Emergence of classical theories from quantum mechanics

International Nuclear Information System (INIS)

Hájícek, P

2012-01-01

Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's 'first kind of dynamics', and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.

Classical mechanics systems of particles and Hamiltonian dynamics

CERN Document Server

Greiner, Walter

2010-01-01

This textbook Classical Mechanics provides a complete survey on all aspects of classical mechanics in theoretical physics. An enormous number of worked examples and problems show students how to apply the abstract principles to realistic problems. The textbook covers Newtonian mechanics in rotating coordinate systems, mechanics of systems of point particles, vibrating systems and mechanics of rigid bodies. It thoroughly introduces and explains the Lagrange and Hamilton equations and the Hamilton-Jacobi theory. A large section on nonlinear dynamics and chaotic behavior of systems takes Classical Mechanics to newest development in physics. The new edition is completely revised and updated. New exercises and new sections in canonical transformation and Hamiltonian theory have been added.

The Dirac equation in classical statistical mechanics

International Nuclear Information System (INIS)

Ord, G.N.

2002-01-01

The Dirac equation, usually obtained by 'quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic continuation, making the model 'self-quantizing'. This provides a new context for the Dirac equation, distinct from its usual context in relativistic quantum mechanics

Classical- and quantum mechanical Coulomb scattering

International Nuclear Information System (INIS)

Gratzl, W.

1987-01-01

Because in textbooks the quantum mechanical Coulomb scattering is either ignored or treated unsatisfactory, the present work attempts to present a physically plausible, mathematically correct but elementary treatment in a way that it can be used in textbooks and lectures on quantum mechanics. Coulomb scattering is derived as a limiting case of a screened Coulomb potential (finite range) within a time dependent quantum scattering theory. The difference in the asymptotic conditions for potentials of finite versus infinite range leads back to the classical Coulomb scattering. In the classical framework many concepts of the quantum theory can be introduced and are useful in an intuitive understanding of the quantum theory. The differences between classical and quantum scattering theory are likewise useful for didactic purposes. (qui)

Bertrand's theorem and virial theorem in fractional classical mechanics

Science.gov (United States)

Yu, Rui-Yan; Wang, Towe

2017-09-01

Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

Quantum Mechanics as Classical Physics

OpenAIRE

Sebens, CT

2015-01-01

Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.

Classical limit for quantum mechanical energy eigenfunctions

International Nuclear Information System (INIS)

Sen, D.; Sengupta, S.

2004-01-01

The classical limit problem is discussed for the quantum mechanical energy eigenfunctions using the Wentzel-Kramers-Brillouin approximation, free from the problem at the classical turning points. A proper perspective of the whole issue is sought to appreciate the significance of the discussion. It is observed that for bound states in arbitrary potential, appropriate limiting condition is definable in terms of a dimensionless classical limit parameter leading smoothly to all observable classical results. Most important results are the emergence of classical phase space, keeping the observable distribution functions non-zero only within the so-called classical region at the limit point and resolution of some well-known paradoxes. (author)

Classical and quantum mechanics of non-abelian gauge fields

International Nuclear Information System (INIS)

Savvidy, G.K.

1984-01-01

Classical and quantum mechanics of non-abelian gauge fields are investigated both with and without spontaneous symmetry breaking. The fundamental subsystem (FS) of Yang-Mills classical mechanics (YMCM) is considered. It is shown to be a Kolmogorov K-system, and hence to have strong statistical properties. Integrable systems are also found, to which in terms of KAM theory Yang-Mills-Higgs classical mechanics (YMHCM) is close. Quantum-mechanical properties of the YM system and their relation to the problem of confinement are discussed. (orig.)

The Weyl representation in classical and quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Almeida, Alfredo M.O. de [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Paris-6 Univ., 75 (France). Inst. Henri Poincare

1996-09-01

The position representation of the evolution operator in quantum mechanics is analogous to the generating function formalism of classical mechanics. Similarly, the Weyl representation is connected to new generating functions described by chords and centres. Both classical and quantal theories rely on the group of translations and reflections through a point in phase space. The composition of small time evolutions leads to new versions of the classical variational principle and to path integrals in quantum mechanics. The restriction of the motion to the energy shell in classical mechanics is the basis for a full review of the semiclassical Wigner function and the theory of scars of periodic orbits. By embedding the theory of scars in a fully uniform approximation, it is shown that the region in which the scar contribution is oscillatory is separated from a decaying region by a caustic that touches the shell along the periodic orbit and widens quadratically within the energy shell. (author). 56 refs., 35 figs.

The Weyl representation in classical and quantum mechanics

International Nuclear Information System (INIS)

Almeida, Alfredo M.O. de; Paris-6 Univ., 75

1996-09-01

The position representation of the evolution operator in quantum mechanics is analogous to the generating function formalism of classical mechanics. Similarly, the Weyl representation is connected to new generating functions described by chords and centres. Both classical and quantal theories rely on the group of translations and reflections through a point in phase space. The composition of small time evolutions leads to new versions of the classical variational principle and to path integrals in quantum mechanics. The restriction of the motion to the energy shell in classical mechanics is the basis for a full review of the semiclassical Wigner function and the theory of scars of periodic orbits. By embedding the theory of scars in a fully uniform approximation, it is shown that the region in which the scar contribution is oscillatory is separated from a decaying region by a caustic that touches the shell along the periodic orbit and widens quadratically within the energy shell. (author). 56 refs., 35 figs

Analogies between classical statistical mechanics and quantum mechanics

International Nuclear Information System (INIS)

Uehara, M.

1986-01-01

Some analogies between nonequilibrium classical statistical mechanics and quantum mechanics, at the level of the Liouville equation and at the kinetic level, are commented on. A theorem, related to the Vlasov equation applied to a plasma, is proved. The theorem presents an analogy with Ehrenfest's theorem of quantum mechanics. An analogy between the plasma kinetic theory and Bohm's quantum theory with 'hidden variables' is also shown. (Author) [pt

Classical Mechanics and Symplectic Integration

DEFF Research Database (Denmark)

Nordkvist, Nikolaj; Hjorth, Poul G.

2005-01-01

Content: Classical mechanics: Calculus of variations, Lagrange’s equations, Symmetries and Noether’s theorem, Hamilton’s equations, cannonical transformations, integrable systems, pertubation theory. Symplectic integration: Numerical integrators, symplectic integrators, main theorem on symplectic...

The Wigner representation of classical mechanics, quantization and classical limit

Energy Technology Data Exchange (ETDEWEB)

Bolivar, A.O. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

2001-08-01

Starting from the Liouvillian formulation of classical physics it is possible by means of a Fourier transform to introduce the Wigner representation and to derive an operator structure to classical mechanisms. The importance of this new representation lies on the fact that it turns out to be suitable route to establish a general method of quantization directly from the equations of motion without alluding to the existence of Hamiltonian and Lagrangian functions. Following this approach we quantize only the motion of a Browian particle with non-linear friction in the Markovian approximation - the thermal bath may be quantum or classical -, thus when the bath is classically described we obtain a master equation which reduces to Caldeira-Legget equation for the linear friction case, and when the reservoir is quantum we get an equation reducing to the one found by Caldeira et al. By neglecting the environmental influence we show that the system can be approximately described by equations of motion in terms of wave function, such as the Schrodinger-Langevin equation and equations of the Caldirola-Kanai type. Finally to make the present study self-consistent we evaluate the classical limit of these dynamical equations employing a new classical limiting method h/2{pi} {yields} 0. (author)

The Wigner representation of classical mechanics, quantization and classical limit

International Nuclear Information System (INIS)

Bolivar, A.O.

2001-08-01

Starting from the Liouvillian formulation of classical physics it is possible by means of a Fourier transform to introduce the Wigner representation and to derive an operator structure to classical mechanisms. The importance of this new representation lies on the fact that it turns out to be suitable route to establish a general method of quantization directly from the equations of motion without alluding to the existence of Hamiltonian and Lagrangian functions. Following this approach we quantize only the motion of a Browian particle with non-linear friction in the Markovian approximation - the thermal bath may be quantum or classical -, thus when the bath is classically described we obtain a master equation which reduces to Caldeira-Legget equation for the linear friction case, and when the reservoir is quantum we get an equation reducing to the one found by Caldeira et al. By neglecting the environmental influence we show that the system can be approximately described by equations of motion in terms of wave function, such as the Schrodinger-Langevin equation and equations of the Caldirola-Kanai type. Finally to make the present study self-consistent we evaluate the classical limit of these dynamical equations employing a new classical limiting method h/2π → 0. (author)

Mechanical Systems, Classical Models

CERN Document Server

Teodorescu, Petre P

2009-01-01

This third volume completes the Work Mechanical Systems, Classical Models. The first two volumes dealt with particle dynamics and with discrete and continuous mechanical systems. The present volume studies analytical mechanics. Topics like Lagrangian and Hamiltonian mechanics, the Hamilton-Jacobi method, and a study of systems with separate variables are thoroughly discussed. Also included are variational principles and canonical transformations, integral invariants and exterior differential calculus, and particular attention is given to non-holonomic mechanical systems. The author explains in detail all important aspects of the science of mechanics, regarded as a natural science, and shows how they are useful in understanding important natural phenomena and solving problems of interest in applied and engineering sciences. Professor Teodorescu has spent more than fifty years as a Professor of Mechanics at the University of Bucharest and this book relies on the extensive literature on the subject as well as th...

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

Science.gov (United States)

Budiyono, Agung; Rohrlich, Daniel

2017-11-03

Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.

Classical particle limit of non-relativistic quantum mechanics

International Nuclear Information System (INIS)

Zucchini, R.

1984-01-01

We study the classical particle limit of non-relativistic quantum mechanics. We show that the unitary group describing the evolution of the quantum fluctuation around any classical phase orbit has a classical limit as h → 0 in the strong operator topology for a very large class of time independent scalar and vector potentials, which in practice covers all physically interesting cases. We also show that the mean values of the quantum mechanical position and velocity operators on suitable states, obtained by time evolution of the product of a Weyl operator centred around the large coordinates and momenta and a fixed n-independent wave function, converge to the solution of the classical equations with initial data as h → 0 for a broad class of repulsive interactions

Supersymmetric classical mechanics: free case

Energy Technology Data Exchange (ETDEWEB)

Rodrigues, R. de Lima [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Paraiba Univ., Cajazeiras, PB (Brazil). Dept. de Ciencias Exatas e da Natureza]. E-mail: rafael@cfp.ufpb.br; Almeida, W. Pires de [Paraiba Univ., Cajazeiras, PB (Brazil). Dept. de Ciencias Exatas e da Natureza; Fonseca Neto, I. [Paraiba Univ., Campina Grande, PB (Brazil). Dept. de Fisica

2001-06-01

We present a review work on Supersymmetric Classical Mechanics in the context of a Lagrangian formalism, with N = 1-supersymmetry. We show that the N = 1 supersymmetry does not allow the introduction of a potencial energy term depending on a single commuting supercoordinate, {phi}(t;{theta}). (author)

Quantum and classical mechanics in the phase space representation

International Nuclear Information System (INIS)

Shirokov, Yu.M.

1979-01-01

The theory of the hamiltonian mechanical systems has been formulated in terms of only such physical and mathematical concepts which are meaningful in both mechanics. For instance the observables in both mechanics are represented as c-number functions of coordinates and momenta. The operations of the usual multiplication of observables as well as Poisson bracket (also treated as a sort of multiplication) are singled out as separate objects which can possess their own structure including h-dependence. This leads to the conclusion that the only primary distinction between classical and quantum mechanics is reduced to the distinction in the form of the algebraic identity for the multiplication operations. All other distinctions are proved to be of the secondary origin. The formalism developed in the paper is especially useful for quantizations and for the transitions (including partial ones) to the classical limits. The transitions in both directions are transparent and accessible for analysis for any quantity at any step of calculations. The unified quantum-classical scattering theory is constructed. The integral quantum Lippman-Schwinder type equation is derived where the free solution term is replaced by the solution of the corresponding classical problem. The iteration of this equation gives the quantum corrections to the classical solution

Perturbation theory via Feynman diagrams in classical mechanics

OpenAIRE

Penco, R.; Mauro, D.

2006-01-01

In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like path integrals and generating functionals.

Teaching Classical Mechanics Using Smartphones

Science.gov (United States)

Chevrier, Joel; Madani, Laya; Ledenmat, Simon; Bsiesy, Ahmad

2013-01-01

A number of articles published in this column have dealt with topics in classical mechanics. This note describes some additional examples employing a smartphone and the new software iMecaProf. Steve Jobs presented the iPhone as "perfect for gaming." Thanks to its microsensors connected in real time to the numerical world, physics…

Teaching classical mechanics using smartphones

Science.gov (United States)

Chevrier, Joel; Madani, Laya; Ledenmat, Simon; Bsiesy, Ahmad

2013-09-01

A number of articles published in this column have dealt with topics in classical mechanics. This note describes some additional examples employing a smartphone and the new software iMecaProf.4 Steve Jobs presented the iPhone as "perfect for gaming."5 Thanks to its microsensors connected in real time to the numerical world, physics teachers could add that smartphones are "perfect for teaching science." The software iMecaProf displays in real time the measured data on a screen. The visual representation is built upon the formalism of classical mechanics. iMecaProf receives data 100 times a second from iPhone sensors through a Wi-Fi connection using the application Sensor Data.6 Data are the three components of the acceleration vector in the smartphone frame and smartphone's orientation through three angles (yaw, pitch, and roll). For circular motion (uniform or not), iMecaProf uses independent measurements of the rotation angle θ, the angular speed dθ/dt, and the angular acceleration d2θ/dt2.

A wave equation interpolating between classical and quantum mechanics

Science.gov (United States)

Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O.

2015-10-01

We derive a ‘master’ wave equation for a family of complex-valued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the Hamilton-Jacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of many-body theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in non-relativistic and relativistic quantum field theory.

A derivation of the classical limit of quantum mechanics and quantum electrodynamics

International Nuclear Information System (INIS)

Ajanapon, P.

1985-01-01

Instead of regarding the classical limit as the h → 0, an alternative view based on the physical interpretation of the elements of the density matrix is proposed. According to this alternative view, taking the classical limit corresponds to taking the diagonal elements and ignoring the off-diagonal elements of the density matrix. As illustrations of this alternative approach, the classical limits of quantum mechanics and quantum electrodynamics are derived. The derivation is carried out in two stages. First, the statistical classical limit is derived. Then with an appropriate initial condition, the deterministic classical limit is obtained. In the case of quantum mechanics, it is found that the classical limit of Schroedinger's wave mechanics is at best statistical, i.e., Schroedinger's wave mechanics does not reduce to deterministic (Hamilton's or Newton's) classical mechanics. In order to obtain the latter, it is necessary to start out initially with a mixture at the level of statistical quantum mechanics. The derivation hinges on the use of the Feynman path integral rigorously defined with the aid of nonstandard analysis. Nonstandard analysis is also applied to extend the method to the case of quantum electrodynamics. The fundamental decoupling problem arising form the use of Grassmann variables is circumvented by the use of c-number electron fields, but antisymmetrically tagged. The basic classical (deterministic) field equations are obtained in the classical limit with appropriate initial conditions. The result raises the question as to what the corresponding classical field equations obtained in the classical limit from the renormalized Lagrangian containing infinite counterterms really mean

Discrete gradients in discrete classical mechanics

International Nuclear Information System (INIS)

Renna, L.

1987-01-01

A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

New mechanism for bubble nucleation: Classical transitions

International Nuclear Information System (INIS)

Easther, Richard; Giblin, John T. Jr; Hui Lam; Lim, Eugene A.

2009-01-01

Given a scalar field with metastable minima, bubbles nucleate quantum mechanically. When bubbles collide, energy stored in the bubble walls is converted into kinetic energy of the field. This kinetic energy can facilitate the classical nucleation of new bubbles in minima that lie below those of the 'parent' bubbles. This process is efficient and classical, and changes the dynamics and statistics of bubble formation in models with multiple vacua, relative to that derived from quantum tunneling.

On possibility of agreement of quantum mechanics with classical probability theory

International Nuclear Information System (INIS)

Slavnov, D.A.

