscopic domain may introduce artifacts, with effects that are difficult to assess and that may compromise the reliability of the calculations. Here is proposed an approach with the aim of minimizing the empirical nature of continuum approximations of solvent effects within the scope of molecular mechanics (MM) approximations in mesoscopic systems. Using quantum chemical methods, the potential generated by the molecular electron density is first decomposed in a multicenter-multipole expansion around predetermined centers. The monopole and dipole terms of the expansion at each site create electric fields that polarize the surrounding aqueous medium whose dielectric properties can be described by the classical theory of polar liquids. Debye's theory allows a derivation of the dielectric profiles created around isolated point charges and dipoles that can incorporate Onsager reaction field corrections. A superposition of screened Coulomb potentials obtained from this theory makes possible a simple derivation of a formal expression for the total electrostatic energy and the polar component of the solvation energy of the system. A discussion is presented on the physical meaning of the model parameters, their transferability, and their convergence to calculable quantities in the limit of simple systems. The performance of this continuum approximation in computer calculations of amino acids in the context of an atomistic force field is discussed. Applications of a continuum model based on screened Coulomb potentials in multinanosecond simulations of peptides and proteins are
No extension of quantum theory can have improved predictive power.
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.
Interplay of Classical and Quantum Mechanics in the Theory of Charged-Particle Stopping
NASA Astrophysics Data System (ADS)
Sigmund, Peter
A quarter of a century ago the author stepped into Jens Oddershede's office and asked for support on a problem involving computation with atomic wave functions in connection with a new theoretical scheme to treat stopping of charged particles at intermediate speed. This visit resulted in two related publications, two joint papers and a number of follow-up studies by Jens and several others. In 1989 a Sanibel Symposium was devoted to aspects of the penetration of charged particles through matter, and since then, quite a few quantum chemists have joined the community of theoreticians dealing with particle penetration. Niels Bohr, a pioneer in both disciplines, emphasized the significance of classical vs. quantal arguments in particle penetration. Not the least in view of the complexity of ab initio computations in this area, such considerations keep being relevant. This note adds new points to an old discussion based on recent developments.
Dirac's equation and the nature of quantum field theory
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2012-11-01
This paper re-examines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.
Ogihara, Yusuke; Yamamoto, Takeshi; Kato, Shigeki
2010-09-23
Triplet ketene exhibits a steplike structure in the experimentally observed dissociation rates, but its mechanism is still unknown despite many theoretical efforts in the past decades. In this paper we revisit this problem by quantum mechanically calculating the reaction probability with multireference-based electronic structure theory. Specifically, we first construct an analytical potential energy surface of triplet state by fitting it to about 6000 ab initio energies computed at the multireference second-order Mller-Plesset perturbation (MRMP2) level. We then evaluate the cumulative reaction probability by using the transition state wave packet method together with an adiabatically constrained Hamiltonian. The result shows that the imaginary barrier frequency on the triplet surface is 328i cm-1, which is close to the CCSD(T) result (321i cm-1) but is likely too large for reproducing the experimentally observed steps. Indeed, our calculated reaction probability exhibits no signature of steps, reflecting too strong tunneling effect along the reaction coordinate. Nevertheless, it is emphasized that the flatness of the potential profile in the transition-state region (which governs the degree of tunneling) depends strongly on the level of electronic structure calculation, thus leaving some possibility that the use of more accurate theories might lead to the observed steps. We also demonstrate that the triplet potential surface differs significantly between the CASSCF and MRMP2 results, particularly in the transition-state region. This fact seems to require more attention when studying the "nonadiabatic" scenario for the steps, in which the crossing seam between S0 and T1 surfaces is assumed to play a central role.
Elementary Concepts of Quantum Theory
ERIC Educational Resources Information Center
Warren, J. W.
1974-01-01
Discusses the importance and difficulties of teaching basic quantum theory. Presents a discussion of wave-particle duality, indeterminacy, the nature of a quantized state of a system, and the exclusion principle. (MLH)
Elementary Concepts of Quantum Theory
ERIC Educational Resources Information Center
Warren, J. W.
1974-01-01
Discusses the importance and difficulties of teaching basic quantum theory. Presents a discussion of wave-particle duality, indeterminacy, the nature of a quantized state of a system, and the exclusion principle. (MLH)
Quantum Theory is an Information Theory
NASA Astrophysics Data System (ADS)
D'Ariano, Giacomo M.; Perinotti, Paolo
2016-03-01
In this paper we review the general framework of operational probabilistic theories (OPT), along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.
Does quantum mechanics tell an atomistic spacetime?
NASA Astrophysics Data System (ADS)
Elze, Hans-Thomas
2009-06-01
The canonical answer to the question posed is "Yes." - tacitly assuming that quantum theory and the concept of spacetime are to be unified by 'quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise as a coarse-grained reflection of the atomistic nature of spacetime? - We speculate that this may indeed be the case. We recall the similarity between evolution of classical and quantum mechanical ensembles, according to Liouville and von Neumann equation, respectively. The classical and quantum mechanical equations are indistinguishable for objects which are free or subject to spatially constant but possibly time dependent, or harmonic forces, if represented appropriately. This result suggests a way to incorporate anharmonic interactions, including fluctuations which are tentatively related to the underlying discreteness of spacetime. Being linear and local at the quantum mechanical level, the model offers a decoherence and natural localization mechanism. However, the relation to primordial deterministic degrees of freedom is nonlocal.
Generalization of the Activated Complex Theory of Reaction Rates. I. Quantum Mechanical Treatment
DOE R&D Accomplishments Database
Marcus, R. A.
1964-01-01
In its usual form activated complex theory assumes a quasi-equilibrium between reactants and activated complex, a separable reaction coordinate, a Cartesian reaction coordinate, and an absence of interaction of rotation with internal motion in the complex. In the present paper a rate expression is derived without introducing the Cartesian assumption. The expression bears a formal resemblance to the usual one and reduces to it when the added assumptions of the latter are introduced.
NASA Astrophysics Data System (ADS)
Stohler, Michael Lehman
2002-01-01
Non-cooperative quantum games have received much attention recently. This thesis defines and divides current works into two major categories of gaming techniques with close attention paid to Nash equilibria, form and possibilities for the payoff functions, and the benefits of using a quantum strategy. In addition to comparing and contrasting these techniques, new applications and calculations are discussed. Finally, the techniques are expanded into 3 x 3 games which allows the study of non-transitive strategies in quantum games.
Quantum spectral dimension in quantum field theory
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe
2016-03-01
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension dS of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension D. In particular, in the presence of higher momentum powers it changes with the scale, dropping from D in the infrared (IR) to a value dSUV ≤ D in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value dSUV = 2 for any dimension D.
Vukmirovic, Nenad; Wang, Lin-Wang
2009-11-10
This review covers the description of the methodologies typically used for the calculation of the electronic structure of self-assembled and colloidal quantum dots. These are illustrated by the results of their application to a selected set of physical effects in quantum dots.
Quantum Theory of the Electron Liquid
NASA Astrophysics Data System (ADS)
Giuliani, Gabriele; Vignale, Giovanni
2005-04-01
Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron liquid. This book introduces the quantum theory of the electron liquid and the mathematical techniques that describe it. The electron liquid's behavior is governed by the laws of quantum mechanics which prevail over the microscopic world of atoms and molecules.
Quantum Information Theory - an Invitation
NASA Astrophysics Data System (ADS)
Werner, Reinhard F.
Quantum information and quantum computers have received a lot of public attention recently. Quantum computers have been advertised as a kind of warp drive for computing, and indeed the promise of the algorithms of Shor and Grover is to perform computations which are extremely hard or even provably impossible on any merely ``classical'' computer.In this article I shall give an account of the basic concepts of quantum information theory is given, staying as much as possible in the area of general agreement.The article is divided into two parts. The first (up to the end of Sect. 2.5) is mostly in plain English, centered around the exploration of what can or cannot be done with quantum systems as information carriers. The second part, Sect. 2.6, then gives a description of the mathematical structures and of some of the tools needed to develop the theory.
Quantum Hamilton-Jacobi theory.
Roncadelli, Marco; Schulman, L S
2007-10-26
Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear operator partial differential equation such as the quantum Hamilton-Jacobi equation (QHJE) has hindered progress along this otherwise promising avenue. We overcome this difficulty. We show that solutions to the QHJE can be constructed by a simple prescription starting from the propagator of the associated Schrödinger equation. Our result opens the possibility of practical use of quantum Hamilton-Jacobi theory. As an application, we develop a surprising relation between operator ordering and the density of paths around a semiclassical trajectory.
Principles and Dynamics of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Efthimiades, Spyros
2009-05-01
Quantum mechanics can be founded on three principles: particle waves, concurrent states and averaged energy relations. The Schrodinger, time-evolution and Dirac equations are derived to be the conditions the wavefunction must satisfy in order to fulfill the corresponding averaged energy relations. Adopting a particle and wave balanced approach we attain a clear, consistent and justified quantum theory.
Quantum mechanics and the generalized uncertainty principle
Bang, Jang Young; Berger, Micheal S.
2006-12-15
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
NASA Astrophysics Data System (ADS)
Scott, Tony C.
It has been shown that the Fokker-Wheeler-Feynman (FWF) model could be rewritten to yield a physically acceptable relativistic many-particle Lagrangian. Contrary to Wheeler and Feynman's postulates, the model satisfies causality and can be generalised to include arbitrary forces. The 1/c power series of the FWF Lagrangian to order (1/c) ^4 contains accelerations. A procedure of quantizing the theory for such a Lagrangian is presented and it is then found that the accelerations approximately introduce an independent harmonic mode which is in agreement with resonances recently observed in Positronium collisions processes. This result may be of fundamental physical importance and requires further investigation. However, the refinement of this calculation requires the creation of new computational tools. To this end, a new method is presented in which both the eigenfunctions and eigenenergies are determined algebraically as power series in the order parameter, where each coefficient of the series is obtained in closed form. This method avoids the complications of a basis set and makes extensive use of symbolic computation. It is then applied to two model problems, namely the one-body Dirac equation for testing purposes and a special case of the two-body Dirac equation for which one obtains previously unknown closed form solutions.
Uncertainty in quantum mechanics: faith or fantasy?
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.
(Studies in quantum field theory)
Not Available
1990-01-01
During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity.
Quantum Gauge Theories : A True Ghost Story
NASA Astrophysics Data System (ADS)
Scharf, Gunter
2001-03-01
An innovative new treatment of particle physics using quantum gauge theory as its basis If regarded as operator theories, ghost fields play a very important role in quantum gauge theory, which forms the basis of modern particle physics. The author argues that all known forces in nature-electromagnetism, weak and strong forces, and gravity-follow in a unique way from the basic principle of quantum gauge invariance. Using that as a starting point, this volume discusses gauge theories as quantum theories, as part of a streamlined modern approach. The simplicity of using only this one method throughout the book allows the reader a clear understanding of the mathematical structure of nature, while this modern and mathematically well-defined approach elucidates the standard theory of particle physics without overburdening the reader with the full range of various ideas and methods. Though the subject matter requires a basic knowledge of quantum mechanics, the book's unprecedented and uncomplicated coverage will offer readers little difficulty. This revolutionary volume is suitable for graduate students and researchers alike and includes a completely new treatment of gravity as well as important new ideas on massive gauge fields.
Penicillin's catalytic mechanism revealed by inelastic neutrons and quantum chemical theory.
Mucsi, Zoltán; Chass, Gregory A; Ábrányi-Balogh, Péter; Jójárt, Balázs; Fang, De-Cai; Ramirez-Cuesta, Annibal J; Viskolcz, Béla; Csizmadia, Imre G
2013-12-21
Penicillin, travels through bodily fluids, targeting and acylatively inactivating enzymes responsible for cell-wall synthesis in gram-positive bacteria. Somehow, it avoids metabolic degradation remaining inactive en route. To resolve this ability to switch from a non-active, to a highly reactive form, we investigated the dynamic structure-activity relationship of penicillin by inelastic neutron spectroscopy, reaction kinetics, NMR and multi-scale theoretical modelling (QM/MM and post-HF ab initio). Results show that by a self-activating physiological pH-dependent two-step proton-mediated process, penicillin changes geometry to activate its irreversibly reactive acylation, facilitated by systemic intramolecular energy management and cooperative vibrations. This dynamic mechanism is confirmed by the first ever reported characterisation of an antibiotic by neutrons, achieved on the TOSCA instrument (ISIS facility, RAL, UK).
The role of relative entropy in quantum information theory
NASA Astrophysics Data System (ADS)
Vedral, V.
2002-01-01
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately, it has emerged that they are in fact intimately related. In this review the author shows how quantum information theory extends traditional information theory by exploring the limits imposed by quantum, rather than classical, mechanics on information storage and transmission. The derivation of many key results differentiates this review from the usual presentation in that they are shown to follow logically from one crucial property of relative entropy. Within the review, optimal bounds on the enhanced speed that quantum computers can achieve over their classical counterparts are outlined using information-theoretic arguments. In addition, important implications of quantum information theory for thermodynamics and quantum measurement are intermittently discussed. A number of simple examples and derivations, including quantum superdense coding, quantum teleportation, and Deutsch's and Grover's algorithms, are also included.
Recoverability in quantum information theory
NASA Astrophysics Data System (ADS)
Wilde, Mark
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities. This is based on arXiv:1505.04661, now accepted for publication in Proceedings of the Royal Society A. I acknowledge support from startup funds from the Department of Physics and Astronomy at LSU, the NSF under Award No. CCF-1350397, and the DARPA Quiness Program through US Army Research Office award W31P4Q-12-1-0019.
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."
Superconducting quantum circuits theory and application
NASA Astrophysics Data System (ADS)
Deng, Xiuhao
Superconducting quantum circuit models are widely used to understand superconducting devices. This thesis consists of four studies wherein the superconducting quantum circuit is used to illustrate challenges related to quantum information encoding and processing, quantum simulation, quantum signal detection and amplification. The existence of scalar Aharanov-Bohm phase has been a controversial topic for decades. Scalar AB phase, defined as time integral of electric potential, gives rises to an extra phase factor in wavefunction. We proposed a superconducting quantum Faraday cage to detect temporal interference effect as a consequence of scalar AB phase. Using the superconducting quantum circuit model, the physical system is solved and resulting AB effect is predicted. Further discussion in this chapter shows that treating the experimental apparatus quantum mechanically, spatial scalar AB effect, proposed by Aharanov-Bohm, can't be observed. Either a decoherent interference apparatus is used to observe spatial scalar AB effect, or a quantum Faraday cage is used to observe temporal scalar AB effect. The second study involves protecting a quantum system from losing coherence, which is crucial to any practical quantum computation scheme. We present a theory to encode any qubit, especially superconducting qubits, into a universal quantum degeneracy point (UQDP) where low frequency noise is suppressed significantly. Numerical simulations for superconducting charge qubit using experimental parameters show that its coherence time is prolong by two orders of magnitude using our universal degeneracy point approach. With this improvement, a set of universal quantum gates can be performed at high fidelity without losing too much quantum coherence. Starting in 2004, the use of circuit QED has enabled the manipulation of superconducting qubits with photons. We applied quantum optical approach to model coupled resonators and obtained a four-wave mixing toolbox to operate photons
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.
Dual field theories of quantum computation
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
2016-06-01
Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N +1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N -torus
Quantum mechanics and the psyche
NASA Astrophysics Data System (ADS)
Galli Carminati, G.; Martin, F.
2008-07-01
In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.
Emerging interpretations of quantum mechanics and recent progress in quantum measurement
NASA Astrophysics Data System (ADS)
Clarke, M. L.
2014-01-01
The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism).
Quantum theory of positronium formation at surfaces
Shindo, S.; Ishii, A.
1987-06-01
A quantum-mechanical theory of positronium formation at surfaces is presented. The neutralization probability of positrons implanted into solids escaping from a surface is calculated. The theory of the resonant neutralization of ions at a surface is improved for positrons by taking into account the quantum effect of the motion of the positrons near the surface. The angular distributions and the energy distributions of the emitted positronium are calculated. We give the relationship of the positronium energy distribution and the density of states at the surface.
Basing quantum theory on information processing
NASA Astrophysics Data System (ADS)
Barnum, Howard
2008-03-01
I consider information-based derivations of the quantum formalism, in a framework encompassing quantum and classical theory and a broad spectrum of theories serving as foils to them. The most ambitious hope for such a derivation is a role analogous to Einstein's development of the dynamics and kinetics of macroscopic bodies, and later of their gravitational interactions, on the basis of simple principles with clear operational meanings and experimental consequences. Short of this, it could still provide a principled understanding of the features of quantum mechanics that account for its greater-than-classical information-processing power, helping guide the search for new quantum algorithms and protocols. I summarize the convex operational framework for theories, and discuss information-processing in theories therein. Results include the fact that information that can be obtained without disturbance is inherently classical, generalized no-cloning and no-broadcasting theorems, exponentially secure bit commitment in all non-classical theories without entanglement, properties of theories that allow teleportation, and properties of theories that allow ``remote steering'' of ensembles using entanglement. Joint work with collaborators including Jonathan Barrett, Matthew Leifer, Alexander Wilce, Oscar Dahlsten, and Ben Toner.
NASA Astrophysics Data System (ADS)
Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Frank
1986-06-01
Beginning students of quantum mechanics frequently experience difficulties separating essential underlying principles from the specific examples to which these principles have been historically applied. Nobel-Prize-winner Claude Cohen-Tannoudji and his colleagues have written this book to eliminate precisely these difficulties. Fourteen chapters provide a clarity of organization, careful attention to pedagogical details, and a wealth of topics and examples which make this work a textbook as well as a timeless reference, allowing to tailor courses to meet students' specific needs. Each chapter starts with a clear exposition of the problem which is then treated, and logically develops the physical and mathematical concept. These chapters emphasize the underlying principles of the material, undiluted by extensive references to applications and practical examples which are put into complementary sections. The book begins with a qualitative introduction to quantum mechanical ideas using simple optical analogies and continues with a systematic and thorough presentation of the mathematical tools and postulates of quantum mechanics as well as a discussion of their physical content. Applications follow, starting with the simplest ones like e.g. the harmonic oscillator, and becoming gradually more complicated (the hydrogen atom, approximation methods, etc.). The complementary sections each expand this basic knowledge, supplying a wide range of applications and related topics as well as detailed expositions of a large number of special problems and more advanced topics, integrated as an essential portion of the text.
Weak Quantum Theory: Formal Framework and Selected Applications
Atmanspacher, Harald; Filk, Thomas; Roemer, Hartmann
2006-01-04
Two key concepts of quantum theory, complementarity and entanglement, are considered with respect to their significance in and beyond physics. An axiomatically formalized, weak version of quantum theory, more general than the ordinary quantum theory of physical systems, is described. Its mathematical structure generalizes the algebraic approach to ordinary quantum theory. The crucial formal feature leading to complementarity and entanglement is the non-commutativity of observables.The ordinary Hilbert space quantum mechanics can be recovered by stepwise adding the necessary features. This provides a hierarchy of formal frameworks of decreasing generality and increasing specificity. Two concrete applications, more specific than weak quantum theory and more general than ordinary quantum theory, are discussed: (i) complementarity and entanglement in classical dynamical systems, and (ii) complementarity and entanglement in the bistable perception of ambiguous stimuli.
NASA Astrophysics Data System (ADS)
Takahashi, Hideaki; Ohno, Hajime; Yamauchi, Toshihiko; Kishi, Ryohei; Furukawa, Shin-ichi; Nakano, Masayoshi; Matubayasi, Nobuyuki
2008-02-01
In the present work, we have performed quantum chemical calculations to determine preferable species among the ionic complexes that are present in ambient water due to the autodissociation of water molecule. First, we have formulated the relative population of the hydrated complexes with respect to the bare ion (H3O+ or OH -) in terms of the solvation free energies of the relevant molecules. The solvation free energies for various ionic species (H3O+, H5O2+, H7O3+, H9O4+ or OH -, H3O2-, H5O3-, H7O4-, H9O5-), categorized as proton or hydroxide ion in solution, have been computed by employing the QM/MM-ER method recently developed by combining the quantum mechanical/molecular mechanical (QM/MM) approach with the theory of energy representation (ER). Then, the computed solvation free energies have been used to evaluate the ratio of the populations of the ionic complexes to that of the bare ion (H3O+ or OH -). Our results suggest that the Zundel form, i.e., H5O2+, is the most preferable in the solution among the cationic species listed above though the Eigen form (H9O4+) is very close to the Zundel complex in the free energy, while the anionic fragment from water molecules mostly takes the form of OH -. It has also been found that the loss of the translational entropy of water molecules associated with the formation of the complex plays a role in determining the preferable size of the cluster.
NASA Astrophysics Data System (ADS)
Arfi, Badredine
2007-02-01
Most game-theoretic studies of strategic interaction assume independent individual strategies as the basic unit of analysis. This paper explores the effects of non-independence on strategic interaction. Two types of non-independence effects are considered. First, the paper considers subjective non-independence at the level of the individual actor by looking at how choice ambivalence shapes the decision-making process. Specifically, how do alternative individual choices superpose with one another to “constructively/destructively” shape each other's role within an actor's decision-making process? This process is termed as quantum superposition of alternative choices. Second, the paper considers how inter-subjective non-independence across actors engenders collective strategies among two or more interacting actors. This is termed as quantum entanglement of strategies. Taking into account both types of non-independence effect makes possible the emergence of a new collective equilibrium, without assuming signaling, prior “contract” agreement or third-party moderation, or even “cheap talk”. I apply these ideas to analyze the equilibrium possibilities of a situation wherein N actors play a quantum social game of cooperation. I consider different configurations of large- N quantum entanglement using the approach of density operator. I specifically consider the following configurations: star-shaped, nearest-neighbors, and full entanglement.
Quantum Field Theory, Revised Edition
NASA Astrophysics Data System (ADS)
Mandl, F.; Shaw, G.
1994-01-01
Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electro-weak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen-sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro-weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical
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.
Formalism and Interpretation in Quantum Theory
NASA Astrophysics Data System (ADS)
Wilce, Alexander
2010-04-01
Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett interpretation.
NASA Astrophysics Data System (ADS)
Moret-Bailly, J.
In the study of experiments of laser spectroscopy, there appears a convergence of the methods of quantum electrodynamics and classical optics: for instance stochastic electrodynamics used for the study of "squeezed states" is common to both theories, and the quantum coherent states are almost classical states. The author shows that this convergence allows to explain the paradoxes of quantum mechanics. The interaction of ultrashort laser pulses with ordinary matter is equivalent to the interaction of incoherent light with extremely dilute gases. Thus, the interaction of light from stars with cosmic gas produces a redshift similar to the Doppler redshift. In a very low pressure gas, the absorption of incoherent light disappears completely, so that the "black matter" could be simply H2 and its products of decomposition by high-frequency radiation.
On the geometrization of quantum mechanics
Tavernelli, Ivano
2016-08-15
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 induced 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.
On the geometrization of quantum mechanics
NASA Astrophysics Data System (ADS)
Tavernelli, Ivano
2016-08-01
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 induced 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.
Relativistic Quantum Information Theory
2007-11-20
systems without reference to a time variable. (a) Papers published in peer-reviewed journals (N/A for none) R.M. Gingrich, A.J. Bergou, C. Adami...Williams, "Random matrix model of quantum computing". Phys. Rev. A 71 (2005) 052324. List of papers submitted or published that acknowledge ARO...support during this reporting period. List the papers , including journal references, in the following categories: (b) Papers published in non-peer
2013-02-15
Universiti Teknikal Malaysia Melaka in Malaysia. The project was then used to partially support a new PhD student, Mr Shanon Vuglar (who is a former...method based on cascade realization of quantum systems is used and a conference and journal paper have been produced. In another approach, a method...based on singular perturbation is used and a conference and journal paper have resulted. This work was extended by the graduate student Shanon Vuglar to
NASA Astrophysics Data System (ADS)
Li, Hui
2009-11-01
Linear response and variational treatment are formulated for Hartree-Fock (HF) and Kohn-Sham density functional theory (DFT) methods and combined discrete-continuum solvation models that incorporate self-consistently induced dipoles and charges. Due to the variational treatment, analytic nuclear gradients can be evaluated efficiently for these discrete and continuum solvation models. The forces and torques on the induced point dipoles and point charges can be evaluated using simple electrostatic formulas as for permanent point dipoles and point charges, in accordance with the electrostatic nature of these methods. Implementation and tests using the effective fragment potential (EFP, a polarizable force field) method and the conductorlike polarizable continuum model (CPCM) show that the nuclear gradients are as accurate as those in the gas phase HF and DFT methods. Using B3LYP/EFP/CPCM and time-dependent-B3LYP/EFP/CPCM methods, acetone S0→S1 excitation in aqueous solution is studied. The results are close to those from full B3LYP/CPCM calculations.
