Relativistic Quantum Mechanics and Field Theory
NASA Astrophysics Data System (ADS)
Gross, Franz
1999-04-01
An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field. Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay. Subsequent chapters prepare readers for advanced work, covering such major topics as gauge theories, path integral techniques, spontaneous symmetry breaking, and an introduction to QCD, chiral symmetry, and the Standard Model. A special chapter is devoted to relativistic bound state wave equations-an important topic that is often overlooked in other books. Clear and concise throughout, Relativistic Quantum Mechanics and Field Theory boasts examples from atomic and nuclear physics as well as particle physics, and includes appendices with background material. It is an essential reference for anyone working in quantum mechanics today.
Quantum mechanics of 4-derivative theories
NASA Astrophysics Data System (ADS)
Salvio, Alberto; Strumia, Alessandro
2016-04-01
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.
Quantum Probability Theory and the Foundations of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Fröhlich, Jürg; Schubnel, Baptiste
By and large, people are better at coining expressions than at filling them with interesting, concrete contents. Thus, it may not be very surprising that there are many professional probabilists who may have heard the expression but do not appear to be aware of the need to develop "quantum probability theory" into a thriving, rich, useful field featured at meetings and conferences on probability theory. Although our aim, in this essay, is not to contribute new results on quantum probability theory, we hope to be able to let the reader feel the enormous potential and richness of this field. What we intend to do, in the following, is to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras).
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.
Quantum Hamilton Mechanics and the Theory of Quantization Conditions
NASA Astrophysics Data System (ADS)
Bracken, Paul
A formulation of quantum mechanics in terms of complex canonical variables is presented. It is seen that these variables are governed by Hamilton's equations. It is shown that the action variables need to be quantized. By formulating a quantum Hamilton equation for the momentum variable, the energies for two different systems are determined. Quantum canonical transformation theory is introduced and the geometrical significance of a set of generalized quantization conditions which are obtained is discussed.
Spin Kinetic Models of Plasmas - Semiclassical and Quantum Mechanical Theory
Brodin, Gert; Marklund, Mattias; Zamanian, Jens
2009-11-10
In this work a recently published semiclassical spin kinetic model, generalizing those of previous authors are discussed. Some previously described properties are reviewed, and a new example illustrating the theory is presented. The generalization to a fully quantum mechanical description is discussed, and the main features of such a theory is outlined. Finally, the main conclusions are presented.
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
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 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
Quantum mechanical model in gravity theory
NASA Astrophysics Data System (ADS)
Losyakov, V. V.
2016-05-01
We consider a model of a real massive scalar field defined as homogeneous on a d-dimensional sphere such that the sphere radius, time scale, and scalar field are related by the equations of the general theory of relativity. We quantize this system with three degrees of freedom, define the observables, and find dynamical mean values of observables in the regime where the scalar field mass is much less than the Planck mass.
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.
"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.
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.
Introduction to Nonequilibrium Statistical Mechanics with Quantum Field Theory
NASA Astrophysics Data System (ADS)
Kita, T.
2010-04-01
In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (i) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (ii) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (iii) to derive an expression of nonequilibrium entropy that evolves with time. In stage (i), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keld ysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Phi-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Phi-derivable approximation, i.e., an issue of how to handle the ``Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy''. Aim (ii) is performed through successive reductions of relevant variables with the Wigner transformation, the gradient expansion based on the Groenewold-Moyal product, and Enskog's expansion from local equilibrium. This part may be helpful for convincing readers that nonequilibrium systems ca n be handled
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
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.
New U-matrix theory in quantum mechanics
NASA Astrophysics Data System (ADS)
Lam, C. C.; Fung, P. C. W.
1983-04-01
We have analyzed Dyson's U-matrix theory of solving the Schrödinger equation in the interaction picture and are able to express the U matrix as a dominant term plus an infinite series involving multiple integrals of time. For a certain rather restrictive class of Hamiltonians, our theory is exact for a general time-dependent problem. For other Hamiltonians, we can only obtain approximate expressions for our U matrix and hence the wave function. Treating a time-independent problem as a special case of the time-dependent situation with a sudden-switching process, we have shown that our U matrix is exact. To demonstrate the working procedures of our theory, we apply it to study the well-known time-independent charged harmonic-oscillator problem and the more general harmonic oscillator with a time-dependent driving force. Compared with other methods, our new theory appears to lead to a result which contains more information than others due to the inclusion of noncommutability properties of operators in the operator Schrödinger equation. It has been shown that the classical Feynman path-integral formalism can be deduced from quantum mechanics with the use of the Green's-function operator. It is interesting to note that apart from a step function, the Green's-function operator is the same as that of our U(s) matrix, which is the U matrix obtained within the regime of the Schrödinger picture for a time-independent Hamiltonian, as a special case of our general time-dependent treatment.
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)].
NASA Astrophysics Data System (ADS)
Schieve, William C.; Horwitz, Lawrence P.
2009-04-01
1. Foundations of quantum statistical mechanics; 2. Elementary examples; 3. Quantum statistical master equation; 4. Quantum kinetic equations; 5. Quantum irreversibility; 6. Entropy and dissipation: the microscopic theory; 7. Global equilibrium: thermostatics and the microcanonical ensemble; 8. Bose-Einstein ideal gas condensation; 9. Scaling, renormalization and the Ising model; 10. Relativistic covariant statistical mechanics of many particles; 11. Quantum optics and damping; 12. Entanglements; 13. Quantum measurement and irreversibility; 14. Quantum Langevin equation: quantum Brownian motion; 15. Linear response: fluctuation and dissipation theorems; 16. Time dependent quantum Green's functions; 17. Decay scattering; 18. Quantum statistical mechanics, extended; 19. Quantum transport with tunneling and reservoir ballistic transport; 20. Black hole thermodynamics; Appendix; Index.
Time-dependent perturbation theory in quantum mechanics and the renormalization group
NASA Astrophysics Data System (ADS)
Bhattacharjee, J. K.; Ray, D. S.
2016-06-01
Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.
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
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
Relativity and Quantum Mechanics
Braendas, Erkki J.
2007-12-26
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.
Quantum set theory and applications
Rodriguez, E.
1984-01-01
The work of von Neumann tells us that the logic of quantum mechanics is not Boolenan. This suggests the formulation of a quantum theory of sets based on quantum logic much as modern set theory is based on Boolean logic. In the first part of this dissertation such a quantum set theory is developed. In the second part, quantum set theory is proposed as a universal language for physics. A quantum topology and the beginnings of a quantum geometry are developed in this language. Finally, a toy model is studied. It gives indications of possible lines for progress in this program.
NASA Astrophysics Data System (ADS)
Kapustin, Anton
2013-06-01
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.
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.
Moving Beyond Quantum Mechanics in Search for a Generalized Theory of Superconductivity
NASA Astrophysics Data System (ADS)
Akpojotor, Godfrey; Animalu, Alexander
2012-02-01
Though there are infinite number of theories currently in the literature in the search for a generalized theory of superconductivity (SC), there may be three domineering mechanisms for the Cooper pair formation (CPF) and their emergent theories of SC. Two of these mechanisms, electron-phonon interactions and electron-electron correlations which are based on the quantum theory axiom of action-at-a distance, may be only an approximation of the third mechanism which is contact interaction of the wavepackets of the two electrons forming the Cooper pair as envisaged in hadronic mechanics to be responsible for natural bonding of elements. The application of this hydronic --type interaction to the superconducting cuprates, iron based compounds and heavy fermions leads to interesting results. It is therefore suggested that the future of the search for the theory of SC may be considered from this natural possible bonding that at short distances, the CPF is by a nonlinear, nonlocal and nonhamiltonian strong hadronic-type interactions due to deep wave-overlapping of spinning particles leading to Hulthen potential that is attractive between two electrons in singlet couplings while at large distances the CPF is by superexchange interaction which is purely a quantum mechanical affairs.
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.''
Orthogonal-state-based cryptography in quantum mechanics and local post-quantum theories
NASA Astrophysics Data System (ADS)
Aravinda, S.; Banerjee, Anindita; Pathak, Anirban; Srikanth, R.
2014-02-01
We introduce the concept of cryptographic reduction, in analogy with a similar concept in computational complexity theory. In this framework, class A of crypto-protocols reduces to protocol class B in a scenario X, if for every instance a of A, there is an instance b of B and a secure transformation X that reproduces a given b, such that the security of b guarantees the security of a. Here we employ this reductive framework to study the relationship between security in quantum key distribution (QKD) and quantum secure direct communication (QSDC). We show that replacing the streaming of independent qubits in a QKD scheme by block encoding and transmission (permuting the order of particles block by block) of qubits, we can construct a QSDC scheme. This forms the basis for the block reduction from a QSDC class of protocols to a QKD class of protocols, whereby if the latter is secure, then so is the former. Conversely, given a secure QSDC protocol, we can of course construct a secure QKD scheme by transmitting a random key as the direct message. Then the QKD class of protocols is secure, assuming the security of the QSDC class which it is built from. We refer to this method of deduction of security for this class of QKD protocols, as key reduction. Finally, we propose an orthogonal-state-based deterministic key distribution (KD) protocol which is secure in some local post-quantum theories. Its security arises neither from geographic splitting of a code state nor from Heisenberg uncertainty, but from post-measurement disturbance.
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.
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)
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...
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. PMID:22654052
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)
Simulik, Volodimir
2016-01-01
The new relativistic equations of motion for the particles with arbitrary spin and nonzero mass have been introduced. The axiomatic level description of the relativistic canonical quantum mechanics of the arbitrary mass and spin has been given. The 64-dimensional ClR(0,6) algebra in terms of Dirac gamma matrices has been suggested. The link between the relativistic canonical quantum mechanics of the arbitrary spin and the covariant local field theory has been found. Different methods of the Dirac equation derivation have been reviewed. The manifestly covariant field equations for an arbitrary spin that follow from the quantum mechanical equations have been considered. The covariant local field theory equations for spin s = (1,1) particle-antiparticle doublet, spin s = (1,0,1,0) particle antiparticle multiplet, spin s = (3/2,3/2) particle-antiparticle doublet, spin s = (2,2) particle-antiparticle doublet, spin s = (2,0,2,0) particle-antiparticle multiplet and spin s = (2,1,2,1) particle-antiparticle multiplet have been introduced. The Maxwell-like equations for the boson with spin s = 1 and nonzero mass have been introduced as well.