2006-01-01

Paper describes a scheme to carry out a construction of the quantum mechanics where the quantum system is assumed to be a pattern of the open classical subsystems. It enables to make use both of the formal classical logic and the classical probability theory in the quantum mechanics. On the other hand, in terms of the mentioned approach one manages to ensure complete reconstruction of the quantum mechanics standard mathematical tool specifying its application limits. The problem dealing with the quantum state reduction is scrutinized [ru

Unified treatment of the classical and quantum mechanics

International Nuclear Information System (INIS)

Shirokov, Yu.M.

1979-01-01

Classical and Quantum Mechanics are unified in the sense that almost all axioms of both mechanics are identical. The only distinction is the explicit form of one algebraic identity. The unified theory is applied to scattering problem. (Z.M.)

On quantization, the generalised Schroedinger equation and classical mechanics

International Nuclear Information System (INIS)

Jones, K.R.W.

1991-01-01

A ψ-dependent linear functional operator, was defined, which solves the problem of quantization in non-relativistic quantum mechanics. Weyl ordering is implemented automatically and permits derivation of many of the quantum to classical correspondences. The parameter λ presents a natural C ∞ deformation of the dynamical structure of quantum mechanics via a non-linear integro-differential 'Generalised Schroedinger Equation', admitting an infinite family of soliton solutions. All these solutions are presented and it is shown that this equation gives an exact dynamic and energetic reproduction of classical mechanics with the correct measurement theoretic limit. 23 refs

Principles of classical statistical mechanics: A perspective from the notion of complementarity

International Nuclear Information System (INIS)

Velazquez Abad, Luisberis

2012-01-01

Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the complementarity between two descriptions that are unified in thermodynamics: (i) the parametrization of the system macrostate in terms of mechanical macroscopic observablesI=(I i ), and (ii) the dynamical description that explains the evolution of a system towards the thermodynamic equilibrium. As expected, such a complementarity is related to the uncertainty relations of classical statistical mechanics ΔI i Δη i ≥k. Here, k is the Boltzmann constant, η i =∂S(I|θ)/∂I i are the restituting generalized forces derived from the entropy S(I|θ) of a closed system, which is found in an equilibrium situation driven by certain control parameters θ=(θ α ). These arguments constitute the central ingredients of a reformulation of classical statistical mechanics from the notion of complementarity. In this new framework, Einstein postulate of classical fluctuation theory dp(I|θ)∼exp[S(I|θ)/k]dI appears as the correspondence principle between classical statistical mechanics and thermodynamics in the limit k→0, while the existence of uncertainty relations can be associated with the non-commuting character of certain operators. - Highlights: ► There exists a direct analogy between quantum and classical statistical mechanics. ► Statistical form of Le Chatellier principle leads to the uncertainty principle. ► Einstein postulate is simply the correspondence principle. ► Complementary quantities are associated with non-commuting operators.

Classical mechanics from Newton to Einstein : a modern introduction

CERN Document Server

McCall, Martin

2011-01-01

This new edition of Classical Mechanics, aimed at undergraduate physics and engineering students, presents in a user-friendly style an authoritative approach to the complementary subjects of classical mechanics and relativity.   The text starts with a careful look at Newton's Laws, before applying them in one dimension to oscillations and collisions. More advanced applications - including gravitational orbits and rigid body dynamics - are discussed after the limitations of Newton's inertial frames have been highlighted through an exposition of Einstein's Special Relativity. Examples gi

Comparative role of potential structure in classical, semiclassical, and quantum mechanics

International Nuclear Information System (INIS)

Judson, R.S.; Shi, S.; Rabitz, H.

1989-01-01

The corresponding effects of features in the potential on classical, semiclassical, and quantum mechanics are probed using the technique of functional sensitivity analysis. It is shown that the classical and quantum functional sensitivities are equivalent in the classical (small (h/2π)) and harmonic limits. Classical and quantum mechanics are known to react in qualitatively similar ways provided that features on the potential are smooth on the length scale of oscillations in the quantum wave function. By using functional sensitivity analysis, we are able to show in detail how the classical and quantum dynamics differ in the way that they sense the potential. Two examples are given, the first of which is the harmonic oscillator. This problem is well understood by other means but is useful to examine because it illustrates the detailed information about the interaction of the potential and the dynamics which can be provided by functional sensitivity analysis, simplifying the analysis of more complex systems. The second example is the collinear H+H 2 reaction. In that case there are a number of detailed and striking differences between the ways that classical and quantum mechanics react to features on the potential. For features which are broad compared to oscillations in the wave function, the two react in qualitatively the same way. The sensitivities are oscillatory, however, and there are phasing differences between the classical and quantum sensitivity functions. This means that using classical mechanics plus experimental data in an inversion scheme intended to find the ''true'' potential will necessarily introduce sizeable errors

Losing energy in classical, relativistic and quantum mechanics

NARCIS (Netherlands)

Atkinson, David

A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. In relativistic mechanics, however,

Novel Evasion Mechanisms of the Classical Complement Pathway.

Science.gov (United States)

Garcia, Brandon L; Zwarthoff, Seline A; Rooijakkers, Suzan H M; Geisbrecht, Brian V

2016-09-15

Complement is a network of soluble and cell surface-associated proteins that gives rise to a self-amplifying, yet tightly regulated system with fundamental roles in immune surveillance and clearance. Complement becomes activated on the surface of nonself cells by one of three initiating mechanisms known as the classical, lectin, and alternative pathways. Evasion of complement function is a hallmark of invasive pathogens and hematophagous organisms. Although many complement-inhibition strategies hinge on hijacking activities of endogenous complement regulatory proteins, an increasing number of uniquely evolved evasion molecules have been discovered over the past decade. In this review, we focus on several recent investigations that revealed mechanistically distinct inhibitors of the classical pathway. Because the classical pathway is an important and specific mediator of various autoimmune and inflammatory disorders, in-depth knowledge of novel evasion mechanisms could direct future development of therapeutic anti-inflammatory molecules. Copyright © 2016 by The American Association of Immunologists, Inc.

Functional methods underlying classical mechanics, relativity and quantum theory

International Nuclear Information System (INIS)

Kryukov, A

2013-01-01

The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is ''made'' of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.

Classical mechanics with Mathematica

CERN Document Server

Romano, Antonio

2018-01-01

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject. Developed by the authors from over 30 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Hamilton—while also painting a clear picture of the most modern developments. The text is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dyna...

From classical to quantum mechanics: ``How to translate physical ideas into mathematical language''

Science.gov (United States)

Bergeron, H.

2001-09-01

Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantum mechanics, we develop a unified mathematical framework for classical and quantum mechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantum mechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantum mechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence

Theoretical physics 1 classical mechanics

CERN Document Server

Nolting, Wolfgang

2016-01-01

This textbook offers a clear and comprehensive introduction to classical mechanics, one of the core components of undergraduate physics courses. The book starts with a thorough introduction to the mathematical tools needed, to make this textbook self-contained for learning. The second part of the book introduces the mechanics of the free mass point and details conservation principles. The third part expands the previous to mechanics of many particle systems. Finally the mechanics of the rigid body is illustrated with rotational forces, inertia and gyroscope movement. Ideally suited to undergraduate students in their first year, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successful German editions, the eight volumes of this series...

Non-classical continuum mechanics a dictionary

CERN Document Server

Maugin, Gérard A

2017-01-01

This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, every entry is followed by a cross-reference to other related subject entries in the dictionary.

Pre-equilibrium nuclear reactions: An introduction to classical and quantum-mechanical models

International Nuclear Information System (INIS)

Koning, A.J.; Akkermans, J.M.

1999-01-01

In studies of light-ion induced nuclear reactions one distinguishes three different mechanisms: direct, compound and pre-equilibrium nuclear reactions. These reaction processes can be subdivided according to time scales or, equivalently, the number of intranuclear collisions taking place before emission. Furthermore, each mechanism preferably excites certain parts of the nuclear level spectrum and is characterized by different types of angular distributions. This presentation includes description of the classical, exciton model, semi-classical models, with some selected results, and quantum mechanical models. A survey of classical versus quantum-mechanical pre-equilibrium reaction theory is presented including practical applications

Classical mechanics and electromagnetism in accelerator physics

CERN Document Server

Stupakov, Gennady

2018-01-01

This self-contained textbook with exercises discusses a broad range of selected topics from classical mechanics and electromagnetic theory that inform key issues related to modern accelerators. Part I presents fundamentals of the Lagrangian and Hamiltonian formalism for mechanical systems, canonical transformations, action-angle variables, and then linear and nonlinear oscillators. The Hamiltonian for a circular accelerator is used to evaluate the equations of motion, the action, and betatron oscillations in an accelerator. From this base, we explore the impact of field errors and nonlinear resonances. This part ends with the concept of the distribution function and an introduction to the kinetic equation to describe large ensembles of charged particles and to supplement the previous single-particle analysis of beam dynamics. Part II focuses on classical electromagnetism and begins with an analysis of the electromagnetic field from relativistic beams, both in vacuum and in a resistive pipe. Plane electromagne...

Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics

International Nuclear Information System (INIS)

Zhang Yi

2011-01-01

This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and the criterion of the symmetry of Hamiltonian of the system are given. A conserved quantity directly derived from the symmetry of Hamiltonian of the generalized classical mechanical system is given. Since a Hamilton system is a special case of the generalized classical mechanics, the results above are equally applicable to the Hamilton system. The results of the paper are the generalization of a theorem known for the existing nonsingular equivalent Lagrangian. Finally, two examples are given to illustrate the application of the results. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Nonlinear wave mechanics from classical dynamics and scale covariance

International Nuclear Information System (INIS)

Hammad, F.

2007-01-01

Nonlinear Schroedinger equations proposed by Kostin and by Doebner and Goldin are rederived from Nottale's prescription for obtaining quantum mechanics from classical mechanics in nondifferentiable spaces; i.e., from hydrodynamical concepts and scale covariance. Some soliton and plane wave solutions are discussed

A stepping stone from classical to quantum mechanics

International Nuclear Information System (INIS)

Tzara, C.

1984-01-01

A microscopic mechanics is constructed in order to incorporate the Planck constant while retaining the concept of particle location. In the one-dimensional stationary case, the first integral of the equation of motion can be solved explicitly with the help of the Schroedinger equation. It is thus shown that, in describing bound-state motions, this mechanics meets a serious difficulty. It can be overcome only by renouncing the classical concepts of trajectories and opting for quantum mechanics

Dynamical chaos: systems of classical mechanics

International Nuclear Information System (INIS)

Loskutov, A Yu

2007-01-01

This article is a methodological manual for those who are interested in chaotic dynamics. An exposition is given on the foundations of the theory of deterministic chaos that originates in classical mechanics systems. Fundamental results obtained in this area are presented, such as elements of the theory of nonlinear resonance and the Kolmogorov-Arnol'd-Moser theory, the Poincare-Birkhoff fixed-point theorem, and the Mel'nikov method. Particular attention is given to the analysis of the phenomena underlying the self-similarity and nature of chaos: splitting of separatrices and homoclinic and heteroclinic tangles. Important properties of chaotic systems - unpredictability, irreversibility, and decay of temporal correlations - are described. Models of classical statistical mechanics with chaotic properties, which have become popular in recent years - billiards with oscillating boundaries - are considered. It is shown that if a billiard has the property of well-developed chaos, then perturbations of its boundaries result in Fermi acceleration. But in nearly-integrable billiard systems, excitations of the boundaries lead to a new phenomenon in the ensemble of particles, separation of particles in accordance their velocities. If the initial velocity of the particles exceeds a certain critical value characteristic of the given billiard geometry, the particles accelerate; otherwise, they decelerate. (methodological notes)

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

International Nuclear Information System (INIS)

Lee, Sang-Bong.

1993-09-01

Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover's and Kubo-Fox-Keizer's approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty

Mathematica for Theoretical Physics Classical Mechanics and Nonlinear Dynamics

CERN Document Server

Baumann, Gerd

2005-01-01

Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A...

Unconstrained SU(2) and SU(3) Yang-Mills classical mechanics

International Nuclear Information System (INIS)

Dahmen, B.; Raabe, B.

1992-01-01

A systematic study of contraints in SU(2) and SU(3) Yang-Mills classical mechanics is performed. Expect for the SU(2) case with spatial angular momenta they turn out to be nonholonomic. The complete elimination of the unphysical gauge and rotatinal degrees of freedom is achieved using Dirac's constraint formalism. We present an effective unconstrained formulation of the general SU(2) Yang-Mills classical mechanics as well as for SU(3) in the subspace of vanishing spatial angular momenta that is well suited for further explicit dynamical investigations. (orig.)

Alternative perturbation approaches in classical mechanics

International Nuclear Information System (INIS)

Amore, Paolo; Raya, Alfredo; Fernandez, Francisco M

2005-01-01

We discuss two alternative methods, based on the Lindstedt-Poincare technique, for the removal of secular terms from the equations of perturbation theory. We calculate the period of an anharmonic oscillator by means of both approaches and show that one of them is more accurate for all values of the coupling constant. We believe that present discussion and comparison may be a suitable exercise for teaching perturbation theory in advanced undergraduate courses on classical mechanics

Explicit integration of some integrable systems of classical mechanics

OpenAIRE

Basak Gancheva, Inna

2011-01-01

The main objective of the thesis is the analytical and geometrical study of several integrable finite-dimentional dynamical systems of classical mechanics, which are closely related, namely: - the classical generalization of the Euler top: the Zhukovski-Volterra (ZV) system describing the free motion of a gyrostat, i.e., a rigid body carrying a symmetric rotator whose axis is fixed in the body; - the Steklov-Lyapunov integrable case of the Kirchhoff equations describing the motio...

Regular behaviors in SU(2) Yang-Mills classical mechanics

International Nuclear Information System (INIS)

Xu Xiaoming

1997-01-01

In order to study regular behaviors in high-energy nucleon-nucleon collisions, a representation of the vector potential A i a is defined with respect to the (a,i)-dependence in the SU(2) Yang-Mills classical mechanics. Equations of the classical infrared field as well as effective potentials are derived for the elastic or inelastic collision of two plane wave in a three-mode model and the decay of an excited spherically-symmetric field

Some connections between relativistic classical mechanics, statistical mechanics, and quantum field theory

International Nuclear Information System (INIS)

Remler, E.A.

1977-01-01

A gauge-invariant version of the Wigner representation is used to relate relativistic mechanics, statistical mechanics, and quantum field theory in the context of the electrodynamics of scalar particles. A unified formulation of quantum field theory and statistical mechanics is developed which clarifies the physics interpretation of the single-particle Wigner function. A covariant form of Ehrenfest's theorem is derived. Classical electrodynamics is derived from quantum field theory after making a random-phase approximation. The validity of this approximation is discussed

Classical and quantum mechanics of the damped harmonic oscillator

International Nuclear Information System (INIS)

Dekker, H.

1981-01-01

The relations between various treatments of the classical linearly damped harmonic oscillator and its quantization are investigated. In the course of a historical survey typical features of the problem are discussed on the basis of Havas' classical Hamiltonian and the quantum mechanical Suessmann-Hasse-Albrecht models as coined by the Muenchen/Garching nuclear physics group. It is then shown how by imposing a restriction on the classical trajectories in order to connect the Hamiltonian with the energy, the time-independent Bateman-Morse-Feshbach-Bopp Hamiltonian leads to the time-dependent Caldirola-Kanai Hamiltonian. Canonical quantization of either formulation entails a violation of Heisenberg's principle. By means of a unified treatment of both the electrical and mechanical semi-infinite transmission line, this defect is related to the disregard of additional quantum fluctuations that are intrinsically connected with the dissipation. The difficulties of these models are discussed. Then it is proved that the Bateman dual Hamiltonian is connected to a recently developed complex symplectic formulation by a simple canonical transformation. (orig.)

Classical and quantum mechanics of complex Hamiltonian systems

Indian Academy of Sciences (India)

Certain aspects of classical and quantum mechanics of complex Hamiltonian systems in one dimension investigated within the framework of an extended complex phase space approach, characterized by the transformation = 1 + 2, = 1 + 2, are revisited. It is argued that Carl Bender inducted P T symmetry in ...