Time and the foundations of quantum mechanics
NASA Astrophysics Data System (ADS)
Pashby, Thomas
Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of `time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on re ection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.
NASA Astrophysics Data System (ADS)
Kawamoto, Noboru; Kugo, Taichiro
String theories seem to have created a breakthrough in theoretical physics. At long last a unified theory of all the fundamental interactions, including gravity, looks possible. This, according to theorist Stephen Hawking, will mark the end of theoretical physics as we have known it, since we will then have a single consistent theory within which to explain all natural phenomena from elementary particles to galactic superclusters. Strings themselves are extremely tiny entities, smaller than the Planck scale, which form loops whose vibrational harmonics can be used to model all the standard elementary particles. Of course the mathematical complexities of the theory are daunting, and physicists are still at a very early stage in understanding how strings and their theoretical cousins superstrings can be used. This proceedings volume gives an overview of the intense recent work in the field and reports latest developments.
Testing quantum mechanics using third-order correlations
NASA Astrophysics Data System (ADS)
Kinsler, Paul
1996-04-01
Semiclassical theories similar to stochastic electrodynamics are widely used in optics. The distinguishing feature of such theories is that the quantum uncertainty is represented by random statistical fluctuations. They can successfully predict some quantum-mechanical phenomena; for example, the squeezing of the quantum uncertainty in the parametric oscillator. However, since such theories are not equivalent to quantum mechanics, they will not always be useful. Complex number representations can be used to exactly model the quantum uncertainty, but care has to be taken that approximations do not reduce the description to a hidden variable one. This paper helps show the limitations of ``semiclassical theories,'' and helps show where a true quantum-mechanical treatment needs to be used. Third-order correlations are a test that provides a clear distinction between quantum and hidden variable theories in a way analogous to that provided by the ``all or nothing'' Greenberger-Horne-Zeilinger test of local hidden variable theories.
Implementation of quantum game theory simulations using Python
NASA Astrophysics Data System (ADS)
Madrid S., A.
2013-05-01
This paper provides some examples about quantum games simulated in Python's programming language. The quantum games have been developed with the Sympy Python library, which permits solving quantum problems in a symbolic form. The application of these methods of quantum mechanics to game theory gives us more possibility to achieve results not possible before. To illustrate the results of these methods, in particular, there have been simulated the quantum battle of the sexes, the prisoner's dilemma and card games. These solutions are able to exceed the classic bottle neck and obtain optimal quantum strategies. In this form, python demonstrated that is possible to do more advanced and complicated quantum games algorithms.
Supersymmetric Quantum Mechanics
NASA Astrophysics Data System (ADS)
David, J.; Fernández, C.
2010-10-01
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulae concerning SUSY QM of first second order for one-dimensional arbitrary systems, we will illustrate the method through the trigonometric Pöschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.
Quantum theory needs no 'Interpretation'
Fuchs, Christopher A.; Peres, Asher
2000-03-01
Purpose of this article is to stress the fact that Quantum Theory does not need an interpretation other than being an algorithm for computing probabilities associated with macroscopic phenomena and measurements. It does not ''describ'' reality, and the wave function is not objective entity, it only gives the evolution of our probabilities for the outcomes potential experiments. (AIP) (c)
de Visser, Sam P
2009-04-01
In this review paper, we will give an overview of recent theoretical studies on the catalytic cycle(s) of NOS (nitric oxide synthase) enzymes and in particular on the later stages of these cycles where experimental work is difficult due to the short lifetime of intermediates. NOS enzymes are vital for human health and are involved in the biosynthesis of toxic nitric oxide. Despite many experimental efforts in the field, the catalytic cycle of this important enzyme is still surrounded by many unknowns and controversies. Our theoretical studies were focused on the grey zones of the catalytic cycle, where intermediates are short-lived and experimental detection is impossible. Thus combined QM/MM (quantum mechanics/molecular mechanics) as well as DFT (density functional theory) studies on NOS enzymes and active site models have established a novel mechanism of oxygen activation and the conversion of L-arginine into N(omega)-hydroxo-arginine. Although NOS enzymes show many structural similarities to cytochrome P450 enzymes, it has long been anticipated that therefore they should have a similar catalytic cycle where molecular oxygen binds to a haem centre and is converted into an Fe(IV)-oxo haem(+*) active species (Compound I). Compound I, however, is elusive in the cytochrome P450s as well as in NOS enzymes, but indirect experimental evidence on cytochrome P450 systems combined with theoretical modelling have shown it to be the oxidant responsible for hydroxylation reactions in cytochrome P450 enzymes. By contrast, in the first catalytic cycle of NOS it has been shown that Compound I is first reduced to Compound II before the hydroxylation of arginine. Furthermore, substrate arginine in NOS enzymes appears to have a dual function, namely first as a proton donor in the catalytic cycle to convert the ferric-superoxo into a ferric-hydroperoxo complex and secondly as the substrate that is hydroxylated in the process leading to N(omega)-hydroxo-arginine.
Studies in the Theory of Quantum Games
NASA Astrophysics Data System (ADS)
Iqbal, Azhar
2005-03-01
Theory of quantum games is a new area of investigation that has gone through rapid development during the last few years. Initial motivation for playing games, in the quantum world, comes from the possibility of re-formulating quantum communication protocols, and algorithms, in terms of games between quantum and classical players. The possibility led to the view that quantum games have a potential to provide helpful insight into working of quantum algorithms, and even in finding new ones. This thesis analyzes and compares some interesting games when played classically and quantum mechanically. A large part of the thesis concerns investigations into a refinement notion of the Nash equilibrium concept. The refinement, called an evolutionarily stable strategy (ESS), was originally introduced in 1970s by mathematical biologists to model an evolving population using techniques borrowed from game theory. Analysis is developed around a situation when quantization changes ESSs without affecting corresponding Nash equilibria. Effects of quantization on solution-concepts other than Nash equilibrium are presented and discussed. For this purpose the notions of value of coalition, backwards-induction outcome, and subgame-perfect outcome are selected. Repeated games are known to have different information structure than one-shot games. Investigation is presented into a possible way where quantization changes the outcome of a repeated game. Lastly, two new suggestions are put forward to play quantum versions of classical matrix games. The first one uses the association of De Broglie's waves, with travelling material objects, as a resource for playing a quantum game. The second suggestion concerns an EPR type setting exploiting directly the correlations in Bell's inequalities to play a bi-matrix game.
Diagrammatic quantum mechanics
NASA Astrophysics Data System (ADS)
Kauffman, Louis H.; Lomonaco, Samuel J.
2015-05-01
This paper explores how diagrams of quantum processes can be used for modeling and for quantum epistemology. The paper is a continuation of the discussion where we began this formulation. Here we give examples of quantum networks that represent unitary transformations by dint of coherence conditions that constitute a new form of non-locality. Local quantum devices interconnected in space can form a global quantum system when appropriate coherence conditions are maintained.
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
Quantum theory of Thomson scattering
NASA Astrophysics Data System (ADS)
Crowley, B. J. B.; Gregori, G.
2014-12-01
The general theory of the scattering of electromagnetic radiation in atomic plasmas and metals, in the non-relativistic regime, in which account is taken of the Kramers-Heisenberg polarization terms in the Hamiltonian, is described from a quantum mechanical viewpoint. As well as deriving the general formula for the double differential Thomson scattering cross section in an isotropic finite temperature multi-component system, this work also considers closely related phenomena such as absorption, refraction, Raman scattering, resonant (Rayleigh) scattering and Bragg scattering, and derives many essential relationships between these quantities. In particular, the work introduces the concept of scattering strength and the strength-density field which replaces the normal particle density field in the standard treatment of scattering by a collection of similar particles and it is the decomposition of the strength-density correlation function into more familiar-looking components that leads to the final result. Comparisons are made with previous work, in particular that of Chihara [1].
Klein's programme and quantum mechanics
NASA Astrophysics Data System (ADS)
Clemente-Gallardo, Jesús; Marmo, Giuseppe
2015-04-01
We review the geometrical formulation of quantum mechanics to identify, according to Klein's programme, the corresponding group of transformations. For closed systems, it is the unitary group. For open quantum systems, the semigroup of Kraus maps contains, as a maximal subgroup, the general linear group. The same group emerges as the exponentiation of the C*-algebra associated with the quantum system, when thought of as a Lie algebra. Thus, open quantum systems seem to identify the general linear group as associated with quantum mechanics and moreover suggest to extend the Klein programme also to groupoids. The usual unitary group emerges as a maximal compact subgroup of the general linear group.
Grounding quantum probability in psychological mechanism.
Love, Bradley C
2013-06-01
Pothos & Busemeyer (P&B) provide a compelling case that quantum probability (QP) theory is a better match to human judgment than is classical probability (CP) theory. However, any theory (QP, CP, or other) phrased solely at the computational level runs the risk of being underconstrained. One suggestion is to ground QP accounts in mechanism, to leverage a wide range of process-level data.
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Quantum simulation of quantum field theories in trapped ions.
Casanova, J; Lamata, L; Egusquiza, I L; Gerritsma, R; Roos, C F; García-Ripoll, J J; Solano, E
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
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.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
An Axiomatic Basis for Quantum Mechanics
NASA Astrophysics Data System (ADS)
Cassinelli, Gianni; Lahti, Pekka
2016-10-01
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Solér which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of Solér's theorem to the theory of symmetry in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions.
The future (and past) of quantum theory after the Higgs boson: a quantum-informational viewpoint.
Plotnitsky, Arkady
2016-05-28
Taking as its point of departure the discovery of the Higgs boson, this article considers quantum theory, including quantum field theory, which predicted the Higgs boson, through the combined perspective of quantum information theory and the idea of technology, while also adopting anon-realistinterpretation, in 'the spirit of Copenhagen', of quantum theory and quantum phenomena themselves. The article argues that the 'events' in question in fundamental physics, such as the discovery of the Higgs boson (a particularly complex and dramatic, but not essentially different, case), are made possible by the joint workings of three technologies: experimental technology, mathematical technology and, more recently, digital computer technology. The article will consider the role of and the relationships among these technologies, focusing on experimental and mathematical technologies, in quantum mechanics (QM), quantum field theory (QFT) and finite-dimensional quantum theory, with which quantum information theory has been primarily concerned thus far. It will do so, in part, by reassessing the history of quantum theory, beginning with Heisenberg's discovery of QM, in quantum-informational and technological terms. This history, the article argues, is defined by the discoveries of increasingly complex configurations of observed phenomena and the emergence of the increasingly complex mathematical formalism accounting for these phenomena, culminating in the standard model of elementary-particle physics, defining the current state of QFT. © 2016 The Author(s).
A Topos for Algebraic Quantum Theory
NASA Astrophysics Data System (ADS)
Heunen, Chris; Landsman, Nicolaas P.; Spitters, Bas
2009-10-01
The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr’s idea that the empirical content of quantum physics is accessible only through classical physics, we show how a noncommutative C*-algebra of observables A induces a topos {mathcal{T}(A)} in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra {A} . According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum {\\underline{Σ}(A)} in {mathcal{T}(A)} , which in our approach plays the role of the quantum phase space of the system. Thus we associate a locale (which is the topos-theoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on {\\underline{Σ}} , and self-adjoint elements of A define continuous functions (more precisely, locale maps) from {\\underline{Σ}} to Scott’s interval domain. Noting that open subsets of {\\underline{Σ}(A)} correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos {mathcal{T}(A)}. These results were inspired by the topos-theoretic approach to quantum physics proposed by Butterfield and Isham, as recently generalized by Döring and Isham.
Geometric Hamiltonian quantum mechanics and applications
NASA Astrophysics Data System (ADS)
Pastorello, Davide
2016-08-01
Adopting a geometric point of view on Quantum Mechanics is an intriguing idea since, we know that geometric methods are very powerful in Classical Mechanics then, we can try to use them to study quantum systems. In this paper, we summarize the construction of a general prescription to set up a well-defined and self-consistent geometric Hamiltonian formulation of finite-dimensional quantum theories, where phase space is given by the Hilbert projective space (as Kähler manifold), in the spirit of celebrated works of Kibble, Ashtekar and others. Within geometric Hamiltonian formulation quantum observables are represented by phase space functions, quantum states are described by Liouville densities (phase space probability densities), and Schrödinger dynamics is induced by a Hamiltonian flow on the projective space. We construct the star-product of this phase space formulation and some applications of geometric picture are discussed.
Inconstancy-theory/quantum-gravity
NASA Astrophysics Data System (ADS)
Murtaza, Faheem
1999-05-01
Inconstancy-theory is the union of "relativity" and "quantum" theories which rests upon the answers of the simple questions. 1) That if only the simple motion of a particle can not be observed without the "reference-frame" then how the whole universe can be expected to be observable without any "reference-frame". 2) Does not the inter-influence (Unity) of space-time-mass suggest that these are generated by common source and might not there be some invisible "flow" (dynamical-equilibrium) that is the cause of space-time-mass,as time itself is a flow. "Inconstancy" proposes, interalia, the principle that "relativity (generalised) is the universal law of nature in each and every respect". For that "inconstancy" admits only the light, being absolute, a real reference-frame and medium(mirror) for the display of relative "space-time-mass". Light as reference-frame in "Inconstancy" unifies "relativity" and "quantum" theories and establishes the inter-connection between "quantum-gravity" and strong-nuclear interactions, which offers the velocity of light in terms of physical and spatial-temporal components. "Inconstancy" introduces another "constant" operative in "quantum-gravity" and unveils the "graviton" location for its novel range as previously "relativity" escaped detection for v<<
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.
A state-dependent noncontextuality inequality in algebraic quantum theory
NASA Astrophysics Data System (ADS)
Kitajima, Yuichiro
2017-08-01
The noncontextuality condition states that a value of any observable is independent of which other compatible observable is measured jointly with it. Klyachko, Can, Binicioğlu, and Shumovsky have introduced an inequality which holds if there is a noncontextual hidden variable theory. It is called KCBS inequality, which is state-dependent. Its violation shows a contradiction between predictions of quantum theory and noncontextual hidden variable theories. In the present paper, it is shown that there is a state which does not violate KCBS inequality in the case of quantum mechanics of finite degrees of freedom, and that any normal state violates it in the case of algebraic quantum field theory. It is a difference between quantum mechanics of finite degrees of freedom and algebraic quantum field theory from a point of view of KCBS inequality.
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.
Creativity and the Quantum Theory.
ERIC Educational Resources Information Center
Goswami, Amit
1988-01-01
The idea that creative acts are quantum jumps in the brain's mechanism is explored. Descriptions of the creative process that support the central role of sudden and discontinuous leaps of thought are cited from various philosophers and scientists. Distinctions between the functions of the brain and of computers are drawn. (VW)
Complementarity and entanglement in quantum information theory
NASA Astrophysics Data System (ADS)
Tessier, Tracey Edward
This research investigates two inherently quantum mechanical phenomena, namely complementarity and entanglement, from an information-theoretic perspective. Beyond philosophical implications, a thorough grasp of these concepts is crucial for advancing our understanding of foundational issues in quantum mechanics, as well as in studying how the use of quantum systems might enhance the performance of certain information processing tasks. The primary goal of this thesis is to shed light on the natures and interrelationships of these phenomena by approaching them from the point of view afforded by information theory. We attempt to better understand these pillars of quantum mechanics by studying the various ways in which they govern the manipulation of information, while at the same time gaining valuable insight into the roles they play in specific applications. The restrictions that nature places on the distribution of correlations in a multipartite quantum system play fundamental roles in the evolution of such systems and yield vital insights into the design of protocols for the quantum control of ensembles with potential applications in the field of quantum computing. By augmenting the existing formalism for quantifying entangled correlations, we show how this entanglement sharing behavior may be studied in increasingly complex systems of both theoretical and experimental significance. Further, our results shed light on the dynamical generation and evolution of multipartite entanglement by demonstrating that individual members of an ensemble of identical systems coupled to a common probe can become entangled with one another, even when they do not interact directly. The findings presented in this thesis support the conjecture that Hilbert space dimension is an objective property of a quantum system since it constrains the number of valid conceptual divisions of the system into subsystems. These arbitrary observer-induced distinctions are integral to the theory since
Dissipative Forces and Quantum Mechanics
ERIC Educational Resources Information Center
Eck, John S.; Thompson, W. J.
1977-01-01
Shows how to include the dissipative forces of classical mechanics in quantum mechanics by the use of non-Hermetian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. (MLH)
Dissipative Forces and Quantum Mechanics
ERIC Educational Resources Information Center
Eck, John S.; Thompson, W. J.
1977-01-01
Shows how to include the dissipative forces of classical mechanics in quantum mechanics by the use of non-Hermetian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. (MLH)
Quantum cellular automaton theory of light
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-01
We present a quantum theory of light based on the recent derivation of Weyl and Dirac quantum fields from general principles ruling the interactions of a countable set of abstract quantum systems, without using space-time and mechanics (D'Ariano and Perinotti, 2014). In a Planckian interpretation of the discreteness, the usual quantum field theory corresponds to the so-called relativistic regime of small wave-vectors. Within the present framework the photon is a composite particle made of an entangled pair of free Weyl Fermions, and the usual Bosonic statistics is recovered in the low photon density limit, whereas the Maxwell equations describe the relativistic regime. We derive the main phenomenological features of the theory in the ultra-relativistic regime, consisting in a dispersive propagation in vacuum, and in the occurrence of a small longitudinal polarization, along with a saturation effect originated by the Fermionic nature of the photon. We then discuss whether all these effects can be experimentally tested, and observe that only the dispersive effects are accessible to the current technology via observations of gamma-ray bursts.
Quantum cellular automaton theory of light
Bisio, Alessandro D’Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-15
We present a quantum theory of light based on the recent derivation of Weyl and Dirac quantum fields from general principles ruling the interactions of a countable set of abstract quantum systems, without using space–time and mechanics (D’Ariano and Perinotti, 2014). In a Planckian interpretation of the discreteness, the usual quantum field theory corresponds to the so-called relativistic regime of small wave-vectors. Within the present framework the photon is a composite particle made of an entangled pair of free Weyl Fermions, and the usual Bosonic statistics is recovered in the low photon density limit, whereas the Maxwell equations describe the relativistic regime. We derive the main phenomenological features of the theory in the ultra-relativistic regime, consisting in a dispersive propagation in vacuum, and in the occurrence of a small longitudinal polarization, along with a saturation effect originated by the Fermionic nature of the photon. We then discuss whether all these effects can be experimentally tested, and observe that only the dispersive effects are accessible to the current technology via observations of gamma-ray bursts.
Quantum mechanics and the physical reality concept
von Borzeszkowski, H.H.; Wahsner, R.
1988-06-01
The difference between the measurement bases of classical and quantum mechanics is often interpreted as a loss of reality arising in quantum mechanics. In this paper it is shown that this apparent loss occurs only if one believes that refined everyday experience determines the Euclidean space as the real space, instead of considering this space, both in classical and quantum mechanics, as a theoretical construction needed for measurement and representing one part of a dualistic space conception. From this point of view, Einstein's program of a unified field theory can be interpreted as the attempt to find a physical theory that is less dualistic. However, if one regards this dualism as resulting from the requirements of measurements, one can hope for a weakening of the dualism but not expect to remove it completely.
On reconciling quantum mechanics and local realism
NASA Astrophysics Data System (ADS)
Graft, Donald A.
2013-10-01
Accepting nonlocal quantum correlations requires us to reject special relativity and/or probability theory. We can retain both by revising our interpretation of quantum mechanics regarding the handling of separated systems, as quantum mechanics conflicts with local realism only in its treatment of separated systems. We cannot use the joint probability formula for cases of separated measurements. We use the marginals (partial traces) together with whatever priors we have from an understanding of the system. This program can reconcile quantum mechanics with local realism. An apparent obstacle to this program is the experimental evidence, but we argue that the experiments have been misinterpreted, and that when correctly interpreted they confirm local realism. We describe a local realistic account of one important Einstein-Poldosky-Rosen-Bohm (EPRB) experiment (Weihs et al6) that claims to demonstrate nonlocal entanglement. We present a local realistic system (experiment) that can be calibrated into both quantum and classical correlation domains via adjustment of parameters (`hidden variables') of the apparatus. Weihs incorrectly dismisses these parameters as uncritical. Nonlocal entanglement is seen to be an error. The rest of quantum mechanics remains intact, and remains highly valued as a powerful probability calculus for observables. Freed from the incoherent idea of nonlocal entanglement, we can leverage powerful classical ideas, such as semiclassical radiation theory, stochastic dynamics, classical noncommutativity/contextuality, measurement effects on state, etc., to augment or complement quantum mechanics. When properly interpreted and applied, quantum mechanics lives in peaceful harmony with the local realist conception, and both perspectives offer useful paradigms for describing systems.
Quantum field theory on a cosmological, quantum space-time
Ashtekar, Abhay; Kaminski, Wojciech; Lewandowski, Jerzy
2009-03-15
In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker space-times arise as well-defined approximations to specific quantum geometries. We initiate the development of a quantum theory of test scalar fields on these quantum geometries. Emphasis is on the new conceptual ingredients required in the transition from classical space-time backgrounds to quantum space-times. These include a ''relational time''a la Leibniz, the emergence of the Hamiltonian operator of the test field from the quantum constraint equation, and ramifications of the quantum fluctuations of the background geometry on the resulting dynamics. The familiar quantum field theory on classical Friedmann-LeMaitre-Robertson-Walker models arises as a well-defined reduction of this more fundamental theory.
Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories
NASA Astrophysics Data System (ADS)
Bonelli, Giulio; Sciarappa, Antonio; Tanzini, Alessandro; Vasko, Petr
2016-11-01
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.
Quantum mechanics, relativity and time
NASA Astrophysics Data System (ADS)
Basini, Giuseppe; Capozziello, Salvatore
2005-01-01
A discussion on quantum mechanics, general relativity and their relations is introduced. The assumption of the absolute validity of conservation laws and the extension to a 5D-space lead to reconsider several shortcomings and paradoxes of modern physics under a new light without the necessity to take into account symmetry breakings. In this picture, starting from first principles, and after a reduction procedure from 5D to 4D, dynamics leads to the natural emergence of two time arrows and ofa scalar-tensor theory of gravity. In this framework, phenomena like entanglement of systems and topology changes can be naturally accounted and, furthermore, several experimental evidences as gamma ray bursts, sizes of astrophysical structures and the observed values of cosmological parameters can be explained. The identification, thanks to conservation laws, of a covariant symplectic structure as a general feature also for gravity can be seen as a deep link common to all the interactions.
Quantum mechanics near closed timelike lines
NASA Astrophysics Data System (ADS)
Deutsch, David
1991-11-01
The methods of the quantum theory of computation are used to analyze the physics of closed timelike lines. This is dominated, even at the macroscopic level, by quantum mechanics. In classical physics the existence of such lines in a spacetime imposes ``paradoxical'' constraints on the state of matter in their past and also provides means for knowledge to be created in ways that conflict with the principles of the philosophy of science. In quantum mechanics the first of these pathologies does not occur. The second is mitigated, and may be avoidable without such spacetimes being ruled out. Several novel and distinctive (but nonparadoxical) quantum-mechanical effects occur on and near closed timelike lines, including violations of the correspondence principle and of unitarity. It becomes possible to ``clone'' quantum systems and to measure the state of a quantum system. A new experimental test of the Everett interpretation against all others becomes possible. Consideration of these and other effects sheds light on the nature of quantum mechanics.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-06
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Quantum mechanics is compatible with realism
Burgos, M.E.
1987-08-01
A new paradox of quantum mechanics has recently been proposed by an author claiming that any attempt to inject realism in physical theory is bound to lead to inconsistencies. In this paper the author shows that the mentioned paradox is not such a one and that at present there are no reasons to reject realism.
BOOK REVIEWS: Quantum Mechanics: Fundamentals
NASA Astrophysics Data System (ADS)
Whitaker, A.
2004-02-01
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried’s well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantum mechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell’s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried’s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried’s book. Gottfried had devoted a
Paul A.M. Dirac's The Principles of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Brown, Laurie M.