NASA Astrophysics Data System (ADS)
Murdin, P.
2000-11-01
A theory based on the premise that, on the microscopic scale, physical quantities have discrete, rather than a continuous range of, values. The theory was devised in the early part of the twentieth century to account for certain phenomena that could not be explained by classical physics. In 1900, the German physicist, Max Planck (1858-1947), was able precisely to describe the previously unexplaine...
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
NASA Astrophysics Data System (ADS)
Escobar-Ruiz, M. A.; Shuryak, E.; Turbiner, A. V.
2016-05-01
We develop a new semiclassical approach, which starts with the density matrix given by the Euclidean time path integral with fixed coinciding end points, and proceed by identifying classical (minimal Euclidean action) path, to be referred to as a flucton, which passes through this end point. Fluctuations around a flucton path are included, by standard Feynman diagrams, previously developed for instantons. We calculate the Green function and evaluate the one loop determinant both by direct diagonalization of the fluctuation equation and also via the trick with the Green functions. The two-loop corrections are evaluated by explicit Feynman diagrams, and some curious cancellation of logarithmic and polylog terms is observed. The results are fully consistent with large-distance asymptotics obtained in quantum mechanics. Two classic examples—quartic double-well and sine-Gordon potentials—are discussed in detail, while powerlike potential and quartic anharmonic oscillator are discussed in brief. Unlike other semiclassical methods, like WKB, we do not use the Schrödinger equation, and all the steps generalize to multidimensional or quantum fields cases straightforwardly.
No-Go Theorems Face Background-Based Theories for Quantum Mechanics
NASA Astrophysics Data System (ADS)
Vervoort, Louis
2016-04-01
Recent experiments have shown that certain fluid-mechanical systems, namely oil droplets bouncing on oil films, can mimic a wide range of quantum phenomena, including double-slit interference, quantization of angular momentum and Zeeman splitting. Here I investigate what can be learned from these systems concerning no-go theorems as those of Bell and Kochen-Specker. In particular, a model for the Bell experiment is proposed that includes variables describing a `background' field or medium. This field mimics the surface wave that accompanies the droplets in the fluid-mechanical experiments. It appears that quite generally such a model can violate the Bell inequality and reproduce the quantum statistics, even if it is based on local dynamics only. The reason is that measurement independence is not valid in such models. This opens the door for local `background-based' theories, describing the interaction of particles and analyzers with a background field, to complete quantum mechanics. Experiments to test these ideas are also proposed.
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…
Effective methods for quantum theories
NASA Astrophysics Data System (ADS)
Brahma, Suddhasattwa
Whenever a full theory is unavailable, effective frameworks serve as powerful tools for examining physical phenomena below some energy scale. However, standard quantum field theory techniques are not always applicable in various exotic, yet physically relevant, systems. This thesis presents a new effective method for quantum theories, which is particularly tailored towards background independent theories such as gravity. Our main motivation is to utilize these techniques to extract the semi-classical dynamics from canonical quantum gravity theories. Application to field theoretic toy models of loop quantum gravity and non-associative quantum mechanics is elaborated in detail. We also extend this framework to fully constrained systems, as is required for gravity, and discuss several consequences for quantum gravity.
NASA Astrophysics Data System (ADS)
Kuwahara, Y.; Nakamura, Y.; Yamanaka, Y.
2013-12-01
The 2×2-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom [1]. We show that the Galley's Hamilton formalism can be extended to quantum field and that the resulting theory is naturally identical with nonequilibrium TFD.
Scalar Theory of Everything model correspondence to the Big Bang model and to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Hodge, John
2014-03-01
We are at a special moment in our scientific evolution that requires the big of cosmology and the small of light and of particle physics be united by a single model. The Scalar Theory of Everything model (STOE) suggests fundamental assumptions with consideration for the successful parts of current models and for the data inconsistent with current models. The STOE has been tested over the last 10 years with data concerning galaxy rotation curves; redshift at galactic, solar system, and earth scales; BH-galaxy disk properties; temperature of the universe; and light interference. The STOE is simpler, corresponds to both General Relativity and quantum mechanics, and solves many current mysteries and inconsistencies. Therefore, the STOE is founded on orthodox science. Data analysis in 2011 confirmed predictions of the STOE made in 2006 that no other model suggested.
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.
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.
Advanced Concepts in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Esposito, Giampiero; Marmo, Giuseppe; Miele, Gennaro; Sudarshan, George
2014-11-01
Preface; 1. Introduction: the need for a quantum theory; 2. Experimental foundations of quantum theory; 3. Waves and particles; 4. Schrödinger picture, Heisenberg picture and probabilistic aspects; 5. Integrating the equations of motion; 6. Elementary applications: 1-dimensional problems; 7. Elementary applications: multidimensional problems; 8. Coherent states and related formalism; 9. Introduction to spin; 10. Symmetries in quantum mechanics; 11. Approximation methods; 12. Modern pictures of quantum mechanics; 13. Formulations of quantum mechanics and their physical implications; 14. Exam problems; Glossary of geometric concepts; References; Index.
NASA Astrophysics Data System (ADS)
Nishimura, Hirokazu
1996-06-01
Machida and Namiki developed a many-Hilbert-spaces formalism for dealing with the interaction between a quantum object and a measuring apparatus. Their mathematically rugged formalism was polished first by Araki from an operator-algebraic standpoint and then by Ozawa for Boolean quantum mechanics, which approaches a quantum system with a compatible family of continuous superselection rules from a notable and perspicacious viewpoint. On the other hand, Foulis and Randall set up a formal theory for the empirical foundation of all sciences, at the hub of which lies the notion of a manual of operations. They deem an operation as the set of possible outcomes and put down a manual of operations at a family of partially overlapping operations. Their notion of a manual of operations was incorporated into a category-theoretic standpoint into that of a manual of Boolean locales by Nishimura, who looked upon an operation as the complete Boolean algebra of observable events. Considering a family of Hilbert spaces not over a single Boolean locale but over a manual of Boolean locales as a whole, Ozawa's Boolean quantum mechanics is elevated into empirical quantum mechanics, which is, roughly speaking, the study of quantum systems with incompatible families of continuous superselection rules. To this end, we are obliged to develop empirical Hilbert space theory. In particular, empirical versions of the square root lemma for bounded positive operators, the spectral theorem for (possibly unbounded) self-adjoint operators, and Stone's theorem for one-parameter unitary groups are established.
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
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. PMID:27305996
Noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
Gamboa, J.; Loewe, M.; Rojas, J. C.
2001-09-01
A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.
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.
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.
Grassmann matrix quantum mechanics
NASA Astrophysics Data System (ADS)
Anninos, Dionysios; Denef, Frederik; Monten, Ruben
2016-04-01
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. 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)
Bender, Carl M.
2015-07-01
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.
NASA Astrophysics Data System (ADS)
Ellerman, David
2014-03-01
In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.
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.
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. PMID:22639577
Quaternionic quantum field theory
Adler, S.L.
1985-08-19
We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second-order wave equation. The theory is initially defined in terms of a quaternion-imaginary Lagrangian using the Feynman sum over histories. A Schroedinger equation can be derived from the functional integral, which identifies the quaternion-imaginary quantum Hamiltonian. Conversely, the transformation theory based on this Hamiltonian can be used to rederive the functional-integral formulation.
Quantum mechanics from invariance principles
NASA Astrophysics Data System (ADS)
Moldoveanu, Florin
2015-07-01
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.
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.
NASA Astrophysics Data System (ADS)
Gardner, David E.
This thesis describes qualitative research conducted to understand the problems students have when learning quantum mechanics. It differs from previous studies on educational issues associated with quantum mechanics in that I have examined the difficulties from the students' perspective. Three questions guided this research: What are the experiences of students learning quantum mechanics? What conceptual difficulties do students have with quantum mechanics? and, How do students approach learning quantum mechanics? From these questions, two themes emerged. First, students do not consider the quantum mechanical concepts of wave-particle duality or the uncertainty principle to be important sources of difficulties for them. Second, many of the difficulties students encounter are not related to conceptual understanding of specific topics, but stem from a mindset that is incongruent with the nature and structure of quantum mechanics. The implications for teaching are that the nature and structure of quantum mechanics should be emphasized and be an explicit part of instruction.
Perturbative N = 2 Supersymmetric Quantum Mechanics and L-Theory with Complex Coefficients
NASA Astrophysics Data System (ADS)
Berwick-Evans, Daniel
2016-01-01
We construct L-theory with complex coefficients from the geometry of 1|2-dimensional perturbative mechanics. Methods of perturbative quantization lead to wrong-way maps that we identify with those coming from the MSO orientation of L-theory tensored with the complex numbers. In particular, the total volume of a space of 1|2-dimensional vacua reads off the signature of a 4 k-dimensional oriented manifold.
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
Supersymmetric Quantum Field Theories
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2005-03-01
We consider some supersymmetric multiplets in a purely quantum framework. A crucial point is to ensure the positivity of the scalar product in the Hilbert space of the quantum system. For the vector multiplet we obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass. The gauge structure is constructed purely deductive and leads to the necessity of introducing scalar ghost superfields, in analogy to the usual gauge theories. Then 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. 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.