Classical and quantum mechanical studies of HF in an intense laser field

International Nuclear Information System (INIS)

Dardi, P.S.; Gray, S.K.

1982-01-01

The behavior of an HF molecule in an intense laser field is investigated with both classical trajectories and quantum dynamics. Vibration-rotation transition probabilities and energy absorption as a function of laser pulse time are calculated for the diatomic initially in its ground state. For comparison, results are also reported for a model nonrotating HF molecule. It is found that classical mechanics does not predict the correct time behavior of the system, nor does it predict the correct rotational state distributions. Classical mechanics does, however, predict pulse time averaged quantities to be the correct order of magnitude. There is also a correct general trend of increased multiphoton excitation for laser frequencies red-shifted from the one-photon resonance, although multiphoton resonance peaks are not observed in the classical results and far too little multiphoton excitation is predicted. The effect of laser phase has also been investigated and shown to be relatively unimportant in both the classical and quantum dynamics

Classical and quantum mechanics of complex Hamiltonian systems ...

Indian Academy of Sciences (India)

Vol. 73, No. 2. — journal of. August 2009 physics pp. 287–297. Classical and quantum mechanics of complex. Hamiltonian systems: An extended complex phase space ... 1Department of Physics, Ramjas College (University Enclave), University of Delhi,. Delhi 110 ... 1.1 Motivation behind the study of complex Hamiltonians.

A remark on the classical mechanics of colored particles

International Nuclear Information System (INIS)

Arodz, H.

1982-04-01

Examples of the motion of a wave packet in external SU(2) gauge fields are analyzed. It is found that the classical mechanics of colored particles gives a wrong qualitative description of this motion. (Auth.)

Reformulating classical and quantum mechanics in terms of a unified set of consistency conditions

International Nuclear Information System (INIS)

Bordley, R.F.

1983-01-01

This paper imposes consistency conditions on the path of a particle and shows that they imply Hamilton's principle in classical contexts and Schroedinger's equation in quantum mechanical contexts. Thus this paper provides a common, intuitive foundation for classical and quantum mechanics. It also provides a very new perspective on quantum mechanics. (author

Noncommutative configuration space. Classical and quantum mechanical aspects

OpenAIRE

Vanhecke, F. J.; Sigaud, C.; da Silva, A. R.

2005-01-01

In this work we examine noncommutativity of position coordinates in classical symplectic mechanics and its quantisation. In coordinates $\\{q^i,p_k\\}$ the canonical symplectic two-form is $\\omega_0=dq^i\\wedge dp_i$. It is well known in symplectic mechanics {\\bf\\cite{Souriau,Abraham,Guillemin}} that the interaction of a charged particle with a magnetic field can be described in a Hamiltonian formalism without a choice of a potential. This is done by means of a modified symplectic two-form $\\ome...

From the attempt of certain classical reformulations of quantum mechanics to quasi-probability representations

International Nuclear Information System (INIS)

Stulpe, Werner

2014-01-01

The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered

Rotating fluid models in classical and quantum mechanics

International Nuclear Information System (INIS)

Arvieu, R.; Troudet, T.

1979-01-01

To describe the behavior of high-spin nuclei it is necessary to refer back to the classical mechanics of fluids in rotation where some results are general enough to apply to the rotational nuclear fluid. It is then shown that the quantum model of rotational oscillator gives a simple classification of rotating configurations [fr

Quantum and classical control of single photon states via a mechanical resonator

International Nuclear Information System (INIS)

Basiri-Esfahani, Sahar; Myers, Casey R; Combes, Joshua; Milburn, G J

2016-01-01

Optomechanical systems typically use light to control the quantum state of a mechanical resonator. In this paper, we propose a scheme for controlling the quantum state of light using the mechanical degree of freedom as a controlled beam splitter. Preparing the mechanical resonator in non-classical states enables an optomechanical Stern–Gerlach interferometer. When the mechanical resonator has a small coherent amplitude it acts as a quantum control, entangling the optical and mechanical degrees of freedom. As the coherent amplitude of the resonator increases, we recover single photon and two-photon interference via a classically controlled beam splitter. The visibility of the two-photon interference is particularly sensitive to coherent excitations in the mechanical resonator and this could form the basis of an optically transduced weak-force sensor. (paper)

Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Facchi, Paolo [Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Kulkarni, Ravi [Vivekananda Yoga Research Foundation, Bangalore 560 080 (India); Man' ko, V.I., E-mail: manko@na.infn.i [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, Giuseppe [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Sudarshan, E.C.G. [Department of Physics, University of Texas, Austin, TX 78712 (United States); Ventriglia, Franco [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy)

2010-11-01

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.

Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

International Nuclear Information System (INIS)

Facchi, Paolo; Kulkarni, Ravi; Man'ko, V.I.; Marmo, Giuseppe; Sudarshan, E.C.G.; Ventriglia, Franco

2010-01-01

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.

On q-deformed supersymmetric classical mechanical models

International Nuclear Information System (INIS)

Colatto, L.P.; Matheus Valle, J.L.

1995-10-01

Based on the idea of quantum groups and paragrassmann variables, we present a generalization of supersymmetric classical mechanics with a deformation parameter q=exp 2πi/k dealing with the k=3 case. The coordinates of the q-superspace are a commuting parameter t and a paragrassmann variable θ, where θ 3 =0. The generator and covariant derivative are obtained, as well as the action for some possible superfields. (author). 13 refs

The difference between the classical and quantum mechanical definitions of scattering cross sections and the problem of the classical limit

International Nuclear Information System (INIS)

Sen, D.; Basu, A.N.; Sengupta, S.

1994-01-01

A critical analysis of the difference between the classical and quantum mechanical definitions of scattering cross sections for particles is presented. This leads to a clarification of the classical limit problem and suggests precise criteria for its validity. In particular these criteria are derived for both finite and infinite range potentials. (orig.)

Classical treatments of quantum mechanical effects in collisions of weakly bound complexes

International Nuclear Information System (INIS)

Lopez, Jose G.; McCoy, Anne B.

2005-01-01

Classical and quantum simulations of Ne + Ar 2 collision dynamics are performed in order to investigate where quantum mechanical effects are most important and where classical simulations provide good descriptions of the dynamics. It is found that when Ar 2 is in a low-lying vibrational state, the differences between the results of quantum and quasiclassical simulations are profound. However, excellent agreement between the results of the quantum and classical simulations can be achieved when the initial conditions for the classical trajectories are sampled from the quantum phase space distribution given by the Wigner function. These effects are largest when collisions occur under constrained geometries or when Ar 2 is in its ground vibrational state. The results of this work suggest that sampling the initial conditions using the Wigner function provides a straightforward way to incorporate the most important quantum mechanical effects in simulations of collisions involving very cold weakly bound complexes

The classical limit in the framework of stochastic mechanics

International Nuclear Information System (INIS)

Claverie, P.

1976-01-01

Thorough qualitative understanding of microphysical phenomena is not really obtained by usual quantum mechanics (QM), whereas statistical mechanics (SM) appears able to bring in substantial conceptual progress. These conceptual improvements in a fringe area of quantum mechanics, namely the so-called transition region to classical mechanics, are described. The difficulties which appear in the framework of usual QM are surveyed and then it is shown how they would disappear in the framework of SM, provided that appropriate dynamical laws are found such that, by using them, SM actually gives the main results of QM (position and velocity probability distributions, mean values of energy, angular momentum, etc.)

Experiments and video analysis in classical mechanics

CERN Document Server

de Jesus, Vitor L B

2017-01-01

This book is an experimental physics textbook on classical mechanics focusing on the development of experimental skills by means of discussion of different aspects of the experimental setup and the assessment of common issues such as accuracy and graphical representation. The most important topics of an experimental physics course on mechanics are covered and the main concepts are explored in detail. Each chapter didactically connects the experiment and the theoretical models available to explain it. Real data from the proposed experiments are presented and a clear discussion over the theoretical models is given. Special attention is also dedicated to the experimental uncertainty of measurements and graphical representation of the results. In many of the experiments, the application of video analysis is proposed and compared with traditional methods.

Real-time dynamics of matrix quantum mechanics beyond the classical approximation

Science.gov (United States)

Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas

2018-03-01

We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.

'Leonard pairs' in classical mechanics

International Nuclear Information System (INIS)

Zhedanov, Alexei; Korovnichenko, Alyona

2002-01-01

Leonard pairs (LP) are matrices with the property of mutual tri-diagonality. We introduce and study a classical analogue of LP. We show that corresponding classical 'Leonard' dynamical variables satisfy non-linear relations of the AW-type with respect to Poisson brackets. (author)

On the Galilean covariance of classical mechanics

International Nuclear Information System (INIS)

Horzela, A.; Kapuscik, E.; Kempczynski, J.; Joint Inst. for Nuclear Research, Dubna

1991-08-01

A Galilean covariant approach to classical mechanics of a single interacting particle is described. In this scheme constitutive relations defining forces are rejected and acting forces are determined by some fundamental differential equations. It is shown that total energy of the interacting particle transforms under Galilean transformations differently from the kinetic energy. The statement is illustrated on the exactly solvable examples of the harmonic oscillator and the case of constant forces and also, in the suitable version of the perturbation theory, for the anharmonic oscillator. (author)

Anyons as spin particles: from classical mechanics to field theory

OpenAIRE

Plyushchay, Mikhail S.

1995-01-01

(2+1)-dimensional relativistic fractional spin particles are considered within the framework of the group-theoretical approach to anyons starting from the level of classical mechanics and concluding by the construction of the minimal set of linear differential field equations.

A Comparison of Kinetic Energy and Momentum in Special Relativity and Classical Mechanics

Science.gov (United States)

Riggs, Peter J.

2016-01-01

Kinetic energy and momentum are indispensable dynamical quantities in both the special theory of relativity and in classical mechanics. Although momentum and kinetic energy are central to understanding dynamics, the differences between their relativistic and classical notions have not always received adequate treatment in undergraduate teaching.…

A morphing approach to couple state-based peridynamics with classical continuum mechanics

KAUST Repository

Han, Fei

2016-01-04

A local/nonlocal coupling technique called the morphing method is developed to couple classical continuum mechanics with state-based peridynamics. State-based peridynamics, which enables the description of cracks that appear and propagate spontaneously, is applied to the key domain of a structure, where damage and fracture are considered to have non-negligible effects. In the rest of the structure, classical continuum mechanics is used to reduce computational costs and to simultaneously satisfy solution accuracy and boundary conditions. Both models are glued by the proposed morphing method in the transition region. The morphing method creates a balance between the stiffness tensors of classical continuum mechanics and the weighted coefficients of state-based peridynamics through the equivalent energy density of both models. Linearization of state-based peridynamics is derived by Taylor approximations based on vector operations. The discrete formulation of coupled models is also described. Two-dimensional numerical examples illustrate the validity and accuracy of the proposed technique. It is shown that the morphing method, originally developed for bond-based peridynamics, can be successfully extended to state-based peridynamics through the original developments presented here.

A morphing approach to couple state-based peridynamics with classical continuum mechanics

KAUST Repository

Han, Fei; Lubineau, Gilles; Azdoud, Yan; Askari, Abe

2016-01-01

A local/nonlocal coupling technique called the morphing method is developed to couple classical continuum mechanics with state-based peridynamics. State-based peridynamics, which enables the description of cracks that appear and propagate spontaneously, is applied to the key domain of a structure, where damage and fracture are considered to have non-negligible effects. In the rest of the structure, classical continuum mechanics is used to reduce computational costs and to simultaneously satisfy solution accuracy and boundary conditions. Both models are glued by the proposed morphing method in the transition region. The morphing method creates a balance between the stiffness tensors of classical continuum mechanics and the weighted coefficients of state-based peridynamics through the equivalent energy density of both models. Linearization of state-based peridynamics is derived by Taylor approximations based on vector operations. The discrete formulation of coupled models is also described. Two-dimensional numerical examples illustrate the validity and accuracy of the proposed technique. It is shown that the morphing method, originally developed for bond-based peridynamics, can be successfully extended to state-based peridynamics through the original developments presented here.

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

Science.gov (United States)

Rohrlich, Daniel

Y. Aharonov and A. Shimony both conjectured that two axioms - relativistic causality (``no superluminal signalling'') and nonlocality - so nearly contradict each other that only quantum mechanics reconciles them. Can we indeed derive quantum mechanics, at least in part, from these two axioms? No: ``PR-box'' correlations show that quantum correlations are not the most nonlocal correlations consistent with relativistic causality. Here we replace ``nonlocality'' with ``retrocausality'' and supplement the axioms of relativistic causality and retrocausality with a natural and minimal third axiom: the existence of a classical limit, in which macroscopic observables commute. That is, just as quantum mechanics has a classical limit, so must any generalization of quantum mechanics. In this limit, PR-box correlations violaterelativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound (a theorem of quantum mechanics) from the three axioms of relativistic causality, retrocausality and the existence of a classical limit. Although the derivation does not assume quantum mechanics, it points to the Hilbert space structure that underlies quantum correlations. I thank the John Templeton Foundation (Project ID 43297) and the Israel Science Foundation (Grant No. 1190/13) for support.

The concept of 'optimal' path in classical mechanics

International Nuclear Information System (INIS)

Passos, E.J.V. de; Cruz, F.F. de S.

1986-01-01

The significance of the concept of 'optimal' path in the framework of classical mechanics is discussed. The derivation of the local harmonic approximation and self-consistent collective coordinate method equations of the optimal path is based on a careful study of the concepts of local maximal decoupling and global maximal decoupling respectively. This exhibits the nature of the differences between these two theories and allows one to establish the conditions under which they become equivalent. (author)

A unified treatment of dynamics and scattering in classical and quantum statistical mechanics

International Nuclear Information System (INIS)

Prugovecki, E.

1978-01-01

The common formal features of classical and quantum statistical mechanics are investigated at three separate levels: at the level of L 2 spaces of wave-packets on GAMMA-space, of Liouville spaces B 2 consisting of density operators constructed from such wave-packets, and of phase-space representation spaces P of GAMMA distribution functions. It is shown that at the last level the formal similarities become so outstanding that all key quantities in P-space, such as Liouville operators, Hamiltonian functions, position and momentum observables, etc., are represented by expressions which to the zeroth order in (h/2π) coincide in the classical and quantum case, and in some instances coincide completely. Scattering theory on the B 2 Liouville spaces takes on the same formal appearance for classical and quantum statistical mechanics, and to the zeroth order in (h/2π) it coincides in both cases. This makes possible the formulation of a classical approximation to quantum scattering, and of a computational scheme for determining rhosup(out) from rhosup(in) for successive order of (h/2π). (Auth.)

An alternative formulation of classical mechanics based on an analogy with thermodynamics

International Nuclear Information System (INIS)

Teruel, Ginés R Pérez

2013-01-01

We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analysed under coordinate transformations. When invariance under different kinds of transformations is considered the new formulation is found to be completely equivalent to the usual Lagrangian formulation, recovering well-established results such as conservation of angular momentum. Furthermore, a natural generalization of the Poisson bracket is found to be inherent to the formalism introduced. On the other hand, we find that with a convenient redefinition of the Lagrangian, L ' =-L, it is possible to establish an exact one-to-one mathematical correspondence between the thermodynamic potentials and the new potentials of classical mechanics. (paper)

Comment on ''a classical model of EPR experiment with quantum mechanical correlations and Bell inequalities''

International Nuclear Information System (INIS)

Aspect, A.

1986-01-01

The author states that ''It is impossible to mimick the quantum mechanical predictions for the EPR correlations, with a reasonable classical-looking model, in the spirit of Einstein's ideas''. The author feels that if he is wrong somebody could make a classical model (i.e. following the laws of classical physics) mimicking all the quantum mechanical predictions for the EPR correlations. He attempts to show that it is not the case for Barut's model for the following reasons: the first version of his model is classical, but doesn't mimick at all an EPR type experiment; and by reinterpretation one can get a model that does mimick the experiment, but this model is no longer ''reasonably classical looking'' since it involves negative probabilities. The claim is put in the form of a challenge. It is shown that the model under discussion can be reinterpreted by adding a chip converting the continuous outputs into two-valved outputs

Some studies on arithmetical chaos in classical and quantum mechanics

International Nuclear Information System (INIS)

Bolte, J.