2006-12-01
Paul A.M. Dirac’s book, The Principles of Quantum Mechanics, summarized the foundations of a new science, much of which was his own creation. It expressed the spirit of the new quantum mechanics, creating a descriptive language that we still use. I discuss the successive editions of Dirac’s book and their critical reception, noting changes, especially in the formulation of the general theory and in its treatment of relativistic quantum theory and quantum electrodynamics. In the case of the later editions, I discuss Dirac’s negative attitude toward renormalized quantum electrodynamics.
The Madelung Picture as a Foundation of Geometric Quantum Theory
NASA Astrophysics Data System (ADS)
Reddiger, Maik
2017-09-01
Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution of a given probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise.
Quantum Mechanics and the Interpretation Problem
NASA Astrophysics Data System (ADS)
Lonney, Lawrence William, Jr.
1990-01-01
Although many well articulated approaches to theory choice exist, no general approach to interpretation choice is available. This lacking is particularly troublesome for quantum mechanics because its mathematical formalism is associated with many well-developed interpretations. The lack of a method for choosing among the various interpretations of quantum mechanics has motivated the construction of this dissertation. The search for an appropriate method focuses on two areas: attempts to establish the superiority of one particular interpretation of quantum mechanics over another and general methods for choosing one theory over another. Regarding the former area, two attempts to choose the Statistical Ensemble interpretation of quantum mechanics over the Copenhagen interpretation are analyzed. One of these is authored by L. E. Ballentine and the other by J. L. Park. The conclusion of this analysis is that both attempts did not succeed and a general approach to interpretation choice could not be extracted from either. The desired approach was eventually found in one of the general methods for choosing among theories. The essential element of this approach to interpretation choice lies in the recognition that each interpretation contains the seed of a unique research program. If the program is cultivated, it can eventually be judged relative to others which have sprouted from the same theory. The criteria for such a judgment are contained in the Methodology of Scientific Research Programmes approach to theory choice. This method is applied to the Statistical Ensemble and Copenhagen interpretations of quantum mechanics. Even though it did not result in an immediate choice between the two, it did provide guidance for identifying what is needed to make such a choice.
Anyons in quantum mechanics with a minimal length
NASA Astrophysics Data System (ADS)
Buisseret, Fabien
2017-02-01
The existence of anyons, i.e. quantum states with an arbitrary spin, is a generic feature of standard quantum mechanics in (2 + 1) -dimensional Minkowski spacetime. Here it is shown that relativistic anyons may exist also in quantum theories where a minimal length is present. The interplay between minimal length and arbitrary spin effects are discussed.
Higher-Order Interference in Extensions of Quantum Theory
NASA Astrophysics Data System (ADS)
Lee, Ciarán M.; Selby, John H.
2016-10-01
Quantum interference, manifest in the two slit experiment, lies at the heart of several quantum computational speed-ups and provides a striking example of a quantum phenomenon with no classical counterpart. An intriguing feature of quantum interference arises in a variant of the standard two slit experiment, in which there are three, rather than two, slits. The interference pattern in this set-up can be written in terms of the two and one slit patterns obtained by blocking one, or more, of the slits. This is in stark contrast with the standard two slit experiment, where the interference pattern cannot be written as a sum of the one slit patterns. This was first noted by Rafael Sorkin, who raised the question of why quantum theory only exhibits irreducible interference in the two slit experiment. One approach to this problem is to compare the predictions of quantum theory to those of operationally-defined `foil' theories, in the hope of determining whether theories that do exhibit higher-order interference suffer from pathological—or at least undesirable—features. In this paper two proposed extensions of quantum theory are considered: the theory of Density Cubes proposed by Dakić, Paterek and Brukner, which has been shown to exhibit irreducible interference in the three slit set-up, and the Quartic Quantum Theory of Życzkowski. The theory of Density Cubes will be shown to provide an advantage over quantum theory in a certain computational task and to posses a well-defined mechanism which leads to the emergence of quantum theory—analogous to the emergence of classical physics from quantum theory via decoherence. Despite this, the axioms used to define Density Cubes will be shown to be insufficient to uniquely characterise the theory. In comparison, Quartic Quantum Theory is a well-defined theory and we demonstrate that it exhibits irreducible interference to all orders. This feature of Życzkowski's theory is argued not to be a genuine phenomenon, but to
Higher-Order Interference in Extensions of Quantum Theory
NASA Astrophysics Data System (ADS)
Lee, Ciarán M.; Selby, John H.
2017-01-01
Quantum interference, manifest in the two slit experiment, lies at the heart of several quantum computational speed-ups and provides a striking example of a quantum phenomenon with no classical counterpart. An intriguing feature of quantum interference arises in a variant of the standard two slit experiment, in which there are three, rather than two, slits. The interference pattern in this set-up can be written in terms of the two and one slit patterns obtained by blocking one, or more, of the slits. This is in stark contrast with the standard two slit experiment, where the interference pattern cannot be written as a sum of the one slit patterns. This was first noted by Rafael Sorkin, who raised the question of why quantum theory only exhibits irreducible interference in the two slit experiment. One approach to this problem is to compare the predictions of quantum theory to those of operationally-defined `foil' theories, in the hope of determining whether theories that do exhibit higher-order interference suffer from pathological—or at least undesirable—features. In this paper two proposed extensions of quantum theory are considered: the theory of Density Cubes proposed by Dakić, Paterek and Brukner, which has been shown to exhibit irreducible interference in the three slit set-up, and the Quartic Quantum Theory of Życzkowski. The theory of Density Cubes will be shown to provide an advantage over quantum theory in a certain computational task and to posses a well-defined mechanism which leads to the emergence of quantum theory—analogous to the emergence of classical physics from quantum theory via decoherence. Despite this, the axioms used to define Density Cubes will be shown to be insufficient to uniquely characterise the theory. In comparison, Quartic Quantum Theory is a well-defined theory and we demonstrate that it exhibits irreducible interference to all orders. This feature of Życzkowski's theory is argued not to be a genuine phenomenon, but to
The principle of stationary variance in quantum field theory
NASA Astrophysics Data System (ADS)
Siringo, Fabio
2014-02-01
The principle of stationary variance is advocated as a viable variational approach to quantum field theory (QFT). The method is based on the principle that the variance of energy should be at its minimum when the state of a quantum system reaches its best approximation for an eigenstate. While not too much popular in quantum mechanics (QM), the method is shown to be valuable in QFT and three special examples are given in very different areas ranging from Heisenberg model of antiferromagnetism (AF) to quantum electrodynamics (QED) and gauge theories.
Construction of relativistic quantum theory: a progress report
Noyes, H.P.
1986-06-01
We construct the particulate states of quantum physics using a recursive computer program that incorporates non-determinism by means of locally arbitrary choices. Quantum numbers and coupling constants arise from the construction via the unique 4-level combinatorial hierarchy. The construction defines indivisible quantum events with the requisite supraluminal correlations, yet does not allow supraluminal communication. Measurement criteria incorporate c, h-bar and m/sub p/ or (not ''and'') G, connected to laboratory events via finite particle number scattering theory and the counter paradigm. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact.
Quantum Mechanics in Insulators
Aeppli, G.
2009-08-20
Atomic physics is undergoing a large revival because of the possibility of trapping and cooling ions and atoms both for individual quantum control as well as collective quantum states, such as Bose-Einstein condensates. The present lectures start from the 'atomic' physics of isolated atoms in semiconductors and insulators and proceed to coupling them together to yield magnets undergoing quantum phase transitions as well as displaying novel quantum states with no classical analogs. The lectures are based on: G.-Y. Xu et al., Science 317, 1049-1052 (2007); G. Aeppli, P. Warburton, C. Renner, BT Technology Journal, 24, 163-169 (2006); H. M. Ronnow et al., Science 308, 392-395 (2005) and N. Q. Vinh et al., PNAS 105, 10649-10653 (2008).
Quantum Theories of Self-Localization
NASA Astrophysics Data System (ADS)
Bernstein, Lisa Joan
In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.
Dynamics of nonrelativistic quantum mechanics
NASA Astrophysics Data System (ADS)
Efthimiades, Spyros
2017-01-01
We show that the wavefunction of an electron interacting with an electric potential is accurately represented by the superposition of plane waves that fulfills the total energy relation. As a result, we explicitly derive the Schrödinger, Pauli, Klein-Gordon, and Dirac equations. While the traditional nonrelativistic quantum dynamics is based on postulates, the dynamics we introduce is theoretically justified, in agreement with experimental measurements, and consistent with the fundamental theory of quantum electrodynamics.
Unusual signs in quantum field theory
NASA Astrophysics Data System (ADS)
O'Connell, Donal
Quantum field theory is by now a mature field. Nevertheless, certain physical phenomena remain difficult to understand. This occurs in some cases because well-established quantum field theories are strongly coupled and therefore difficult to solve; in other cases, our current understanding of quantum field theory seems to be inadequate. In this thesis, we will discuss various modifications of quantum field theory which can help to alleviate certain of these problems, either in their own right or as a component of a greater computational scheme. The modified theories we will consider all include unusual signs in some aspect of the theory. We will also discuss limitations on what we might expect to see in experiments, imposed by sign constraints in the customary formulation of quantum field theory.
[The concepts of quantum theory can be introduced into psychophysiology].
Shuĭkin, N N
1998-01-01
There are some ideas in the quantum mechanics, which may be assimilated by psychophysiology. The concept of interference alternatives, advanced by Richard Feynman, may extend the subject matter of the notion of need. The quantum theory assumes virtual transitions. The idea of the physical virtual process may be the rational basis for subjective reality.
Noncommuting observables in quantum detection and estimation theory
NASA Technical Reports Server (NTRS)
Helstrom, C. W.
1971-01-01
In quantum detection theory, the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. In addition, the lower bounds on mean square errors of parameter estimates, predicted by the quantum mechanical Cramer-Rao inequality, cannot be reduced by such means.
Noncommunting observables in quantum detection and estimation theory
NASA Technical Reports Server (NTRS)
Helstrom, C. W.
1971-01-01
In quantum detection theory the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. The lower bounds on mean square errors of parameter estimates predicted by the quantum-mechanical Cramer-Rao inequality can also not be reduced by such means.
Quantum mechanics in complex systems
NASA Astrophysics Data System (ADS)
Hoehn, Ross Douglas
. These nodes are spaced far enough from each other to minimized the electronic repulsion of the electrons, while still providing adequate enough attraction so as to bind the excess elections into orbitals. We have found that even with relativistic considerations these species are stably bound within the field. It was also found that performing the dimensional scaling calculations for systems within the confines of laser fields to be a much simpler and more cost-effective method than the supporting D=3 SCF method. The dimensional scaling method is general and can be extended to include relativistic corrections to describe the stability of simple molecular systems in super-intense laser fields. Chapter 3, we delineate the model, and aspects therein, of inelastic electron tunneling and map this model to the protein environment. G protein-coupled receptors (GPCRs) constitute a large family of receptors that sense molecules outside of a cell and activate signal transduction pathways inside the cell. Modeling how an agonist activates such a receptor is important for understanding a wide variety of physiological processes and it is of tremendous value for pharmacology and drug design. Inelastic electron tunneling spectroscopy (IETS) has been proposed as the mechanism by which olfactory GPCRs are activated by an encapsulated agonist. In this note we apply this notion to GPCRs within the mammalian nervous system using ab initio quantum chemical modeling. We found that non-endogenous agonists of the serotonin receptor share a singular IET spectral aspect both amongst each other and with the serotonin molecule: a peak that scales in intensity with the known agonist activities. We propose an experiential validation of this model by utilizing lysergic acid dimethylamide (DAM-57), an ergot derivative, and its isotopologues in which hydrogen atoms are replaced by deuterium. If validated our theory may provide new avenues for guided drug design and better in silico prediction of
A minimalist approach to conceptualization of time in quantum theory
NASA Astrophysics Data System (ADS)
Kitada, Hitoshi; Jeknić-Dugić, Jasmina; Arsenijević, Momir; Dugić, Miroljub
2016-12-01
Ever since Schrödinger, Time in quantum theory is postulated Newtonian for every reference frame. With the help of certain known mathematical results, we show that the concept of the so-called Local Time allows avoiding the postulate. In effect, time appears as neither fundamental nor universal on the quantum-mechanical level while being consistently attributable to every, at least approximately, closed quantum system as well as to every of its (conservative or not) subsystems.
Quantum chemistry simulation on quantum computers: theories and experiments.
Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng
2012-07-14
It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.
Geometrical description of algebraic structures: Applications to Quantum Mechanics
Carinena, J. F.; Ibort, A.; Marmo, G.; Morandi, G.
2009-05-06
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to quantum mechanics. We will concentrate our attention into quantum theories and we will show how to use in a systematic way the transition from algebraic to geometrical structures to explore their geometry, mainly its Jordan-Lie structure.
Space--Time from Topos Quantum Theory
NASA Astrophysics Data System (ADS)
Flori, Cecilia
One of the main challenges in theoretical physics in the past 50 years has been to define a theory of quantum gravity, i.e. a theory which consistently combines general relativity and quantum theory in order to define a theory of space-time itself seen as a fluctuating field. As such, a definition of space-time is of paramount importance, but it is precisely the attainment of such a definition which is one of the main stumbling blocks in quantum gravity. One of the striking features of quantum gravity is that although both general relativity and quantum theory treat space-time as a four-dimensional (4D) manifold equipped with a metric, quantum gravity would suggest that, at the microscopic scale, space-time is somewhat discrete. Therefore the continuum structure of space-time suggested by the two main ingredients of quantum gravity seems to be thrown into discussion by quantum gravity itself. This seems quite an odd predicament, but it might suggest that perhaps a different mathematical structure other than a smooth manifold should model space-time. These considerations seem to shed doubts on the use of the continuum in general in a possible theory of quantum gravity. An alternative would be to develop a mathematical formalism for quantum gravity in which no fundamental role is played by the continuum and where a new concept of space-time, not modeled on a differentiable manifold, will emerge. This is precisely one of the aims of the topos theory approach to quantum theory and quantum gravity put forward by Isham, Butterfield, and Doering and subsequently developed by other authors. The aim of this article is to precisely elucidate how such an approach gives rise to a new definition of space-time which might be more appropriate for quantum gravity.
Whiteheadian process and quantum theory
Stapp, H.
1998-08-01
There are deep similarities between Whitehead's idea of the process by which nature unfolds and the ideas of quantum theory. Whitehead says that the world is made of ''actual occasions'', each of which arises from potentialities created by prior actual occasions. These actual occasions are happenings modeled on experiential events, each of which comes into being and then perishes, only to be replaced by a successor. It is these experience-like happenings that are the basic realities of nature, according to Whitehead, not the persisting physical particles that Newtonian physics took be the basic entities. Similarly, Heisenberg says that what is really happening in a quantum process is the emergence of an actual from potentialities created by prior actualities. In the orthodox Copenhagen interpretation of quantum theory the actual things to which the theory refer are increments in ''our knowledge''. These increments are experiential events. The particles of classical physics lose their fundamental status: they dissolve into diffuse clouds of possibilities. At each stage of the unfolding of nature the complete cloud of possibilities acts like the potentiality for the occurrence of a next increment in knowledge, whose occurrence can radically change the cloud of possibilities/potentialities for the still-later increments in knowledge. The fundamental difference between these ideas about nature and the classical ideas that reigned from the time of Newton until this century concerns the status of the experiential aspects of nature. These are things such as thoughts, ideas, feelings, and sensations. They are distinguished from the physical aspects of nature, which are described in terms of quantities explicitly located in tiny regions of space and time. According to the ideas of classical physics the physical world is made up exclusively of things of this latter type, and the unfolding of the physical world is determined by causal connections involving only these things
A nilpotent symmetry of quantum gauge theories
NASA Astrophysics Data System (ADS)
Lahiri, Amitabha
2001-09-01
For the Becchi-Rouet-Stora-Tyutin invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the construction of the quantum effective action. Generalizations for nonlinear gauges and actions with higher-order ghost terms are also possible.
Is quantum theory predictably complete?
NASA Astrophysics Data System (ADS)
Kupczynski, M.
2009-07-01
Quantum theory (QT) provides statistical predictions for various physical phenomena. To verify these predictions a considerable amount of data has been accumulated in the 'measurements' performed on the ensembles of identically prepared physical systems or in the repeated 'measurements' on some trapped 'individual physical systems'. The outcomes of these measurements are, in general, some numerical time series registered by some macroscopic instruments. The various empirical probability distributions extracted from these time series were shown to be consistent with the probabilistic predictions of QT. More than 70 years ago the claim was made that QT provided the most complete description of 'individual' physical systems and outcomes of the measurements performed on 'individual' physical systems were obtained in an intrinsically random way. Spin polarization correlation experiments (SPCEs), performed to test the validity of Bell inequalities, clearly demonstrated the existence of strong long-range correlations and confirmed that the beams hitting far away detectors somehow preserve the memory of their common source which would be destroyed if the individual counts of far away detectors were purely random. Since the probabilities describe the random experiments and are not the attributes of the 'individual' physical systems, the claim that QT provides a complete description of 'individual' physical systems seems not only unjustified but also misleading and counter productive. In this paper, we point out that we even do not know whether QT is predictably complete because it has not been tested carefully enough. Namely, it was not proven that the time series of existing experimental data did not contain some stochastic fine structures that could have been averaged out by describing them in terms of the empirical probability distributions. In this paper, we advocate various statistical tests that could be used to search for such fine structures in the data and to
Kowalevski top in quantum mechanics
Matsuyama, A.
2013-09-15
The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra. -- Highlights: •Quantum spectra of the Kowalevski top are calculated. •Semiclassical quantization is carried out by the EBK formulation. •Quantum states are labeled by the semiclassical integer quantum numbers. •Multiplicity of the classical torus makes the spectra nearly degenerate. •Symmetries, quantum numbers and near-degenerate spectra are closely related.
NASA Astrophysics Data System (ADS)
Bennett, Charles L.
1987-11-01
It is pointed out that both classical Wheeler-Feynman electrodynamics and its finite quantized generalization inevitably lead to microscopic causality violation. As there is some evidence for such effects in proton Compton scattering, there is possibly reason to prefer such absorber theories of action at a distance over field theories as the more reasonable microscopic description of nature.
Quantum Mechanics and Narratability
NASA Astrophysics Data System (ADS)
Myrvold, Wayne C.
2016-07-01
As has been noted by several authors, in a relativistic context, there is an interesting difference between classical and quantum state evolution. For a classical system, a state history of a quantum system given along one foliation uniquely determines, without any consideration of the system's dynamics, a state history along any other foliation. This is not true for quantum state evolution; there are cases in which a state history along one foliation is compatible with multiple distinct state histories along some other, a phenomenon that David Albert has dubbed "non-narratability." In this article, we address the question of whether non-narratability is restricted to the sorts of special states that so far have been used to illustrate it. The results of the investigation suggest that there has been a misplaced emphasis on underdetermination of state histories; though this is generic for the special cases that have up until now been considered, involving bipartite systems in pure entangled states, it fails generically in cases in which more component systems are taken into account, and for bipartite systems that have some entanglement with their environment. For such cases, if we impose relativistic causality constraints on the evolution, then, except for very special states, a state history along one foliation uniquely determines a state history along any other. But this in itself is a marked difference between classical and quantum state evolution, because, in a classical setting, no considerations of dynamics at all are needed to go from a state history along one foliation to a state history along another.
The Compton effect: Transition to quantum mechanics
NASA Astrophysics Data System (ADS)
Stuewer, R. H.
2000-11-01
The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925-1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light-quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite Robert A. Millikan's confirmation of Einstein's equation of the photoelectric effect in 1915. I then follow in some detail the experimental and theoretical research program that Arthur Holly Compton pursued between 1916 and 1922 at the University of Minnesota, the Westinghouse Lamp Company, the Cavendish Laboratory, and Washington University that culminated in his discovery of the Compton effect. Surprisingly, Compton was not influenced directly by Einstein's light-quantum hypothesis, in contrast to Peter Debye and H.A. Kramers, who discovered the quantum theory of scattering independently. I close by discussing the most significant response to that discovery, the Bohr-Kramers-Slater theory of 1924, its experimental refutation, and its influence on the emerging new quantum mechanics.
Quantum Mechanics from Periodic Dynamics: the bosonic case
Dolce, Donatello
2010-05-04
Enforcing the periodicity hypothesis of the 'old' formulation of Quantum Mechanics we show the possibility for a new scenario where Special Relativity and Quantum Mechanics are unified in a deterministic field theory. A novel interpretation of the AdS/CFT conjecture is discussed.
Quantum mechanical coherence, resonance, and mind
Stapp, H.P.
1995-03-26
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Einstein's opposition to the quantum theory
NASA Astrophysics Data System (ADS)
Deltete, Robert; Guy, Reed
1990-07-01
Einstein's opposition to the quantum theory is well known to physicists, but his reasons for being dissatisfied are not. Einstein regarded the theory as not only incomplete, but as fundamentally inadequate. He believed that the only reasonable interpretation of the quantum formalism was an ``ensemble interpretation,'' but he also thought that this interpretation and others were incomplete and irremediably inadequate, because they failed to describe the objective, real states of individual systems. He hoped, and expected, that a better theory would be developed—one expressed in terms of individuals having their own real states and from which the quantum theory could be recovered as an approximation.
Self-Referential Quantum Mechanics
NASA Astrophysics Data System (ADS)
Mitchell, Mark Kenneth
1993-01-01
A nonlinear quantum mechanics based upon the nonlinear logarithmic Schrodinger equation, is developed which has the property of self-reference, that is, the nonlinear term is dependent upon the square of the wavefunction. The self-referential system is examined in terms of its mathematical properties, the definition of the wavefunction, and the nonlinear system in the feedback between equation and solution. Theta operators are introduced which make possible new operations in the quantum phase. Two interpretations are presented utilizing the nonlinear quantum system: the idealistic interpretation based upon consciousness focused upon the measurement problem, and the statistical interpretation focused upon stochastic quantum fluctuations. Experimental properties are examined, beginning with a proposed analog of the Bohm-Aharonov experiment. Interference due to difference in path length for a split electron beam is effected in a region of spacetime where electromagnetic field and the vector potential are enclosed within but screened to be zero at the paths. If the wavefunction's geometrical phase contribution along the paths is different, then there should be interference induced purely by the wave-function alone. A positive result would be due to a purely wavefunction dependent effect. The spin phase of the wavefunction is postulated to be the source of the zitterbewegung of the electron. Reduction of the wavefunction in measurement is examined for self -referential quantum systems arising from consciousness and then arising from a stochastic quantum spacetime model. These results are applied to the mind-brain as a quantum processor producing a behavioral double slit experiment (ideation experiments) and nonlocal transferred potentials in an EPR-style experiment. Looking at the universe as a whole as a quantum self-referential system, leads to a modified zitterbewegung Wheeler-DeWitt equation; and, the transition from quantum-to-classical on a cosmological scale for
The geometrical structure of quantum theory as a natural generalization of information geometry
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 using geometrical quantities. This suggests that quantum theory has its roots in information geometry.
Indirect Acquisition of Information in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Ballesteros, M.; Fraas, M.; Fröhlich, J.; Schubnel, B.
2016-02-01
Long sequences of successive direct (projective) measurements or observations of just a few "uninteresting" physical quantities pertaining to a quantum system, such as clicks of some detectors, may reveal indirect, but precise and unambiguous information on the values of some very "interesting" observables of the system. In this paper, the mathematics underlying this claim is developed; i.e., we attempt to contribute to a mathematical theory of indirect and, in particular, non-demolition observations and measurements in quantum mechanics. Our attempt leads us to make some novel uses of classical notions and results of probability theory, such as the "algebra of functions measurable at infinity", the Central Limit Theorem, results concerning relative entropy and its role in the theory of large deviations, etc.
Why Quantum Theory is Possibly Wrong
NASA Astrophysics Data System (ADS)
Lyre, Holger
2010-10-01
Quantum theory is a tremendously successful physical theory, but nevertheless suffers from two serious problems: the measurement problem and the problem of interpretational underdetermination. The latter, however, is largely overlooked as a genuine problem of its own. Both problems concern the doctrine of realism, but pull, quite curiously, into opposite directions. The measurement problem can be captured such that due to scientific realism about quantum theory common sense anti-realism follows, while theory underdetermination usually counts as an argument against scientific realism. I will also consider the more refined distinctions of ontic and epistemic realism and demonstrate that quantum theory in its most viable interpretations conflicts with at least one of the various realism claims. A way out of the conundrum is to come to the bold conclusion that quantum theory is, possibly, wrong (in the realist sense).