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)
Akhmeteli, Andrey
2013-03-01
Is it possible to offer a ``no drama'' quantum theory? Something as simple (in principle) as classical electrodynamics - a theory described by a system of partial differential equations (PDE) in 3+1 dimensions, but reproducing unitary evolution of a quantum field theory in the Fock space? The following results suggest an affirmative answer: 1. The scalar field can be algebraically eliminated from scalar electrodynamics; the resulting equations describe independent evolution of the electromagnetic field (EMF). 2. After introduction of a complex 4-potential (producing the same EMF as the standard real 4-potential), the spinor field can be algebraically eliminated from spinor electrodynamics; the resulting equations describe independent evolution of EMF. 3. The resulting theories for EMF can be embedded into quantum field theories. Another fundamental result: in a general case, the Dirac equation is equivalent to a 4th order PDE for just one component, which can be made real by a gauge transform. Issues related to the Bell theorem are discussed. A. Akhmeteli, Int'l Journal of Quantum Information, Vol. 9, Suppl., 17-26 (2011) A. Akhmeteli, Journal of Mathematical Physics, Vol. 52, 082303 (2011) A. Akhmeteli, quant-ph/1111.4630 A. Akhmeteli, J. Phys.: Conf. Ser., Vol. 361, 012037 (2012)
NASA Astrophysics Data System (ADS)
Akhmeteli, Andrey
2012-02-01
Is it possible to offer a ``no drama'' quantum theory? Something as simple (in principle) as classical electrodynamics - a theory described by a system of partial differential equations (PDE) in 3+1 dimensions, but reproducing unitary evolution of a quantum field theory in the configuration space? The following results suggest an affirmative answer: 1. The scalar field can be algebraically eliminated from scalar electrodynamics; the resulting equations describe independent evolution of the electromagnetic field (EMF). 2. After introduction of a complex 4-potential (producing the same EMF as the standard real 4-potential), the spinor field can be algebraically eliminated from spinor electrodynamics; the resulting equations describe independent evolution of EMF. 3. The resulting theories for EMF can be embedded into quantum field theories. Another fundamental result: in a general case, the Dirac equation is equivalent to a 4th order PDE for just one component, which can be made real by a gauge transform. Issues related to the Bell theorem are discussed. A. Akhmeteli, Int'l Journal of Quantum Information, Vol. 9, Suppl., 17-26 (2011) A. Akhmeteli, Journal of Mathematical Physics, Vol. 52, 082303 (2011) A. Akhmeteli, quant-ph/1108.1588
Emergent mechanics, quantum and un-quantum
NASA Astrophysics Data System (ADS)
Ralston, John P.
2013-10-01
There is great interest in quantum mechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantum mechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantum mechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications
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/
Unified theory of exactly and quasiexactly solvable ''discrete'' quantum mechanics. I. Formalism
Odake, Satoru; Sasaki, Ryu
2010-08-15
We present a simple recipe to construct exactly and quasiexactly solvable Hamiltonians in one-dimensional ''discrete'' quantum mechanics, in which the Schroedinger equation is a difference equation. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. The recipe also predicts several new ones. An essential role is played by the sinusoidal coordinate, which generates the closure relation and the Askey-Wilson algebra together with the Hamiltonian. The relationship between the closure relation and the Askey-Wilson algebra is clarified.
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.
Barnett, Stephen M.; Cresser, James D.
2005-08-15
We present a Markovian quantum theory of friction. Our approach is based on the idea that collisions between a Brownian particle and single molecules of the surrounding medium constitute, as far as the particle is concerned, instantaneous simultaneous measurements of its position and momentum.
Feynman's simple quantum mechanics
NASA Astrophysics Data System (ADS)
Taylor, Edwin F.
1997-03-01
This sample class presents an alternative to the conventional introduction to quantum mechanics and describes its current use in a credit course. This alternative introduction rests on theory presented in professional and popular writings by Richard Feynman. Feynman showed that Nature gives a simple command to the electron: "Explore all paths." All of nonrelativistic quantum mechanics, among other fundamental results, comes from this command. With a desktop computer the student points and clicks to tell a modeled electron which paths to follow. The computer then shows the results, which embody the elemental strangeness and paradoxical behaviors of the world of the very small. Feynman's approach requires few equations and provides a largely non-mathematical introduction to the wave function of conventional quantum mechanics. Draft software and materials already used for two semesters in an e-mail computer conference credit university course show that Feynman's approach works well with a variety of students. The sample class explores computer and written material and describes the next steps in its development.
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.
Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces
NASA Astrophysics Data System (ADS)
Gulden, Tobias; Janas, Michael; Kamenev, Alex
2014-03-01
Statistical mechanics of 1D Coulomb gases may be mapped onto (in general) non-Hermitian quantum mechanics. We use this example to develop non-Hermitian instanton calculus. Treating momentum and coordinate as independent complex variables, constant energy manifolds are given by Riemann surfaces of genus g >= 1 . The actions along principal cycles on these surfaces obey an ODE in the moduli space of the Riemann surface known as the Picard-Fuchs equation. Solving the Picard-Fuchs equation yields semiclassical spectra as well as instanton effects such as width of Bloch bands (the latter determines energy barrier for charge transport). Both are shown to be in perfect agreement with numerical simulations. Applications include transport through biological ion channels as well as nanofluidics, e.g water filled nanotubes. The work was supported by NSF grant DMR1306734.
NASA Astrophysics Data System (ADS)
Akhmeteli, Andrey
2012-05-01
Is it possible to offer a "no drama" quantum theory? Something as simple (in principle) as classical electrodynamics - a theory described by a system of partial differential equations in 3+1 dimensions, but reproducing unitary evolution of a quantum field theory in the configuration space? The following results suggest an affirmative answer: 1. The scalar field can be algebraically eliminated from scalar electrodynamics; the resulting equations describe independent evolution of the electromagnetic field. 2. After introduction of a complex 4-potential (producing the same electromagnetic field as the standard real 4-potential), the spinor field can be algebraically eliminated from spinor electrodynamics; the resulting equations describe independent evolution of the electromagnetic field. 3. The resulting theories for the electromagnetic field can be embedded into quantum field theories. Another fundamental result: in a general case, the Dirac equation is equivalent to a 4th order partial differential equations for just one component, which can be made real by a gauge transform. Issues related to the Bell theorem are discussed.
PT quantum mechanics - Recent results
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2012-09-01
Most quantum physicists believe that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under matrix transposition and complex conjugation) to be sure that the energy eigenvalues are real and that time evolution is unitary. However, the non-Dirac-hermitian Hamiltonian H = p2+ix3 has a real positive discrete spectrum and generates unitary time evolution and defines a fully consistent and physical quantum theory. Evidently, Dirac Hermiticity is too restrictive. While H = p2+ix3 is not Dirac Hermitian, it is PT symmetric (invariant under combined space reflection P and time reversal T). Another PT-symmetric Hamiltonian whose energy levels are real, positive and discrete is H = p2-x4, which contains an upside-down potential. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics and quantum field theory are extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past two years some of these properties have been verified in laboratory experiments. Here, we first discuss PT-symmetric Hamiltonians at a simple intuitive level and explain why the energy levels of such Hamiltonians may be real, positive, and discrete. Second, we describe a recent experiment in which the PT phase transition was observed. Third, we briefly mention that PT-symmetric theories can be useful at a fundamental level. While the double-scaling limit of an O(N)-symmetric gφ4 quantum field theory appears to be inconsistent because the critical value of g is negative, this limit is in fact not inconsistent because the critical theory is PT symmetric.
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. PMID:17020371
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.
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.
Emergence of four dimensional quantum mechanics from a deterministic theory in 11 dimensions
NASA Astrophysics Data System (ADS)
Doyen, G.; Drakova, D.
2015-07-01
We develop a deterministic theory which accounts for the coupling of a high dimensional continuum of environmental excitations (called gravonons) to massive particle in a very localized and very weak fashion. For the model presented Schrödinger's equation can be solved practically exactly in 11 spacetime dimensions and the result demonstrates that as a function of time an incoming matter wave incident on a screen extinguishes, except at a single interaction center on the detection screen. This transition is reminiscent of the wave - particle duality arising from the ’’collapse” (also called ’’process one”) postulated in the Copenhagen-von Neumann interpretation. In our theory it is replaced by a sticking process of the particle from the vacuum to the surface of the detection screen. This situation was verified in experiments by using massive molecules. In our theory this ”wave-particle transition” is connected to the different dimensionalities of the space for particle motion and the gravonon dynamics, the latter propagating in the hidden dimensions of 11 dimensional spacetime. The fact that the particle is detected at apparently statistically determined points on the screen is traced back to the weakness and locality of the interaction with the gravonons which allows coupling on the energy shell alone. Although the theory exhibits a completely deterministic ”chooser” mechanism for single site sticking, an apparent statistical character results, as it is found in the experiments, due to small heterogeneities in the atomic and gravonon structures.
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.
The Quantum Underground: Early quantum theory textbooks
NASA Astrophysics Data System (ADS)
Gearhart, Clayton
2011-04-01
Quantum theory had its beginnings in 1900, when Max Planck derived his famous formula for the energy density of black-body radiation. But the early quantum theory textbooks we remember today--for example, those of Arnold Summerfeld (1919), Fritz Reiche (1921), and a shorter Report by James Jeans (1914), did not appear until some years later, and all were written by physicists who were themselves active participants in early quantum theory. Surprisingly, not all early texts fit this pattern. Reiche himself had written a review article on quantum theory for general readers in Die Naturwissenschaften in 1913, long before his research had shifted to quantum topics. And a year later, textbooks by Hermann Sieveking and Sigfried Valentiner treated quantum theory for students and non-specialists, although neither was active in quantum theoretical research. A third and better known author, Owen Richardson, also treated quantum theory in a 1914 book on electromagnetism. I will describe these early and little-known treatments of quantum theory, all of which were written by physicists whose primary research and professional interests lay elsewhere.