1993-04-01

Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. The latter consists of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose corresponding fundamental groups are supplied with an arithmetic structure. It is shown that the arithmetical features of the considered systems lead to exceptional properties of the corresponding spectra of lengths of closed geodesics (periodic orbits). The most significant one is an exponential growth of degeneracies in these geodesic length spectra. Furthermore, the arithmetical systems are distinguished by a structure that appears as a generalization of geometric symmetries. These pseudosymmetries occur in the quantization of the classical arithmetic systems as Hecke operators, which form an infinite algebra of self-adjoint operators commuting with the Hamiltonian. The statistical properties of quantum energies in the arithmetical systems have previously been identified as exceptional. They do not fit into the general scheme of random matrix theory. It is shown with the help of a simplified model for the spectral form factor how the spectral statistics in arithmetical quantum chaos can be understood by the properties of the corresponding classical geodesic length spectra. A decisive role is played by the exponentially increasing multiplicities of lengths. The model developed for the level spacings distribution and for the number variance is compared to the corresponding quantities obtained from quantum energies for a specific arithmetical system. Finally, the convergence properties of a representation for the Selberg zeta function as a Dirichlet series are studied. It turns out that the exceptional classical and quantum mechanical properties shared by the arithmetical systems prohibit a convergence of this important function in the physically interesting domain. (orig.)

Why irreversibility? The formulation of classical and quantum mechanics for nonintegrable systems

International Nuclear Information System (INIS)

Prigogine, I.

1995-01-01

Nonintegrable Poincare systems with a continuous spectrum lead to the appearance of diffusive terms in the frame of classical or quantum dynamics. These terms break time symmetry. They lead, therefore, to limitations to classical trajectory theory and of wave-function formalism. These diffusive terms correspond to well-defined classes of dynamical processes. The diffusive effects are amplified in situations corresponding to persistent interactions. As a result, we have to include, already, in the fundamental dynamical description the two basic aspects, probability and irreversibility, which are so conspicuous on the macroscopic level. We have to formulate both classical and quantum mechanics on the Liouville level of probability distributions. For integrable systems, we recover the usual formulation of classical or quantum mechanics. Instead of being primitive concepts, which cannot be further analyzed, trajectories and wave functions appear as special solutions of the Liouville-von Neumann equations. This extension of classical and quantum dynamics permits us to unify the two concepts of nature that we inherited from the nineteenth century, based, on the one hand, on dynamical time-reversible laws and, on the other, on an evolutionary view associated to entropy. It leads also to a unified formulation of quantum theory, avoiding the conventional dual structure based on Schroedinger's equation, on the one hand, and on the open-quotes collapseclose quotes of the wave function, on the other. A dynamical interpretation is given to processes such as decoherence or approach to equilibrium without any appeal to extra dynamic considerations. There is a striking parallelism between classical and quantum theory. For large Poincare systems (LPS), we have, in general, both a open-quotes collapseclose quotes of trajectories and of wave functions. In both cases, we need a generalized formulation of dynamics in terms of probability distributions or density matrices

Classical mechanics including an introduction to the theory of elasticity

CERN Document Server

Hentschke, Reinhard

2017-01-01

This textbook teaches classical mechanics as one of the foundations of physics. It describes the mechanical stability and motion in physical systems ranging from the molecular to the galactic scale. Aside from the standard topics of mechanics in the physics curriculum, this book includes an introduction to the theory of elasticity and its use in selected modern engineering applications, e.g. dynamic mechanical analysis of viscoelastic materials. The text also covers many aspects of numerical mechanics, ranging from the solution of ordinary differential equations, including molecular dynamics simulation of many particle systems, to the finite element method. Attendant Mathematica programs or parts thereof are provided in conjunction with selected examples. Numerous links allow the reader to connect to related subjects and research topics. Among others this includes statistical mechanics (separate chapter), quantum mechanics, space flight, galactic dynamics, friction, and vibration spectroscopy. An introductory...

Quantum flesh on classical bones: Semiclassical bridges across the quantum-classical divide

Energy Technology Data Exchange (ETDEWEB)

Bokulich, Alisa [Center for Philosophy and History of Science, Boston University, Boston, MA (United States)

2014-07-01

Traditionally quantum mechanics is viewed as having made a sharp break from classical mechanics, and the concepts and methods of these two theories are viewed as incommensurable with one another. A closer examination of the history of quantum mechanics, however, reveals that there is a strong sense in which quantum mechanics was built on the backbone of classical mechanics. As a result, there is a considerable structural continuity between these two theories, despite their important differences. These structural continuities provide a ground for semiclassical methods in which classical structures, such as trajectories, are used to investigate and model quantum phenomena. After briefly tracing the history of semiclassical approaches, I show how current research in semiclassical mechanics is revealing new bridges across the quantum-classical divide.

A Primer on Elliptic Functions with Applications in Classical Mechanics

Science.gov (United States)

Brizard, Alain J.

2009-01-01

The Jacobi and Weierstrass elliptic functions used to be part of the standard mathematical arsenal of physics students. They appear as solutions of many important problems in classical mechanics: the motion of a planar pendulum (Jacobi), the motion of a force-free asymmetric top (Jacobi), the motion of a spherical pendulum (Weierstrass) and the…

Visualizing the solutions for the circular infinite well in quantum and classical mechanics

International Nuclear Information System (INIS)

Robinett, R.W.

1996-01-01

The classical and quantum mechanical problem of a particle in the infinite circular well has recently surfaced in two quite different manifestations: (i) the observation of open-quote open-quote electron standing waves close-quote close-quote in circular open-quote open-quote corrals close-quote close-quote of atoms adsorbed on surfaces and (ii) as a benchmark example of an integrable system for comparison to the classical and quantum chaotic behavior of the open-quote open-quote stadium billiards close-quote close-quote problem. Motivated by this, we review the quantum and classical probability distributions for both position and momentum for this familiar problem, focusing on the visualization of the quantum wave functions and classical trajectories as well as the semiclassical connections between the two. copyright 1996 American Association of Physics Teachers

Blow-up Mechanism of Classical Solutions to Quasilinear Hyperbolic Systems in the Critical Case

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

This paper deals with the blow-up phenomenon, particularly, the geometric blow-up mechanism, of classical solutions to the Cauchy problem for quasilinear hyperbolic systems in the critical case. We prove that it is still the envelope of the same family of characteristics which yields the blowup of classical solutions to the Cauchy problem in the critical case.

That's why, sort of ....; Classical Mechanics derived from Self-evident Axioms

NARCIS (Netherlands)

Sonneveld, P.

2015-01-01

Classical point-mechanics is derived from three principles —called axioms— that are based on observations of simple kinematical phenomena. Predefined concepts of ‘force’ and ‘mass’ are not required. The concept ’mass’ and corresponding concepts of momentum and energy follow from the first and second

Is classical mechanics based on Newton's laws or Eulers analytical equations?

Directory of Open Access Journals (Sweden)

H.Iro

2005-01-01

Full Text Available In an example I illustrate how my picture of physics is enriched due to my frequent conversations with Reinhard Folk. The subject is: Who wrote down the basic equations of motion of classical mechanics for the first time? (To be sure, it was not Newton.

Classical and Quantum-Mechanical State Reconstruction

Science.gov (United States)

Khanna, F. C.; Mello, P. A.; Revzen, M.

2012-01-01

The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that…

Classical antiparticles

International Nuclear Information System (INIS)

Costella, J.P.; McKellar, B.H.J.; Rawlinson, A.A.

1997-03-01

We review how antiparticles may be introduced in classical relativistic mechanics, and emphasize that many of their paradoxical properties can be more transparently understood in the classical than in the quantum domain. (authors)

Reason of method of density functional in classical and quantum statistical mechanisms

International Nuclear Information System (INIS)

Dinariev, O.Yu.

2000-01-01

Interaction between phenomenological description of a multi-component mixture on the basis of entropy functional with members, square in terms of component density gradients and temperature, on the one hand, and description in the framework of classical and quantum statistical mechanics, on the other hand, was investigated. Explicit expressions for the entropy functional in the classical and quantum theory were derived. Then a square approximation for the case of minor disturbances of uniform state was calculated. In the approximation the addends square in reference to the gradient were singlet out. It permits calculation of the relevant phenomenological coefficients from the leading principles [ru

Quantum models of classical systems

International Nuclear Information System (INIS)

Hájíček, P

2015-01-01

Quantum statistical methods that are commonly used for the derivation of classical thermodynamic properties are extended to classical mechanical properties. The usual assumption that every real motion of a classical mechanical system is represented by a sharp trajectory is not testable and is replaced by a class of fuzzy models, the so-called maximum entropy (ME) packets. The fuzzier are the compared classical and quantum ME packets, the better seems to be the match between their dynamical trajectories. Classical and quantum models of a stiff rod will be constructed to illustrate the resulting unified quantum theory of thermodynamic and mechanical properties. (paper)

Stochastic theory for classical and quantum mechanical systems

International Nuclear Information System (INIS)

Pena, L. de la; Cetto, A.M.

1975-01-01

From first principles a theory of stochastic processes in configuration space is formulated. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schroedinger equation, which is derived with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section

Atomic collision experiments at the border line between classical and quantum mechanics

International Nuclear Information System (INIS)

Aquilanti, V.

1984-01-01

In order to understand atomic and molecular interactions, one has to learn how to live with the wave-particle duality, considering classical nuclei and quantum electrons. A better way, illustrated by reference to experiments, is by quasiclassical (or semi-classical) mechanics, governing a world with a quasi-zero Planck's constant. One thus explains optical analogs (shadows, rainbows, glories) as interference effects in atomic collisions. Reference is also made to Wheeler's 'black bird' on the inversion problem from spectroscopy and scattering to molecular structure. The paper concludes outlining a journey in the hyperspace to escape from Einstein's torus and to find interferences and resonances in three body scattering and reactions. (Auth.)

On the connections between the classical and quantum-mechanical Kepler problems

International Nuclear Information System (INIS)

Dahl, J.P.; Jorgensen, T.G.

1993-01-01

The Runge-Lenz vector, which accounts for the accidental degeneracy of the non-relativistic Kepler problem, has been the subject matter of many studies, both in quantum mechanics and in classical mechanics. Much less attention has been paid to the Johnson-Lippmann operator which accounts for the accidental degeneracy of the relativistic Kepler problem in Dirac's quantum-mechanical description. In the present communication we discuss the properties of the Johnson-Lippmann operator. We show its relation to the non-relativistic Runge-Lenz vector and draw a connection to Sommerfield's early discussion of the relativistic Kepler problem. This enables us, inter alia, to give an explanation of the apparent coincidence of the energy expressions of the two theories

Turbulent Evolution of a Plasma Described Through Classical Mechanics Only

International Nuclear Information System (INIS)

Escande, D.F.; Elskens, Y.

2003-01-01

For the first time an old dream of the XIXth century comes true: the non trivial evolution of a macroscopic many-body system is described through classical mechanics only. This is done for the relaxation of a warm electron beam in a plasma, which results in the generation of Langmuir turbulence and in the formation of a plateau in the velocity distribution function of the electrons. Our derivation starts from the hamiltonian describing the one-dimensional N-body system corresponding to the beam and plasma bulk electrons in electrostatic interaction. For such a system, the dynamics can be reduced to the resonant interaction of M Langmuir waves with N'( > 1 Langmuir waves with N' >> 1 beam particles. This yields the proof of the classical quasilinear equations describing the coupled evolution of the wave spectrum and of the beam velocity distribution function in the strongly nonlinear regime where their validity is the matter of a longstanding controversy

The conservation laws of nonrelativistic classical and quantum mechanics for a system of interacting particles

International Nuclear Information System (INIS)

Havas, P.

1978-01-01

The various classical or quantum mechanical equations describing a system of N particles with central two-body interactions are invariant under the 10 transformations of the Galilei group, and for interaction potential inversely proportional to the squares of the particle separations also under two further transformations. From the invariance of the corresponding classical and quantum mechanical variation principles under this 12-parameter conformal extension of the Galilei group, the 'Jacobi-Schroedinger group', the 12 well-known conservation laws of Newtonian dynamics as well as 12 local conservation laws implied by the Schroedinger equation are obtained via Noether's theorem. Under appropriate conditions on the wave functions, these local laws yield 12 global conservation laws which are analogous to the Newtonian ones. The Hamiltonian-Jacobi equation implies a classical equation differing from the Schroedinger equation only by a potential-like term involving the Van Vleck determinant, from which 12 local balance equations and the corresponding global equations are obtained, which under certain conditions reduce the true conservation laws. (Auth.)

Principles of physics from quantum field theory to classical mechanics

CERN Document Server

Jun, Ni

2014-01-01

This book starts from a set of common basic principles to establish the formalisms in all areas of fundamental physics, including quantum field theory, quantum mechanics, statistical mechanics, thermodynamics, general relativity, electromagnetic field, and classical mechanics. Instead of the traditional pedagogic way, the author arranges the subjects and formalisms in a logical-sequential way, i.e. all the formulas are derived from the formulas before them. The formalisms are also kept self-contained. Most of the required mathematical tools are also given in the appendices. Although this book covers all the disciplines of fundamental physics, the book is concise and can be treated as an integrated entity. This is consistent with the aphorism that simplicity is beauty, unification is beauty, and thus physics is beauty. The book may be used as an advanced textbook by graduate students. It is also suitable for physicists who wish to have an overview of fundamental physics. Readership: This is an advanced gradua...

Seven steps towards the classical world

International Nuclear Information System (INIS)

Allori, Valia; Duerr, Detlef; Goldstein, Shelly; Zanghi, Nino

2002-01-01

Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard quantum mechanics only the wavefunctions or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical limit becomes very simple: when do the Bohmian trajectories look Newtonian?

Wave Mechanics or Wave Statistical Mechanics

International Nuclear Information System (INIS)

Qian Shangwu; Xu Laizi

2007-01-01

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.

Hannay angle. Yet another symmetry-protected topological order parameter in classical mechanics

International Nuclear Information System (INIS)

Kariyado, Toshikaze; Hatsugai, Yasuhiro

2016-01-01

The topological way of thinking now goes beyond quantum solids, and topological characters of classical mechanical systems obeying Newton's law are attracting current interest. To provide a physical insight into the topological numbers in mechanics, we demonstrate the use of the Hannay angle, a “classical” Berry phase, as a symmetry-protected topological order parameter. The Hannay angle is derived using a canonical transformation that maps Newton's equation to a Schrödinger-type equation, and the condition for the quantization is discussed in connection with the symmetry in mechanics. Also, we demonstrate the use of the Hannay angle for a topological characterization of a spring-mass model focusing on the bulk-edge correspondence. (author)

Some problems in classical mechanics and relativistic astrophysics

International Nuclear Information System (INIS)

Hut, P.

1981-01-01

The first part of this thesis is indirectly related to high energy astrophysics. It concerns the study of binary systems consisting of a normal star and a neutronstar or a black hole. To interpret the observations from such a system; in X-ray, UV, optical, infrared and radio wavelengths; it is helpful to have a general idea of the evolution of the orbital and rotational parameters. Here we enter the old field of classical mechanics, in the form of celestial mechanics. In particular the effects of tidal interaction, precession, and sudden mass loss are treated. The second part starts with an article on thought experiments with a charged black hole enclosed in a huge box and in equilibrium with its own radiation. In this way the thermodynamic aspects of the Hawking radiation are fully explored. The connection between physical and kinematical cosmological parameters, as predicted by general relativity are explored. It is shown how the standard big bang model of cosmology restricts the possible properties of some elementary particle types. The theory of white dwarf structure is compared with observations in order to put low-energy constraints on (super) gravity theories. (Auth.)