Quantum Mechanical Earth: Where Orbitals Become Orbits
ERIC Educational Resources Information Center
Keeports, David
2012-01-01
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
Quantum Mechanical Earth: Where Orbitals Become Orbits
ERIC Educational Resources Information Center
Keeports, David
2012-01-01
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
Quantum Detection Theory for the Free-Space Channel
NASA Astrophysics Data System (ADS)
Vilnrotter, V.; Lau, C.-W.
2001-04-01
The fundamental performance limits of optical communications over the free-space channel are developed using quantum theory, and presented in terms of concepts familiar to communications engineers. The compact Dirac notation generally employed in quantum mechanics is defined, and key concepts necessary for understanding quantum projection measurements are reviewed. A derivation that provides significant insights into the quantum measurement performed by the optimum receiver is developed by interpreting the familiar technique of photon counting in terms of quantum projection operators. The performance of the optimum quantum receiver for on-off keying and optical binary phase-shift-keying (BPSK) modulation is treated first as a noise-free (or pure-state) problem, then extended to include the effects of background radiation. The performance of the optimum quantum receiver is compared to that of classical optical receivers employing photon-counting and coherent detection techniques, and it is shown to be exponentially better in most cases.
Quantum and semiclassical theories of chemical reaction rates
Miller, W.H. |
1995-09-01
A rigorous quantum mechanical theory (and a semiclassical approximation thereto) is described for calculating chemical reaction rates ``directly``, i.e., without having to solve the complete state-to-state reactive scattering problem. The approach has many vestiges of transition state theory, for which it may be thought of as the rigorous generalization.
QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.
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.
Historical Review of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Prashant, Prashant
2007-03-01
Quantum Mechanics is being taught for the last many decades at both undergraduate as well as post graduate levels in universities world over. Inclusion of historical background i.e. development of the subject in chronological order, description of Gedanken experiments, information regarding Solvay, Copenhagen Conferences and biographies of well known contributors in this field may definitely give a broader understanding of the subject. This may create an interest in understanding the new developments and this article is an attempt in that direction to highlight the rich past of Quantum Mechanics and how it got shaped by great minds to its present form. Keywords: Quantum mechanics, historical, Copenhagen, Solvay, Bohr, Einstein. note: http://www.arxiv.org/abs/physics/0512104
Energy conservation in quantum mechanics
NASA Astrophysics Data System (ADS)
Prentis, Jeffrey J.; Fedak, William A.
2004-05-01
In the classical mechanics of conservative systems, the position and momentum evolve deterministically such that the sum of the kinetic energy and potential energy remains constant in time. This canonical trademark of energy conservation is absent in the standard presentations of quantum mechanics based on the Schrödinger picture. We present a purely canonical proof of energy conservation that focuses exclusively on the time-dependent position x(t) and momentum p(t) operators. This treatment of energy conservation serves as an introduction to the Heisenberg picture and illuminates the classical-quantum connection. We derive a quantum-mechanical work-energy theorem and show explicitly how the time dependence of x and p and the noncommutivity of x and p conspire to bring about a perfect temporal balance between the evolving kinetic and potential parts of the total energy operator.
Quantum equivalence of dual field theories
NASA Astrophysics Data System (ADS)
Fradkin, E. S.; Tseytlin, A. A.
1985-06-01
Motivated by the study of ultraviolet properties of different versions of supergravities duality transformations at the quantum level are discussed. Using the background field method it is proven on shell quantum equivalence for several pairs of dual field theories known to be classically equivalent. The examples considered include duality in chiral model, duality of scalars and second rank antisymmetric gauge tensors, vector duality and duality of the Einstein theory with cosmological term and the Eddington-Schrödinger theory.
A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2015-10-01
This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation of the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall also consider Heisenberg's earlier work leading him to the discovery of quantum mechanics, which inspired Dirac's work. I argue that Heisenberg's and Dirac's work was guided by their adherence to and their confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by D'Ariano and coworkers on the principles of quantum information theory, which extend quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equations from these principles alone, without using the principles of relativity.
3D quantum gravity and effective noncommutative quantum field theory.
Freidel, Laurent; Livine, Etera R
2006-06-09
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.
Intrusion Detection With Quantum Mechanics: A Photonic Quantum Fence
2008-12-01
computing and quantum key distribution (QKD). Some of the most remarkable examples include quantum teleportation for the non-local transfer of...1 INTRUSION DETECTION WITH QUANTUM MECHANICS: A PHOTONIC QUANTUM FENCE T. S. Humble*, R. S. Bennink, and W. P. Grice Oak Ridge National...use of quantum -mechanically entangled photons for sensing intrusions across a physical perimeter. Our approach to intrusion detection uses the no
A new introductory quantum mechanics curriculum
NASA Astrophysics Data System (ADS)
Kohnle, Antje; Bozhinova, Inna; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth
2014-01-01
The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum-mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of the interpretive aspects of quantum mechanics and quantum information theory. This paper gives an overview of the resources available from the IOP website. The core text includes around 80 articles which are co-authored by leading experts, arranged in themes, and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is included in the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways, from being supplemental to existing courses to forming a complete programme.
Quantum Mechanical Aspects of Free Electron Lasers.
NASA Astrophysics Data System (ADS)
Saritepe, Selcuk
Scope of study. A 2-D quantum theory of the Free Electron Laser (FEL) has been developed based on the solutions of Dirac equation for the motion of electrons moving in various wiggler geometries, uniform, tapered and enhanced by an axial guide field. It is shown that these solutions can be written in terms of Mathieu functions of fractional order. Using these solutions a perturbational analysis is carried out to calculate the frequencies and the gain of the FEL in each magnet configuration. Finally, an optical model for the FEL interaction is developed to explain the saturation behaviour and the short-pulse effects such as Laser Lethargy. Findings and conclusions. It is found that the quantum mechanical effects due to transverse momentum correction were gamma (Lorentz factor) times larger than the quantum recoil and spin effects and therefore important for the short wavelength FELs. These quantum mechanical effects cause a broadening in the spontaneous emission lineshape, a decrease in gain and an increase in the rate of harmonic frequency generation. In the presence of an axial field, gain is increased, harmonic frequency rate is reduced and Dirac solutions exhibit instability. The optical model developed in this thesis correctly predicts the oscillator rise time and uses a simpler algorithm to calculate the nonlinear saturation behaviour. Optical model also incorporates inhomogeneous broadening and quantum mechanical effects and explains the Laser Lethargy effect as an optical pulse compression phenomenon.
Canonical Transformations in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Anderson, A.
1994-06-01
Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary transformations for constructing solutions of the Schrödinger equation is discussed. Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can be realized quantum mechanically as a product of these transformations. Each transformation corresponds to a familiar tool used in solving differential equations, and the procedure of solving a differential equation is systematized by the use of the canonical transformations. Several examples are done to illustrate the use of the canonical transformations.
Quantum theory of surface-plasmon polariton scattering
Ballester, D.; Tame, M. S.; Kim, M. S.
2010-07-15
We introduce the quantum mechanical formalism for treating surface plasmon polariton scattering at an interface. Our developed theory--which differs fundamentally from the analogous photonic scenario--is used to investigate the possibility of plasmonic beam splitters at the quantum level. Remarkably, we find that a wide range of splitting ratios can be reached. As an application, we characterize a 50:50 plasmonic beam splitter and investigate first-order quantum interference of surface plasmon polaritons. The results of this theoretical study show that surface plasmon beam splitters are able to reliably and efficiently operate in the quantum domain.
Minkowski Space and Quantum Mechanics
NASA Astrophysics Data System (ADS)
O'Hara, Paul
A paradigm shift distinguishes general relativity from classical mechanics. In general relativity the energy-momentum tensor is the effective cause of the ontological space-time curvature and vice-versa, while in classical physics, the structure of space-time is treated as an accidental cause, serving only as a backdrop against which the laws of physics unfold. This split in turn is inherited by quantum mechanics, which is usually developed by changing classical (including special relativity) Hamiltonians into quantum wave equations.
Hidden variables and nonlocality in quantum mechanics
NASA Astrophysics Data System (ADS)
Hemmick, Douglas Lloyd
1997-05-01
Most physicists hold a skeptical attitude toward a 'hidden variables' interpretation of quantum theory, despite David Bohm's successful construction of such a theory and John S. Bell's strong arguments in favor of the idea. The first reason for doubt concerns certain mathematical theorems (von Neumann's, Gleason's, Kochen and Specker's, and Bell's) which can be applied to the hidden variables issue. These theorems are often credited with proving that hidden variables are indeed 'impossible', in the sense that they cannot replicate the predictions of quantum mechanics. Many who do not draw such a strong conclusion nevertheless accept that hidden variables have been shown to exhibit prohibitively complicated features. The second concern is that the most sophisticated example of a hidden variables theory-that of David Bohm-exhibits non-locality, i.e., consequences of events at one place can propagate to other places instantaneously. However, neither the mathematical theorems in question nor the attribute of nonlocality detract from the importance of a hidden variables interpretation of quantum theory. Nonlocality is present in quantum mechanics itself, and is a required characteristic of any theory that agrees with the quantum mechanical predictions. We first discuss the earliest analysis of hidden variables-that of von Neumann's theorem-and review John S. Bell's refutation of von Neumann's 'impossibility proof'. We recall and elaborate on Bell's arguments regarding the theorems of Gleason, and Kochen and Specker. According to Bell, these latter theorems do not imply that hidden variables interpretations are untenable, but instead that such theories must exhibit contextuality, i.e., they must allow for the dependence of measurement results on the characteristics of both measured system and measuring apparatus. We demonstrate a new way to understand the implications of both Gleason's theorem and Kochen and Specker's theorem by noting that they prove a result we call
Effective equations for the quantum pendulum from momentous quantum mechanics
Hernandez, Hector H.; Chacon-Acosta, Guillermo
2012-08-24
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.
Emergent "Quantum" Theory in Complex Adaptive Systems.
Minic, Djordje; Pajevic, Sinisa
2016-04-30
Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective "Planck constant" associated with such emergent "quantum" theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.
Quantum mechanics of time travel through post-selected teleportation
NASA Astrophysics Data System (ADS)
Lloyd, Seth; Maccone, Lorenzo; Garcia-Patron, Raul; Giovannetti, Vittorio; Shikano, Yutaka
2011-07-01
This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is inequivalent to Deutsch’s theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum-field theory in curved space-time). We derive the dynamical equations that a chronology-respecting system interacting with a CTC will experience. We discuss the possibility of time travel in the absence of general-relativistic closed-timelike curves, and investigate the implications of P-CTCs for enhancing the power of computation.
Ruling out multi-order interference in quantum mechanics.
Sinha, Urbasi; Couteau, Christophe; Jennewein, Thomas; Laflamme, Raymond; Weihs, Gregor
2010-07-23
Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born's rule--one of the axioms of quantum mechanics--could be violated. Born's rule predicts that quantum interference, as shown by a double-slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multipath (i.e., higher-order) interference, thus leading to a deviation from the theory. We performed a three-slit experiment with photons and bounded the magnitude of three-path interference to less than 10(-2) of the expected two-path interference, thus ruling out third- and higher-order interference and providing a bound on the accuracy of Born's rule. Our experiment is consistent with the postulate both in semiclassical and quantum regimes.
Emergent quantum mechanics of finances
NASA Astrophysics Data System (ADS)
Nastasiuk, Vadim A.
2014-06-01
This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price-time continuum having fractal properties. The main steps of this development are the statistical scaling, the non-differentiability hypothesis, and the equations of motion entailed by this hypothesis. From perspective of the proposed theory the dynamics of S&P500 index are analyzed.
Supersymmetric quantum mechanics and its applications
Sukumar, C.V.
2004-12-23
The Hamiltonian in Supersymmetric Quantum Mechanics is defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of the component parts that constitute the supersymmetric system are explored. The implications of supersymmetry for the solutions of the Schroedinger equation, the Dirac equation, the inverse scattering theory and the multi-soliton solutions of the KdV equation are examined. Applications to scattering problems in Nuclear Physics with specific reference to singular potentials which arise from considerations of supersymmetry will be discussed.
``Haunted'' measurements in quantum theory
NASA Astrophysics Data System (ADS)
Greenberger, Daniel M.; Yasin, Alaine
1989-06-01
Sometimes it is possible in quantum theory for a system to interact with another system in such a way that the information contained in the wave function becomes very scrambled and apparently incoherent. We produce an example which is exactly calculable, in which a macroscopic change is induced in the environment, and all phase information for the system is apparently lost, so that a measurement has seemingly been made. But actually, although the wave function has been badly scrambled, all the original information is still present. We call this situation one of “latent order.” Subsequently, the system interacts again with the environment, wiping out the macroscopic change, and the wave function once again becomes manifestly coherent. Thus the apparent measurement has been undone, and leaves no aftereffect. Thus, our “measurement” has disappeared without a trace. We call such a measurement a “haunted measurement,” and we believe that until the measurement process is rigorously understood, the concept of measurement is ambiguous. It is just not good enough to say that an amplification stage occurs “somewhere” in the process. We also point out the connection between the haunted measurement and delayed-choice experiments and discuss a haunted version of the “Schrödinger's Cat” experiment and of the Einstein-Podolsky-Rosen experiment.
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.
Theory of coherent control with quantum light
NASA Astrophysics Data System (ADS)
Schlawin, Frank; Buchleitner, Andreas
2017-01-01
We develop a coherent control theory for multimode quantum light. It allows us to examine a fundamental problem in quantum optics: what is the optimal pulse form to drive a two-photon-transition? In formulating the question as a coherent control problem, we show that—and quantify how much—the strong frequency quantum correlations of entangled photons enhance the transition compared to shaped classical pulses. In ensembles of collectively driven two-level systems, such enhancement requires nonvanishing interactions.
A Free Object in Quantum Information Theory
2010-01-01
process of teleporting quantum information with a given entangled state. The third is purely a mathematical construction, the free affine monoid over the...Klein four group. We prove that all three of these objects are isomorphic. Keywords: Information Theory, Quantum Channel, Category, Teleportation ...information theoretic properties are easy to calculate. What are their higher dimensional analogues? (iv) If we attempt to teleport quantum information
Pilot-wave theory and quantum fields
NASA Astrophysics Data System (ADS)
Struyve, Ward
2010-10-01
Pilot-wave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on pilot-wave theories in which the additional variables are field configurations. The first such theory was proposed by Bohm for the free electromagnetic field. Since Bohm, similar pilot-wave theories have been proposed for other quantum fields. The purpose of this paper is to present an overview and further development of these proposals. We discuss various bosonic quantum field theories such as the Schrödinger field, the free electromagnetic field, scalar quantum electrodynamics and the Abelian Higgs model. In particular, we compare the pilot-wave theories proposed by Bohm and by Valentini for the electromagnetic field, finding that they are equivalent. We further discuss the proposals for fermionic fields by Holland and Valentini. In the case of Holland's model we indicate that further work is required in order to show that the model is capable of reproducing the standard quantum predictions. We also consider a similar model, which does not seem to reproduce the standard quantum predictions. In the case of Valentini's model we point out a problem that seems hard to overcome.
Emergent Quantum Mechanics and the Origin of Quantum Non-local Correlations
NASA Astrophysics Data System (ADS)
Torromé, Ricardo Gallego
2017-10-01
A geometric interpretation for quantum correlations and entanglement according to a particular framework of emergent quantum mechanics is developed. The mechanism described is based on two ingredients: 1. At an hypothetical sub-quantum level description of physical systems, the dynamics has a regime where it is partially ergodic and 2. A formal projection from a two-dimensional time mathematical formalism of the emergent quantum theory to the usual one-dimensional time formalism of quantum dynamics. Observable consequences of the theory are obtained. Among them we show that quantum correlations must be instantaneous from the point of view of the spacetime description, but the spatial distance up to which they can be observed must be bounded. It is argued how our mechanism avoids Bell theorem and Kochen-Specken theorem. Evidence for non-signaling faster than the speed of light in our proposal is discussed.
Quantum Hall Physics Equals Noncommutive Field Theory
Rammsdonk , Mark van
2001-08-09
In this note, we study a matrix-regularized version of non-commutative U(1) Chern-Simons theory proposed recently by Polychronakos. We determine a complete minimal basis of exact wavefunctions for the theory at arbitrary level k and rank N and show that these are in one-to-one correspondence with Laughlin-type wavefunctions describing excitations of a quantum Hall droplet composed of N electrons at filling fraction 1/k. The finite matrix Chern-Simons theory is shown to be precisely equivalent to the theory of composite fermions in the lowest Landau level, believed to provide an accurate description of the filling fraction 1/k fractional quantum Hall state. In the large N limit, this implies that level k noncommutative U(1) Chern-Simons theory is equivalent to the Laughlin theory of the filling fraction 1k quantum Hall fluid, as conjectured recently by Susskind.
An approach to nonstandard quantum mechanics
NASA Astrophysics Data System (ADS)
Raab, A.
2004-12-01
We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to nonrelativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the Mo/ller wave operators and the S-matrix.
Quantum Decision Theory in Simple Risky Choices
Favre, Maroussia; Wittwer, Amrei; Heinimann, Hans Rudolf; Yukalov, Vyacheslav I.; Sornette, Didier
2016-01-01
Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker’s choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) data, and find that the results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. This article revisits the formalism of QDT along a concrete example and offers a practical guide to researchers who are interested in applying QDT to a dataset of binary lotteries in the domain of gains. PMID:27936217
Quantum Decision Theory in Simple Risky Choices.
Favre, Maroussia; Wittwer, Amrei; Heinimann, Hans Rudolf; Yukalov, Vyacheslav I; Sornette, Didier
2016-01-01
Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker's choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) data, and find that the results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. This article revisits the formalism of QDT along a concrete example and offers a practical guide to researchers who are interested in applying QDT to a dataset of binary lotteries in the domain of gains.
Mathematical model I. Electron and quantum mechanics
NASA Astrophysics Data System (ADS)
Gadre, Nitin Ramchandra
2011-03-01
The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Steps in the philosophy of quantum theory
NASA Astrophysics Data System (ADS)
Görnitz, Th.; Weizsäcker, C. F. V.
1. Interpretation. The Copenhagen Interpretation (CI) is a minimal semantics to quantum theory, expressing what we know at least. It can be extended into a universal Quantum Theory, applied to the observer as well as to the observed object. 2. A Universal Theory as a Philosophical Problem. A circular epistemology is proposed, consisting of nonhierarchical realism, empirism, apriorism and evolutionism, combined in a description of time: past. as discrete facts, future as continuous possibilities. 3. Quantum Logic and the Reconstruction of Quantum Theory. Non-distributive logic and Bell's theorem are discussed following Doebner and Lücke. Reconstruction is briefly described. 4. Further Philosophical Questions. Mind-body problem and holism are briefly discussed.
Teaching Quantum Theory in the Introductory Course.
ERIC Educational Resources Information Center
Hobson, Art
1996-01-01
Describes an approach to teaching quantum theory without math with emphasis on some innovative approaches and topics such as nonlocality and Bell's theorem. Written in the form of suggestions to prospective instructors. (JRH)
Teaching Quantum Theory in the Introductory Course.
ERIC Educational Resources Information Center
Hobson, Art
1996-01-01
Describes an approach to teaching quantum theory without math with emphasis on some innovative approaches and topics such as nonlocality and Bell's theorem. Written in the form of suggestions to prospective instructors. (JRH)
Machine Learning and Quantum Mechanics
NASA Astrophysics Data System (ADS)
Chapline, George
The author has previously pointed out some similarities between selforganizing neural networks and quantum mechanics. These types of neural networks were originally conceived of as away of emulating the cognitive capabilities of the human brain. Recently extensions of these networks, collectively referred to as deep learning networks, have strengthened the connection between self-organizing neural networks and human cognitive capabilities. In this note we consider whether hardware quantum devices might be useful for emulating neural networks with human-like cognitive capabilities, or alternatively whether implementations of deep learning neural networks using conventional computers might lead to better algorithms for solving the many body Schrodinger equation.
Quantum feedback control and classical control theory
Doherty, Andrew C.; Habib, Salman; Jacobs, Kurt; Mabuchi, Hideo; Tan, Sze M.
2000-07-01
We introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences. We describe the application of state-observer-based control laws, familiar in classical control theory, to quantum systems and apply our methods to the particular case of switching the state of a particle in a double-well potential. (c) 2000 The American Physical Society.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Improving student understanding of quantum mechanics
NASA Astrophysics Data System (ADS)
Singh, Chandralekha
2015-04-01
Learning quantum mechanics is challenging for many students. We are investigating the difficulties that upper-level students have in learning quantum mechanics. To help improve student understanding of quantum concepts, we are developing quantum interactive learning tutorials (QuILTs) and tools for peer-instruction. Many of the QuILTs employ computer simulations to help students visualize and develop better intuition about quantum phenomena. We will discuss the common students' difficulties and research-based tools we are developing to bridge the gap between quantitative and conceptual aspects of quantum mechanics and help students develop a solid grasp of quantum concepts. Support from the National Science Foundation is gratefully acknowledged.
A supersymmetric extension of quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Scharf, G.
2003-01-01
We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge models in the Epstein-Glaser framework for perturbative field theory. Accordingly, all the arguments are completely of quantum nature without reference to a classical supersymmetric theory. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
Quantum Gauge Symmetry of Reducible Gauge Theory
NASA Astrophysics Data System (ADS)
Dwivedi, Manoj Kumar
2017-05-01
We derive the gaugeon formalism of the Kalb-Ramond field theory, a reducible gauge theory, which discusses the quantum gauge freedom. In gaugeon formalism, theory admits quantum gauge symmetry which leaves the action form-invariant. The BRST symmetric gaugeon formalism is also studied which introduces the gaugeon ghost fields and gaugeon ghosts of ghosts fields. To replace the Yokoyama subsidiary conditions by a single Kugo-Ojima type condition the virtue of BRST symmetry is utilized. Under generalized BRST transformations, we show that the gaugeon fields appear naturally in the reducible gauge theory.
Kinetic potentials in quantum mechanics
NASA Astrophysics Data System (ADS)
Hall, Richard L.
1984-09-01
Suppose that the Hamiltonian H=-Δ+vf(r) represents the energy of a particle which moves in an attractive central potential and obeys nonrelativistic quantum mechanics. The discrete eigenvalues Enl=Fnl(v) of H may be expressed as a Legendre transformation Fnl(v)=mins≳0(s+vf¯nl(s)), n=1,2,3,..., l=0,1,2,..., where the ``kinetic potentials'' f¯nl(s) associated with f(r) are defined by f¯nl(s) =infDnl supψ∈Dnl, ∥ψ∥=1 ∫ ψ(r) f ([ψ,-Δψ)/s]1/2r)ψ(r)d3r, and Dnl is an n-dimensional subspace of L2(R3) labeled by Ylm(θ,φ), m=0, and contained in the domain D(H) of H. If the potential has the form f(r)=∑Ni=1 g(i)( f(i)(r)) then in many interesting cases it turns out that the corresponding kinetic potentials can be closely approximated by ∑Ni=1 g(i)( f¯nl(i)(s)). This nice behavior of the kinetic potentials leads to a constructive global approximation theory for Schrödinger eigenvalues. As an illustration, detailed recipes are provided for arbitrary linear combinations of power-law potentials and the log potential. For the linear plus Coulomb potential and the quartic anharmonic oscillator the approximate eigenvalues are compared to accurate values found by numerical integration.
Quantum theory of the generalised uncertainty principle
NASA Astrophysics Data System (ADS)
Bruneton, Jean-Philippe; Larena, Julien
2017-04-01
We extend significantly previous works on the Hilbert space representations of the generalized uncertainty principle (GUP) in 3 + 1 dimensions of the form [X_i,P_j] = i F_{ij} where F_{ij} = f({{P}}^2) δ _{ij} + g({{P}}^2) P_i P_j for any functions f. However, we restrict our study to the case of commuting X's. We focus in particular on the symmetries of the theory, and the minimal length that emerge in some cases. We first show that, at the algebraic level, there exists an unambiguous mapping between the GUP with a deformed quantum algebra and a quadratic Hamiltonian into a standard, Heisenberg algebra of operators and an aquadratic Hamiltonian, provided the boost sector of the symmetries is modified accordingly. The theory can also be mapped to a completely standard Quantum Mechanics with standard symmetries, but with momentum dependent position operators. Next, we investigate the Hilbert space representations of these algebraically equivalent models, and focus specifically on whether they exhibit a minimal length. We carry the functional analysis of the various operators involved, and show that the appearance of a minimal length critically depends on the relationship between the generators of translations and the physical momenta. In particular, because this relationship is preserved by the algebraic mapping presented in this paper, when a minimal length is present in the standard GUP, it is also present in the corresponding Aquadratic Hamiltonian formulation, despite the perfectly standard algebra of this model. In general, a minimal length requires bounded generators of translations, i.e. a specific kind of quantization of space, and this depends on the precise shape of the function f defined previously. This result provides an elegant and unambiguous classification of which universal quantum gravity corrections lead to the emergence of a minimal length.