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
Entangled states in quantum mechanics
NASA Astrophysics Data System (ADS)
Ruža, Jānis
2010-01-01
In some circles of quantum physicists, a view is maintained that the nonseparability of quantum systems-i.e., the entanglement-is a characteristic feature of quantum mechanics. According to this view, the entanglement plays a crucial role in the solution of quantum measurement problem, the origin of the “classicality” from the quantum physics, the explanation of the EPR paradox by a nonlocal character of the quantum world. Besides, the entanglement is regarded as a cornerstone of such modern disciplines as quantum computation, quantum cryptography, quantum information, etc. At the same time, entangled states are well known and widely used in various physics areas. In particular, this notion is widely used in nuclear, atomic, molecular, solid state physics, in scattering and decay theories as well as in other disciplines, where one has to deal with many-body quantum systems. One of the methods, how to construct the basis states of a composite many-body quantum system, is the so-called genealogical decomposition method. Genealogical decomposition allows one to construct recurrently by particle number the basis states of a composite quantum system from the basis states of its forming subsystems. These coupled states have a structure typical for entangled states. If a composite system is stable, the internal structure of its forming basis states does not manifest itself in measurements. However, if a composite system is unstable and decays onto its forming subsystems, then the measurables are the quantum numbers, associated with these subsystems. In such a case, the entangled state has a dynamical origin, determined by the Hamiltonian of the corresponding decay process. Possible correlations between the quantum numbers of resulting subsystems are determined by the symmetries-conservation laws of corresponding dynamical variables, and not by the quantum entanglement feature.
Quantum algorithms for quantum field theories
NASA Astrophysics Data System (ADS)
Jordan, Stephen
2015-03-01
Ever since Feynman's original proposal for quantum computers, one of the primary applications envisioned has been efficient simulation of other quantum systems. In fact, it has been conjectured that quantum computers would be universal simulators, which can simulate all physical systems using computational resources that scale polynomially with the system's number of degrees of freedom. Quantum field theories have posed a challenge in that the set of degrees of freedom is formally infinite. We show how quantum computers, if built, could nevertheless efficiently simulate certain quantum field theories at bounded energy scales. Our algorithm includes a new state preparation technique which we believe may find additional applications in quantum algorithms. Joint work with Keith Lee and John Preskill.
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.
Informational derivation of quantum theory
NASA Astrophysics Data System (ADS)
Chiribella, Giulio; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2011-07-01
We derive quantum theory from purely informational principles. Five elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—define a broad class of theories of information processing that can be regarded as standard. One postulate—purification—singles out quantum theory within this class.
Quantum Information Theory for Quantum Communication
NASA Astrophysics Data System (ADS)
Koashi, Masato
This chapter gives a concise description of the fundamental concepts of quantum information and quantum communication, which is pertinent to the discussions in the subsequent chapters. Beginning with the basic set of rules that dictate quantum mechanics, the chapter explains the most general ways to describe quantum states, measurements, and state transformations. Convenient mathematical tools are also presented to provide an intuitive picture of a qubit, which is the simplest unit of quantum information. The chapter then elaborates on the distinction between quantum communication and classical communication, with emphasis on the role of quantum entanglement as a communication resource. Quantum teleportation and dense coding are then explained in the context of optimal resource conversions among quantum channels, classical channels, and entanglement.
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. PMID:23509390
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.
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. PMID:22946645
BOOK REVIEW: Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Antoine, J.-P.
2004-01-01
The aim of relativistic quantum mechanics is to describe the finer details of the structure of atoms and molecules, where relativistic effects become nonnegligible. It is a sort of intermediate realm, between the familiar nonrelativistic quantum mechanics and fully relativistic quantum field theory, and thus it lacks the simplicity and elegance of both. Yet it is a necessary tool, mostly for quantum chemists. Pilkuhn's book offers to this audience an up-to-date survey of these methods, which is quite welcome since most previous textbooks are at least ten years old. The point of view of the author is to start immediately in the relativistic domain, following the lead of Maxwell's equations rather than classical mechanics, and thus to treat the nonrelativistic version as an approximation. Thus Chapter 1 takes off from Maxwell's equations (in the noncovariant Coulomb gauge) and gradually derives the basic aspects of Quantum Mechanics in a rather pedestrian way (states and observables, Hilbert space, operators, quantum measurement, scattering,. Chapter 2 starts with the Lorentz transformations, then continues with the Pauli spin equation and the Dirac equation and some of their applications (notably the hydrogen atom). Chapter 3 is entitled `Quantum fields and particles', but falls short of treating quantum field theory properly: only creation/annihilation operators are considered, for a particle in a box. The emphasis is on two-electron states (the Pauli principle, the Foldy--Wouthuysen elimination of small components of Dirac spinors, Breit projection operators. Chapter 4 is devoted to scattering theory and the description of relativistic bound states. Chapter 5, finally, covers hyperfine interactions and radiative corrections. As we said above, relativistic quantum mechanics is by nature limited in scope and rather inelegant and Pilkuhn's book is no exception. The notation is often heavy (mostly noncovariant) and the mathematical level rather low. The central topic
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).
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.
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.
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.
A general theory of quantum relativity
NASA Astrophysics Data System (ADS)
Minic, Djordje; Tze, Chia-Hsiung
2004-02-01
The geometric form of standard quantum mechanics is compatible with the two postulates: (1) the laws of physics are invariant under the choice of experimental setup and (2) every quantum observation or event is intrinsically statistical. These postulates remain compatible within a background independent extension of quantum theory with a local intrinsic time implying the relativity of the concept of a quantum event. In this extension the space of quantum events becomes dynamical and only individual quantum events make sense observationally. At the core of such a general theory of quantum relativity is the three-way interplay between the symplectic form, the dynamical metric and non-integrable almost complex structure of the space of quantum events. Such a formulation provides a missing conceptual ingredient in the search for a background independent quantum theory of gravity and matter. The crucial new technical element in our scheme derives from a set of recent mathematical results on certain infinite-dimensional almost Kahler manifolds which replace the complex projective spaces of standard quantum mechanics.
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.
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.
NASA Astrophysics Data System (ADS)
Błaszak, Maciej; Domański, Ziemowit
2012-02-01
This paper develops an alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative ⋆-product and the deformation of the Poisson bracket to an appropriate Lie bracket are the key elements in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of any smooth Hamiltonian function and for a very wide class of deformations. The considered class of deformations and the corresponding ⋆-products contains as a special case all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of ⋆-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the ⋆-multiplication. The most important result of the paper shows that developed formalism is more fundamental than the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. The equivalence of two formulations of quantum mechanics is proved by observing that the Wigner-Moyal transform has all properties of the tensor product. This observation allows writing many previous results found in the literature in a transparent way, from which the equivalence of the two formulations of quantum mechanics follows naturally. In addition, examples of a free particle and a simple harmonic
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.
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.
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 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.
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
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.
Categorical aspects of reconstructing quantum theory
NASA Astrophysics Data System (ADS)
Lal, Raymond; Coecke, Bob
2012-02-01
We present steps towards a new understanding of reconstructions of quantum theory. Chiribella, D'Ariano, and Perinotti (CDP) have recently produced a fascinating reconstruction of the formalism of quantum theory, which brings to light its operational origins. We use parts of the formalism of categorical quantum mechanics to expose the underlying mathematical structures of information flow in the CDP reconstruction. Our results include an elegant relation between teleportation and local tomography, and an equivalence betweeen a purely category-theoretic description of the purification of a mixed state, and the purification axiom of CDP.
Fundamentals of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Tang, C. L.
2005-06-01
Quantum mechanics has evolved from a subject of study in pure physics to one with a wide range of applications in many diverse fields. The basic concepts of quantum mechanics are explained in this book in a concise and easy-to-read manner emphasising applications in solid state electronics and modern optics. Following a logical sequence, the book is focused on the key ideas and is conceptually and mathematically self-contained. The fundamental principles of quantum mechanics are illustrated by showing their application to systems such as the hydrogen atom, multi-electron ions and atoms, the formation of simple organic molecules and crystalline solids of practical importance. It leads on from these basic concepts to discuss some of the most important applications in modern semiconductor electronics and optics. Containing many homework problems and worked examples, the book is suitable for senior-level undergraduate and graduate level students in electrical engineering, materials science and applied physics. Clear exposition of quantum mechanics written in a concise and accessible style Precise physical interpretation of the mathematical foundations of quantum mechanics Illustrates the important concepts and results by reference to real-world examples in electronics and optoelectronics Contains homeworks and worked examples, with solutions available for instructors
Studies in quantum field theory
NASA Astrophysics Data System (ADS)
Polmar, S. K.
The theoretical physics group at Washington University has been devoted to the solution of problems in theoretical and mathematical physics. All of the personnel on this task have a similar approach to their research in that they apply sophisticated analytical and numerical techniques to problems primarily in quantum field theory. Specifically, this group has worked on quantum chromodynamics, classical Yang-Mills fields, chiral symmetry breaking condensates, lattice field theory, strong-coupling approximations, perturbation theory in large order, nonlinear waves, 1/N expansions, quantum solitons, phase transitions, nuclear potentials, and early universe calculations.
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.
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.
Quantum Mechanics Beyond Hilbert Space
NASA Astrophysics Data System (ADS)
Antoine, J.-P.
Going Beyond Hilbert Space Why? The Different Formalisms What Does One Obtain? The Mathematical Formalism Rigged Hilbert Spaces Scales and Lattices of Hilbert Spaces Partial Inner Product Spaces Operators on PIP-Spaces Application in Quantum Mechanics: The Fock-Bargmann Representation - Revisited A RHS of Entire Functions A LHS of Entire Functions Around ℑ Application in Scattering Theory RHS: Resonances, Gamow Vectors, Arrow of Time LHS: Integral Equations vs. Complex Scaling Conclusion
NASA Astrophysics Data System (ADS)
Katzarov, Ivaylo H.; Pashov, Dimitar L.; Paxton, Anthony T.
2013-08-01
We present calculations of free energy barriers and diffusivities as functions of temperature for the diffusion of hydrogen in α-Fe. This is a fully quantum mechanical approach since the total energy landscape is computed using a self-consistent, transferable tight binding model for interstitial impurities in magnetic iron. Also the hydrogen nucleus is treated quantum mechanically and we compare here two approaches in the literature both based in the Feynman path integral formulation of statistical mechanics. We find that the quantum transition state theory which admits greater freedom for the proton to explore phase space gives result in better agreement with experiment than the alternative which is based on fixed centroid calculations of the free energy barrier. This will have an impact on future modeling and the simulation of hydrogen trapping and diffusion.