Introductory quantum mechanics a traditional approach emphasizing connections with classical physics

CERN Document Server

Berman, Paul R

2018-01-01

This book presents a basic introduction to quantum mechanics at the undergraduate level. Depending on the choice of topics, it can be used for a one-semester or two-semester course. An attempt has been made to anticipate the conceptual problems students encounter when they first study quantum mechanics. Wherever possible, examples are given to illustrate the underlying physics associated with the mathematical equations of quantum mechanics. To this end, connections are made with corresponding phenomena in classical mechanics and electromagnetism. The problems at the end of each chapter are intended to help students master the course material and to explore more advanced topics. Many calculations exploit the extraordinary capabilities of computer programs such as Mathematica, MatLab, and Maple. Students are urged to use these programs, just as they had been urged to use calculators in the past. The treatment of various topics is rather complete, in that most steps in derivations are included. Several of the ch...

Sum rules in classical scattering

International Nuclear Information System (INIS)

Bolle, D.; Osborn, T.A.

1981-01-01

This paper derives sum rules associated with the classical scattering of two particles. These sum rules are the analogs of Levinson's theorem in quantum mechanics which provides a relationship between the number of bound-state wavefunctions and the energy integral of the time delay of the scattering process. The associated classical relation is an identity involving classical time delay and an integral over the classical bound-state density. We show that equalities between the Nth-order energy moment of the classical time delay and the Nth-order energy moment of the classical bound-state density hold in both a local and a global form. Local sum rules involve the time delay defined on a finite but otherwise arbitrary coordinate space volume S and the bound-state density associated with this same region. Global sum rules are those that obtain when S is the whole coordinate space. Both the local and global sum rules are derived for potentials of arbitrary shape and for scattering in any space dimension. Finally the set of classical sum rules, together with the known quantum mechanical analogs, are shown to provide a unified method of obtaining the high-temperature expansion of the classical, respectively the quantum-mechanical, virial coefficients

Quantum manifestations of classical resonance zones

International Nuclear Information System (INIS)

De Leon, N.; Davis, M.J.; Heller, E.J.

1984-01-01

We examine the concept of nodal breakup of wave functions as a criterion for quantum mechanical ergodicity. We find that complex nodal structure of wave functions is not sufficient to determine quantum mechanical ergodicity. The influence of classical resonances [which manifest themselves as classical resonance zones (CRZ)] may also be responsible for the seeming complexity of nodal structure. We quantify this by reexamining one of the two systems studied by Stratt, Handy, and Miller [J. Chem. Phys. 71, 3311 (1974)] from both a quantum mechanical and classical point of view. We conclude that quasiperiodic classical motion can account for highly distorted quantum eigenstates. One should always keep this in mind when addressing questions regarding quantum mechanical ergodicity

Optimum Onager: The Classical Mechanics of a Classical Siege Engine

Science.gov (United States)

Denny, Mark

2009-01-01

The onager is a throwing weapon of classical antiquity, familiar to both the ancient Greeks and Romans. Here we analyze the dynamics of onager operation and derive the optimum angle for launching a projectile to its maximum range. There is plenty of scope for further considerations about increasing onager range, and so by thinking about how this…

Manifestations of classical phase space structures in quantum mechanics

International Nuclear Information System (INIS)

Bohigas, O.; Ullmo, D.; Tomsovic, S.; Paris-11 Univ., 91 - Orsay

1992-11-01

Using two coupled quartic oscillators for illustration, the quantum mechanics of simple systems whose classical analogues have varying degrees of non-integrability is investigated. By taking advantage of discrete symmetries and dynamical quasidegeneracies it is shown that Percival's semiclassical classification scheme, i.e. eigenstates may be separated into a regular or an irregular group, basically works. Some observations of intermediate status states are made. Generalized ensembles are constructed which apply equally well to both spectral and eigenstate properties. They typically show non-universal, but nevertheless characteristic level fluctuations. In addition, they predict 'semiclassical localization' of eigenfunctions and 'quantum suppression of chaos' which are quantitatively borne out in the quantum systems. (author) 101 refs.; 27 figs.; 6 tabs

Scaling, scattering, and blackbody radiation in classical physics

International Nuclear Information System (INIS)

Boyer, Timothy H

2017-01-01

Here we discuss blackbody radiation within the context of classical theory. We note that nonrelativistic classical mechanics and relativistic classical electrodynamics have contrasting scaling symmetries which influence the scattering of radiation. Also, nonrelativistic mechanical systems can be accurately combined with relativistic electromagnetic radiation only provided the nonrelativistic mechanical systems are the low-velocity limits of fully relativistic systems. Application of the no-interaction theorem for relativistic systems limits the scattering mechanical systems for thermal radiation to relativistic classical electrodynamic systems, which involve the Coulomb potential. Whereas the naive use of nonrelativistic scatterers or nonrelativistic classical statistical mechanics leads to the Rayleigh–Jeans spectrum, the use of fully relativistic scatterers leads to the Planck spectrum for blackbody radiation within classical physics. (paper)

Quantum-classical hybrid dynamics – a summary

International Nuclear Information System (INIS)

Elze, Hans-Thomas

2013-01-01

A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of classical Hamiltonian mechanics suitably extended to quantum mechanics.

Classical and quantum dynamics from classical paths to path integrals

CERN Document Server

Dittrich, Walter

2017-01-01

Graduate students who wish to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name just a few topics. Well-chosen and detailed examples illustrate perturbation theory, canonical transformations and the action principle, and demonstrate the usage of path integrals. The fifth edition has been revised and enlarged to include chapters on quantum electrodynamics, in particular, Schwinger’s proper time method and the treatment of classical and quantum mechanics with Lie brackets and pseudocanonical transformations. It is shown that operator quantum electrodynamics can be equivalently described with c-numbers, as demonstrated by calculating the propagation function for an electron in a prescribed classical electromagnetic field.

Mathematical methods of classical physics

CERN Document Server

Cortés, Vicente

2017-01-01

This short primer, geared towards students with a strong interest in mathematically rigorous approaches, introduces the essentials of classical physics, briefly points out its place in the history of physics and its relation to modern physics, and explains what benefits can be gained from a mathematical perspective. As a starting point, Newtonian mechanics is introduced and its limitations are discussed. This leads to and motivates the study of different formulations of classical mechanics, such as Lagrangian and Hamiltonian mechanics, which are the subjects of later chapters. In the second part, a chapter on classical field theories introduces more advanced material. Numerous exercises are collected in the appendix.

Continuous quantum measurement and the quantum to classical transition

International Nuclear Information System (INIS)

Bhattacharya, Tanmoy; Habib, Salman; Jacobs, Kurt

2003-01-01

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

Zwitters: Particles between quantum and classical

International Nuclear Information System (INIS)

Wetterich, C.

2012-01-01

We describe both quantum particles and classical particles in terms of a classical statistical ensemble, with a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same quantum formalism. Quantum particles are characterized by a specific choice of observables and time evolution of the probability density. Then interference and tunneling are found within classical statistics. Zwitters are (effective) one-particle states for which the time evolution interpolates between quantum and classical particles. Experimental bounds on a small parameter can test quantum mechanics. -- Highlights: ► Quantum particles can be described within classical statistics. ► Classical particles are formulated in quantum formalism. ► Zwitters interpolate between classical and quantum particles. ► Zwitters allow for quantitative tests of quantum mechanics. ► Zwitters could be effective one-particle descriptions of droplets.

New application of functional integrals to classical mechanics

International Nuclear Information System (INIS)

Zherebtsov, Anton; Ilinski, Kirill

2005-01-01

In this Letter a new functional integral representation for classical dynamics is introduced. It is achieved by rewriting the Liouville picture in terms of bosonic creation-annihilation operators and utilizing the standard derivation of functional integrals for dynamical quantities in the coherent states representation. This results in a new class of functional integrals which are exactly solvable and can be found explicitly when the underlying classical systems are integrable

Classical trajectory methods in molecular collisions

International Nuclear Information System (INIS)

Porter, R.N.; Raff, L.M.

1976-01-01

The discussion of classical trajectory methods in molecular collisions includes classical dynamics, Hamiltonian mechanics, classical scattering cross sections and rate coefficients, statistical averaging, the selection of initial states, integration of equations of motion, analysis of final states, consecutive collisions, and the prognosis for classical molecular scattering calculations. 61 references

Particle spin dynamics as the grassmann variant of classical mechanics

International Nuclear Information System (INIS)

Berezin, F.A.; Marinov, M.S.

1976-01-01

A generalization of the calssical mechanics is presented. The dynamical variables are assumed to be elements of an algebra with anticommuting generators (The Grassmann algebra). The action functional and the Poisson brackets are defined. The equations of motion are deduced from the variational principle. The dynamics is described also by means of the Liouville equation for the phase-space distribution. The canonical quantization lead phase-space path integral approach to the quantum theory is also formulated. The theory is applied to describe the particle spin. Classical description of the spin precession and of the spin-orbital forces is given. The phase-space distribution and the interaction with an external field are also considered

Classical dynamics and its quantum analogues

International Nuclear Information System (INIS)

Park, D.

1979-01-01

In this book the author establishes mathematical connections between classical and quantum mechanics, between ray optics and wave optics. The approach is to consider classical mechanics as a limiting case of quantum mechanics, and ray optics as a limiting case of wave optics. The conceptual background is discussed where necessary, so the reader should be already fairly familiar with it. The main goal of this approach is the revelation that classical and quantum theory are not so different conceptually as one thinks at first exposure. The first chapters recall the basic facts about light waves and light rays and demonstrate the construction of Newtonian orbits from Schroedinger waves. In the following the Lagrangian and Hamiltonian formulation of few-body system is developed showing as often as possible the relations to the corresponding quantum systems. To illustrate the theory planetary motion using perturbation theory is treated in some detail and several calculations in general relativity such as the deflection and retardation of light by the sun and the precession of planetary perikelia are included. The final parts deal with the motions of systems of many particles. The quantum mechanics of rigid bodies is presented in analogy with the classical theory and contrasts are noted. There is also a discussion of the roles of spinors in the two theories. The book is intended as a text in classical mechanics for readers which have already some knowledge in classical and quantum mechanics. It may help to deepen their understanding of the relation between the old and new theory and show something of the ways in which new discoveries are made. (orig.) 891 HJ/orig. 892 BRE

Angular distribution of electrons ejected by charged particles. IV. Combined classical and quantum-mechanical treatment

NARCIS (Netherlands)

Boesten, L.G.J.; Bonsen, T.F.M.

1975-01-01

Angular distributions of electrons ejected from helium by 100 and 300 keV protons have been calculated by a method which is a comination of the classical three-body collision theory and the quantum-mechanical Born approximation. The results of this theory have been compared with the corresponding

How to quantize forces (?): An academic essay on how the strings could enter classical mechanics

Czech Academy of Sciences Publication Activity Database

Kochan, Denis

2010-01-01

Roč. 60, č. 2 (2010), s. 219-229 ISSN 0393-0440 R&D Projects: GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : Line element contact bundle * Classical mechanics * Dissipative systems Subject RIV: BE - Theoretical Physics Impact factor: 0.652, year: 2010

Solved problems in classical mechanics analytical and numerical solutions with comments

CERN Document Server

de Lange, O L

2010-01-01

Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation androtation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used to obtain andanalyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and...

Quantization in classical mechanics and its relation to the Bohmian Ψ-field

International Nuclear Information System (INIS)

Rusov, V.D.; Vlasenko, D.S.; Mavrodiev, S.Cht.

2011-01-01

Research highlights: →The Schroedinger equation is derived from the classical Hamiltonian mechanics. →This derivation is based on the Chetaev theorem on stable dynamical trajectories. →The conditions for correctness of trajectory quantum mechanics are discussed. - Abstract: Based on the Chetaev theorem on stable dynamical trajectories in the presence of dissipative forces, we obtain the generalized condition for stability of Hamilton systems in the form of the Schroedinger equation. It is shown that the energy of dissipative forces, which generate the Chetaev generalized condition of stability, coincides exactly with the Bohm 'quantum' potential. Within the frame-work of Bohmian quantum mechanics supplemented by the generalized Chetaev theorem and on the basis of the principle of least action for dissipative forces, we show that the squared amplitude of a wave function in the Schroedinger equation is equivalent semantically and syntactically to the probability density function for the number of particle trajectories, relative to which the velocity and the position of the particle are not hidden parameters. The conditions for the correctness of trajectory interpretation of quantum mechanics are discussed.

Quantum epistemology from subquantum ontology: Quantum mechanics from theory of classical random fields

Science.gov (United States)

Khrennikov, Andrei

2017-02-01

The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations. In classical mechanics the phase space description can be considered as the ontic description, here states are given by points λ =(x , p) of phase space. The dynamics of the ontic state is given by the system of Hamiltonian equations.We can also consider probability distributions on the phase space (or equivalently random variables valued in it). We call them probabilistic ontic states. Dynamics of probabilistic ontic states is given by the Liouville equation.In classical physics we can (at least in principle) measure both the coordinate and momentum and hence ontic states can be treated as epistemic states as well (or it is better to say that here epistemic states can be treated as ontic states). Probabilistic ontic states represent probabilities for outcomes of joint measurement of position and momentum.However, this was a very special, although very important, example of

Quantum formalism for classical statistics

Science.gov (United States)

Wetterich, C.

2018-06-01

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

Computation of disordered system from the first principles of classical mechanics and ℕℙ hard problem

Energy Technology Data Exchange (ETDEWEB)

Gevorkyan, A. S., E-mail: g-ashot@sci.am; Sahakyan, V. V. [National Academy of Sciences of the Republic of Armenia, Institute for Informatics and Automation Problems (Armenia)

2017-03-15

We study the classical 1D Heisenberg spin glasses in the framework of nearest-neighboring model. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from the first principles of classical mechanics lead to ℕℙ hard problem, that however in the limit of the statistical equilibrium can be calculated by ℙ algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.

Transport cross sections based on a screened interaction potential: Comparison of classical and quantum-mechanical results

International Nuclear Information System (INIS)

Vincent, R.; Juaristi, J.I.; Nagy, I.

2005-01-01

Standard classical and quantum-mechanical methods are used to characterize the momentum-transfer cross section needed in energy-loss calculations and simulations for heavy, swift charges moving in an electron gas. By applying a well-known, finite-range screened Coulombic potential energy to model the two-body collision, the quantitative applicability range of the classical cross section is investigated as a function of charge (Z), screening length (R), and scattering relative velocity (v). The a posteriori condition (Z/R)/v 2 <1, as an upper bound for heavy charges, is deduced for this applicability range from the comparative study performed

Quantum dynamics in open quantum-classical systems.

Science.gov (United States)

Kapral, Raymond

2015-02-25

Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.

Classical dynamics of particles and systems

CERN Document Server

Marion, Jerry B

1965-01-01

Classical Dynamics of Particles and Systems presents a modern and reasonably complete account of the classical mechanics of particles, systems of particles, and rigid bodies for physics students at the advanced undergraduate level. The book aims to present a modern treatment of classical mechanical systems in such a way that the transition to the quantum theory of physics can be made with the least possible difficulty; to acquaint the student with new mathematical techniques and provide sufficient practice in solving problems; and to impart to the student some degree of sophistication in handl

The statistical mechanics of the classical two-dimensional Coulomb gas is exactly solved

International Nuclear Information System (INIS)

Samaj, L

2003-01-01

The model under consideration is a classical 2D Coulomb gas of pointlike positive and negative unit charges, interacting via a logarithmic potential. In the whole stability range of temperatures, the equilibrium statistical mechanics of this fluid model is exactly solvable via an equivalence with the integrable 2D sine-Gordon field theory. The exact solution includes the bulk thermodynamics, special cases of the surface thermodynamics and the large-distance asymptotic behaviour of the two-body correlation functions

The classical behavior of measuring instruments

International Nuclear Information System (INIS)

Kraus, K.

1986-01-01

This paper constructs a quantum mechanical model of a counter monitoring the decay of an unstable microsystem. In spite of its quantum mechanical nature, the counter may be assumed to behave classically during the measurement. The relevance of this result for a particular interpretation of quantum mechanics is discussed. The quantum mechanical nature of the model counter could be easily detected in measurements of counter observables which do not commute with the observable P/sub +/. The statistical predictions for such measurements will be definitely incompatible with classical concepts

Feeding Behavior of Aplysia: A Model System for Comparing Cellular Mechanisms of Classical and Operant Conditioning

Science.gov (United States)

Baxter, Douglas A.; Byrne, John H.