Random matrix techniques in quantum information theory
Collins, Benoît; Nechita, Ion
2016-01-15
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Theory of smeared quantum phase transitions.
Hoyos, José A; Vojta, Thomas
2008-06-20
We present an analytical strong-disorder renormalization group theory of the quantum phase transition in the dissipative random transverse-field Ising chain. For Ohmic dissipation, we solve the renormalization flow equations analytically, yielding asymptotically exact results for the low-temperature properties of the system. We find that the interplay between quantum fluctuations and Ohmic dissipation destroys the quantum critical point by smearing. We also determine the phase diagram and the behavior of observables in the vicinity of the smeared quantum phase transition.
Random matrix techniques in quantum information theory
NASA Astrophysics Data System (ADS)
Collins, Benoît; Nechita, Ion
2016-01-01
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Quantum Mechanics in the Light of Quantum Cosmology
NASA Astrophysics Data System (ADS)
Gell-Mann, Murray; Hartle, James B.
We sketch a quantum-mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the "quasiclassical domain" of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities (approximately obeying the rules of probability theory) can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative histories of the universe. A quasiclassical domain consists of a branching set of alternative decohering histories, described by a coarse graining that is, in an appropriate sense, maximally refined consistent with decoherence, with individual branches that exhibit a high level of classical correlation in time. We pose the problem of making these notions precise and quantitative. A quasiclassical domain is emergent in the universe as a consequence of the initial condition and the action function of the elementary particles. It is an important question whether all the quasiclassical domains are roughly equivalent or whether there are various essentially inequivalent ones. A measurement is a correlation with variables in a quasiclassical domain. An "observer" (or information gathering and utilizing system) is a complex adaptive system that has evolved to exploit the relative predictability of a quasiclassical domain, or rather a set of such domains among which it cannot discriminate because of its own very coarse graining. We suggest that resolution of many of the problems of interpretation presented by quantum mechanics is to be accomplished, not by further scrutiny of the subject as it applies to reproducible laboratory situations, but rather by an examination of alternative histories of the universe, stemming from its
Quantum Uncertainty and Decision-Making in Game Theory
NASA Astrophysics Data System (ADS)
Asano, M.; Ohya, M.; Tanaka, Y.; Khrennikov, A.; Basieva, I.
2011-01-01
Recently a few authors pointed to a possibility to apply the mathematical formalism of quantum mechanics to cognitive psychology, in particular, to games of the Prisoners Dilemma (PD) type.6_18 In this paper, we discuss the problem of rationality in game theory and point out that the quantum uncertainty is similar to the uncertainty of knowledge, which a player feels subjectively in his decision-making.
Toward a physical theory of quantum cognition.
Takahashi, Taiki
2014-01-01
Recently, mathematical models based on quantum formalism have been developed in cognitive science. The target articles in this special issue of Topics in Cognitive Science clearly illustrate how quantum theoretical formalism can account for various aspects of human judgment and decision making in a quantitatively and mathematically rigorous manner. In this commentary, we show how future studies in quantum cognition and decision making should be developed to establish theoretical foundations based on physical theory, by introducing Taketani's three-stage theory of the development of science. Also, implications for neuroeconomics (another rapidly evolving approach to human judgment and decision making) are discussed.
Quantum kinetic theory of the filamentation instability
Bret, A.; Haas, F.
2011-07-15
The quantum electromagnetic dielectric tensor for a multi-species plasma is re-derived from the gauge-invariant Wigner-Maxwell system and presented under a form very similar to the classical one. The resulting expression is then applied to a quantum kinetic theory of the electromagnetic filamentation instability. Comparison is made with the quantum fluid theory including a Bohm pressure term and with the cold classical plasma result. A number of analytical expressions are derived for the cutoff wave vector, the largest growth rate, and the most unstable wave vector.
Generalizing Prototype Theory: A Formal Quantum Framework
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436
Generalizing Prototype Theory: A Formal Quantum Framework.
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2011-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
NASA Astrophysics Data System (ADS)
Zhang, Xiangdong; Ma, Yongge
2011-09-01
As modified gravity theories, the four-dimensional metric f(R) theories are cast into connection-dynamical formalism with real su(2) connections as configuration variables. This formalism enables us to extend the nonperturbative loop quantization scheme of general relativity to any metric f(R) theories. The quantum kinematical framework of f(R) gravity is rigorously constructed, where the quantum dynamics can be launched. Both Hamiltonian constraint operator and master constraint operator for f(R) theories are well defined. Our results show that the nonperturbative quantization procedure of loop quantum gravity are valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.
NASA Astrophysics Data System (ADS)
Cui, Ping
The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO
Quantum-Mechanical Prediction of Nanoscale Photovoltaics.
Zhang, Yu; Meng, LingYi; Yam, ChiYung; Chen, GuanHua
2014-04-03
Previous simulations of photovoltaic devices are based on classical models, which neglect the atomistic details and quantum-mechanical effects besides the dependence on many empirical parameters. Here, within the nonequilibrium Green's function formalism, we present a quantum-mechanical study of the performance of inorganic nanowire-based photovoltaic devices. On the basis of density-functional tight-binding theory, the method allows simulation of current-voltage characteristics and optical properties of photovoltaic devices without relying on empirical parameters. Numerical studies of silicon nanowire-based devices of realistic sizes with 10 000 atoms are performed, and the results indicate that atomistic details and nonequilibrium conditions have a clear impact on the photoresponse of the devices.
Projection quantum mechanics and neutrino mixing
NASA Astrophysics Data System (ADS)
Góźdź, A.; Góźdź, M.
2017-03-01
The theory of neutrino oscillations rests on the assumption, that the interaction basis and the physical (mass) basis of neutrino states are different. Therefore neutrino is produced in a certain welldefined superposition of three mass eigenstates, which propagate separately and may be detected as a different superposition. This is called flavor oscillations. It is, however, not clear why neutrinos behave this way, i.e., what is the underlying mechanism which leads to the production of a superposition of physical states in a single reaction. In this paper we argue, that one of the reasons may be connected with the temporal structure of the process. In order to discuss the role of time in processes on the quantum level, we use a special formulation of the quantum mechanics, which is based on the projection time evolution. We arrive at the conclusion, that for short reaction times the formation of a superposition of states of similar masses is natural.
Quantum mechanics of black holes.
Witten, Edward
2012-08-03
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
Quantum communication between remote mechanical resonators
NASA Astrophysics Data System (ADS)
Felicetti, S.; Fedortchenko, S.; Rossi, R.; Ducci, S.; Favero, I.; Coudreau, T.; Milman, P.
2017-02-01
Mechanical resonators represent one of the most promising candidates to mediate the interaction between different quantum technologies, bridging the gap between efficient quantum computation and long-distance quantum communication. Here, we introduce an interferometric scheme where the interaction of a mechanical resonator with input-output quantum pulses is controlled by an independent classical drive. We design protocols for state teleportation and direct quantum state transfer, between distant mechanical resonators. The proposed device, feasible with state-of-the-art technology, can serve as a building block for the implementation of long-distance quantum networks of mechanical resonators.
Quantum Algorithms for Fermionic Quantum Field Theories
2014-04-28
preskill@theory.caltech.edu 1 Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for the collection of information is...NAME OF RESPONSIBLE PERSON a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98...operators of momentum modes. (The choice between these forms of measurement depends on the application.) 2.3 Complexity In this section we bound the
Statistical mechanics of quantum-classical systems with holonomic constraints.
Sergi, Alessandro
2006-01-14
The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained systems arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear-response function of constrained quantum-classical systems contains nontrivial additional terms which are absent in the response of unconstrained systems.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; Weedbrook, Christian
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.
Quantum simulation of quantum field theory using continuous variables
NASA Astrophysics Data System (ADS)
Marshall, Kevin; Pooser, Raphael; Siopsis, George; Weedbrook, Christian
2015-12-01
The year 1982 is often credited as the year that theoretical quantum computing was started with a keynote speech by Richard Feynman, who proposed a universal quantum simulator, the idea being that if you had such a machine you could in principle "imitate any quantum system, including the physical world." With that in mind, we present an algorithm for a continuous-variable quantum computing architecture which gives an exponential speedup over the best-known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on continuous-variable states that is feasible with today's technology.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; ...
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less
Geometrical Phases in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
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.
Paschoal, Diego; Santos, Hélio F Dos
2013-05-01
In this paper, we assessed the quantum mechanical level of theory for prediction of linear and nonlinear optical (NLO) properties of push-pull organic molecules. The electric dipole moment (μ), mean polarizability ([Symbol: see text]α[Symbol: see text]) and total static first hyperpolarizability (βt) were calculated for a set of benzene, styrene, biphenyl and stilbene derivatives using HF, MP2 and DFT (31 different functionals) levels and over 71 distinct basis sets. In addition, we propose two new basis sets, NLO-V and aNLO-V, for NLO properties calculations. As the main outcomes it is shown that long-range corrected DFT functionals such as M062X, ωB97, cam-B3LYP, LC-BLYP and LC-ωPBE work satisfactorily for NLO properties when appropriate basis sets such as those proposed here (NLO-V or aNLO-V) are used. For most molecules with β ranging from 0 to 190 esu, the average absolute deviation was 13.2 esu for NLO-V basis sets, compared to 27.2 esu for the standard 6-31 G(2d) basis set. Therefore, we conclude that the new basis sets proposed here (NLO-V and aNLO-V), together with the cam-B3LYP functional, make an affordable calculation scheme to predict NLO properties of large organic molecules.
de Oliveira-Filho, Antonio G S; Ornellas, Fernando R; Peterson, Kirk A; Mielke, Steven L
2013-12-05
The O((3)P) + HBr → OH + Br and O((3)P) + DBr → OD + Br reactions are studied on a recent high-quality ab initio-based potential energy surface. Thermal rate constants over the 200-1000 K temperature range, calculated using variational transition-state theory (VTST) with the small-curvature tunneling (SCT) correction and quantum mechanical methods with the J-shifting approximation (QM/JS) for zero total angular momentum (J = 0), are reported. These results are compared to the available experimental data, which lie in the ranges of 221-554 and 295-419 K for O + HBr and O + DBr, respectively. The rate constants, in cm(3) molecule(-1) s(-1) and at 298 K, for the O + HBr reaction are 3.66 × 10(-14) for VTST, 3.80 × 10(-14) for QM/JS, and 3.66 × 10(-14) for the average of eight experimental measurements.
Quantum mechanics with coordinate dependent noncommutativity
NASA Astrophysics Data System (ADS)
Kupriyanov, V. G.
2013-11-01
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
Quantum mechanics with coordinate dependent noncommutativity
Kupriyanov, V. G.
2013-11-15
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
Quantum theory of laser-stimulated desorption
NASA Technical Reports Server (NTRS)
Slutsky, M. S.; George, T. F.
1978-01-01
A quantum theory of laser-stimulated desorption (LSDE) is presented and critically analyzed. It is shown how LSDE depends on laser-pulse characteristics and surface-lattice dynamics. Predictions of the theory for a Debye model of the lattice dynamics are compared to recent experimental results.
Space-time resolved quantum field theory
NASA Astrophysics Data System (ADS)
Grobe, R.
2009-11-01
We have solved simplified model versions of the time-dependent Dirac and Yukawa equation numerically to study the time evolution of electrons, positrons and photons with full spatial resolution. The goal is to better understand how various particle creation and annihilation processes that require quantum field theory can be visualized. There are many open ended questions that we will address. Are particles and their antimatter companions created instantly, or do they require a certain minimum amount of time? Are they created at precisely the same location? What is the difference between a bare and a physical particle? Forces between two particles are usually understood on a microscopic level as the result of an exchange of bosonic particles. How can the same microscopic exchange mechanism lead to a repulsion as well as an attraction? Do these force intermediating particles ``know'' about the charges of the two interacting particles? How can one visualize this exchange? Does it really make sense to distinguish between virtual and real particles? We also examine how a bare electron can trigger the creation of a cloud of virtual photons around it.[4pt] In collaboration with R. Wagner, Intense Laser Physics Theory Unit, Illinois State University; C. Gerry, Lehman College and ILP-ISU; T. Cheng and Q. Su, Intense Laser Physics Theory Unit, Illinois State University.
Solving the simplest theory of quantum gravity
NASA Astrophysics Data System (ADS)
Dubovsky, Sergei; Flauger, Raphael; Gorbenko, Victor
2012-09-01
We solve what is quite likely the simplest model of quantum gravity, the worldsheet theory of an infinitely long, free bosonic string in Minkowski space. Contrary to naive expectations, this theory is non-trivial. We illustrate this by constructing its exact factorizable S-matrix. Despite its simplicity, the theory exhibits many of the salient features expected from more mature quantum gravity models, including the absence of local off-shell observables, a minimal length, as well as (integrable relatives of) black holes. All these properties follow from the exact S-matrix. We show that the complete finite volume spectrum can be reconstructed analytically from this S-matrix with the help of the thermodynamic Bethe Ansatz. We argue that considered as a UV complete relativistic 2-dimensional quantum field theory the model exhibits a new type of renormalization group flow behavior, "asymptotic fragility". Asymptotically fragile flows do not originate from a UV fixed point.
Faster than Hermitian Quantum Mechanics
Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.; Meister, Bernhard K.
2007-01-26
Given an initial quantum state vertical bar {psi}{sub I}> and a final quantum state vertical bar {psi}{sub F}>, there exist Hamiltonians H under which vertical bar {psi}{sub I}> evolves into vertical bar {psi}{sub F}>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time {tau}? For Hermitian Hamiltonians {tau} has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, {tau} can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from vertical bar {psi}{sub I}> to vertical bar {psi}{sub F}> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.
Facets of contextual realism in quantum mechanics
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.
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.
Scaling theory for anomalous semiclassical quantum transport
NASA Astrophysics Data System (ADS)
Sena-Junior, M. I.; Macêdo, A. M. S.
2016-01-01
Quantum transport through devices coupled to electron reservoirs can be described in terms of the full counting statistics (FCS) of charge transfer. Transport observables, such as conductance and shot-noise power are just cumulants of FCS and can be obtained from the sample's average density of transmission eigenvalues, which in turn can be obtained from a finite element representation of the saddle-point equation of the Keldysh (or supersymmetric) nonlinear sigma model, known as quantum circuit theory. Normal universal metallic behavior in the semiclassical regime is controlled by the presence of a Fabry-Pérot singularity in the average density of transmission eigenvalues. We present general conditions for the suppression of Fabry-Pérot modes in the semiclassical regime in a sample of arbitrary shape, a disordered conductor or a network of ballistic quantum dots, which leads to an anomalous metallic phase. Through a double-scaling limit, we derive a scaling equation for anomalous metallic transport, in the form of a nonlinear differential equation, which generalizes the ballistic-diffusive scaling equation of a normal metal. The two-parameter stationary solution of our scaling equation generalizes Dorokhov's universal single-parameter distribution of transmission eigenvalues. We provide a simple interpretation of the stationary solution using a thermodynamic analogy with a spin-glass system. As an application, we consider a system formed by a diffusive wire coupled via a barrier to normal-superconductor reservoirs. We observe anomalous reflectionless tunneling, when all perfectly transmitting channels are suppressed, which cannot be explained by the usual mechanism of disorder-induced opening of tunneling channels.
NASA Astrophysics Data System (ADS)
Liu, Jian; Miller, William H.
2011-03-01
We have reformulated and generalized our recent work [J. Liu and W. H. Miller, J. Chem. Phys. 126, 234110 (2007)] into an approach for generating a family of trajectory-based dynamics methods in the phase space formulation of quantum mechanics. The approach (equilibrium Liouville dynamics) is in the spirit of Liouville's theorem in classical mechanics. The trajectory-based dynamics is able to conserve the quantum canonical distribution for the thermal equilibrium system and approaches classical dynamics in the classical (ℏ → 0), high temperature (β → 0), and harmonic limits. Equilibrium Liouville dynamics provides the framework for the development of novel theoretical/computational tools for studying quantum dynamical effects in large/complex molecular systems.
Liu, Jian; Miller, William H
2011-03-14
We have reformulated and generalized our recent work [J. Liu and W. H. Miller, J. Chem. Phys. 126, 234110 (2007)] into an approach for generating a family of trajectory-based dynamics methods in the phase space formulation of quantum mechanics. The approach (equilibrium Liouville dynamics) is in the spirit of Liouville's theorem in classical mechanics. The trajectory-based dynamics is able to conserve the quantum canonical distribution for the thermal equilibrium system and approaches classical dynamics in the classical (ℏ → 0), high temperature (β → 0), and harmonic limits. Equilibrium Liouville dynamics provides the framework for the development of novel theoretical∕computational tools for studying quantum dynamical effects in large∕complex molecular systems.
Quantum processes: A Whiteheadian interpretation of quantum field theory
NASA Astrophysics Data System (ADS)
Bain, Jonathan
Quantum processes: A Whiteheadian interpretation of quantum field theory is an ambitious and thought-provoking exercise in physics and metaphysics, combining an erudite study of the very complex metaphysics of A.N. Whitehead with a well-informed discussion of contemporary issues in the philosophy of algebraic quantum field theory. Hättich's overall goal is to construct an interpretation of quantum field theory. He does this by translating key concepts in Whitehead's metaphysics into the language of algebraic quantum field theory. In brief, this Hättich-Whitehead (H-W, hereafter) interpretation takes "actual occasions" as the fundamental ontological entities of quantum field theory. An actual occasion is the result of two types of processes: a "transition process" in which a set of initial possibly-possessed properties for the occasion (in the form of "eternal objects") is localized to a space-time region; and a "concrescence process" in which a subset of these initial possibly-possessed properties is selected and actualized to produce the occasion. Essential to these processes is the "underlying activity", which conditions the way in which properties are initially selected and subsequently actualized. In short, under the H-W interpretation of quantum field theory, an initial set of possibly-possessed eternal objects is represented by a Boolean sublattice of the lattice of projection operators determined by a von Neumann algebra R (O) associated with a region O of Minkowski space-time, and the underlying activity is represented by a state on R (O) obtained by conditionalizing off of the vacuum state. The details associated with the H-W interpretation involve imposing constraints on these representations motivated by principles found in Whitehead's metaphysics. These details are spelled out in the three sections of the book. The first section is a summary and critique of Whitehead's metaphysics, the second section introduces the formalism of algebraic quantum field
Quantum Field Theory and the Standard Model
NASA Astrophysics Data System (ADS)
Schwartz, Matthew D.
2014-03-01
Part I. Field Theory: 1. Microscopic theory of radiation; 2. Lorentz invariance and second quantization; 3. Classical Field Theory; 4. Old-fashioned perturbation theory; 5. Cross sections and decay rates; 6. The S-matrix and time-ordered products; 7. Feynman rules; Part II. Quantum Electrodynamics: 8. Spin 1 and gauge invariance; 9. Scalar QED; 10. Spinors; 11. Spinor solutions and CPT; 12. Spin and statistics; 13. Quantum electrodynamics; 14. Path integrals; Part III. Renormalization: 15. The Casimir effect; 16. Vacuum polarization; 17. The anomalous magnetic moment; 18. Mass renormalization; 19. Renormalized perturbation theory; 20. Infrared divergences; 21. Renormalizability; 22. Non-renormalizable theories; 23. The renormalization group; 24. Implications of Unitarity; Part IV. The Standard Model: 25. Yang-Mills theory; 26. Quantum Yang-Mills theory; 27. Gluon scattering and the spinor-helicity formalism; 28. Spontaneous symmetry breaking; 29. Weak interactions; 30. Anomalies; 31. Precision tests of the standard model; 32. QCD and the parton model; Part V. Advanced Topics: 33. Effective actions and Schwinger proper time; 34. Background fields; 35. Heavy-quark physics; 36. Jets and effective field theory; Appendices; References; Index.
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)
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)
Changing Views of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Weinberg, Steven
2010-03-01
The first part of this talk reviews changes in our views regarding quantum field theory since its beginnings, leading eventually to the modern view that our most successful field theories may in fact be effective field theories, valid only as low energy approximations to an underlying theory that may not be a field theory at all. In the second part, I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory, and finally cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe. The second part is substantially the same as a talk given a month earlier at the 6th International Workshop on Chiral Dynamics, at the University of Bern, which is reproduced here.
Deformation of noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
Jiang, Jian-Jian; Chowdhury, S. Hasibul Hassan
2016-09-01
In this paper, the Lie group GNC α , β , γ , of which the kinematical symmetry group GNC of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero α, β, and γ, is three-parameter deformation quantized using the method suggested by Ballesteros and Musso [J. Phys. A: Math. Theor. 46, 195203 (2013)]. A certain family of QUE algebras, corresponding to GNC α , β , γ with two of the deformation parameters approaching zero, is found to be in agreement with the existing results of the literature on quantum Heisenberg group. Finally, we dualize the underlying QUE algebra to obtain an expression for the underlying star-product between smooth functions on GNC α , β , γ .
Matrix quantum mechanics from qubits
NASA Astrophysics Data System (ADS)
Hartnoll, Sean A.; Huijse, Liza; Mazenc, Edward A.
2017-01-01
We introduce a transverse field Ising model with order N 2 spins interacting via a nonlocal quartic interaction. The model has an O( N, ℤ), hyperoctahedral, symmetry. We show that the large N partition function admits a saddle point in which the symmetry is enhanced to O( N). We further demonstrate that this `matrix saddle' correctly computes large N observables at weak and strong coupling. The matrix saddle undergoes a continuous quantum phase transition at intermediate couplings. At the transition the matrix eigenvalue distribution becomes disconnected. The critical excitations are described by large N matrix quantum mechanics. At the critical point, the low energy excitations are waves propagating in an emergent 1 + 1 dimensional spacetime.
Quantum-mechanical twin paradox
NASA Astrophysics Data System (ADS)
Franson, J. D.
2016-10-01
In the twin paradox of special relativity, an observer that travels along an accelerated trajectory at a high velocity will experience a smaller amount of elapsed time than an observer that remains at rest. This illustrates the fact that time is relative unlike the situation in classical physics where time is absolute. In a recent paper, Bushev et al (2016 New J. Phys. 18 093050) showed that the twin paradox can also be demonstrated using a single electron that functions as a quantum-mechanical clock. The wave function of the electron can travel along two different paths simultaneously, which allows a measurement of the difference in proper times along the two trajectories using a single particle. Quantum interference effects show that time cannot be thought of as a classical parameter even when associated with a single clock or observer.
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.
Hunting for Snarks in Quantum Mechanics
Hestenes, David
2009-12-08
A long-standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger's wave function {psi} for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school(led by Bohr, Heisenberg and Pauli) holds that {psi} provides a complete description of a single electron state; hence the probability interpretation of {psi}{psi}* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school(led by Einstein, de Broglie, Bohm and Jaynes) holds that {psi} represents a statistical ensemble of possible electron states; hence it is an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung(first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in {psi}. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark{exclamation_point}.
Numerical approach of the quantum circuit theory
NASA Astrophysics Data System (ADS)
Silva, J. J. B.; Duarte-Filho, G. C.; Almeida, F. A. G.
2017-03-01
In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.
Consistent interpretations of quantum mechanics
Omnes, R. )
1992-04-01
Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counterexamples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.
BiHermitian supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Zucchini, Roberto
2007-04-01
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kähler manifolds recently developed by Gualtieri in [33]. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li in [9].
NASA Astrophysics Data System (ADS)
Doyen, G.; Drakova, D.