No extension of quantum theory can have improved predictive power.
Colbeck, Roger; Renner, Renato
2011-01-01
According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory that removes this indeterminism, as suspected by Einstein, Podolsky and Rosen. Although this has been shown to be impossible, existing results do not imply that the current theory is maximally informative. Here we ask the more general question of whether any improved predictions can be achieved by any extension of quantum theory. Under the assumption that measurements can be chosen freely, we answer this question in the negative: no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself. Our result has significance for the foundations of quantum mechanics, as well as applications to tasks that exploit the inherent randomness in quantum theory, such as quantum cryptography. PMID:21811240
Quantum theory of Manakov solitons
Rand, Darren; Prucnal, Paul R.; Steiglitz, Ken
2005-05-15
A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schroedinger representations, followed by an analytical, linearized quantum theory of Manakov solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and dispersion in Manakov soliton propagation. Calculations of the position, polarization angle, and polarization state fluctuations show an increase in collision-induced noise with a decrease in the relative velocity between the two solitons, as expected because of an increase in the interaction length. Fluctuations in both the polarization angle and state are shown to be independent of propagation distance, opening up possibilities for communications, switching, and logic, exploiting these properties of Manakov solitons. Calculations of the phase noise reveal, surprisingly, that the collision-induced fluctuations can be reduced slightly below the level of fluctuations in the absence of collision, due to cross-correlation effects between the collision-induced phase and amplitude fluctuations of the soliton. The squeezing effect of Manakov solitons is also studied and proven, unexpectedly, to have the same theoretical optimum as scalar solitons.
Choi, B.H.; Poe, R.T.
1985-08-01
We present a systematic formulation of the atom--surface scattering dynamics which includes the vibrational states of the atoms in the solid (phonons). The properties of the total scattering wave function of the system, a representation of the interaction potential matrix, and the characteristics of the independent physical solutions are all derived from the translational invariance of the full Hamiltonian. The scattering equations in the integral forms as well as the related Green functions were also obtained. The configurational representations of the Green functions, in particular, are quite different from those of the conventional scattering theory where the collision partners are spatially localized. Various versions of the integral expression of scattering, transition, and reactance matrices were also obtained. They are useful for introducing approximation schemes. From the present formulation, some specific theoretical schemes which are more realistic compared to those that have been employed so far and at the same time capable of yielding effective ab initio computation are derived in the following paper. The time reversal invariance and the microscopic reversibility of the atom--surface scattering were discussed. The relations between the in and outgoing scattering wave functions which are satisfied in the atom--surface system and important in the transition matrix methods were presented. The phonon annihilation and creation, and the adsorption and desorption of the atom are related through the time reversal invariance, and thus the microscopic reversibility can be tested by the experiment.
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)
Spacetime states and covariant quantum theory
NASA Astrophysics Data System (ADS)
Reisenberger, Michael; Rovelli, Carlo
2002-06-01
In its usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended configuration space. Such covariant formulations are natural for relativistic gravitational systems, where general covariance conflicts with the notion of a preferred physical-time variable. The standard presentation of quantum mechanics, in turn, again gives time a very special role, raising well known difficulties for quantum gravity. Is there a covariant form of (canonical) quantum mechanics? We observe that the preferred role of time in quantum theory is the consequence of an idealization: that measurements are instantaneous. Canonical quantum theory can be given a covariant form by dropping this idealization. States prepared by noninstantaneous measurements are described by ``spacetime smeared states.'' The theory can be formulated in terms of these states, without making any reference to a special time variable. The quantum dynamics is expressed in terms of the propagator, an object covariantly defined on the extended configuration space.
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.
Knot theory and statistical mechanics
Jones, V.F.R. )
1990-11-01
Certain algebraic relations used to solve models in statistical mechanics were key to describing a mathematical property of knots known as a polynomial invariant. This connection, tenuous at first, has since developed into a significant flow of ideas. The appearance of such common ground is not atypical of recent developments in mathematics and physics--ideas from different fields interact and produce unexpected results. Indeed, the discovery of the connection between knots and statistical mechanics passed through a theory intimately related to the mathematical structure of quantum physics. This theory, called von Neumann algebras, is distinguished by the idea of continuous dimensionality. Spaces typically have dimensions that are natural numbers, such as 2, 3 or 11, but in von Neumann algebras dimensions such as 2 or {pi} are equally possible. This possibility for continuous dimension played a key role in joining knot theory and statistical mechanics. In another direction, the knot invariants were soon found to occur in quantum field theory. Indeed, Edward Witten of the Institute for Advanced Study in Princeton, N.J., has shown that topological quantum field theory provides a natural way of expressing the new ideas about knots. This advance, in turn, has allowed a beautiful generalization about the invariants of knots in more complicated three-dimensional spaces known as three-manifolds, in which space itself may contain holes and loops.
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. PMID:17995307
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.
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.
(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.
Causal structure in categorical quantum mechanics
NASA Astrophysics Data System (ADS)
Lal, Raymond Ashwin
Categorical quantum mechanics is a way of formalising the structural features of quantum theory using category theory. It uses compound systems as the primitive notion, which is formalised by using symmetric monoidal categories. This leads to an elegant formalism for describing quantum protocols such as quantum teleportation. In particular, categorical quantum mechanics provides a graphical calculus that exposes the information flow of such protocols in an intuitive way. However, the graphical calculus also reveals surprising features of these protocols; for example, in the quantum teleportation protocol, information appears to flow `backwards-in-time'. This leads to question of how causal structure can be described within categorical quantum mechanics, and how this might lead to insight regarding the structural compatibility between quantum theory and relativity. This thesis is concerned with the project of formalising causal structure in categorical quantum mechanics. We begin by studying an abstract view of Bell-type experiments, as described by `no-signalling boxes', and we show that under time-reversal no-signalling boxes generically become signalling. This conflicts with the underlying symmetry of relativistic causal structure. This leads us to consider the framework of categorical quantum mechanics from the perspective of relativistic causal structure. We derive the properties that a symmetric monoidal category must satisfy in order to describe systems in such a background causal structure. We use these properties to define a new type of category, and this provides a formal framework for describing protocols in spacetime. We explore this new structure, showing how it leads to an understanding of the counter-intuitive information flow of protocols in categorical quantum mechanics. We then find that the formal properties of our new structure are naturally related to axioms for reconstructing quantum theory, and we show how a reconstruction scheme based on
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. PMID:22042902
The Measurement Problem in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Ogawa, Shuzo
2001-02-01
Since the establishment of quantum mechanics in the 20s of this century, the controversial discussions 1 have ever continued about its basis, that is the measurement problem of quantum mechanics. Strangely those discussions are prevailed mainly in the circle of theoretical group, while the experimental physicists who are directly concerned with the measurement, indifferently to the discussion have performed their study works, showing firmly the validity of quantum theory. This curious affair seems to be stemmed from the situation that the discussions overlooked by basing on what quantum theoretic ground the experimental equipments are installed, its sure operations are examined and the obtained results are explained, etc. In this talk 2 we shall aim to make clear the relation between the experiment and the structure of quantum mechanics, and to present some epistemological considerations on the quantum mechanics.
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.
Neutron Interference Experiments and Quantum Measurement Theory
NASA Astrophysics Data System (ADS)
Namiko, M.; Otake, Y.; Soshi, H.
1987-03-01
Physical and epistemological implications of recent experiments on the neutron interference are discussed from the viewpoint of the Machida-Namiki theory of measurement in quantum mechanics, without resort to discussion on the number-phase uncertainty relation. The same idea is also applied to the neutrino oscillation problem.
Backlund Transformation in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Burt, Philip
1996-11-01
Solutions of nonlinear field equations with polynomial nonlin earities are well known(P.B.Burt,Quantum Mechanics and Nonlinear Waves,Harwood Academic,Chur,1981).These solutions have been used to describe spin zero systems with self interactions. General- izations to systmes of fermions and bosons with various inter- actions lend themselves to description of quantum field theories with proper normalization. No ultraviolet divergences occur in such theories. The solutions themselves represent weak Backlund transformation of the nonlinear field equations and the related Klein Gordonequation(C.Rogers and W.F.Ames,Nonlinear Boundary Value Problems in Science and Engineering, Academic Press,New York,1989).
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.
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
Supersymmetry in quantum mechanics
Lahiri, A. ); Roy, P.K. ); Bagghi, B. )
1990-04-20
A pedagogical review on supersymmetry in quantum mechanics is presented which provides a comprehensive coverage of the subject. First, the key ingredients of the quantization of the systems with anticommuting variables are discussed. The supersymmetric Hamiltonian in quantum mechanics is then constructed by emphasizing the role of partner potentials and the superpotentials. The authors also make explicit the mathematical formulation of the Hamiltonian by considering in detail the N = 1 and N = 2 supersymmetric (quantum) mechanics. Supersymmetry is then discussed in the context of one-dimensional problems and the importance of the factorization method is highlighted. They treat in detail the technique of constructing a hierarchy of Hamiltonians employing the so-called 'shape-invariance' of potentials. To make transparent the relationship between supersymmetry and solvable potentials, they also solve several examples. They then go over the formulation of supersymmetry in radial problems, paying a special attention to the Coulomb and isotropic oscillator potentials. They show that the ladder operator technique may be suitable modified in higher dimensions for generating isospectral Hamiltonians. Next, the criteria for the breaking of supersymmetry is considered and their range of applicability is examined by suitably modifying he definition of Witten's index. Finally, the authors perform some numerical calculations for a class of potentials to show how a modified WKB approximation works in supersymmetric cases.
NASA Astrophysics Data System (ADS)
Fan, Hong-Yi; Lou, Sen-Yue
2015-07-01
Based on the operator Hermite polynomials method (OHPM), we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications. As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials. Project supported by the National Natural Science Foundation of China (Grant No. 11175113).
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.
PT-Symmetric Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2011-09-01
In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.
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
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.
Experimental status of quaternionic quantum mechanics
NASA Astrophysics Data System (ADS)
Brumby, S. P.; Joshi, G. C.