2006-01-01

Feeding behavior of Aplysia provides an excellent model system for analyzing and comparing mechanisms underlying appetitive classical conditioning and reward operant conditioning. Behavioral protocols have been developed for both forms of associative learning, both of which increase the occurrence of biting following training. Because the neural…

There is no quantum ontology without classical ontology

Energy Technology Data Exchange (ETDEWEB)

Fink, Helmut [Institut fuer Theoretische Physik, Univ. Erlangen-Nuernberg (Germany)

2011-07-01

The relation between quantum physics and classical physics is still under debate. In his recent book ''Rational Reconstructions of Modern Physics'', Peter Mittelstaedt explores a route from classical to quantum mechanics by reduction and elimination of (some of) the ontological hypotheses underlying classical mechanics. While, according to Mittelstaedt, classical mechanics describes a fictitious world that does not exist in reality, he claims to achieve a universal quantum ontology that can be improved by incorporating unsharp properties and equipped with Planck's constant without any need to refer to classical concepts. In this talk, we argue that quantum ontology in Mittelstaedt's sense is not enough. Quantum ontology can never be universal as long as the difference between potential and real properties is not represented adequately. Quantum properties are potential, not (yet) real, be they sharp or unsharp. Hence, preparation and measurement presuppose classical concepts, even in quantum theory. We end up with a classical-quantum sandwich ontology, which is still less extravagant than Bohmian or many-worlds ontologies are.

Progress in classical and quantum variational principles

International Nuclear Information System (INIS)

Gray, C G; Karl, G; Novikov, V A

2004-01-01

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The reciprocal Maupertuis principle is the classical limit of Schroedinger's variational principle of wave mechanics and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems. '... the most beautiful and important discovery of Mechanics.' Lagrange to Maupertuis (November 1756)

Understanding the Planck blackbody spectrum and Landau diamagnetism within classical electromagnetism

International Nuclear Information System (INIS)

Boyer, Timothy H

2016-01-01

Electromagnetism is a relativistic theory, and one must exercise care in coupling this theory with nonrelativistic classical mechanics and with nonrelativistic classical statistical mechanics. Indeed historically, both the blackbody radiation spectrum and diamagnetism within classical theory have been misunderstood because of two crucial failures: (1) the neglect of classical electromagnetic zero-point radiation, and (2) the use of erroneous combinations of nonrelativistic mechanics with relativistic electrodynamics. Here we review the treatment of classical blackbody radiation, and show that the presence of Lorentz-invariant classical electromagnetic zero-point radiation can explain both the Planck blackbody spectrum and Landau diamagnetism at thermal equilibrium within classical electromagnetic theory. The analysis requires that relativistic electromagnetism is joined appropriately with simple nonrelativistic mechanical systems which can be regarded as the zero-velocity limits of relativistic systems, and that nonrelativistic classical statistical mechanics is applied only in the low-frequency limit when zero-point energy makes no contribution. (paper)

Comparison Of Quantum Mechanical And Classical Trajectory Calculations Of Cross Sections For Ion-Atom Impact Ionization of Negative - And Positive -Ions For Heavy Ion Fusion Applications

International Nuclear Information System (INIS)

Kaganovich, Igor D.; Startsev, Edward A.; Davidson, Ronald C.

2003-01-01

Stripping cross sections in nitrogen have been calculated using the classical trajectory approximation and the Born approximation of quantum mechanics for the outer shell electrons of 3.2GeV I - and Cs + ions. A large difference in cross section, up to a factor of six, calculated in quantum mechanics and classical mechanics, has been obtained. Because at such high velocities the Born approximation is well validated, the classical trajectory approach fails to correctly predict the stripping cross sections at high energies for electron orbitals with low ionization potential

Mechanical and Thermal Analysis of Classical Functionally Graded Coated Beam

Directory of Open Access Journals (Sweden)

Toudehdehghan Abdolreza

2018-01-01

Full Text Available The governing equation of a classical rectangular coated beam made of two layers subjected to thermal and uniformly distributed mechanical loads are derived by using the principle of virtual displacements and based on Euler-Bernoulli deformation beam theory (EBT. The aim of this paper was to analyze the static behavior of clamped-clamped thin coated beam under thermo-mechanical load using MATLAB. Two models were considered for composite coated. The first model was consisting of ceramic layer as a coated and substrate which was metal (HC model. The second model was consisting of Functionally Graded Material (FGM as a coated layer and metal substrate (FGC model. From the result it was apparent that the superiority of the FGC composite against conventional coated composite has been demonstrated. From the analysis, the stress level throughout the thickness at the interface of the coated beam for the FGC was reduced. Yet, the deflection in return was observed to increase. Therefore, this could cater to various new engineering applications where warrant the utilization of material that has properties that are well-beyond the capabilities of the conventional or yesteryears materials.

Mechanisms explaining Coulomb's electric force & Lorentz's magnetic force from a classical perspective

Science.gov (United States)

Correnti, Dan S.

2018-06-01

The underlying mechanisms of the fundamental electric and magnetic forces are not clear in current models; they are mainly mathematical constructs. This study examines the underlying physics from a classical viewpoint to explain Coulomb's electric force and Lorentz's magnetic force. This is accomplished by building upon already established physics. Although no new physics is introduced, extension of existing models is made by close examination. We all know that an electron carries a bound cylindrical B-field (CBF) as it translates. Here, we show how the electron CBF plays an intrinsic role in the generation of the electric and magnetic forces.

Integrable systems and lie symmetries in classical mechanics

International Nuclear Information System (INIS)

Sen, T.

1986-01-01

The interrelationship between integrability and symmetries in classical mechanics is studied. Two-dimensional time- and velocity-independent potentials form the domain of the study. It is shown that, contrary to folklore, existence of a single finite symmetry does not ensure integrability. A method due to Darboux is used to construct potentials that admit a time-independent invariant. All potentials admitting invariants linear or quadratic in the momentum coordinates are constructed. These are the only integrable potentials which can be expressed as arbitrary functions of certain arguments. A complete construction of potentials admitting higher-order invariants does not seem possible. However, the necessary general forms for potentials that admit a particular invariant of arbitrary order are found. These invariants must be spherically symmetric in the leading terms. Two kinds of symmetries are studied: point Lie symmetries of the Newtonian equations of motion for conservative potentials, and point Noether symmetries of the action functionals obtained from the standard Lagrangians associated with these potentials. All conservative potentials which admit these symmetries are constructed. The class of potentials admitting Noether symmetries is shown to be a subclass of those admitting Lie symmetries

Interaction between classical and quantum systems

International Nuclear Information System (INIS)

Sherry, T.N.; Sudarshan, E.C.G.

1977-10-01

An unconventional approach to the measurement problem in quantum mechanics is considered--the apparatus is treated as a classical system, belonging to the macro-world. In order to have a measurement the apparatus must interact with the quantum system. As a first step, the classical apparatus is embedded into a large quantum mechanical structure, making use of a superselection principle. The apparatus and system are coupled such that the apparatus remains classical (principle of integrity), and unambiguous information of the values of a quantum observable are transferred to the variables of the apparatus. Further measurement of the classical apparatus can be done, causing no problems of principle. Thus interactions causing pointers to move (which are not treated) can be added. The restrictions placed by the principle of integrity on the form of the interaction between classical and quantum systems are examined and illustration is given by means of a simple example in which one sees the principle of integrity at work

Semi-classical limit of relativistic quantum mechanics

Indian Academy of Sciences (India)

It is shown that the semi-classical limit of solutions to the Klein–Gordon equation gives the particle probability density that is in direct proportion to the inverse of the particle velocity. It is also shown that in the case of the Dirac equation a different result is obtained.

Quantum dynamics of classical stochastic systems

Energy Technology Data Exchange (ETDEWEB)

Casati, G

1983-01-01

It is shown that one hand Quantum Mechanics introduces limitations to the manifestations of chaotic motion resulting, for the case of the periodically kicked rotator, in the limitation of energy growth; also, as it is confirmed by numerical experiments, phenomena like the exponential instability of orbits, inherent to strongly chaotic systems, are absent here and therefore Quantum Mechanics appear to be more stable and predictable than Classical Mechanics. On the other hand, we have seen that nonrecurrent behavior may arise in Quantum Systems and it is connected to the presence of singular continuous spectrum. We conjecture that the classical chaotic behavior is reflected, at least partially, in the nature of the spectrum and the singular-continuity of the latter may possess a self-similar structure typical of classical chaos.

New derivation of quantum equations from classical stochastic arguments

OpenAIRE

Bergeron, H.

2003-01-01

In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This procedure was based on a Koopman-von Neumann approach where classical equations are reformulated into a quantumlike form. In this article, we develop a different derivation of quantum equations, based on purely classical stochastic arguments, taking some elem...

Integrable models in classical and quantum mechanics

International Nuclear Information System (INIS)

Jurco, B.

1991-01-01

Integrable systems are investigated, especially the rational and trigonometric Gaudin models. The Gaudin models are diagonalized for the case of classical Lie algebras. Their relation to the other integrable models and to the quantum inverse scattering method is investigated. Applications in quantum optics and plasma physics are discussed. (author). 94 refs

The Wigner transform and the semi-classical approximations

International Nuclear Information System (INIS)

Shlomo, S.

1985-01-01

The Wigner transform provides a reformulation of quantum mechanics in terms of classical concepts. Some properties of the Wigner transform of the density matrix which justify its interpretation as the quantum-mechanical analog of the classical phase-space distribution function are presented. Considering some applications, it is demonstrated that the Wigner distribution function serves as a good starting point for semi-classical approximations to properties of the (nuclear) many-body system

Modeling the classical nova outburst. I. Exploring the physics of a new mechanism

International Nuclear Information System (INIS)

Kutter, G.S.; Sparks, W.M.

1989-01-01

Model calculations were performed to describe a mechanism that produces classical nova outbursts on white dwarfs of 1 solar mass or less and for accretion rates of 4 x 10 to the -10th solar mass/yr or greater, i.e., the parameters corresponding to observed data of nova systems. Calculations point to four factors that can induce nuclear runaways of sufficient strength to eject about 0.0001 solar mass at speeds of several hundred to a few thousand km per second, as is observed in classical novae. These are (1) the effects of storage of angular momentum in the star's envelope during the accretion phase; (2) the reduction of centrifugal forces in the star's outer layers during the early nuclear runaway phase, through the inward transport of angular momentum; (3) the inward movement of the zone of peak nuclear burning through the convectively induced shear instability during the runaway phase; and (4) the mixing of original CO stellar matter and H-rich matter, also through the convectively induced shear instability. 58 refs

Advances in classical and analytical mechanics: A reviews of author’s results

Directory of Open Access Journals (Sweden)

Hedrih-Stevanović Katica R.

2013-01-01

Full Text Available A review, in subjective choice, of author’s scientific results in area of: classical mechanics, analytical mechanics of discrete hereditary systems, analytical mechanics of discrete fractional order system vibrations, elastodynamics, nonlinear dynamics and hybrid system dynamics is presented. Main original author’s results were presented through the mathematical methods of mechanics with examples of applications for solving problems of mechanical real system dynamics abstracted to the theoretical models of mechanical discrete or continuum systems, as well as hybrid systems. Paper, also, presents serries of methods and scientific results authored by professors Mitropolyski, Andjelić and Rašković, as well as author’s of this paper original scientific research results obtained by methods of her professors. Vector method based on mass inertia moment vectors and corresponding deviational vector components for pole and oriented axis, defined in 1991 by K. Hedrih, is presented. Results in construction of analytical dynamics of hereditary discrete system obtained in collaboration with O. A. Gorosho are presented. Also, some selections of results author’s postgraduate students and doctorantes in area of nonlinear dynamics are presented. A list of scientific projects headed by author of this paper is presented with a list of doctoral dissertation and magister of sciences thesis which contain scientific research results obtained under the supervision by author of this paper or their fist doctoral candidates. [Projekat Ministarstva nauke Republike Srbije, br. ON174001: Dynamics of hybrid systems with complex structures

Classical Yang-Mills mechanics. Nonlinear colour oscillations

International Nuclear Information System (INIS)

Matinyan, S.G.; Savvidi, G.K.; Ter-Arutyunyan-Savvidi, N.G.

1981-01-01

A novel class of solutions of the classical Yang-Mills equations in the Minkowsky space which leads to nonlinear colour oscillations is studied. The system discribing these oscillations is apparently stochastic. Periodic trajectories corresponding to the solutions are found and studied and it is demonstrated that they constitute at least an enumerable set [ru

Hybrid Quantum Mechanical-Quasi-Classical Model for Evaluating Ionization and Stripping Cross Sections in Atom-Ion Collisions

CERN Document Server

Kaganovich, I D; Startsev, E

2005-01-01

Ion-atom ionization cross sections are needed in many applications employing the propagation of fast ions through matter. When experimental data or full-scale theoretical calculations are non-existent, approximate methods must be used. The most robust and easy-to-use approximations include the Born approximation of quantum mechanics and the quasi-classical approach utilizing classical mechanics together with the Bohr-Sommerfeld quantization rule.* The simplest method to extend the validity of both approaches is to combine them, i.e., use the two different approaches but only for the regions of impact parameters in which they are valid, and sum the results to obtain the total cross section. We have recently investigated theoretically and experimentally the stripping of more than 18 different pairs of projectile and target atoms in the range of 3-38 MeV/amu to study the range of validity of various approximations. The results of the modified approach agree better with the experimental data than either the Born ...

Photonic Rutherford scattering: A classical and quantum mechanical analogy in ray and wave optics

Science.gov (United States)

Selmke, Markus; Cichos, Frank

2013-06-01

Using Fermat's least-optical-path principle, the family of ray trajectories through a special (but common) type of a gradient refractive index lens n(r)=n0+ΔnR /r is solved analytically. The solution gives a ray equation r(ϕ) that is closely related to Rutherford scattering trajectories; we therefore refer to this refraction process as "photonic Rutherford scattering." It is shown that not only do the classical limits correspond but also the wave-mechanical pictures coincide—the time-independent Schrödingier equation and the Helmholtz equation permit the same mapping between the scattering of massive particles and optical scalar waves. Scattering of narrow beams of light finally recovers the classical trajectories. The analysis suggests that photothermal single-particle microscopy measures photonic Rutherford scattering in specific limits and allows for an individual single-scatterer probing. A macroscopic experiment is demonstrated to directly measure the scattering angle to impact parameter relation, which is otherwise accessible only indirectly in Rutherford-scattering experiments.

Elementary classical hydrodynamics

CERN Document Server

Chirgwin, B H; Langford, W J; Maxwell, E A; Plumpton, C

1967-01-01

Elementary Classical Hydrodynamics deals with the fundamental principles of elementary classical hydrodynamics, with emphasis on the mechanics of inviscid fluids. Topics covered by this book include direct use of the equations of hydrodynamics, potential flows, two-dimensional fluid motion, waves in liquids, and compressible flows. Some general theorems such as Bernoulli's equation are also considered. This book is comprised of six chapters and begins by introducing the reader to the fundamental principles of fluid hydrodynamics, with emphasis on ways of studying the motion of a fluid. Basic c

Classical-quantum correspondence in electron-positron pair creation

International Nuclear Information System (INIS)

Chott, N. I.; Su, Q.; Grobe, R.

2007-01-01

We examine the creation of electron-positron pairs in a very strong force field. Using numerical solutions to quantum field theory we calculate the spatial and momentum probability distributions for the created particles. A comparison with classical mechanical phase space calculations suggests that despite the fully relativistic and quantum mechanical nature of the matter creation process, most aspects can be reproduced accurately in terms of classical mechanics

Stochasticity of Yang-Mills classical mechanics and its elimination by higgs mechanism

International Nuclear Information System (INIS)

Matinyan, S.G.; Savvidy, G.K.; Ter-Arutunyan-Savvidy, N.G.

1981-01-01

Phases of classical gauge systems with spontaneous symmetry breaking are considered. The two-dimensional case is studied in detail. The critical value of the parameter πsub(c) which determines phase transformations is calculated

On the Calculation of Quantum Mechanical Ground States from Classical Geodesic Motion on Certain Spaces of Constant Negative Curvature

CERN Document Server

Tomaschitz, R

1989-01-01

We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are bounded and recurrent in both directions of the time evolution a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schrodinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories.