2015-08-01
We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle-wave characteristics of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources (massive particles). The final world model treated here contains only gravonons and a scalar matter field. The gravonons are localized in the environment of the massive particles which generate them. The solution of the Schrödinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: (i) There is a chooser mechanism for the selection of the localization site. (ii) The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which at present cannot be controlled experimentally and therefore let the choice appear statistical. (iii) The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. (iv) The times at which telegraph like jumps occur depend on subtleties of the gravonon structure which at present cannot be controlled experimentally and therefore let the telegraph-like jumps appear statistical. (v) The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of CQM is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave
Information and Entropy in Quantum Theory
NASA Astrophysics Data System (ADS)
Maroney, O. J. E.
2004-11-01
We look at certain thought experiments based upon the 'delayed choice' and 'quantum eraser' interference experiments, which present a complementarity between information gathered from a quantum measurement and interference effects. It has been argued that these experiments show the Bohm interpretation of quantum theory is untenable. We demonstrate that these experiments depend critically upon the assumption that a quantum optics device can operate as a measuring device, and show that, in the context of these experiments, it cannot be consistently understood in this way. By contrast, we then show how the notion of 'active information' in the Bohm interpretation provides a coherent explanation of the phenomena shown in these experiments. We then examine the relationship between information and entropy. The thought experiment connecting these two quantities is the Szilard Engine version of Maxwell's Demon, and it has been suggested that quantum measurement plays a key role in this. We provide the first complete description of the operation of the Szilard Engine as a quantum system. This enables us to demonstrate that the role of quantum measurement suggested is incorrect, and further, that the use of information theory to resolve Szilard's paradox is both unnecessary and insufficient. Finally we show that, if the concept of 'active information' is extended to cover thermal density matrices, then many of the conceptual problems raised by this paradox appear to be resolved.
Physical properties of quantum field theory measures
NASA Astrophysics Data System (ADS)
Mourão, J. M.; Thiemann, T.; Velhinho, J. M.
1999-05-01
Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the Ashtekar-Lewandowski (AL) measure on spaces of connections. In particular we prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the Ashtekar-Isham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve.
Reasonable fermionic quantum information theories require relativity
NASA Astrophysics Data System (ADS)
Friis, Nicolai
2016-03-01
We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be encoded in the fermionic Fock space, the unrestricted theory has a peculiar feature: the marginals of bipartite pure states need not have identical entropies, which leads to an ambiguous definition of entanglement. We solve this problem, by proving that it is removed by relativity, i.e., by the parity superselection rule that arises from Lorentz invariance via the spin-statistics connection. Our results hence unveil a fundamental conceptual inseparability of quantum information and the causal structure of relativistic field theory.
Statistical Mechanics of Quantum Integrable Systems
NASA Astrophysics Data System (ADS)
Wadati, Miki; Kato, Go; Iida, Toshiaki
Recent developments in statistical mechanics of quantum integrable systems are reviewed. Those studies are fundamental and have a renewed interest related to newly developing fields such as atomic Bose-Einstein condensations, photonic crystals and quantum computations. After a brief summary of the basic concepts and methods, the following three topics are discussed. First, by the thermal Bethe ansatz (TBA), a hard-core Bose gas is exactly solved. The model includes fully the effect of excluded volume and is identified to be a c=1 conformal field theory. Second, the cluster expansion method based on the periodic boundary condition for the Bethe wave function, which we call the Bethe ansatz cluster expansion (BACE) method, is developed for a δ-function gas and the XXX Heisenberg chain. This directly proves the TBA and reveals intrinsic properties of quantum integrable systems. Third, for a δ-function gas, the integral equations for the distribution functions of the quasi-momentum and the quasi-particle energy are solved in the form of power series. In the weak coupling case, the results reproduce those of Bogoliubov theory.
Quantum Mechanics - Fundamentals and Applications to Technology
NASA Astrophysics Data System (ADS)
Singh, Jasprit
1996-10-01
Explore the relationship between quantum mechanics and information-age applications This volume takes an altogether unique approach to quantum mechanics. Providing an in-depth exposition of quantum mechanics fundamentals, it shows how these concepts are applied to most of today's information technologies, whether they are electronic devices or materials. No other text makes this critical, essential leap from theory to real-world applications. The book's lively discussion of the mathematics involved fits right in with contemporary multidisciplinary trends in education: Once the basic formulation has been derived in a given chapter, the connection to important technological problems is summarily described. The many helpful features include * Twenty-eight application-oriented sections that focus on lasers, transistors, magnetic memories, superconductors, nuclear magnetic resonance (NMR), and other important technology-driving materials and devices * One hundred solved examples, with an emphasis on numerical results and the connection between the physics and its applications * End-of-chapter problems that ground the student in both fundamental and applied concepts * Numerous figures and tables to clarify the various topics and provide a global view of the problems under discussion * Over two hundred illustrations to highlight problems and text A book for the information age, Quantum Mechanics: Fundamentals and Applications to Technology promises to become a standard in departments of electrical engineering, applied physics, and materials science, as well as physics. It is an excellent text for senior undergraduate and graduate students, and a helpful reference for practicing scientists, engineers, and chemists in the semiconductor and electronic industries.
Quantum theory of light propagation - Linear medium
NASA Astrophysics Data System (ADS)
Abram, I.
1987-06-01
A quantum-mechanical formalism has been developed which permits the treatment of light propagation within the conceptual framework of quantum optics. The formalism rests on the calculation of the momentum operator for the radiation field, and yields directly a description for the spatial progression of the electromagnetic waves. In this paper, a quantum-mechanical treatment for refraction and reflection is given by applying the formalism to propagation through a linear dielectric. The fidelity with which this formalism reproduces all results known from classical optics demonstrates its validity.
Mechanism for quantum speedup in open quantum systems
NASA Astrophysics Data System (ADS)
Liu, Hai-Bin; Yang, W. L.; An, Jun-Hong; Xu, Zhen-Yu
2016-02-01
The quantum speed limit (QSL) time for open system characterizes the most efficient response of the system to the environmental influences. Previous results showed that the non-Markovianity governs the quantum speedup. Via studying the dynamics of a dissipative two-level system, we reveal that the non-Markovian effect is only the dynamical way of the quantum speedup, while the formation of the system-environment bound states is the essential reason for the quantum speedup. Our attribution of the quantum speedup to the energy-spectrum character can supply another vital path for experiments when the quantum speedup shows up without any dynamical calculations. The potential experimental observation of our quantum speedup mechanism in the circuit QED system is discussed. Our results may be of both theoretical and experimental interest in exploring the ultimate QSL in realistic environments, and may open new perspectives for devising active quantum speedup devices.
Nonequilibrium quantum mechanics: A "hot quantum soup" of paramagnons
NASA Astrophysics Data System (ADS)
Scammell, H. D.; Sushkov, O. P.
2017-01-01
Motivated by recent measurements of the lifetime (decay width) of paramagnons in quantum antiferromagnet TlCuCl3, we investigate paramagnon decay in a heat bath and formulate an appropriate quantum theory. Our formulation can be split into two regimes: (i) a nonperturbative, "hot quantum soup" regime where the paramagnon width is comparable to its energy; (ii) a usual perturbative regime where the paramagnon width is significantly lower than its energy. Close to the Neel temperature, the paramagnon width becomes comparable to its energy and falls into the hot quantum soup regime. To describe this regime, we develop a new finite frequency, finite temperature technique for a nonlinear quantum field theory; the "golden rule of quantum kinetics." The formulation is generic and applicable to any three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point. Specifically, we apply our results to TlCuCl3 and find agreement with experimental data. Additionally, we show that logarithmic running of the coupling constant in the upper critical dimension changes the commonly accepted picture of the quantum disordered and quantum critical regimes.
Quantum Walks: Theory, Application, and Implementation
NASA Astrophysics Data System (ADS)
Schmitz, Albert Thomas
The quantum walk is a method for conceptualizing and designing quantum computing algorithms and it comes in two forms: the continuous-time and discrete-time quantum walk. The thesis is organized into three parts, each of which looks to develop the concept and uses of the quantum walk. The first part is the theory of the quantum walk. This includes definitions and considerations for the various incarnations of the discrete-time quantum walk and a discussion on the general method for connecting the continuous-time and discrete-time versions. As a result, it is shown that most versions of the discrete-time quantum walk can be put into a general form and this can be used to simulate any continuous-time quantum walk. The second part uses these results for a hypothetical application. The application presented is a search algorithm that appears to scale in the time for completion independent of the size of the search space. This behavior is then elaborated upon and shown to have general qualitative agreement with simulations to within the approximations that are made. The third part introduces a method of implementation. Given a universal quantum computer, the method is discussed and shown to simulate an arbitrary discrete-time quantum walk. Some of the benefits of this method are that half the unitary evolution can be achieved without the use of any gates and there may be some possibility for error detection. The three parts combined suggest a possible experiment, given a quantum computing scheme of sufficient robustness.
Information theory, spectral geometry, and quantum gravity.
Kempf, Achim; Martin, Robert
2008-01-18
We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well-known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.
Quantum Field Theory and Decoherence in the Early Universe
NASA Astrophysics Data System (ADS)
Koksma, J. F.
2011-06-01
Quantum field theory is indispensable for understanding many aspects of cosmology, both in the early Universe and today. For example, quantum processes could be paramount to understand the nature of the mysterious dark energy resulting in the Universe’s recently observed accelerated expansion. Inspired by these considerations, this PhD thesis is concerned with two aspects of quantum field theory relevant to cosmology: quantum backreaction and decoherence. Quantum backreaction is a line of research where the impact of quantum fluctuations on the background spacetime geometry in perturbative quantum gravity is investigated. The cosmological constant problem and the process of quantum backreaction are intimately related: quantum backreaction might provide us with a dynamical mechanism to effectively make the cosmological constant almost vanish. We investigate the quantum backreaction of the trace anomaly and of fermions. We find that the trace anomaly does not dynamically influence the effective value of the cosmological constant. We furthermore evaluate the fermion propagator in FLRW spacetimes with constant deceleration. Although the dynamics resulting from the one-loop stress-energy tensor need yet to be investigated, we find that we certainly cannot exclude a significant effect due to the quantum backreaction on the Universe’s expansion. Decoherence is a quantum theory which addresses the quantum-to-classical transition of a particular system. The idea of the decoherence formalism is that a macroscopic system cannot be separated from its environment. The framework of decoherence is widely used, e.g. in quantum computing, black hole physics, inflationary perturbation theory, and in elementary particle physics, such as electroweak baryogenesis models. We formulate a novel “correlator approach” to decoherence: neglecting observationally inaccessible correlators gives rise to an increase in entropy of the system, as perceived by an observer. This is inspired
Models on the boundary between classical and quantum mechanics.
Hooft, Gerard 't
2015-08-06
Arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there cannot be physical laws that require 'conspiracy'. It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In this report, several such counterexamples are shown. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. So now the question is asked: how can such a model feature 'conspiracy', and how bad is that? Is there conspiracy in the vacuum fluctuations? Arguments concerning Bell's theorem are further sharpened.
Mathematical foundations of quantum mechanics: An advanced short course
NASA Astrophysics Data System (ADS)
Moretti, Valter
2016-08-01
This paper collects and extends the lectures I gave at the “XXIV International Fall Workshop on Geometry and Physics” held in Zaragoza (Spain) during September 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (C∗-) algebraic formulation of quantum theories.
Quantum localization of classical mechanics
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.
2016-07-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Photon physics: from wave mechanics to quantum electrodynamics
NASA Astrophysics Data System (ADS)
Keller, Ole
2009-05-01
When rewritten in an appropriate manner, the microscopic Maxwell-Lorentz equations appear as a wave-mechanical theory for photons, and their quantum physical interaction with matter. A natural extension leads from photon wave mechanics to quantum electrodynamics (QED). In its modern formulation photon wave mechanics has given us valuable new insight in subjects such as spatial photon localization, near-field photon dynamics, transverse photon mass, photon eikonal theory, photon tunneling, and rim-zone electrodynamics. The present review is based on my plenary lecture at the SPIE-Europe 2009 Optics and Optoelectronics International Symposium in Prague.
Integrable structures in quantum field theory
NASA Astrophysics Data System (ADS)
Negro, Stefano
2016-08-01
This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q-operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only.
Boolean approach to dichotomic quantum measurement theories
NASA Astrophysics Data System (ADS)
Nagata, K.; Nakamura, T.; Batle, J.; Abdalla, S.; Farouk, A.
2017-02-01
Recently, a new measurement theory based on truth values was proposed by Nagata and Nakamura [Int. J. Theor. Phys. 55, 3616 (2016)], that is, a theory where the results of measurements are either 0 or 1. The standard measurement theory accepts a hidden variable model for a single Pauli observable. Hence, we can introduce a classical probability space for the measurement theory in this particular case. Additionally, we discuss in the present contribution the fact that projective measurement theories (the results of which are either +1 or -1) imply the Bell, Kochen, and Specker (BKS) paradox for a single Pauli observable. To justify our assertion, we present the BKS theorem in almost all the two-dimensional states by using a projective measurement theory. As an example, we present the BKS theorem in two-dimensions with white noise. Our discussion provides new insight into the quantum measurement problem by using this measurement theory based on the truth values.
Categorical quantum mechanics II: Classical-quantum interaction
NASA Astrophysics Data System (ADS)
Coecke, Bob; Kissinger, Aleks
2016-08-01
This is the second part of a three-part overview, in which we derive the category-theoretic backbone of quantum theory from a process ontology, treating quantum theory as a theory of systems, processes and their interactions. In this part, we focus on classical-quantum interaction. Classical and quantum systems are treated as distinct types, of which the respective behavioral properties are specified in terms of processes and their compositions. In particular, classicality is witnessed by ‘spiders’ which fuse together whenever they connect. We define mixedness and show that pure processes are extremal in the space of all processes, and we define entanglement and show that quantum theory indeed exhibits entanglement. We discuss the classification of tripartite qubit entanglement and show that both the GHZ-state and the W-state come from spider-like families of processes, which differ only in how they behave when they are connected by two or more wires. We define measurements and provide fully comprehensive descriptions of several quantum protocols involving classical data flow. Finally, we give a notion of ‘genuine quantumness’, from which special processes called ‘phase spiders’ arise, and get a first glimpse of quantum nonlocality.
Quantum field theory of treasury bonds
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
2001-07-01
The Heath-Jarrow-Morton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a two-dimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract.
Quantum field theory of treasury bonds.
Baaquie, B E
2001-07-01
The Heath-Jarrow-Morton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a two-dimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract.
Bridging classical and quantum mechanics
NASA Astrophysics Data System (ADS)
Haddad, D.; Seifert, F.; Chao, L. S.; Li, S.; Newell, D. B.; Pratt, J. R.; Williams, C.; Schlamminger, S.
2016-10-01
Using a watt balance and a frequency comb, a mass-energy equivalence is derived. The watt balance compares mechanical power measured in terms of the meter, the second, and the kilogram to electrical power measured in terms of the volt and the ohm. A direct link between mechanical action and the Planck constant is established by the practical realization of the electrical units derived from the Josephson and the quantum Hall effects. By using frequency combs to measure velocities and acceleration of gravity, the unit of mass can be realized from a set of three defining constants: the Planck constant h, the speed of light c, and the hyperfine splitting frequency of 133Cs.
Statistical origin of classical mechanics and quantum mechanics
NASA Astrophysics Data System (ADS)
Chu, Shu-Yuan
1993-11-01
The classical action for interacting strings, obtained by generalizing the time-symmetric electrodynamics of Wheeler and Feynman, is exactly additive. The additivity of the string action suggests a connection between the area of the string world sheets and entropy. We find that the action principle of classical mechanics is the condition that the total entropy of the strings be at an extremum, and the path-integral representation of the quantum density matrix element is an approximation to the partition function of the string theory.
Quantum mechanical light harvesting mechanisms in photosynthesis
NASA Astrophysics Data System (ADS)
Scholes, Gregory
2012-02-01
More than 10 million billion photons of light strike a leaf each second. Incredibly, almost every red-coloured photon is captured by chlorophyll pigments and initiates steps to plant growth. Last year we reported that marine algae use quantum mechanics in order to optimize photosynthesis [1], a process essential to its survival. These and other insights from the natural world promise to revolutionize our ability to harness the power of the sun. In a recent review [2] we described the principles learned from studies of various natural antenna complexes and suggested how to utilize that knowledge to shape future technologies. We forecast the need to develop ways to direct and regulate excitation energy flow using molecular organizations that facilitate feedback and control--not easy given that the energy is only stored for a billionth of a second. In this presentation I will describe new results that explain the observation and meaning of quantum-coherent energy transfer. [4pt] [1] Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer, and Gregory D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature 463, 644-648 (2010).[0pt] [2] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro and Rienk van Grondelle, ``Lessons from nature about solar light harvesting'' Nature Chem. 3, 763-774 (2011).
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-06
In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory.
Quantum Bayesianism as the basis of general theory of decision-making.
Khrennikov, Andrei
2016-05-28
We discuss the subjective probability interpretation of the quantum-like approach to decision making and more generally to cognition. Our aim is to adopt the subjective probability interpretation of quantum mechanics, quantum Bayesianism (QBism), to serve quantum-like modelling and applications of quantum probability outside of physics. We analyse the classical and quantum probabilistic schemes of probability update, learning and decision-making and emphasize the role of Jeffrey conditioning and its quantum generalizations. Classically, this type of conditioning and corresponding probability update is based on the formula of total probability-one the basic laws of classical probability theory. © 2016 The Author(s).
Quantum Bayesianism as the basis of general theory of decision-making
2016-01-01
We discuss the subjective probability interpretation of the quantum-like approach to decision making and more generally to cognition. Our aim is to adopt the subjective probability interpretation of quantum mechanics, quantum Bayesianism (QBism), to serve quantum-like modelling and applications of quantum probability outside of physics. We analyse the classical and quantum probabilistic schemes of probability update, learning and decision-making and emphasize the role of Jeffrey conditioning and its quantum generalizations. Classically, this type of conditioning and corresponding probability update is based on the formula of total probability—one the basic laws of classical probability theory. PMID:27091160
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.
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.
Operational quantum theory without predefined time
NASA Astrophysics Data System (ADS)
Oreshkov, Ognyan; Cerf, Nicolas J.
2016-07-01
The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally probabilistic in character. Here, we propose a generalized formulation of quantum theory without predefined time or causal structure, building upon a recently introduced operationally time-symmetric approach to quantum theory. The key idea is a novel isomorphism between transformations and states which depends on the symmetry transformation of time reversal. This allows us to express the time-symmetric formulation in a time-neutral form with a clear physical interpretation, and ultimately drop the assumption of time. In the resultant generalized formulation, operations are associated with regions that can be connected in networks with no directionality assumed for the connections, generalizing the standard circuit framework and the process matrix framework for operations without global causal order. The possible events in a given region are described by positive semidefinite operators on a Hilbert space at the boundary, while the connections between regions are described by entangled states that encode a nontrivial symmetry and could be tested in principle. We discuss how the causal structure of space-time could be understood as emergent from properties of the operators on the boundaries of compact space-time regions. The framework is compatible with indefinite causal order, timelike loops, and other acausal structures.
Multiparameter deformation theory for quantum confined systems
Aleixo, A. N. F.; Balantekin, A. B.
2009-11-15
We introduce a generalized multiparameter deformation theory applicable to all supersymmetric and shape-invariant systems. Taking particular choices for the deformation factors used in the construction of the deformed ladder operators, we show that we can generalize the one-parameter quantum-deformed harmonic oscillator models and build alternative multiparameter deformed models that are also shape invariant like the primary undeformed system.
Unification of quantum theory and classical physics
Stapp, H.P.
1985-07-01
A program is described for unifying quantum theory and classical physics on the basis of the Copenhagen-interpretation idea of external reality and a recently discovered classical part of the electromagnetic field. The program effects an integration of the intuitions of Heisenberg, Bohr, and Einstein.
Diffeomorphism groups, gauge groups, and quantum theory
Goldin, G.A.; Menikoff, R.; Sharp, D.H.
1983-12-19
Unitary representations of the infinite parameter group Diff(R/sup 3/) are presented which describe particles with spin as well as tightly bound composite particles. These results support the idea that Diff(R/sup 3/) can serve as a ''universal group'' for quantum theory.
Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries.
Sun, Qiming; Chan, Garnet Kin-Lic
2014-09-09
Motivated by recent work in density matrix embedding theory, we define exact link orbitals that capture all quantum mechanical (QM) effects across arbitrary quantum mechanics/molecular mechanics (QM/MM) boundaries. Exact link orbitals are rigorously defined from the full QM solution, and their number is equal to the number of orbitals in the primary QM region. Truncating the exact set yields a smaller set of link orbitals optimal with respect to reproducing the primary region density matrix. We use the optimal link orbitals to obtain insight into the limits of QM/MM boundary treatments. We further analyze the popular general hybrid orbital (GHO) QM/MM boundary across a test suite of molecules. We find that GHOs are often good proxies for the most important optimal link orbital, although there is little detailed correlation between the detailed GHO composition and optimal link orbital valence weights. The optimal theory shows that anions and cations cannot be described by a single link orbital. However, expanding to include the second most important optimal link orbital in the boundary recovers an accurate description. The second optimal link orbital takes the chemically intuitive form of a donor or acceptor orbital for charge redistribution, suggesting that optimal link orbitals can be used as interpretative tools for electron transfer. We further find that two optimal link orbitals are also sufficient for boundaries that cut across double bonds. Finally, we suggest how to construct "approximately" optimal link orbitals for practical QM/MM calculations.
Aspects of nonlocality in quantum field theory, quantum gravity and cosmology
NASA Astrophysics Data System (ADS)
Barvinsky, A. O.
2015-02-01
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures. Euclidean version of the Schwinger-Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter (dS) cosmological evolution at an arbitrary value of Λ — a model of dark energy with the dynamical scale selected by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of a scalar mediated gravity and the short distance general relativistic limit in a special metric frame related by a nonlocal conformal transformation to the original metric.
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
Riemann hypothesis and quantum mechanics
NASA Astrophysics Data System (ADS)
Planat, Michel; Solé, Patrick; Omar, Sami
2011-04-01
In their 1995 paper, Jean-Benoît Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β), where β is an inverse temperature. We formulate Riemann hypothesis (RH) as a property of the low-temperature Kubo-Martin-Schwinger (KMS) states of this theory. More precisely, the expectation value of the BC phase operator can be written as \\phi _{\\beta }(q)=N_{q-1}^{\\beta -1} \\psi _{\\beta -1}(N_q), where Nq = ∏qk = 1pk is the primorial number of order q and ψb is a generalized Dedekind ψ function depending on one real parameter b as \\psi _b (q)=q \\prod _{p \\in {P,}p \\vert q}\\frac{1-1/p^b}{1-1/p}. Fix a large inverse temperature β > 2. The RH is then shown to be equivalent to the inequality N_q |\\phi _\\beta (N_q)|\\zeta (\\beta -1) \\gt e^\\gamma log log N_q, for q large enough. Under RH, extra formulas for high-temperature KMS states (1.5 < β < 2) are derived. 'Number theory is not pure Mathematics. It is the Physics of the world of Numbers.' Alf van der Poorten
NASA Astrophysics Data System (ADS)
Oss, Stefano; Rosi, Tommaso
2015-04-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.
Towards a Constructive Foundation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Smilga, Walter
2016-11-01
I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space-time has a discrete spectrum, relative to classical observers in space-time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.
Towards a Constructive Foundation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Smilga, Walter
2017-01-01
I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space-time has a discrete spectrum, relative to classical observers in space-time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.
Domain Walls, Black Holes and Supersymmetric Quantum Mechanics.
Shmakova, Marina
2001-07-25
Supersymmetric solutions, such as BPS domain walls or black holes, in four- and five-dimensional supergravity theories with eight supercharges can be described by effective quantum mechanics with a potential term. We show how properties of the latter theory can help us to learn about the physics of supersymmetric vacua and BPS solutions in these supergravity theories. The general approach is illustrated in a number of specific examples where scalar fields of matter multiplets take values in symmetric coset spaces.
NASA Astrophysics Data System (ADS)
Blanchard, Philippe; Hellmich, Mario; Ługiewicz, Piotr; Olkiewicz, Robert
Quantum mechanics is the greatest revision of our conception of the character of the physical world since Newton. Consequently, David Hilbert was very interested in quantum mechanics. He and John von Neumann discussed it frequently during von Neumann's residence in Göttingen. He published in 1932 his book Mathematical Foundations of Quantum Mechanics. In Hilbert's opinion it was the first exposition of quantum mechanics in a mathematically rigorous way. The pioneers of quantum mechanics, Heisenberg and Dirac, neither had use for rigorous mathematics nor much interest in it. Conceptually, quantum theory as developed by Bohr and Heisenberg is based on the positivism of Mach as it describes only observable quantities. It first emerged as a result of experimental data in the form of statistical observations of quantum noise, the basic concept of quantum probability.