1996-05-01
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We review the only direct search for quaternionic quantum mechanics yet carried out and outline a recent proposal by the present authors to look for quaternionic effects in correlated multi-particle systems. We set out how such experiments might distinguish between the several quaternionic models proposed in the literature.
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)
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
Interpretation and Predictability of Quantum Mechanics and Quantum Cosmology
NASA Astrophysics Data System (ADS)
Wada, Sumio
A non-probabilistic interpretation of quantum mechanics asserts that we get a prediction only when a wave function has a peak. Taking this interpretation seriously, we discuss how to find a peak in the wave function of the universe, by using some minisuperspace models with homogeneous degrees of freedom and also a model with cosmological perturbations. Then we show how to recover our classical picture of the universe from the quantum theory, and comment on the physical meaning of the backreaction equation.
Massive supersymmetric quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Gut, M.; Scharf, G.
2005-08-01
We continue the study of the supersymmetric vector multiplet in a purely quantum framework. We obtain some new results which make the connection with the standard literature. First we construct the one-particle physical Hilbert space taking into account the (quantum) gauge structure of the model. Then we impose the condition of positivity for the scalar product only on the physical Hilbert space. Finally we obtain a full supersymmetric coupling which is gauge invariant in the supersymmetric sense in the first order of perturbation theory. By integrating out the Grassmann variables we get an interacting Lagrangian for a massive Yang-Mills theory related to ordinary gauge theory; however the number of ghost fields is doubled so we do not obtain the same ghost couplings as in the standard model Lagrangian.
Consistency of PT-symmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Brody, Dorje C.
2016-03-01
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully consistent with standard quantum mechanics. This follows from the surprising fact that the much-discussed metric operator on Hilbert space is not physically observable. In particular, for closed quantum systems in finite dimensions there is no statistical test that one can perform on the outcomes of measurements to determine whether the Hamiltonian is Hermitian in the conventional sense, or PT-symmetric—the two theories are indistinguishable. Nontrivial physical effects arising as a consequence of PT symmetry are expected to be observed, nevertheless, for open quantum systems with balanced gain and loss.
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].
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. PMID:26930454
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.
Testing foundations of quantum mechanics with photons
NASA Astrophysics Data System (ADS)
Shadbolt, Peter; Mathews, Jonathan C. F.; Laing, Anthony; O'Brien, Jeremy L.
2014-04-01
Quantum mechanics continues to predict effects at odds with a classical understanding of nature. Experiments with light at the single-photon level have historically been at the forefront of fundamental tests of quantum theory and the current developments in photonic technologies enable the exploration of new directions. Here we review recent photonic experiments to test two important themes in quantum mechanics: wave-particle duality, which is central to complementarity and delayed-choice experiments; and Bell nonlocality, where the latest theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different experiments.
Intrusion Detection with Quantum Mechanics: A Photonic Quantum Fence
Humble, Travis S; Bennink, Ryan S; Grice, Warren P; Owens, Israel J
2008-01-01
We describe the use of quantum-mechanically entangled photons for sensing intrusions across a physical perimeter. Our approach to intrusion detection uses the no-cloning principle of quantum information science as protection against an intruder s ability to spoof a sensor receiver using a classical intercept-resend attack. We explore the bounds on detection using quantum detection and estimation theory, and we experimentally demonstrate the underlying principle of entanglement-based detection using the visibility derived from polarization-correlation measurements.
An Axiomatic Basis for Quantum Mechanics
NASA Astrophysics Data System (ADS)
Cassinelli, Gianni; Lahti, Pekka
2016-06-01
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.
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.
NASA Astrophysics Data System (ADS)
Huang, Yi-Ping; Hermele, Michael
Some pyrochlore oxides realize novel dipolar-octupolar (DO) doublets on the sites of the pyrochlore lattice of corner-sharing tetrahedra. With magnetic field along the (111) direction, such systems can approximately be described as decoupled layers of a S =1/2 XYZ model on Kagome planes, with perpendicular magnetic field. A recent quantum Monte Carlo study found a zero temperature disordered phase in this model, dubbed quantum kagome ice, and proposed that it is a type of Z2 quantum spin liquid (J. Carrasquilla, Z. Hao and R. G. Melko, Nat. Comm., 6, 7421). We will describe an effective theory for this putative Z2 spin liquid, and present results on its symmetry fractionalization and resulting properties that may be tested in future numerical simulations. the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award # DE-SC0014415.
Quantum Mechanics Based Multiscale Modeling of Materials
NASA Astrophysics Data System (ADS)
Lu, Gang
2013-03-01
We present two quantum mechanics based multiscale approaches that can simulate extended defects in metals accurately and efficiently. The first approach (QCDFT) can treat multimillion atoms effectively via density functional theory (DFT). The method is an extension of the original quasicontinuum approach with DFT as its sole energetic formulation. The second method (QM/MM) has to do with quantum mechanics/molecular mechanics coupling based on the constrained density functional theory, which provides an exact framework for a self-consistent quantum mechanical embedding. Several important materials problems will be addressed using the multiscale modeling approaches, including hydrogen-assisted cracking in Al, magnetism-controlled dislocation properties in Fe and Si pipe diffusion along Al dislocation core. We acknowledge the support from the Office of Navel Research and the Army Research Office.
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<<
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.
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)
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.
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. PMID:27091170
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 theory of bilayer quantum Hall smectics
NASA Astrophysics Data System (ADS)
Papa, Emiliano; Schliemann, John; MacDonald, A. H.; Fisher, Matthew P.
2003-03-01
Mean-field theory predicts that bilayer quantum Hall systems at odd integer total filling factors can have stripe ground states, in which the top Landau level is occupied alternately by electrons in one of the two layers. We report on an analysis of the properties of these states based on a coupled-Luttinger-liquid description that is able to account for quantum fluctuations of charge-density and position along each stripe edge. The soft modes associated with the broken symmetries of the stripe state lead to an unusual coupled-Luttinger-liquid system with strongly enhanced low-temperature heat capacity and strongly suppressed low-energy tunneling density of states. We assess the importance of the intralayer and interlayer backscattering terms in the microscopic Hamiltonian, which are absent in the Luttinger liquid description, by employing a perturbative renormalization group approach which rescales time and length along but not transverse to the stripes. With interlayer backscattering interactions present the Luttinger-liquid states are unstable either to an incompressible striped state that has spontaneous interlayer phase coherence and a sizable charge gap even at relatively large layer separations, or to Wigner crystal states. Our quantitative estimates of the gaps produced by backscattering interactions are summarized in Fig. 11 by a schematic phase diagram intended to represent predicted experimental findings in very high mobility bilayer systems at dilution refrigerator temperatures as a function of layer separation and bilayer density balance. We predict that the bilayer will form incompressible isotropic interlayer phase-coherent states for small layer separations, say d⩽1.5l. At larger interlayer spacings, however, the bilayer will tend to form one of several different anisotropic states depending on the layer charge balance, which we parametrize by the fractional filling factor ν contributed by one of the two layers. For large charge imbalances (
Conformal quantum mechanics and holographic quench
NASA Astrophysics Data System (ADS)
Järvelä, Jarkko; Keränen, Ville; Keski-Vakkuri, Esko
2016-02-01
Recently, there has been much interest in holographic computations of two-point nonequilibrium Green functions from anti-de Sitter- (AdS-)Vaidya backgrounds. In the strongly coupled quantum field theory on the boundary, the dual interpretation of the background is an equilibration process called a holographic quench. The two-dimensional AdS-Vaidya spacetime is a special case, dual to conformal quantum mechanics. We study how the quench is incorporated into a Hamiltonian H +θ (t )Δ H and into correlation functions. With the help of recent work on correlation functions in conformal quantum mechanics, we first rederive the known two-point functions, and then compute nonequilibrium three- and four-point functions. We also compute the three-point function Witten diagram in the two-dimensional AdS-Vaidya background, and find agreement with the conformal quantum mechanics result.
Space and time from quantum mechanics
Chew, G.F.
1992-09-16
Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over collapse of the quantum-mechanical state vector when measurement is performed. Additionally, pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.
Space and time from quantum mechanics
NASA Astrophysics Data System (ADS)
Chew, G. F.
1992-09-01
Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over the collapse of the quantum-mechanical state vector when measurement is performed. Additionally, the pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as a coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.
Gravity and Quantum Theory Unified
NASA Astrophysics Data System (ADS)
Warren, Gary
Historic arguments against Aether theories disappear if the Aether is a 4D compressible hyperfluid in which each particle is our observation of a hypervortex, formed in and comprised of hyperfluid. Such Aether resolves ``spooky action at a distance'' which allows unification of gravity and quantum theory. Light is transverse waves in free space (away from hypervortices) in the hyperfluid. Their detailed behavior is why we observe a curved 3D Lorentz universe - a slice through the 4D hyperverse. Meanwhile, detailed hypervortex behavior, including faster-than-light longitudinal waves in and along hypervortices, explain quantum phenomena. A particular Lagrangian for such a hyperfluid regenerates Maxwell's equations, plus an equation for gravity, and an equation for electric charge. Couplings among these equations generate a discrete spectrum of hypervortex solutions that we observe as a spectrum of particles. Gravity results from gradients in the fluid density near vortices. Observed clock rates depend on fluid density, and vortex motion thus intertwining gravity, clock rates and quantum phenomena. Implied experiments will be discussed.
From Entropic Dynamics to Quantum Theory
Caticha, Ariel
2009-12-08
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the configuration space is a statistical manifold. The dynamics then follows from a principle of inference, the method of Maximum Entropy. The concept of time is introduced as a convenient way to keep track of change. The resulting theory resembles both Nelson's stochastic mechanics and general relativity. The statistical manifold is a dynamical entity: its geometry determines the evolution of the probability distribution which, in its turn, reacts back and determines the evolution of the geometry. There is a new quantum version of the equivalence principle: 'osmotic' mass equals inertial mass. Mass and the phase of the wave function are explained as features of purely statistical origin.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-01
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. PMID:26124252
Subjective and objective probabilities in quantum mechanics
Srednicki, Mark
2005-05-15
We discuss how the apparently objective probabilities predicted by quantum mechanics can be treated in the framework of Bayesian probability theory, in which all probabilities are subjective. Our results are in accord with earlier work by Caves, Fuchs, and Schack, but our approach and emphasis are different. We also discuss the problem of choosing a noninformative prior for a density matrix.