Quantum-mechanical machinery for rational decision-making in classical guessing game

Science.gov (United States)

Bang, Jeongho; Ryu, Junghee; Pawłowski, Marcin; Ham, Byoung S.; Lee, Jinhyoung

2016-02-01

In quantum game theory, one of the most intriguing and important questions is, “Is it possible to get quantum advantages without any modification of the classical game?” The answer to this question so far has largely been negative. So far, it has usually been thought that a change of the classical game setting appears to be unavoidable for getting the quantum advantages. However, we give an affirmative answer here, focusing on the decision-making process (we call ‘reasoning’) to generate the best strategy, which may occur internally, e.g., in the player’s brain. To show this, we consider a classical guessing game. We then define a one-player reasoning problem in the context of the decision-making theory, where the machinery processes are designed to simulate classical and quantum reasoning. In such settings, we present a scenario where a rational player is able to make better use of his/her weak preferences due to quantum reasoning, without any altering or resetting of the classically defined game. We also argue in further analysis that the quantum reasoning may make the player fail, and even make the situation worse, due to any inappropriate preferences.

Quantum-mechanical machinery for rational decision-making in classical guessing game.

Science.gov (United States)

Bang, Jeongho; Ryu, Junghee; Pawłowski, Marcin; Ham, Byoung S; Lee, Jinhyoung

2016-02-15

In quantum game theory, one of the most intriguing and important questions is, "Is it possible to get quantum advantages without any modification of the classical game?" The answer to this question so far has largely been negative. So far, it has usually been thought that a change of the classical game setting appears to be unavoidable for getting the quantum advantages. However, we give an affirmative answer here, focusing on the decision-making process (we call 'reasoning') to generate the best strategy, which may occur internally, e.g., in the player's brain. To show this, we consider a classical guessing game. We then define a one-player reasoning problem in the context of the decision-making theory, where the machinery processes are designed to simulate classical and quantum reasoning. In such settings, we present a scenario where a rational player is able to make better use of his/her weak preferences due to quantum reasoning, without any altering or resetting of the classically defined game. We also argue in further analysis that the quantum reasoning may make the player fail, and even make the situation worse, due to any inappropriate preferences.

Persistent entanglement in the classical limit

Energy Technology Data Exchange (ETDEWEB)

Everitt, M J [Centre for Physical Electronics and Quantum Technology, School of Science and Technology, University of Sussex, Falmer, Brighton BN1 9QT (United Kingdom); Clark, T D [Centre for Physical Electronics and Quantum Technology, School of Science and Technology, University of Sussex, Falmer, Brighton BN1 9QT (United Kingdom); Stiffell, P B [Centre for Physical Electronics and Quantum Technology, School of Science and Technology, University of Sussex, Falmer, Brighton BN1 9QT (United Kingdom); Ralph, J F [Department of Electrical and Electronic Engineering, Liverpool University, Brownlow Hill, Liverpool L69 3GJ (United Kingdom); Bulsara, A R [Space and Naval Warfare Systems Center, Code 2363, 53560 Hull Street, San Diego, CA 92152-5001 (United States); Harland, C J [Centre for Physical Electronics and Quantum Technology, School of Science and Technology, University of Sussex, Falmer, Brighton BN1 9QT (United Kingdom)

2005-02-01

The apparent difficulty in recovering classical nonlinear dynamics and chaos from standard quantum mechanics has been the subject of a great deal of interest over the last 20 years. For open quantum systems-those coupled to a dissipative environment and/or a measurement device-it has been demonstrated that chaotic-like behaviour can be recovered in the appropriate classical limit. In this paper, we investigate the entanglement generated between two nonlinear oscillators, coupled to each other and to their environment. Entanglement-the inability to factorize coupled quantum systems into their constituent parts-is one of the defining features of quantum mechanics. Indeed, it underpins many of the recent developments in quantum technologies. Here, we show that the entanglement characteristics of two 'classical' states (chaotic and periodic solutions) differ significantly in the classical limit. In particular, we show that significant levels of entanglement are preserved only in the chaotic-like solutions.

Decoherence and the quantum-to-classical transition

International Nuclear Information System (INIS)

Schlosshauer, M.A.

2007-01-01

The ultimate introduction, textbook, and reference on decoherence and the quantum-to-classical transition. This detailed but accessible text describes the concepts, formalism, interpretation, and experimental observation of decoherence and explains how decoherence is responsible for the emergence, from the realm of quantum mechanics, of the classical world of our experience. Topics include: - Foundational problems at the quantum-classical border; - The role of the environment and entanglement; - Environment-induced loss of coherence and superselection; - Scattering-induced decoherence and spatial localization; - Master equations; - Decoherence models; - Experimental realization of ''Schroedinger's kittens'' and their decoherence; - Quantum computing, quantum error correction, and decoherence-free subspaces; - Implications of decoherence for interpretations of quantum mechanics and for the ''measurement problem''; - Decoherence in the brain. Written in a lucid and concise style that is accessible to all readers with a basic knowledge of quantum mechanics, this stimulating book tells the ''classical from quantum'' story in a comprehensive and coherent manner that brings together the foundational, technical, and experimental aspects of decoherence. It will be an indispensable resource for newcomers and experts alike. (orig.)

On second quantization methods applied to classical statistical mechanics

International Nuclear Information System (INIS)

Matos Neto, A.; Vianna, J.D.M.

1984-01-01

A method of expressing statistical classical results in terms of mathematical entities usually associated to quantum field theoretical treatment of many particle systems (Fock space, commutators, field operators, state vector) is discussed. It is developed a linear response theory using the 'second quantized' Liouville equation introduced by Schonberg. The relationship of this method to that of Prigogine et al. is briefly analyzed. The chain of equations and the spectral representations for the new classical Green's functions are presented. Generalized operators defined on Fock space are discussed. It is shown that the correlation functions can be obtained from Green's functions defined with generalized operators. (Author) [pt

Logical reformulation of quantum mechanics. III. Classical limit and irreversibility

International Nuclear Information System (INIS)

Omnes, R.

1988-01-01

This paper deals with two questions: (1) It contains a proof of the fact that consistent quantum representations of logic tend to the classical representation of logic when Planck's constant tends to zero. This result is obtained by using the microlocal analysis of partial differential equations and the Weyl calculus, which turn out to be the proper mathematical framework for this type of problems. (2) The analysis of the limitations of this proof turn out to be of physical significance, in particular when one considers quantum systems having for their classical version a Kolmogorov K-system. These limitations are used to show the existence of a best classical description for such a system leading to an objective definition of entropy. It is shown that in such a description the approach to equilibrium is strictly reduced to a Markov process

Biophysical mechanisms complementing "classical" cell biology.

Science.gov (United States)

Funk, Richard H W

2018-01-01

This overview addresses phenomena in cell- and molecular biology which are puzzling by their fast and highly coordinated way of organization. Generally, it appears that informative processes probably involved are more on the biophysical than on the classical biochemical side. The coordination problem is explained within the first part of the review by the topic of endogenous electrical phenomena. These are found e.g. in fast tissue organization and reorganization processes like development, wound healing and regeneration. Here, coupling into classical biochemical signaling and reactions can be shown by modern microscopy, electronics and bioinformatics. Further, one can follow the triggered reactions seamlessly via molecular biology till into genetics. Direct observation of intracellular electric processes is very difficult because of e.g. shielding through the cell membrane and damping by other structures. Therefore, we have to rely on photonic and photon - phonon coupling phenomena like molecular vibrations, which are addressed within the second part. Molecules normally possess different charge moieties and thus small electromagnetic (EMF) patterns arise during molecular vibration. These patterns can now be measured best within the optical part of the spectrum - much less in the lower terahertz till kHz and lower Hz part (third part of this review). Finally, EMFs facilitate quantum informative processes in coherent domains of molecular, charge and electron spin motion. This helps to coordinate such manifold and intertwined processes going on within cells, tissues and organs (part 4). Because the phenomena described in part 3 and 4 of the review still await really hard proofs we need concerted efforts and a combination of biophysics, molecular biology and informatics to unravel the described mysteries in "physics of life".

On the calculation of quantum mechanical ground states from classical geodesic motion on certain spaces of constant negative curvature

International Nuclear Information System (INIS)

Tomaschitz, R.

1989-01-01

We consider geodesic motion on three-dimensional Riemannian manifolds of constant negative curvature, topologically equivalent to S x ]0,1[, S a compact surface of genus two. To those trajectories which are recurrent in both directions of the time evolution t → +∞, t → -∞ a fractal limit set is associated whose Hausdorff dimension is intimately connected with the quantum mechanical energy ground state, determined by the Schroedinger operator on the manifold. We give a rather detailed and pictorial description of the hyperbolic spaces we have in mind, discuss various aspects of classical and quantum mechanical motion on them as far as they are needed to establish the connection between energy ground state and Hausdorff dimension and give finally some examples of ground state calculations in terms of Hausdorff dimensions of limit sets of classical trajectories. (orig.)

Classical counterexamples to Bell's inequalities

International Nuclear Information System (INIS)

Orlov, Yuri F.

2002-01-01

This paper shows that a classical system containing a conventional yes/no decision-making component can behave like a quantum system of spin measurements in many ways (although it lacks a wave function) when, in principle, there are no deterministic decision procedures to govern the decision making, and when probabilistic decision procedures consistent with the system are introduced. Most notably, the system violates Bell's inequalities. Moreover, since the system is simple and macroscopic, its similarities to quantum systems arguably provide an insight into quantum mechanics and, in particular, EPR experiments. Thus, from the qualitative correspondences, decisions↔quantum measurements and the impossibility of deterministic decision procedures↔quantum noncommutativity, we conclude that the violation of Bell's inequalities in quantum mechanics does not require the existence of an unknown nonclassical nonlocality. It can merely be a result of local noncommutativity combined with nonlocalities of the classical type. The proposed classical decision-making system is a nonquantum theoretical construct possessing complementarity features in Bohr's sense

CLASSICAL AND NON-CLASSICAL PHILOSOPHICAL ANTHROPOLOGY: COMPARATIVE ANALYSIS

Directory of Open Access Journals (Sweden)

T. A. Kozlova

2018-01-01

Full Text Available Introduction: The goals and values of human life, the search for the meaning of human existence contain the potential for a meaningful, progressive development of philosophical and anthropological ideas at any time in history. One of the tasks of philosophical anthropology is the formation of the image of man, the choice of ways to achieve the ideal, the methods of comprehension and resolution of universal problems. The increasing processes of differentiation in science led to the formation of different views on the nature of man, to the distinction between classical and non-classical philosophical anthropology. А comparative analysis of these trends is given in this article.Materials and methods: The dialectical method is preferred in the question of research methodology, the hermeneutic and phenomenological approaches are used.Results: The development of philosophical anthropology correlates with the challenges of modernity. By tracking the trends of human change, philosophical anthropology changes the approach to the consideration of its main subject of research. The whole array of disciplines that study man comes to new discoveries, new theories, and philosophical anthropology changes its view of the vision, challenging the principles of classical philosophical anthropology.Classical philosophical anthropology elevates the biological nature of man to a pedestal, non-classical philosophical anthropology actualizes questions of language, culture, thinking, understanding, actualizes the hermeneutic and phenomenological approaches. The desire to understand a person in classical philosophical anthropology is based on the desire to fully reveal the biological mechanisms in a person. The perspective of treating a person in nonclassical philosophical anthropology is polyformen: man as a text, as a dreaming self, as an eternal transition. Non-classical philosophical anthropology, goes from the idea of identity to the idea of variability, from

Classical and semiclassical aspects of chemical dynamics

International Nuclear Information System (INIS)

Gray, S.K.

1982-08-01

Tunneling in the unimolecular reactions H 2 C 2 → HC 2 H, HNC → HCN, and H 2 CO → H 2 + CO is studied with a classical Hamiltonian that allows the reaction coordinate and transverse vibrational modes to be considered directly. A combination of classical perturbation theory and the semiclassical WKB method allows tunneling probabilities to be obtained, and a statistical theory (RRKM) is used to construct rate constants for these reactions in the tunneling regime. In this fashion, it is found that tunneling may be important, particularly for low excitation energies. Nonadiabatic charge transfer in the reaction Na + I → Na + + I - is treated with classical trajectories based on a classical Hamiltonian that is the analogue of a quantum matrix representation. The charge transfer cross section obtained is found to agree reasonably well with the exact quantum results. An approximate semiclassical formula, valid at high energies, is also obtained. The interaction of radiation and matter is treated from a classical viewpoint. The excitation of an HF molecule in a strong laser is described with classical trajectories. Quantum mechanical results are also obtained and compared to the classical results. Although the detailed structure of the pulse time averaged energy absorption cannot be reproduced classically, classical mechanics does predict the correct magnitude of energy absorption, as well as certain other qualitative features. The classical behavior of a nonrotating diatomic molecule in a strong laser field is considered further, by generating a period advance map that allows the solution over many periods of oscillation of the laser to be obtained with relative ease. Classical states are found to form beautiful spirals in phase space as time progresses. A simple pendulum model is found to describe the major qualitative features

Is Classical Statistical Mechanics Self-Consistent? (A paper in honor of C. F. von Weizsäcker, 1912-2007

Directory of Open Access Journals (Sweden)

Enders P.

2007-07-01

Full Text Available In addition to his outstanding achievements in physics and activities in policy, C.-F. von Weizsäcker is famous for his talks, given as a member of the Academy Leopoldina. Due to the latter, I could learn quite a lot from his methodological writings. In particular, he is the only modern thinker I’m aware of who has pointed to the difference between Newton’s and Laplace’s notions of state. But this difference is essential for the relationship between classical and quantum physics. Moreover it is the clue to overcoming Gibbs’ paradox within classical statistical mechanics itself.

[Today's meaning of classical authors of political thinking].

Science.gov (United States)

Weinacht, Paul-Ludwig

2005-01-01

How can classical political authors be actualised? The question is asked in a discipline which is founded in old traditions: the political science. One of its great matters is the history of political ideas. Classic authors are treated in many books, but they are viewed in different perspectives; colleagues do not agree with shining and bad examples. For actualising classic we have to go a methodically reflected way: historic not historicistic, with sensibility for classic and christian norms without dogmatism or scepticism. Searching the permanent problems we try to translate the original concepts of the classic authors carefully in our time. For demonstrating our method of actualising, we choose the French classical author Montesquieu. His famous concept of division of powers is misunderstood as a "liberal" mechanism which works in itself in favour of freedom (such as Kant made work a "natural mechanism" in a people of devils in favour of their legality); in reality Montesquieu acknoledges that constitutional und organisational work cannot stabilise themselves but must be found in social character and in human virtues.

Quantum versus classical dynamics in the optical centrifuge

Science.gov (United States)

Armon, Tsafrir; Friedland, Lazar

2017-09-01

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

Evolution of the Stability Work from Classic Retaining Walls to Mechanically Stabilized Earth Walls

Directory of Open Access Journals (Sweden)

Anghel Stanciu

2008-01-01

Full Text Available For the consolidation of soil mass and the construction of the stability works for roads infrastructure it was studied the evolution of these kinds of works from classical retaining walls - common concrete retaining walls, to the utilization in our days of the modern and competitive methods - mechanically stabilized earth walls. Like type of execution the variety of the reinforced soil is given by the utilization of different types of reinforcing inclusions (steel strips, geosynthetics, geogrids or facing (precast concrete panels, dry cast modular blocks, metal sheets and plates, gabions, and wrapped sheets of geosynthetics.

Collagen V haploinsufficiency in a murine model of classic Ehlers-Danlos syndrome is associated with deficient structural and mechanical healing in tendons.