Quantum field theory based on birefringent modified Maxwell theory
NASA Astrophysics Data System (ADS)
Schreck, M.
2014-04-01
In the current paper the properties of a birefringent Lorentz-violating extension of quantum electrodynamics is considered. The theory results from coupling modified Maxwell theory, which is a CPT-even Lorentz-violating extension of the photon sector, to a Dirac theory of standard spin-1/2 particles. It is then restricted to a special birefringent case with one nonzero Lorentz-violating coefficient. The modified dispersion laws of electromagnetic waves are obtained plus their phase and group velocities are considered. After deriving the photon propagator and the polarization vectors for a special momentum configuration we prove both unitarity at tree level and microcausality for the quantum field theory based on this Lorentz-violating modification. These analytical proofs are done for a spatial momentum with two vanishing components and the proof of unitarity is supported by numerical investigations in case all components are nonvanishing. The upshot is that the theory is well behaved within the framework of our assumptions where there is a possible issue for negative Lorentz-violating coefficients. The paper shall provide a basis for the future analysis of alternative birefringent quantum field theories.
Introduction to the Quantum Theory of Elementary Cycles
NASA Astrophysics Data System (ADS)
Dolce, Donatello
Elementary Cycles Theory (ECT) is a novel exact formulation of quantum-relativistic mechanics. Here, we present an introduction to its basic quantum aspects. On the one hand, Newton's law of inertia states that every isolated particle has persistent motion, i.e. constant energy and momentum. On the other hand, undulatory mechanics associates, by means of the Planck constant, a recurrence in time and space to the energy and the momentum of an elementary particle, respectively. Paraphrasing these two fundamental principles of modern physics, ECT postulates that every elementary constituent of nature (every elementary particle) is characterized by persistent intrinsic periodicity (as long it does not interact) whose space-time duration determines its kinematical state (energy and momentum). In other words, undulatory mechanics is imposed as constraint "overdetermining" relativistic mechanics, with fundamental motivations on Einstein's proposal of unification of quantum and relativistic theories. Every free particle is a (de Broglie) "periodic phenomenon" which can also be regarded as a reference clock and every system is decomposable in modulated elementary cycles. Indeed, ECT introduces a cyclic nature to the ordinary relativistic space-time coordinates. The resulting classical-relativistic mechanics turns out to be fully consistent with relativity and, at the same time, reproduces exactly all the fundamental aspects of ordinary quantum-relativistic mechanics (without any explicit quantisation). Relativity only fixes the differential structure of space-time without giving any prescription about the boundary of space-time, and the constraint of covariant periodicity (or similar relativistic boundary conditions) is allowed by the variational principle for relativistic theories. The constraint of intrinsic periodicity enforces the local nature of relativistic space-time and the wave-particle duality. Besides such unified description of relativistic and quantum dynamics
Quantum mechanics without potential function
Alhaidari, A. D.; Ismail, M. E. H.
2015-07-15
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.
Quantum mechanics of Proca fields
NASA Astrophysics Data System (ADS)
Zamani, Farhad; Mostafazadeh, Ali
2009-05-01
We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries.
Relationship between quantum walks and relativistic quantum mechanics
Chandrashekar, C. M.; Banerjee, Subhashish; Srikanth, R.
2010-06-15
Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This article revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled forms of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schroedinger form. By showing the coin to be a means to make the walk reversible and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modeled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. The Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of the quantum walk, the maximum speed of walk propagation, and earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two-state system to which the study can be extended.
Supersymmetric Liouville theory: A statistical mechanical approach
Barrozo, M.C.; Belvedere, L.V.
1996-02-01
The statistical mechanical system associated with the two-dimensional supersymmetric Liouville theory is obtained through an infrared-finite perturbation expansion. Considering the system confined in a finite volume and in the presence of a uniform neutralizing background, we show that the grand-partition function of this system describes a one-component gas, in which the Boltzmann factor is weighted by an integration over the Grassmann variables. This weight function introduces the dimensional reduction phenomenon. After performing the thermodynamic limit, the resulting supersymmetric quantum theory is translationally invariant. {copyright} {ital 1996 The American Physical Society.}
Solvay 1927: Quantum Theory at the Crossroads
NASA Astrophysics Data System (ADS)
Valentini, Antony
2011-04-01
We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. The proceedings of the conference contain much unexpected material, and are remarkable for their clear identification of key issues that remain controversial to this day. After providing a general overview, we focus on the extensive discussions of de Broglie's pilot-wave theory, which de Broglie presented for a many-body system, including the much misunderstood critique by Pauli.
Towards a Quantum Theory of Humour
NASA Astrophysics Data System (ADS)
Gabora, Liane; Kitto, Kirsty
2016-12-01
This paper proposes that cognitive humour can be modelled using the mathematical framework of quantum theory, suggesting that a Quantum Theory of Humour (QTH) is a viable approach. We begin with brief overviews of both research on humour, and the generalized quantum framework. We show how the bisociation of incongruous frames or word meanings in jokes can be modelled as a linear superposition of a set of basis states, or possible interpretations, in a complex Hilbert space. The choice of possible interpretations depends on the context provided by the set-up versus the punchline of a joke. We apply QTH first to a verbal pun, and then consider how this might be extended to frame blending in cartoons. An initial study of 85 participant responses to 35 jokes (and a number of variants) suggests that there is reason to believe that a quantum approach to the modelling of cognitive humour is a viable new avenue of research for the field of quantum cognition.
The uncertainty principle determines the nonlocality of quantum mechanics.
Oppenheim, Jonathan; Wehner, Stephanie
2010-11-19
Two central concepts of quantum mechanics are Heisenberg's uncertainty principle and a subtle form of nonlocality that Einstein famously called "spooky action at a distance." These two fundamental features have thus far been distinct concepts. We show that they are inextricably and quantitatively linked: Quantum mechanics cannot be more nonlocal with measurements that respect the uncertainty principle. In fact, the link between uncertainty and nonlocality holds for all physical theories. More specifically, the degree of nonlocality of any theory is determined by two factors: the strength of the uncertainty principle and the strength of a property called "steering," which determines which states can be prepared at one location given a measurement at another.
Study on a Possible Darwinian Origin of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Baladrón, C.
2011-03-01
A sketchy subquantum theory deeply influenced by Wheeler's ideas (Am. J. Phys. 51:398-404, 1983) and by the de Broglie-Bohm interpretation (Goldstein in Stanford Encyclopedia of Philosophy, 2006) of quantum mechanics is further analyzed. In this theory a fundamental system is defined as a dual entity formed by bare matter and a methodological probabilistic classical Turing machine. The evolution of the system would be determined by three Darwinian informational regulating principles. Some progress in the derivation of the postulates of quantum mechanics from these regulating principles is reported. The entanglement in a bipartite system is preliminarily considered.
Kindergarten Quantum Mechanics: Lecture Notes
Coecke, Bob
2006-01-04
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns 'doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I which subsumes my Logic of Entanglement. For a survey on the 'what', the 'why' and the 'hows' I refer to a previous set of lecture notes. In a last section we provide some pointers to the body of technical literature on the subject.
Quantum mechanics: A new chapter?
NASA Astrophysics Data System (ADS)
Hofer, Werner A.
2012-12-01
We review the conceptual problems in quantum mechanics on a fundamental level. It is shown that the proposed model of extended electrons and a clear understanding of rotations in three dimensional space solve a large part of these problems, in particular the problems related to the ontological status and physical meaning of wavefunctions. It also solves the problem of non-locality. The experimental results obtained in Yves Couder's group and theoretical results by Gerdard Grössing indicate that the wave-like distribution of trajectories of electrons in interference experiments are most likely due to the quantized interactions leading to a discrete set of transferred momenta. A separate experimental confirmation of this interpretation for double-slit interferometry of photons has been given by the group of Steinberg.
Complex numbers in quantum theory
NASA Astrophysics Data System (ADS)
Maynard, Glenn
In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: "What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function." This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. (Abstract shortened by ProQuest.).
"Mysticism" in Quantum Mechanics: The Forgotten Controversy
ERIC Educational Resources Information Center
Marin, Juan Miguel
2009-01-01
This paper argues that a European controversy over a "mystical" hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s--birth of quantum theory--and concluding…
"Mysticism" in Quantum Mechanics: The Forgotten Controversy
ERIC Educational Resources Information Center
Marin, Juan Miguel
2009-01-01
This paper argues that a European controversy over a "mystical" hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s--birth of quantum theory--and concluding…
Thermodynamic integration from classical to quantum mechanics.
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
Quantum Mechanics and physical calculations
NASA Astrophysics Data System (ADS)
Karayan, H. S.
2014-03-01
We suggest to realize the computer simulation and calculation by the algebraic structure built on the basis of the logic inherent to processes in physical systems (called physical computing). We suggest a principle for the construction of quantum algorithms of neuroinformatics of quantum neural networks. The role of academician Sahakyan is emphasized in the development of quantum physics in Armenia.
Theory of fractional quantum Hall interferometers
NASA Astrophysics Data System (ADS)
Levkivskyi, Ivan P.; Fröhlich, Jürg; Sukhorukov, Eugene V.
2012-12-01
Interference of fractionally charged quasiparticles is expected to lead to Aharonov-Bohm oscillations with periods larger than the flux quantum. However, according to the Byers-Yang theorem, observables of an electronic system are invariant under an adiabatic insertion of a quantum of singular flux. We resolve this seeming paradox by considering a microscopic model of electronic interferometers made from a quantum Hall liquid at filling factor 1/m with the shape of a Corbino disk. In such interferometers, the quantum Hall edge states are utilized in place of optical beams, the quantum point contacts play the role of beam splitters connecting different edge channels, and Ohmic contacts represent a source and drain of quasiparticle currents. Depending on the position of Ohmic contacts, one distinguishes interferometers of Fabry-Pérot (FP) and Mach-Zehnder (MZ) type. An approximate ground state of such interferometers is described by a Laughlin-type wave function, and low-energy excitations are incompressible deformations of this state. We construct a low-energy effective theory by restricting the microscopic Hamiltonian of electrons to the space of incompressible deformations and show that the theory of the quantum Hall edge so obtained is a generalization of a chiral conformal field theory. In our theory, a quasiparticle tunneling operator is found to be a single-valued function of tunneling point coordinates, and its phase depends on the topology determined by the positions of Ohmic contacts. We describe strong coupling of the edge states to Ohmic contacts and the resulting quasiparticle current through the interferometer with the help of a master equation. We find that the coherent contribution to the average quasiparticle current through MZ interferometers does not vanish after summation over quasiparticle degrees of freedom. However, it acquires oscillations with the electronic period, in agreement with the Byers-Yang theorem. Importantly, our theory does not
Nhu, Nguyen Van; Singh, Mahendra; Leonhard, Kai
2008-05-08
We have computed molecular descriptors for sizes, shapes, charge distributions, and dispersion interactions for 67 compounds using quantum chemical ab initio and density functional theory methods. For the same compounds, we have fitted the three perturbed-chain polar statistical associating fluid theory (PCP-SAFT) equation of state (EOS) parameters to experimental data and have performed a statistical analysis for relations between the descriptors and the EOS parameters. On this basis, an analysis of the physical significance of the parameters, the limits of the present descriptors, and the PCP-SAFT EOS has been performed. The result is a method that can be used to estimate the vapor pressure curve including the normal boiling point, the liquid volume, the enthalpy of vaporization, the critical data, mixture properties, and so on. When only two of the three parameters are predicted and one is adjusted to experimental normal boiling point data, excellent predictions of all investigated pure compound and mixture properties are obtained. We are convinced that the methodology presented in this work will lead to new EOS applications as well as improved EOS models whose predictive performance is likely to surpass that of most present quantum chemically based, quantitative structure-property relationship, and group contribution methods for a broad range of chemical substances.
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.
Physics on the boundary between classical and quantum mechanics
NASA Astrophysics Data System (ADS)
't Hooft, Gerard
2014-04-01
Nature's laws in the domain where relativistic effects, gravitational effects and quantum effects are all comparatively strong are far from understood. This domain is called the Planck scale. Conceivably, a theory can be constructed where the quantum nature of phenomena at such scales can be attributed to something fundamentally simpler. However, arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there can't be physical laws that require "conspiracy". It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In the lecture we will show several such counterexamples. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. This theory is often portrayed as to underly the quantum field theory of the subatomic particles, including the "Standard Model". So now the question is asked: how can this model feature "conspiracy", and how bad is that? Is there conspiracy in the vacuum fluctuations?
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.
Elucidating reaction mechanisms on quantum computers.
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.
Causal quantum theory and the collapse locality loophole
Kent, Adrian
2005-07-15
Causal quantum theory is an umbrella term for ordinary quantum theory modified by two hypotheses: state vector reduction is a well-defined process, and strict local causality applies. The first of these holds in some versions of Copenhagen quantum theory and need not necessarily imply practically testable deviations from ordinary quantum theory. The second implies that measurement events which are spacelike separated have no nonlocal correlations. To test this prediction, which sharply differs from standard quantum theory, requires a precise definition of state vector reduction. Formally speaking, any precise version of causal quantum theory defines a local hidden variable theory. However, causal quantum theory is most naturally seen as a variant of standard quantum theory. For that reason it seems a more serious rival to standard quantum theory than local hidden variable models relying on the locality or detector efficiency loopholes. Some plausible versions of causal quantum theory are not refuted by any Bell experiments to date, nor is it evident that they are inconsistent with other experiments. They evade refutation via a neglected loophole in Bell experiments--the collapse locality loophole--which exists because of the possible time lag between a particle entering a measurement device and a collapse taking place. Fairly definitive tests of causal versus standard quantum theory could be made by observing entangled particles separated by {approx_equal}0.1 light seconds.
Quantum Mechanics with a Little Less Mystery
ERIC Educational Resources Information Center
Cropper, William H.
1969-01-01
Suggests the "route of the inquiring mind in presenting the esoteric quantum mechanical postulates and concepts in an understandable form. Explains that the quantum mechanical postulates are but useful mathematical forms to express thebroader principles of superposition and correspondence. Briefly describes some of the features which makes the…
Deriving quantum theory from its local structure and reversibility.
de la Torre, Gonzalo; Masanes, Lluís; Short, Anthony J; Müller, Markus P
2012-08-31
We investigate the class of physical theories with the same local structure as quantum theory but potentially different global structure. It has previously been shown that any bipartite correlations generated by such a theory can be simulated in quantum theory but that this does not hold for tripartite correlations. Here we explore whether imposing an additional constraint on this space of theories-that of dynamical reversibility-will allow us to recover the global quantum structure. In the particular case in which the local systems are identical qubits, we show that any theory admitting at least one continuous reversible interaction must be identical to quantum theory.
Physical theories, eternal inflation, and the quantum universe
NASA Astrophysics Data System (ADS)
Nomura, Yasunori
2011-11-01
Infinities in eternal inflation have long been plaguing cosmology, making any predictions highly sensitive to how they are regulated. The problem exists already at the level of semi-classical general relativity, and has a priori nothing to do with quantum gravity. On the other hand, we know that certain problems in semi-classical gravity, for example physics of black holes and their evaporation, have led to understanding of surprising, quantum natures of spacetime and gravity, such as the holographic principle and horizon complementarity. In this paper, we present a framework in which well-defined predictions are obtained in an eternally inflating multiverse, based on the principles of quantum mechanics. We propose that the entire multiverse is described purely from the viewpoint of a single "observer," who describes the world as a quantum state defined on his/her past light cones bounded by the (stretched) apparent horizons. We find that quantum mechanics plays an essential role in regulating infinities. The framework is "gauge invariant," i.e. predictions do not depend on how spacetime is parametrized, as it should be in a theory of quantum gravity. Our framework provides a fully unified treatment of quantum measurement processes and the multiverse. We conclude that the eternally inflating multiverse and many worlds in quantum mechanics are the same. Other important implications include: global spacetime can be viewed as a derived concept; the multiverse is a transient phenomenon during the world relaxing into a supersymmetric Minkowski state. We also present a model of "initial conditions" for the multiverse. By extrapolating our framework to the extreme, we arrive at a picture that the entire multiverse is a fluctuation in the stationary, fractal "mega-multiverse," in which an infinite sequence of multiverse productions occurs. The framework discussed here does not suffer from problems/paradoxes plaguing other measures proposed earlier, such as the youngness
Local Tomography and the Jordan Structure of Quantum Theory
NASA Astrophysics Data System (ADS)
Barnum, Howard; Wilce, Alexander
2014-02-01
Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection rules is the only non-signaling probabilistic theory in which (i) individual systems are Jordan algebras (equivalently, their cones of unnormalized states are homogeneous and self-dual), (ii) composites are locally tomographic (meaning that states are determined by the joint probabilities they assign to measurement outcomes on the component systems) and (iii) at least one system has the structure of a qubit. Using this result, we also characterize finite dimensional quantum theory among probabilistic theories having the structure of a dagger-monoidal category.
The operator tensor formulation of quantum theory.
Hardy, Lucien
2012-07-28
In this paper, we provide what might be regarded as a manifestly covariant presentation of discrete quantum theory. A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation (e.g. B(b(2)a(3))(a(1))) can have zero or more quantum systems inputted into it and zero or more quantum systems outputted from it. The operation B(b(2)a(3))(a(1)) has one system of type a inputted, and one system of type b and one system of type a outputted. We can wire together operations to form circuits, for example, A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Each repeated integer label here denotes a wire connecting an output to an input of the same type. As each operation in a circuit has an outcome associated with it, a circuit represents a set of outcomes that can happen in a run of the experiment. In the operator tensor formulation of quantum theory, each operation corresponds to an operator tensor. For example, the operation B(b(2)a(3))(a(1)) corresponds to the operator tensor B(b(2)a(3))(a(1)). Further, the probability for a general circuit is given by replacing operations with corresponding operator tensors as in Prob(A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3))) = Â(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Repeated integer labels indicate that we multiply in the associated subspace and then take the partial trace over that subspace. Operator tensors must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).
Differentiability of correlations in realistic quantum mechanics
Cabrera, Alejandro; Faria, Edson de; Pujals, Enrique; Tresser, Charles
2015-09-15
We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumed to be twice differentiable at the origin, then we arrive at a version of Bell’s theorem. On the one hand, we are showing that any realistic theory of quantum mechanics which incorporates the kinematic aspects of relativity must lead to this type of rough correlation function that is once but not twice differentiable. On the other hand, this study brings us a single degree of differentiability away from a relativistic von Neumann no hidden variables theorem.
Molecular model with quantum mechanical bonding information.
Bohórquez, Hugo J; Boyd, Russell J; Matta, Chérif F
2011-11-17
The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules.
NASA Astrophysics Data System (ADS)
Takahashi, Hideaki; Tanabe, Kohsuke; Aketa, Masataka; Kishi, Ryohei; Furukawa, Shin-ichi; Nakano, Masayoshi
2007-02-01
The Beckmann rearrangement of acetone oxime promoted by proton transfers in the supercritical water has been investigated by means of the hybrid quantum mechanical/molecular mechanical approach combined with the theory of energy representation (QM/MM-ER) recently developed. The transition state (TS) structures have been explored by ab initio calculations for the reaction of hydrated acetone oxime on the assumption that the reaction is catalyzed by proton transfers along the hydrogen bonds connecting the solute and the solvent water molecules. Up to two water molecules have been considered as reactants that take part in the proton transfers. As a result of the density functional theory calculations with B3LYP functional and aug-cc-pVDZ basis set, it has been found that participation of two water molecules in the reaction reduces the activation free energy by -12.3kcal/mol. Furthermore, the QM/MM-ER simulations have revealed that the TS is more stabilized than the reactant state in the supercritical water by 2.7kcal/mol when two water molecules are involved in the reaction. Solvation free energies of the reactant and the TS have been decomposed into terms due to the electronic polarization of the solute, electron density fluctuation, and others to elucidate the origin of the stabilization of the TS as compared with the reactant. It has been revealed that the promotion of the chemical reaction due to the hydration mainly originates from the interaction between the nonpolarized solute and the solvent water molecules at the supercritical state.
Optimal state discrimination and unstructured search in nonlinear quantum mechanics
NASA Astrophysics Data System (ADS)
Childs, Andrew M.; Young, Joshua
2016-02-01
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.
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.
Why space has three dimensions: A quantum mechanical explanation
NASA Astrophysics Data System (ADS)
Marcer, Peter; Schempp, Walter
2000-05-01
The theoretical physics of a quantum mechanical model of space, relativistic quantum holography, is described. It specifies three dimensions, such as is validated by the nature of our spatial experience, but where additionally, quantum non-locality, which Feynman described as the only mystery of quantum theory, is made manifest by means of observable phase relationships. For example, synchronicity between events, and other phenomena such as are described by the geometric/Berry phase, etc., which are outside the bounds of classical explanation. It can therefore be hypothesized: a) that we live in a entirely quantum mechanical world/universe and not a classical mechanical one (where quantum phenomena are confined to the microscopic scale) as is the current generally held scientific view, b) that three spatial dimensions are a fundamental consequence of quantum mechanics, c) that quantum holography is a natural candidate to explain quantum gravity, such that mass/inertia concerns not the eigenvalues of some operator, but rather the observable gauge invariant phases of a state vector, postulated to be that of the universe itself, as a whole, and d) that this model provides a natural explanation in terms of relativistic quantum signal processing of any each individual's perception and cognition will be of a three dimensional world, defined similarly in relation to each individual's quantum state vector, describing its mind/body and associated gauge invariant phases or mindset, which have observable consequences, such that mental processes and events can cause neural events and processes! These testable hypotheses, if validated, will have profound implications for our understanding, radically changing our scientific perspective on the world, as we enter the new millennium. .
ysteries, Puzzles, and Paradoxes in Quantum Mechanics. Proceedings
Rodolfo, B.
1999-02-01
These proceedings represent papers presented at the Mysteries, Puzzles, and Paradoxes in Quantum Mechanics Workshop held in Italy, in August 1998. The Workshop was devoted to recent experimental and theoretical advances such as new interference, effects, the quantum eraser, non{minus}disturbing and Schroedinger{minus}cat{minus}like states, experiments, EPR correlations, teleportation, superluminal effects, quantum information and computing, locality and causality, decoherence and measurement theory. Tachyonic information transfer was also discussed. There were 45 papers presented at the conference,out of which 2 have been abstracted for the Energy,Science and Technology database.(AIP)
The statistical theory of quantum dots
NASA Astrophysics Data System (ADS)
Alhassid, Y.
2000-10-01
A quantum dot is a sub-micron-scale conducting device containing up to several thousand electrons. Transport through a quantum dot at low temperatures is a quantum-coherent process. This review focuses on dots in which the electron's dynamics are chaotic or diffusive, giving rise to statistical properties that reflect the interplay between one-body chaos, quantum interference, and electron-electron interactions. The conductance through such dots displays mesoscopic fluctuations as a function of gate voltage, magnetic field, and shape deformation. The techniques used to describe these fluctuations include semiclassical methods, random-matrix theory, and the supersymmetric nonlinear σ model. In open dots, the approximation of noninteracting quasiparticles is justified, and electron-electron interactions contribute indirectly through their effect on the dephasing time at finite temperature. In almost-closed dots, where conductance occurs by tunneling, the charge on the dot is quantized, and electron-electron interactions play an important role. Transport is dominated by Coulomb blockade, leading to peaks in the conductance that at low temperatures provide information on the dot's ground-state properties. Several statistical signatures of electron-electron interactions have been identified, most notably in the dot's addition spectrum. The dot's spin, determined partly by exchange interactions, can also influence the fluctuation properties of the conductance. Other mesoscopic phenomena in quantum dots that are affected by the charging energy include the fluctuations of the cotunneling conductance and mesoscopic Coulomb blockade.
Topics in Theories of Quantum Gravity
Perelstein, M.