Collective field theory for quantum Hall states
NASA Astrophysics Data System (ADS)
Laskin, M.; Can, T.; Wiegmann, P.
2015-12-01
We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian field theory arise from the covariant ultraviolet regularization of the theory, which produces the gravitational anomaly. These corrections are described by a theory closely related to the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.
Modern Quantum Field Theory II - Proceeeings of the International Colloquium
NASA Astrophysics Data System (ADS)
Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.
1995-08-01
The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory
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
Phase space quantum mechanics - Direct
Nasiri, S.; Sobouti, Y.; Taati, F.
2006-09-15
Conventional approach to quantum mechanics in phase space (q,p), is to take the operator based quantum mechanics of Schroedinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of the formalism are demonstrated throughout the text.
Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
NASA Astrophysics Data System (ADS)
Grössing, Gerhard
2015-10-01
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...
Quantum field perturbation theory revisited
NASA Astrophysics Data System (ADS)
Matone, Marco
2016-03-01
Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in D dimension with exponential interactions, such as μDexp (α ϕ ). In particular, we use the relation exp (α δ/δ J (x ) )exp (-Z0[J ])=exp (-Z0[J +αx]) with J the external source, and αx(y )=α δ (y -x ). Such a shift is strictly related to the normal ordering of exp (α ϕ ) and to a scaling relation which follows by renormalizing μ . Next, we derive a new formulation of perturbation theory for the potentials V (ϕ )=λ/n ! :ϕn: , using the generating functional associated to :exp (α ϕ ):. The Δ (0 )-terms related to the normal ordering are absorbed at once. The functional derivatives with respect to J to compute the generating functional are replaced by ordinary derivatives with respect to auxiliary parameters. We focus on scalar theories, but the method is general and similar investigations extend to other theories.
Quantum mechanics from classical statistics
Wetterich, C.
2010-04-15
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.
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.
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.
Quantum Mechanics in Insulators
NASA Astrophysics Data System (ADS)
Aeppli, G.
2009-08-01
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 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).
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.
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.
Interpretation and predictability of quantum mechanics and quantum cosmology
Wada, S.
1988-06-01
A non-probabilistic interpretation of quantum mechanics asserts that the authors get a prediction only when a wave function has a peak. Taking this interpretation seriously, the authors discuss how to find a peak in the wave function of the universe, by using some minisuperspace models. With homogeneous degrees of freedom and also a model with cosmological perturbations. Then the authors show how to recover their classical picture of the universe from the quantum theory, and comment on the physical meaning of the backreaction equation.
Consecutive Measurements in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Glick, Jennifer R.; Adami, Christoph
The physics of quantum measurement still continues to puzzle with no resolution in sight between competing interpretations, in particular because no interpretation has so far produced predictions that would be falsifiable via experiment. Here we present an analysis of consecutive projective measurements performed on a quantum state using quantum information theory, where the entanglement between the quantum system and a measuring device is explicitly taken into account, and where the consecutive measurements increase the joint Hilbert space while the wavefunction of the joint system never collapses. Using this relative-state formalism we rederive well-known results for the pairwise correlation between any two measurement devices, but show that considering the joint as well as conditional entropy of three devices reveals a difference between the collapse and no-collapse pictures of quantum measurement that is experimentally testable. This research was funded by a Michigan State University Enrichment Fellowship.
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
Superstrings and the Foundations of Quantum Mechanics
NASA Astrophysics Data System (ADS)
't Hooft, Gerard
2014-05-01
It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell's powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.
Measurement and Fundamental Processes in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Jaeger, Gregg
2015-07-01
In the standard mathematical formulation of quantum mechanics, measurement is an additional, exceptional fundamental process rather than an often complex, but ordinary process which happens also to serve a particular epistemic function: during a measurement of one of its properties which is not already determined by a preceding measurement, a measured system, even if closed, is taken to change its state discontinuously rather than continuously as is usual. Many, including Bell, have been concerned about the fundamental role thus given to measurement in the foundation of the theory. Others, including the early Bohr and Schwinger, have suggested that quantum mechanics naturally incorporates the unavoidable uncontrollable disturbance of physical state that accompanies any local measurement without the need for an exceptional fundamental process or a special measurement theory. Disturbance is unanalyzable for Bohr, but for Schwinger it is due to physical interactions' being borne by fundamental particles having discrete properties and behavior which is beyond physical control. Here, Schwinger's approach is distinguished from more well known treatments of measurement, with the conclusion that, unlike most, it does not suffer under Bell's critique of quantum measurement. Finally, Schwinger's critique of measurement theory is explicated as a call for a deeper investigation of measurement processes that requires the use of a theory of quantum fields.
Emergent quantum mechanics without wavefunctions
NASA Astrophysics Data System (ADS)
Mesa Pascasio, J.; Fussy, S.; Schwabl, H.; Grössing, G.
2016-03-01
We present our model of an Emergent Quantum Mechanics which can be characterized by “realism without pre-determination”. This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like “surreal” trajectories, which are obtained classically, i.e. without the use of any quantum mechanical tool such as wavefunctions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantum mechanics in a high-low intesity double slit scenario gives rise to the “quantum sweeper effect” with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques.
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.
Uncertainty relation revisited from quantum estimation theory
Watanabe, Yu; Sagawa, Takahiro; Ueda, Masahito
2011-10-15
We use quantum estimation theory to formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two noncommuting observables satisfy Heisenberg-type uncertainty relation, find the achievable bound, and propose a strategy to achieve it.
Multiscale quantum simulation of quantum field theory using wavelets
NASA Astrophysics Data System (ADS)
Brennen, Gavin K.; Rohde, Peter; Sanders, Barry C.; Singh, Sukhwinder
2015-09-01
A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis—a multiscale description of the theory. Since wavelet families can be constructed to have compact support at all resolutions, this encoding allows for quantum simulations to create particle excitations which are local at some chosen scale and provides a natural way to associate observables in the theory to finite-resolution detectors.
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
Three Attempts at Two Axioms for Quantum Mechanics
NASA Astrophysics Data System (ADS)
Rohrlich, Daniel
The axioms of nonrelativistic quantum mechanics lack clear physical meaning. In particular, they say nothing about nonlocality. Yet quantum mechanics is not only nonlocal, it is twice nonlocal: there are nonlocal quantum correlations, and there is the Aharonov-Bohm effect, which implies that an electric or magnetic field here may act on an electron there. Can we invert the logical hierarchy? That is, can we adopt nonlocality as an axiom for quantum mechanics and derive quantum mechanics from this axiom and an additional axiom of causality? Three versions of these two axioms lead to three different theories, characterized by "maximal nonlocal correlations", "jamming" and "modular energy". Where is quantum mechanics in these theories?
Conservation of information and the foundations of quantum mechanics
NASA Astrophysics Data System (ADS)
Chiribella, Giulio; Scandolo, Carlo Maria
2015-05-01
We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory [1, 2]. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems.
Quantum Mechanics and Narratability
NASA Astrophysics Data System (ADS)
Myrvold, Wayne C.
2016-05-01
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.
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.
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.
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 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.
Reconstruction and Reinvention in Quantum Theory
NASA Astrophysics Data System (ADS)
Dickson, Michael
2015-10-01
I consider the fact that there are a number of interesting ways to `reconstruct' quantum theory, and suggest that, very broadly speaking, a form of `instrumentalism' makes good sense of the situation. This view runs against some common wisdom, which dismisses instrumentalism as `cheap'. In contrast, I consider how an instrumentalist might think about the reconstruction theorems, and, having made a distinction between `reconstructing' quantum theory and `reinventing' quantum theory, I suggest that there is an adequate (not `cheap') instrumentalist approach to the theory (and to these theorems) that invokes both.
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
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.
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.
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.
The geometrical structure of quantum theory as a natural generalization of information geometry
NASA Astrophysics Data System (ADS)
Reginatto, Marcel
2015-01-01
Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.
Beyond relativity and quantum mechanics: space physics
NASA Astrophysics Data System (ADS)
Lindner, Henry H.
2011-09-01
Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.
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.
Emergence of quantum mechanics from a sub-quantum statistical mechanics
NASA Astrophysics Data System (ADS)
Grössing, Gerhard
2014-07-01
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wavefunctions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" non-locality.
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…
Interpretation neutrality in the classical domain of quantum theory
NASA Astrophysics Data System (ADS)
Rosaler, Joshua
2016-02-01
I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie-Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified picture that treats reduction as a matter of simply taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest's Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest's Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity.
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.
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 |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(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 |psi(I)> to |psi(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. PMID:17358747
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.
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
Interpreting Quantum Mechanics according to a Pragmatist Approach
NASA Astrophysics Data System (ADS)
Bächtold, Manuel
2008-09-01
The aim of this paper is to show that quantum mechanics can be interpreted according to a pragmatist approach. The latter consists, first, in giving a pragmatic definition to each term used in microphysics, second, in making explicit the functions any theory must fulfil so as to ensure the success of the research activity in microphysics, and third, in showing that quantum mechanics is the only theory which fulfils exactly these functions.