2005-04-05
In this thesis, the author addresses several issues involving gravity. The first half of the thesis is devoted to studying quantum properties of Einstein gravity and its supersymmetric extensions in the perturbative regime. String theory suggests that perturbative scattering amplitudes in the theories of gravity are related to the amplitudes in gauge theories. This connection has been studied at classical (tree) level by Kawai, Lewellen and Tye. Here, they will explore the relationship between gravity and gauge theory at quantum (loop) level. This relationship, together with the cut-based approach to computing loop amplitudes, allow us to obtain new non-trivial results for quantum gravity. IN particular, they present two infinite sequences of one-loop n-graviton scattering amplitudes: the maximally helicity violating amplitudes in N = 8 supergravity, and the ''all-plus'' helicity amplitudes in Einstein gravity with any minimally coupled massless matter content. The results for n {le} 6 will be obtained by an explicit calculation, while those for n > 6 is inferred from the soft and collinear properties of the amplitudes. They also present an explicit expression for the two-loop contribution to the four-particle scattering amplitude in N = 8 supergravity, and observe a simple relation between this result and its counterpart in N = 4 super-Yang-Mills theory. Furthermore, the simple structure of the two-particle unitarity cuts in these theories suggests that similar relations exist to all loop orders. If this is the case, the first ultraviolet divergence in N = 8 supergravity should appear at five loops, contrary to the earlier expectation of a three-loop counterterm.
Effective Particles in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Głazek, Stanisław D.; Trawiński, Arkadiusz P.
2017-03-01
The concept of effective particles is introduced in the Minkowski space-time Hamiltonians in quantum field theory using a new kind of the relativistic renormalization group procedure that does not integrate out high-energy modes but instead integrates out the large changes of invariant mass. The new procedure is explained using examples of known interactions. Some applications in phenomenology, including processes measurable in colliders, are briefly presented.
On space of integrable quantum field theories
NASA Astrophysics Data System (ADS)
Smirnov, F. A.; Zamolodchikov, A. B.
2017-02-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (T T bar) built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by X1 are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
Quantum Mechanical Models Of The Fermi Shuttle
Sternberg, James
2011-06-01
The Fermi shuttle is a mechanism in which high energy electrons are produced in an atomic collision by multiple collisions with a target and a projectile atom. It is normally explained purely classically in terms of the electron's orbits prescribed in the collision. Common calculations to predict the Fermi shuttle use semi-classical methods, but these methods still rely on classical orbits. In reality such collisions belong to the realm of quantum mechanics, however. In this paper we discuss several purely quantum mechanical calculations which can produce the Fermi shuttle. Being quantum mechanical in nature, these calculations produce these features by wave interference, rather than by classical orbits.
Keldysh field theory for driven open quantum systems.
Sieberer, L M; Buchhold, M; Diehl, S
2016-09-01
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Keldysh field theory for driven open quantum systems
NASA Astrophysics Data System (ADS)
Sieberer, L. M.; Buchhold, M.; Diehl, S.
2016-09-01
Recent experimental developments in diverse areas—ranging from cold atomic gases to light-driven semiconductors to microcavity arrays—move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Spin and Uncertainty in the Interpretation of Quantum Mechanics.
ERIC Educational Resources Information Center
Hestenes, David
1979-01-01
Points out that quantum mechanics interpretations, using Heisenberg's Uncertainty Relations for the position and momentum of an electron, have their drawbacks. The interpretations are limited to the Schrodinger theory and fail to take into account either spin or relativity. Shows why spin cannot be ignored. (Author/GA)
The History of Teaching Quantum Mechanics in Greece
ERIC Educational Resources Information Center
Tampakis, Constantin; Skordoulis, Constantin
2007-01-01
In this work, our goal is to examine the attitude of the Greek scientific community towards Quantum Mechanics and establish the history of teaching of this theory in Greece. We have examined Physics textbooks written by professors of the University of Athens, as well as records of public speeches, university yearbooks from 1923 to 1970, articles…
Completeness of the Coulomb Wave Functions in Quantum Mechanics
ERIC Educational Resources Information Center
Mukunda, N.
1978-01-01
Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)
Elementary Quantum Mechanics in a High-Energy Process
ERIC Educational Resources Information Center
Denville, A.; And Others
1978-01-01
Compares two approaches to strong absorption in elementary quantum mechanics; the black sphere and a model based on the continuum theory of nuclear reactions. Examines the application to proton-antiproton interactions at low momenta and concludes that the second model is the appropriate and simplest to use. (Author/GA)
Time Symmetric Quantum Mechanics and Causal Classical Physics ?
NASA Astrophysics Data System (ADS)
Bopp, Fritz W.
2017-04-01
A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual "near future" macroscopic phenomena is attributed to a cosmological asymmetry and to rules governing the transition between microscopic to macroscopic observations. Our interest is a heuristic understanding of the resulting macroscopic physics.
The History of Teaching Quantum Mechanics in Greece
ERIC Educational Resources Information Center
Tampakis, Constantin; Skordoulis, Constantin
2007-01-01
In this work, our goal is to examine the attitude of the Greek scientific community towards Quantum Mechanics and establish the history of teaching of this theory in Greece. We have examined Physics textbooks written by professors of the University of Athens, as well as records of public speeches, university yearbooks from 1923 to 1970, articles…
Spin and Uncertainty in the Interpretation of Quantum Mechanics.
ERIC Educational Resources Information Center
Hestenes, David
1979-01-01
Points out that quantum mechanics interpretations, using Heisenberg's Uncertainty Relations for the position and momentum of an electron, have their drawbacks. The interpretations are limited to the Schrodinger theory and fail to take into account either spin or relativity. Shows why spin cannot be ignored. (Author/GA)
Completeness of the Coulomb Wave Functions in Quantum Mechanics
ERIC Educational Resources Information Center
Mukunda, N.
1978-01-01
Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)
Quasi-Hermitian quantum mechanics in phase space
Curtright, Thomas; Veitia, Andrzej
2007-10-15
We investigate quasi-Hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact results are easily obtained. We emphasize spatially periodic solutions, compute various distribution functions and phase-space metrics, and explore the relationships between them.
Elementary Quantum Mechanics in a High-Energy Process
ERIC Educational Resources Information Center
Denville, A.; And Others
1978-01-01
Compares two approaches to strong absorption in elementary quantum mechanics; the black sphere and a model based on the continuum theory of nuclear reactions. Examines the application to proton-antiproton interactions at low momenta and concludes that the second model is the appropriate and simplest to use. (Author/GA)
Time Symmetric Quantum Mechanics and Causal Classical Physics ?
NASA Astrophysics Data System (ADS)
Bopp, Fritz W.
2017-02-01
A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual "near future" macroscopic phenomena is attributed to a cosmological asymmetry and to rules governing the transition between microscopic to macroscopic observations. Our interest is a heuristic understanding of the resulting macroscopic physics.
The role of type III factors in quantum field theory
NASA Astrophysics Data System (ADS)
Yngvason, Jakob
2005-02-01
One of von Neumann's motivations for developing the theory of operator algebras and his and Murray's 1936 classification of factors was the question of possible decompositions of quantum systems into independent parts. For quantum systems with a finite number of degrees of freedom the simplest possibility, i.e. factors of type I in the terminology of Murray and von Neumann, are perfectly adequate. In relativistic quantum field theory (RQFT), on the other hand, factors of type III occur naturally. The same holds true in quantum statistical mechanics of infinite systems. In this brief review some physical consequences of the type III property of the von Neumann algebras corresponding to localized observables in RQFT and their difference from the type I case will be discussed. The cumulative effort of many people over more than 30 years has established a remarkable uniqueness result: The local algebras in RQFT are generically isomorphic to the unique, hyperfinite type III, factor in Connes' classification of 1973. Specific theories are characterized by the net structure of the collection of these isomorphic algebras for different space-time regions, i.e. the way they are embedded into each other
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.
Strange Bedfellows: Quantum Mechanics and Data Mining
Weinstein, Marvin; /SLAC
2009-12-16
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.
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.
String theory, quantum phase transitions, and the emergent Fermi liquid.
Cubrović, Mihailo; Zaanen, Jan; Schalm, Koenraad
2009-07-24
A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.
New theory of diffusive and coherent nature of optical wave via a quantum walk
NASA Astrophysics Data System (ADS)
Ide, Yusuke; Konno, Norio; Matsutani, Shigeki; Mitsuhashi, Hideo
2017-08-01
We propose a new theory on a relation between diffusive and coherent nature in one dimensional wave mechanics based on a quantum walk. It is known that the quantum walk in homogeneous matrices provides the coherent property of wave mechanics. Using the recent result of a localization phenomenon in a one-dimensional quantum walk (Konno, 2010), we numerically show that the randomized localized matrices suppress the coherence and give diffusive nature.
Finite quantum theory of the harmonic oscillator
NASA Astrophysics Data System (ADS)
Shiri-Garakani, Mohsen
We apply the Segal process of group simplification to the linear harmonic oscillator. The result is a finite quantum theory with three quantum constants h, h', h″ instead of the usual one. We compare the classical (CLHO), quantum (QLHO), and finite (FLHO) linear harmonic oscillators and their canonical or unitary groups. The FLHO is isomorphic to a dipole rotator with N = l(l + 1) ˜ 1/(h ' h″) states and Hamiltonian H = A(Lx)2 + B(Ly)2, and the physically interesting case has N ≫ 1. The position and momentum variables are quantized with uniform finite spectra. For fixed quantum constants and large N ≫ 1 there are three broad classes of FLHO: soft, medium, and hard, with B/A ≪ 1, B/A ˜ 1, and B/A ≫ 1 respectively. The field oscillators responsible for infra-red and ultraviolet divergences are soft and hard respectively. Medium oscillators have B/A ˜ 1 and approximate the QLHO. They have ˜ N low-lying states with nearly the same zero-point energy and level spacing as the QLHO, and nearly obeying the Heisenberg uncertainty principle and the equipartition principle. The corresponding rotators are nearly polarized along the z axis with Lz ˜ +/-l. The soft and hard FLHO's have infinitesimal 0-point energy and grossly violate equipartition and the Heisenberg uncertainty principle. They do not resemble the QLHO at all. Their low-lying energy states correspond to rotators with Lx ˜ 0 or Ly ˜ 0 instead of Lz ˜ +/-l. Soft oscillators have frozen momentum, because their maximum potential energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to excite one quantum of position.
On the theory of quantum measurement
NASA Technical Reports Server (NTRS)
Haus, Hermann A.; Kaertner, Franz X.
1994-01-01
Many so called paradoxes of quantum mechanics are clarified when the measurement equipment is treated as a quantized system. Every measurement involves nonlinear processes. Self consistent formulations of nonlinear quantum optics are relatively simple. Hence optical measurements, such as the quantum nondemolition (QND) measurement of photon number, are particularly well suited for such a treatment. It shows that the so called 'collapse of the wave function' is not needed for the interpretation of the measurement process. Coherence of the density matrix of the signal is progressively reduced with increasing accuracy of the photon number determination. If the QND measurement is incorporated into the double slit experiment, the contrast ratio of the fringes is found to decrease with increasing information on the photon number in one of the two paths.
On space of integrable quantum field theories
Smirnov, F. A.; Zamolodchikov, A. B.
2016-12-21
Here, we study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as “effective field theories”, with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field View the MathML source(TT¯) built frommore » the components of the energy–momentum tensor. The deformations of quantum field theories generated by X1 are “solvable” in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. Lastly, we also make some remarks on the problem of UV completeness of such integrable deformations.« less
A modern solvation theory: quantum chemistry and statistical chemistry.
Sato, Hirofumi
2013-05-28
This perspective highlights recent developments in the field of statistical mechanics for molecular liquids, i.e. the integral equation (IE) theory, especially focusing on hybrid approaches incorporating quantum chemistry and IE theory. The electronic structure of solvated molecules is characterized, followed by recent developments and applications. The latter includes for some specific systems: evaluation of acidity, basicity, pH and pKa, chemical equilibrium and molecular structure, chemical reactions, ionization and electron transfer reactions, as well as excited states and their free energy.
Failure of random matrix theory to correctly describe quantum dynamics.
Kottos, T; Cohen, D
2001-12-01
Consider a classically chaotic system that is described by a Hamiltonian H(0). At t=0 the Hamiltonian undergoes a sudden change (H)0-->H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it cannot be analyzed using a conventional random-matrix theory (RMT) approach. Conventional RMT can be trusted only to the extent that it gives trivial results that are implied by first-order perturbation theory. Nonperturbative effects are sensitive to the underlying classical dynamics, and therefore the Planck's over 2 pi-->0 behavior for effective RMT models is strikingly different from the correct semiclassical limit.
Extending quantum mechanics entails extending special relativity
NASA Astrophysics Data System (ADS)
Aravinda, S.; Srikanth, R.
2016-05-01
The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an ontological extension for quantum mechanics (QMs) through the oblivious embedding of a sound simulation protocol in a Newtonian spacetime. Minkowski or other intermediate spacetimes are ruled out as the locus of the embedding by virtue of hidden influence inequalities. The complementarity transferred from a simulation to the extension unifies a number of results about quantum non-locality, and implies that special relativity has a different significance for the ontological model and for the operational theory it reproduces. Only the latter, being experimentally accessible, is required to be Lorentz covariant. There may be certain Lorentz non-covariant elements at the ontological level, but they will be inaccessible at the operational level in a valid extension. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime at the ontological level has Minkowski causal structure.
Quantum mechanics on profinite groups and partial order
NASA Astrophysics Data System (ADS)
Vourdas, A.
2013-02-01
Inverse limits and profinite groups are used in a quantum mechanical context. Two cases are considered: a quantum system with positions in the profinite group { {Z}}_p and momenta in the group { {Q}}_p/{ {Z}}_p, and a quantum system with positions in the profinite group {\\widehat{ {Z}}} and momenta in the group { {Q}}/{ {Z}}. The corresponding Schwatz-Bruhat spaces of wavefunctions and the Heisenberg-Weyl groups are discussed. The sets of subsystems of these systems are studied from the point of view of partial order theory. It is shown that they are directed-complete partial orders. It is also shown that they are topological spaces with T0-topologies, and this is used to define continuity of various physical quantities. The physical meaning of profinite groups, non-Archimedean metrics, partial orders and T0-topologies, in a quantum mechanical context, is discussed.
Relational quadrilateralland II: The Quantum Theory
NASA Astrophysics Data System (ADS)
Anderson, Edward; Kneller, Sophie
2014-04-01
We provide the quantum treatment of the relational quadrilateral. The underlying reduced configuration spaces are ℂℙ2 and the cone over this. We consider exact free and isotropic HO potential cases and perturbations about these. Moreover, our purely relational kinematical quantization is distinct from the usual one for ℂℙ2, which turns out to carry absolutist connotations instead. Thus, this paper is the first to note absolute-versus-relational motion distinctions at the kinematical rather than dynamical level. It is also an example of value to the discussion of kinematical quantization along the lines of Isham, 1984. The relational quadrilateral is the simplest RPM whose mathematics is not standard in atomic physics (the triangle and four particles on a line are both based on 𝕊2 and ℝ3 mathematics). It is far more typical of the general quantum relational N-a-gon than the previously studied case of the relational triangle. We consider useful integrals as regards perturbation theory and the peaking interpretation of quantum cosmology. We subsequently consider problem of time (PoT) applications of this: quantum Kuchař beables, the Machian version of the semiclassical approach and the timeless naïve Schrödinger interpretation. These go toward extending the combined Machian semiclassical-Histories-Timeless Approach of [Int. J. Mod. Phys. D23 (2014) 1450014] to the case of the quadrilateral, which will be treated in subsequent papers.
Quantum mechanics: The subtle pull of emptiness
Seife, C.
1997-01-10
Classic physics dictates that the vacuum is devoid not only of matter but also of energy. But quantum mechanics often seems to depart from common sense. A paper in the Physical Review Letters describes the first successful measurement of the ultimate quantum free lunch: the Casimir force, a pressure exerted by empty space. This paper describes the background and the experiment.
Orientable Objects in Relativistic Quantum Theory
NASA Astrophysics Data System (ADS)
Gitman, D. M.; Shelepin, A. L.
2017-03-01
An approach to the quantum description of the orientation of relativistic particles, generalizing the approach to nonrelativistic objects possessing orientation (in particular, a rotator) is proposed, based on the self-consistent use of two reference frames. The realization of such an approach is connected with the introduction of wave functions f (x, z) on the Poincaré group M(3,1), which depend on the coordinates x μ of the Minkowski space M(3,1)/Spin(3,1) and orientational variables assigned by the elements z {β/α} of the matrix Z ∈Spin(3,1).The field f (x, z) is the generating function for ordinary spin-tensor fields and admits a number of symmetries. Besides the Lorentz transformations (corresponding to the action of the Poincaré group from the left and interpretable as external symmetries), transformations of a reference frame associated with an orientable object (corresponding to the action of the Poincaré group from the right and interpretable as internal symmetries) are applicable to orientable objects. In addition to the six quantum numbers assigned by the Casimir operators and the left generators, quantum numbers arise here that are assigned by the right generators and are associated with internal symmetries. The assumption that the internal symmetries of the theory of orientable objects are local leads to gauge theories describing the electroweak and gravitational interactions.
Measurement theory in local quantum physics
Okamura, Kazuya Ozawa, Masanao
2016-01-15
In this paper, we aim to establish foundations of measurement theory in local quantum physics. For this purpose, we discuss a representation theory of completely positive (CP) instruments on arbitrary von Neumann algebras. We introduce a condition called the normal extension property (NEP) and establish a one-to-one correspondence between CP instruments with the NEP and statistical equivalence classes of measuring processes. We show that every CP instrument on an atomic von Neumann algebra has the NEP, extending the well-known result for type I factors. Moreover, we show that every CP instrument on an injective von Neumann algebra is approximated by CP instruments with the NEP. The concept of posterior states is also discussed to show that the NEP is equivalent to the existence of a strongly measurable family of posterior states for every normal state. Two examples of CP instruments without the NEP are obtained from this result. It is thus concluded that in local quantum physics not every CP instrument represents a measuring process, but in most of physically relevant cases every CP instrument can be realized by a measuring process within arbitrary error limits, as every approximately finite dimensional von Neumann algebra on a separable Hilbert space is injective. To conclude the paper, the concept of local measurement in algebraic quantum field theory is examined in our framework. In the setting of the Doplicher-Haag-Roberts and Doplicher-Roberts theory describing local excitations, we show that an instrument on a local algebra can be extended to a local instrument on the global algebra if and only if it is a CP instrument with the NEP, provided that the split property holds for the net of local algebras.
NASA Astrophysics Data System (ADS)
Pope, D. T.; Drummond, P. D.; Munro, W. J.
2000-10-01
Intracavity and external third order correlations in the damped nondegenerate parametric oscillator are calculated for quantum mechanics and stochastic electrodynamics (SED), a semiclassical theory. The two theories yield greatly different results, with the correlations of quantum mechanics being cubic in the system's nonlinear coupling constant and those of SED being linear in the same constant. In particular, differences between the two theories are present in at least a mesoscopic regime. They also exist when realistic damping is included. Such differences illustrate distinctions between quantum mechanics and a hidden variable theory for continuous variables.
Delirium Quantum Or, where I will take quantum mechanics if it will let me
NASA Astrophysics Data System (ADS)
Fuchs, Christopher A.
2007-02-01
Once again, I take advantage of the wonderfully liberal and tolerant mood Andrei Khrennikov sets at his yearly conferences by submitting a nonstandard paper for the proceedings. This pseudo-paper consists of excerpts drawn from two of my samizdats [Quantum States: What the Hell Are They? and Darwinism All the Way Down (and Probabilism All the Way Back Up)] that I think best summarize what I am aiming for on the broadest scale with my quantum foundations program. Section 1 tries to draw a picture of a physical world whose essence is "Darwinism all the way down." Section 2 outlines how quantum theory should be viewed in light of that, i.e., as being an expression of probabilism (in Bruno de Finetti or Richard Jeffrey's sense) all the way back up. Section 3 describes how the idea of "identical" quantum measurement outcomes, though sounding atomistic in character, nonetheless meshes well with a William Jamesian style "radical pluralism." Sections 4 and 5 further detail how quantum theory should not be viewed so much as a "theory of the world," but rather as a theory of decision-making for agents immersed within a quantum world—that is, a world in continual creation. Finally, Sections 6 and 7 attempt to sketch once again the very positive sense in which quantum theory is incomplete, but still just as complete is it can be. In total, I hope these heady speculations convey some of the excitement and potential I see for the malleable world quantum mechanics hints of.
Mechanical equivalent of quantum heat engines.
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.
The trouble with orbits: The Stark effect in the old and the new quantum theory
NASA Astrophysics Data System (ADS)
Duncan, Anthony; Janssen, Michel
2014-11-01
The old quantum theory and Schrödinger's wave mechanics (and other forms of quantum mechanics) give the same results for the line splittings in the first-order Stark effect in hydrogen, the leading terms in the splitting of the spectral lines emitted by a hydrogen atom in an external electric field. We examine the account of the effect in the old quantum theory, which was hailed as a major success of that theory, from the point of view of wave mechanics. First, we show how the new quantum mechanics solves a fundamental problem that one runs into in the old quantum theory with the Stark effect. It turns out that, even without an external field, it depends on the coordinates in which the quantum conditions are imposed which electron orbits are allowed in a hydrogen atom. The allowed energy levels and hence the line splittings are independent of the coordinates used but the size and eccentricity of the orbits are not. In the new quantum theory, this worrisome non-uniqueness of orbits turns into the perfectly innocuous non-uniqueness of bases in Hilbert space. Second, we review how the so-called WKB (Wentzel-Kramers-Brillouin) approximation method for solving the Schrödinger equation reproduces the quantum conditions of the old quantum theory amended by some additional half-integer terms. These extra terms remove the need for some arbitrary extra restrictions on the allowed orbits that the old quantum theory required over and above the basic quantum conditions.
Microscopic theory and quantum simulation of atomic heat transport
NASA Astrophysics Data System (ADS)
Marcolongo, Aris; Umari, Paolo; Baroni, Stefano
2016-01-01
Quantum simulation methods based on electronic-structure theory are deemed unfit to cope with atomic heat transport within the Green-Kubo formalism, because quantum-mechanical energy densities and currents are inherently ill-defined at the atomic scale. We show that, although this difficulty would also affect classical simulations, thermal conductivity is indeed insensitive to such ill-definedness by virtue of a kind of gauge invariance resulting from energy extensivity and conservation. On the basis of these findings, we derive an expression for the adiabatic energy flux from density-functional theory, which allows heat transport to be simulated using ab initio equilibrium molecular dynamics. Our methodology is demonstrated by comparing its predictions to those of classical equilibrium and ab initio non-equilibrium (Müller-Plathe) simulations for a liquid-argon model, and by applying it to heavy water at ambient conditions.
NASA Astrophysics Data System (ADS)
Babaei, Hassan; Mostafazadeh, Ali
2017-08-01
A first-quantized free photon is a complex massless vector field A =(Aμ ) whose field strength satisfies Maxwell's equations in vacuum. We construct the Hilbert space H of the photon by endowing the vector space of the fields A in the temporal-Coulomb gauge with a positive-definite and relativistically invariant inner product. We give an explicit expression for this inner product, identify the Hamiltonian for the photon with the generator of time translations in H , determine the operators representing the momentum and the helicity of the photon, and introduce a chirality operator whose eigenfunctions correspond to fields having a definite sign of energy. We also construct a position operator for the photon whose components commute with each other and with the chirality and helicity operators. This allows for the construction of the localized states of the photon with a definite sign of energy and helicity. We derive an explicit formula for the latter and compute the corresponding electric and magnetic fields. These turn out to diverge not just at the point where the photon is localized but on a plane containing this point. We identify the axis normal to this plane with an associated symmetry axis and show that each choice of this axis specifies a particular position operator, a corresponding position basis, and a position representation of the quantum mechanics of a photon. In particular, we examine the position wave functions determined by such a position basis, elucidate their relationship with the Riemann-Silberstein and Landau-Peierls wave functions, and give an explicit formula for the probability density of the spatial localization of the photon.
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.
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, common sense, and the black hole information paradox
NASA Astrophysics Data System (ADS)
Danielsson, Ulf H.; Schiffer, Marcelo
1993-11-01
The purpose of this paper is to analyze, in the light of information theory and with the arsenal of (elementary) quantum mechanics (EPR, correlations, copying machines, teleportation, mixing produced in subsystems owing to a trace operation, etc.) the scenarios available on the market to resolve the so-called black hole information paradox. We shall conclude that the only plausible ones are those where either the unitary evolution of quantum mechanics is given up, in which information leaks continuously in the course of black hole evaporation through nonlocal processes, or those in which the world is polluted by an infinite number of metastable remnants.