Asymptotic theory of quantum statistical inference
NASA Astrophysics Data System (ADS)
Hayashi, Masahito
Part I: Hypothesis Testing: Introduction to Part I -- Strong Converse and Stein's lemma in quantum hypothesis testing/Tomohiro Ogawa and Hiroshi Nagaoka -- The proper formula for relative entropy and its asymptotics in quantum probability/Fumio Hiai and Dénes Petz -- Strong Converse theorems in Quantum Information Theory/Hiroshi Nagaoka -- Asymptotics of quantum relative entropy from a representation theoretical viewpoint/Masahito Hayashi -- Quantum birthday problems: geometrical aspects of Quantum Random Coding/Akio Fujiwara -- Part II: Quantum Cramèr-Rao Bound in Mixed States Model: Introduction to Part II -- A new approach to Cramèr-Rao Bounds for quantum state estimation/Hiroshi Nagaoka -- On Fisher information of Quantum Statistical Models/Hiroshi Nagaoka -- On the parameter estimation problem for Quantum Statistical Models/Hiroshi Nagaoka -- A generalization of the simultaneous diagonalization of Hermitian matrices and its relation to Quantum Estimation Theory/Hiroshi Nagaoka -- A linear programming approach to Attainable Cramèr-Rao Type Bounds/Masahito Hayashi -- Statistical model with measurement degree of freedom and quantum physics/Masahito Hayashi and Keiji Matsumoto -- Asymptotic Quantum Theory for the Thermal States Family/Masahito Hayashi -- State estimation for large ensembles/Richard D. Gill and Serge Massar -- Part III: Quantum Cramèr-Rao Bound in Pure States Model: Introduction to Part III-- Quantum Fisher Metric and estimation for Pure State Models/Akio Fujiwara and Hiroshi Nagaoka -- Geometry of Quantum Estimation Theory/Akio Fujiwara -- An estimation theoretical characterization of coherent states/Akio Fujiwara and Hiroshi Nagaoka -- A geometrical approach to Quantum Estimation Theory/Keiji Matsumoto -- Part IV: Group symmetric approach to Pure States Model: Introduction to Part IV -- Optimal extraction of information from finite quantum ensembles/Serge Massar and Sandu Popescu -- Asymptotic Estimation Theory for a Finite-Dimensional Pure
Cloning in nonlinear Hamiltonian quantum and hybrid mechanics
NASA Astrophysics Data System (ADS)
Arsenović, D.; Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.
2014-10-01
The possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is then demonstrated that the addition of the cloning machine, treated as a quantum or as a classical system, makes cloning possible by nonlinear Hamiltonian evolution. However, a special type of quantum-classical theory, known as the mean-field Hamiltonian hybrid mechanics, does not admit cloning by natural evolution. The latter represents an example of a theory where it appears to be possible to communicate between two quantum systems at superluminal speed, but at the same time it is impossible to clone quantum pure states.
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.
Quantum Theory of Laser Amplifiers.
NASA Astrophysics Data System (ADS)
Mander, Gillian Linda
Available from UMI in association with The British Library. Requires signed TDF. We calculate the input-output characteristics of a below threshold laser amplifier. Expressions are derived for the output second- and fourth-order spectral and temporal correlation functions in terms of the corresponding input quantities, and for the photocount first and second factorial moments for both homodyne and direct detection. The general results are applied to several cases of practical interest, including specific non-classical input states. We show that a maximum of twofold amplification is permitted if squeezing in the input is to survive at the output. Similarly, for preservation of photon antibunching in amplification we show that only very small gains are allowed. The model treated here provides a detailed example of the amplifier noise limitations imposed by quantum mechanics. In particular, we show that minimum noise occurs in a cavity that is asymmetric with respect to the mirror reflectivities. The latter part of this work treats the above threshold laser amplifier. The laser output is back-scattered from a moving target to provide a weak Doppler-shifted signal which re-enters the laser cavity and is amplified. We show that the three-level atomic lasing medium is equivalent to a two-level medium pumped by an inverted bath. We use the methods of quantum statistical analysis to obtain time -evolution equations for the c-number amplitudes of the laser and signal fields. We show that the results may be applied to the below threshold regime for appropriate values of the pump parameter. By considering the amplitude differential gain we show explicitly that the behaviour of the laser around threshold is characteristic of a second -order phase transition. We calculate the output intensity gain appropriate to a heterodyne detection process, and find good agreement between the predicted gain profiles and measured data for both carbon dioxide and argon-ion lasers.
Hermeneutics, Underdetermination and Quantum Mechanics.
ERIC Educational Resources Information Center
Cushing, James T.
1995-01-01
States that the existence of an essential underdetermination in the interpretation of the formalism of quantum mechanics, in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics, legitimizes the analysis of hermeneutics in science education. (LZ)
Renormalization group in quantum mechanics
Polony, J.
1996-12-01
The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright {copyright} 1996 Academic Press, Inc.
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.
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.
NASA Astrophysics Data System (ADS)
Oriols, X.
2016-03-01
Exact predictions for most quantum systems are computationally inaccessible. This is the so-called many body problem, which is present in most common interpretations of quantum mechanics. Therefore, predictions of natural quantum phenomena have to rely on some approximations (assumptions or simplifications). In the literature, there are different types of approximations, ranging from those whose justification is basically based on theoretical developments to those whose justification lies on the agreement with experiments. This last type of approximations can convert a quantum theory into an “unfalsifiable” quantum theory, true by construction. On the practical side, converting some part of a quantum theory into an “unfalsifiable” one ensures a successful modeling (i.e. compatible with experiments) for quantum engineering applications. An example of including irreversibility and dissipation in the Bohmian modeling of open systems is presented. On the ontological level, however, the present-day foundational problems related to controversial quantum phenomena have to avoid (if possible) being contaminated by the unfalsifiability originated from the many body problem. An original attempt to show how the Bohmian theory itself (minimizing the role of many body approximations) explains the transitions from a microscopic quantum system towards a macroscopic classical one is presented.
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)
Quantum Mechanics and the Role of Time:. are Quantum Systems Markovian?
NASA Astrophysics Data System (ADS)
Durt, Thomas
2013-06-01
The predictions of the Quantum Theory have been verified so far with astonishingly high accuracy. Despite of its impressive successes, the theory still presents mysterious features such as the border line between the classical and quantum world, or the deep nature of quantum nonlocality. These open questions motivated in the past several proposals of alternative and/or generalized approaches. We shall discuss in the present paper alternative theories that can be infered from a reconsideration of the status of time in quantum mechanics. Roughly speaking, quantum mechanics is usually formulated as a memory free (Markovian) theory at a fundamental level, but alternative, nonMarkovian, formulations are possible, and some of them can be tested in the laboratory. In our paper we shall give a survey of these alternative proposals, describe related experiments that were realized in the past and also formulate new experimental proposals.
Quantum theory - essential from cosmos to consciousness
NASA Astrophysics Data System (ADS)
Görnitz, T.
2010-06-01
Quantum theory is the most successful physical theory. About one third of the gross national product in the developed countries results from its applications. But very often quantum theory is still declared as "crazy" or "not understandable". However, quantum theory has a clear mathematical structure that expresses well-known experiences from every day life: A whole is often more than the sum of its parts, and not only the facts also the possibilities can act. If such structures become important then the consequences differ from the models of classical physics which rests on the fundamental differences between matter and motion, material and force, localization and extension, fullness and emptiness. From quantum theory one can learn that all these differences are useful in many cases but are not fundamental. There are equivalences between them, and these can be extended even to the equivalence between matter, energy and abstract quantum information. It is cosmological funded and is denominated as "Protyposis" to avoid the connotation of information and meaning. Protyposis enables a fundamentally new understanding of matter which can be seen as "formed", "condensed" or "designed" abstract quantum information. One result of the Protyposis is a derivation of Einstein's equations from the abstract quantum information. Another consequence is the ontological reality of the mind and its connection to a brain which can be explained without any dualistic model.
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.
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.
The decoupling approach to quantum information theory
NASA Astrophysics Data System (ADS)
Dupuis, Frédéric
2010-04-01
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and have as corollaries entanglement-assisted and unassisted asymptotic coding theorems. The entanglement-assisted asymptotic versions can, in both cases, be considered as quantum versions of the best coding theorems known for the classical versions of these problems. The last chapter deals with a purely quantum phenomenon called locking. We demonstrate that it is possible to encode a classical message into a quantum state such that, by removing a subsystem of logarithmic size with respect to its total size, no measurement can have significant correlations with the message. The message is therefore "locked" by a logarithmic-size key. This thesis presents the first locking protocol for which the success criterion is that the trace distance between the joint distribution of the message and the measurement result and the product of their marginals be sufficiently small.
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.
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
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2010-04-01
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.
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.
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
Quantum mechanics of black holes.
Witten, Edward
2012-08-01
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. PMID:22859480
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. PMID:24482329
Quantum mechanics without the projection postulate
NASA Astrophysics Data System (ADS)
Bub, Jeffrey
1992-05-01
I show that the quantum state ω can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with ω and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of “determinate” quantities (selected by ω and the boundary conditions) can have values. The probabilities defined by ω (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate.
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.
Three-space from quantum mechanics
Chew, G.F.; Stapp, H.P.
1988-08-01
We formulate a discrete quantum-mechanical precursor to spacetime geometry. The objective is to provide the foundation for a quantum mechanics that is rooted exclusively in quantum-mechanical concepts, with all classical features, including the three-dimensional spatial continuum, emerging dynamically.
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
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
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. PMID:21405150
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.
Hermeneutics, underdetermination and quantum mechanics
NASA Astrophysics Data System (ADS)
Cushing, James T.
1995-04-01
There exists an essential underdetermination in the interpretation of the formalism of quantum mechanics and this extends even to the question of whether or not physical phenomena at the most fundamental level are irreducibly and ineliminably indeterministic or absolutely deterministic. This is true in spite of the widespread belief that logic and empirical considerations alone demand an indeterministic world view in physics. This lends support to Martin Eger's analysis of a role for hermeneutics in science education.
Quantum mechanics and heat conduction
Bajpai, S.D. ); Mishra, S. )
1991-08-01
One of the fundamental problems in quantum mechanics is to find a solution of Schroedinger equation for different forms of potentials. The object of this paper is to obtain a series solution of a particular one-dimensional, time-dependent Schroedinger equation involving Hermite polynomials. The authors also show a relationship of their particular one-dimensional, time-dependent Schroedinger equation with an equation of heat conduction.
Complementarity in Categorical Quantum Mechanics
NASA Astrophysics Data System (ADS)
Heunen, Chris
2012-07-01
We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a `point-free' definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.