Science.gov (United States)

Johnston, Jessica M; Connizzo, Brianne K; Shetye, Snehal S; Robinson, Kelsey A; Huegel, Julianne; Rodriguez, Ashley B; Sun, Mei; Adams, Sheila M; Birk, David E; Soslowsky, Louis J

2017-12-01

Classic Ehlers-Danlos syndrome (EDS) patients suffer from connective tissue hyperelasticity, joint instability, skin hyperextensibility, tissue fragility, and poor wound healing due to heterozygous mutations in COL5a1 or COL5a2 genes. This study investigated the roles of collagen V in establishing structure and function in uninjured patellar tendons as well as in the injury response using a Col5a1 +/- mouse, a model for classic EDS. These analyses were done comparing tendons from a classic EDS model (Col5a1 +/- ) with wild-type controls. Tendons were subjected to mechanical testing, histological, and fibril analysis before injury as well as 3 and 6 weeks after injury. We found that Col5a1 +/- tendons demonstrated diminished recovery of mechanical competency after injury as compared to normal wild-type tendons, which recovered their pre-injury values by 6 weeks post injury. Additionally, the Col5a1 +/- tendons demonstrated altered fibril morphology and diameter distributions compared to the wild-type tendons. This study indicates that collagen V plays an important role in regulating collagen fibrillogenesis and the associated recovery of mechanical integrity in tendons after injury. In addition, the dysregulation with decreased collagen V expression in EDS is associated with a diminished injury response. The results presented herein have the potential to direct future targeted therapeutics for classic EDS patients. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2707-2715, 2017. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk Formulations

Science.gov (United States)

Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

2012-06-01

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics.

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner–Rusk Formulations

International Nuclear Information System (INIS)

Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

2012-01-01

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner–Rusk formulation on classical mechanics.

Classical Limit and Quantum Logic

Science.gov (United States)

Losada, Marcelo; Fortin, Sebastian; Holik, Federico

2018-02-01

The analysis of the classical limit of quantum mechanics usually focuses on the state of the system. The general idea is to explain the disappearance of the interference terms of quantum states appealing to the decoherence process induced by the environment. However, in these approaches it is not explained how the structure of quantum properties becomes classical. In this paper, we consider the classical limit from a different perspective. We consider the set of properties of a quantum system and we study the quantum-to-classical transition of its logical structure. The aim is to open the door to a new study based on dynamical logics, that is, logics that change over time. In particular, we appeal to the notion of hybrid logics to describe semiclassical systems. Moreover, we consider systems with many characteristic decoherence times, whose sublattices of properties become distributive at different times.

Bohmian measures and their classical limit

KAUST Repository

Markowich, Peter

2010-09-01

We consider a class of phase space measures, which naturally arise in the Bohmian interpretation of quantum mechanics. We study the classical limit of these so-called Bohmian measures, in dependence on the scale of oscillations and concentrations of the sequence of wave functions under consideration. The obtained results are consequently compared to those derived via semi-classical Wigner measures. To this end, we shall also give a connection to the theory of Young measures and prove several new results on Wigner measures themselves. Our analysis gives new insight on oscillation and concentration effects in the semi-classical regime. © 2010 Elsevier Inc.

Information transport in classical statistical systems

Science.gov (United States)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

Classical-limit S-matrix for heavy ion scattering

International Nuclear Information System (INIS)

Donangelo, R.J.

1977-01-01

An integral representation for the classical limit of the quantum mechanical S-matrix is developed and applied to heavy-ion Coulomb excitation and Coulomb-nuclear interference. The method combines the quantum principle of superposition with exact classical dynamics to describe the projectile-target system. A detailed consideration of the classical trajectories and of the dimensionless parameters that characterize the system is carried out. The results are compared, where possible, to exact quantum mechanical calculations and to conventional semiclassical calculations. It is found that in the case of backscattering the classical limit S-matrix method is able to almost exactly reproduce the quantum-mechanical S-matrix elements, and therefore the transition probabilities, even for projectiles as light as protons. The results also suggest that this approach should be a better approximation for heavy-ion multiple Coulomb excitation than earlier semiclassical methods, due to a more accurate description of the classical orbits in the electromagnetic field of the target nucleus. Calculations using this method indicate that the rotational excitation probabilities in the Coulomb-nuclear interference region should be very sensitive to the details of the potential at the surface of the nucleus, suggesting that heavy-ion rotational excitation could constitute a sensitive probe of the nuclear potential in this region. The application to other problems as well as the present limits of applicability of the formalism are also discussed

An investigation of student understanding of classical ideas related to quantum mechanics: Potential energy diagrams and spatial probability density

Science.gov (United States)

Stephanik, Brian Michael

This dissertation describes the results of two related investigations into introductory student understanding of ideas from classical physics that are key elements of quantum mechanics. One investigation probes the extent to which students are able to interpret and apply potential energy diagrams (i.e., graphs of potential energy versus position). The other probes the extent to which students are able to reason classically about probability and spatial probability density. The results of these investigations revealed significant conceptual and reasoning difficulties that students encounter with these topics. The findings guided the design of instructional materials to address the major problems. Results from post-instructional assessments are presented that illustrate the impact of the curricula on student learning.

On singular interaction potentials in classical statistical mechanics

International Nuclear Information System (INIS)

Zagrebnov, V.A.; Pastur, L.A.

1978-01-01

A classical system of particles with stable two-body interaction potential is considered. It is shown that for a certain class of highly singular stable two-body potentials a cut-off procedure preserves the stability of the potential. The thermodynamical potentials (pressure and free energy density) and correlation functions are proved to have the property of asymptotic independence with respect to the continuation of the interaction potentials near singularity

Mathematics of classical and quantum physics

CERN Document Server

Byron, Frederick W

Well-organized text designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Topics include theory of vector spaces, analytic function theory, Green's function method of solving differential and partial differential equations, theory of groups, more. Many problems, suggestions for further reading.

Decoherence and the quantum-to-classical transition

CERN Document Server

Schlosshauer, Maximilian

2007-01-01

The ultimate introduction, textbook, and reference on decoherence and the quantum-to-classical transition. This detailed but accessible text describes the concepts, formalism, interpretation, and experimental observation of decoherence and explains how decoherence is responsible for the emergence, from the realm of quantum mechanics, of the classical world of our experience. Topics include: • Foundational problems at the quantum–classical border; • The role of the environment and entanglement; • Environment-induced loss of coherence and superselection; • Scattering-induced decoherence and spatial localization; • Master equations; • Decoherence models; • Experimental realization of "Schrödinger kittens" and their decoherence; • Quantum computing, quantum error correction, and decoherence-free subspaces; • Implications of decoherence for interpretations of quantum mechanics and for the "measurement problem"; • Decoherence in the brain. Written in a lucid and concise style that is accessib...

Quantum-classical correspondence for the inverted oscillator

Science.gov (United States)

Maamache, Mustapha; Ryeol Choi, Jeong

2017-11-01

While quantum-classical correspondence for a system is a very fundamental problem in modern physics, the understanding of its mechanism is often elusive, so the methods used and the results of detailed theoretical analysis have been accompanied by active debate. In this study, the differences and similarities between quantum and classical behavior for an inverted oscillator have been analyzed based on the description of a complete generalized Airy function-type quantum wave solution. The inverted oscillator model plays an important role in several branches of cosmology and particle physics. The quantum wave packet of the system is composed of many sub-packets that are localized at different positions with regular intervals between them. It is shown from illustrations of the probability density that, although the quantum trajectory of the wave propagation is somewhat different from the corresponding classical one, the difference becomes relatively small when the classical excitation is sufficiently high. We have confirmed that a quantum wave packet moving along a positive or negative direction accelerates over time like a classical wave. From these main interpretations and others in the text, we conclude that our theory exquisitely illustrates quantum and classical correspondence for the system, which is a crucial concept in quantum mechanics. Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1A09919503)

Mechanism of the Glycosidic Bond Cleavage of Mismatched Thymine in Human Thymine DNA Glycosylase Revealed by Classical Molecular Dynamics and Quantum Mechanical/Molecular Mechanical Calculations.

Science.gov (United States)

Kanaan, Natalia; Crehuet, Ramon; Imhof, Petra

2015-09-24

Base excision of mismatched or damaged nucleotides catalyzed by glycosylase enzymes is the first step of the base excision repair system, a machinery preserving the integrity of DNA. Thymine DNA glycosylase recognizes and removes mismatched thymine by cleaving the C1'-N1 bond between the base and the sugar ring. Our quantum mechanical/molecular mechanical calculations of this reaction in human thymine DNA glycosylase reveal a requirement for a positive charge in the active site to facilitate C1'-N1 bond scission: protonation of His151 significantly lowers the free energy barrier for C1'-N1 bond dissociation compared to the situation with neutral His151. Shuttling a proton from His151 to the thymine base further reduces the activation free energy for glycosidic bond cleavage. Classical molecular dynamics simulations of the H151A mutant suggest that the mutation to the smaller, neutral, residue increases the water accessibility of the thymine base, rendering direct proton transfer from the bulk feasible. Quantum mechanical/molecular mechanical calculations of the glycosidic bond cleavage reaction in the H151A mutant show that the activation free energy is slightly lower than in the wild-type enzyme, explaining the experimentally observed higher reaction rates in this mutant.

Photosynthetic Energy Transfer at the Quantum/Classical Border.

Science.gov (United States)

Keren, Nir; Paltiel, Yossi

2018-06-01

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

Quantum healing of classical singularities in power-law spacetimes

Energy Technology Data Exchange (ETDEWEB)

Helliwell, T M [Department of Physics, Harvey Mudd College, Claremont, CA 91711 (United States); Konkowski, D A [Department of Mathematics, US Naval Academy, Annapolis, MD 21402 (United States)

2007-07-07

We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. Among these four-parameter 'power-law' metrics, we identify those parameters for which the spacetimes have classical singularities as r {yields} 0. We show that a large set of such classically-singular spacetimes is nevertheless non-singular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint, so that the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities. Using these metrics, the broadest class yet studied to compare classical with quantum singularities, we explore the physical reasons why some that are singular classically are 'healed' quantum mechanically, while others are not. We show that most (but not all) of the remaining quantum-mechanically singular spacetimes can be excluded if either the weak energy condition or the dominant energy condition is invoked, and we briefly discuss the effect of this work on the strong cosmic censorship conjecture.

The Ups and Downs of Classical and Quantum Formulations of Magnetic Resonance

DEFF Research Database (Denmark)

Hanson, Lars G.

2015-01-01

in the connection between the seemingly very different classical and quantum descriptions. Such understanding is needed by students, authors, and lecturers, in particular. With limited complexity, the text introduces probabilistic classical and quantum mechanics with emphasis on similarities and differences......), which gives insight into the resonance phenomenon itself as well as spectral features resulting from intramolecular J-coupling of atomic nuclei. It is discussed how classical and quantum mechanics give rise to similar expectations for basic NMR and why a classical understanding is central....

MYC translocation-negative classical Burkitt lymphoma cases: an alternative pathogenetic mechanism involving miRNA deregulation

DEFF Research Database (Denmark)

Leucci, E; Cocco, M; Onnis, A

2008-01-01

at the standardization of FISH procedures in lymphoma diagnosis, we found that five cases out of 35 classic endemic BLs were negative for MYC translocations by using a split-signal as well as a dual-fusion probe. Here we investigated the expression pattern of miRNAs predicted to target c-Myc, in BL cases, to clarify...... whether alternative pathogenetic mechanisms may be responsible for lymphomagenesis in cases lacking the MYC translocation. miRNAs are a class of small RNAs that are able to regulate gene expression at the post-transcriptional level. Several studies have reported their involvement in cancer...

Factorizations of one-dimensional classical systems

International Nuclear Information System (INIS)

Kuru, Senguel; Negro, Javier

2008-01-01

A class of one-dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra. These two functions lead directly to two time-dependent integrals of motion from which the phase motions are derived algebraically. The systems so obtained constitute the classical analogues of the well known factorizable one-dimensional quantum mechanical systems

The dynamics of the H(+) + D(2) reaction: a comparison of quantum mechanical wavepacket, quasi-classical and statistical-quasi-classical results.

Science.gov (United States)

Jambrina, P G; Aoiz, F J; Bulut, N; Smith, Sean C; Balint-Kurti, G G; Hankel, M

2010-02-07

A detailed study of the proton exchange reaction H(+) + D(2)(v = 0, j = 0) --> HD + D(+) on its ground 1(1)A' potential energy surface has been carried out using 'exact' close-coupled quantum mechanical wavepacket (WP-EQM), quasi-classical trajectory (QCT), and statistical quasi-classical trajectory (SQCT) calculations for a range of collision energies starting from the reaction threshold to 1.3 eV. The WP-EQM calculations include all total angular momenta up to J(max) = 50, and therefore the various dynamical observables are converged up to 0.6 eV. It has been found that it is necessary to include all Coriolis couplings to obtain reliable converged results. Reaction probabilities obtained using the different methods are thoroughly compared as a function of the total energy for a series of J values. Comparisons are also made of total reaction cross sections as function of the collision energy, and rate constants. In addition, opacity functions, integral cross sections (ICS) and differential cross sections (DCS) are presented at 102 meV, 201.3 meV and 524.6 meV collision energy. The agreement between the three sets of results is only qualitative. The QCT calculations fail to describe the overall reactivity and most of the dynamical observables correctly. At low collision energies, the QCT method is plagued by the lack of conservation of zero point energy, whilst at higher collision energies and/or total angular momenta, the appearance of an effective repulsive potential associated with the centrifugal motion "over" the well causes a substantial decrease of the reactivity. In turn, the statistical models overestimate the reactivity over the whole range of collision energies as compared with the WP-EQM method. Specifically, at sufficiently high collision energies the reaction cannot be deemed to be statistical and important dynamical effects seem to be present. In general the WP-EQM results lie in between those obtained using the QCT and SQCT methods. One of the main

Beyond quantum-classical analogies: high time for agreement?

Science.gov (United States)

Marrocco, Michele

Lately, many quantum-classical analogies have been investigated and published in many acknowledged journals. Such a surge of research on conceptual connections between quantum and classical physics forces us to ask whether the correspondence between the quantum and classical interpretation of the reality is deeper than the correspondence principle stated by Bohr. Here, after a short introduction to quantum-classical analogies from the recent literature, we try to examine the question from the perspective of a possible agreement between quantum and classical laws. A paradigmatic example is given in the striking equivalence between the classical Mie theory of electromagnetic scattering from spherical scatterers and the corresponding quantum-mechanical wave scattering analyzed in terms of partial waves. The key features that make the correspondence possible are examined and finally employed to deal with the fundamental blackbody problem that marks the initial separation between classical and quantum physics. The procedure allows us to recover the blackbody spectrum in classical terms and the proof is rich in consequences. Among them, the strong analogy between the quantum vacuum and its classical counterpart.

How far can radiation from atoms be represented by classical models

International Nuclear Information System (INIS)

Haar, D. Ter; Wergeland, H.

1978-01-01

In recent years some phenomena currently assumed to be essentially quantal have found an accurate description in classical terms. An example is Lamb's semiclassical theory of the laser. Consequently many physicists are discussing in how far a full quantum mechanical treatment is necessary. A good many of the formulae for the radiation from atoms can certainly be obtained by classical methods. But these methods fail already at the question of the line profiles. Even though the damping is a simple mechanism - classically speaking. It seems inevitible that the semi-classical formulae must be limited to those phenomena which essentially only involve the averages of photon numbers. (JIW)

Classical mechanics with calculus of variations and optimal control an intuitive introduction

CERN Document Server

Levi, Mark

2014-01-01

This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this boo...

To quantum averages through asymptotic expansion of classical averages on infinite-dimensional space

International Nuclear Information System (INIS)

Khrennikov, Andrei

2007-01-01

We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of scaling of the covariation operator of a Gaussian measure and the second (Frechet) derivative of a functional. In this way we couple classical average (given by an infinite-dimensional Gaussian integral) and quantum average (given by the von Neumann trace formula). We can interpret this mathematical construction as a procedure of 'dequantization' of quantum mechanics. We represent quantum mechanics as an asymptotic projection of classical statistical mechanics with infinite-dimensional phase space. This space can be represented as the space of classical fields, so quantum mechanics is represented as a projection of 'prequantum classical statistical field theory'

On the paramagnetism of spin in the classical limit

International Nuclear Information System (INIS)

Hogreve, H.

1985-12-01

We consider particles with spin 1/2 in external electromagnetic fields. Although in many quantum mechanical situations they show a paramagnetic behaviour, within non-relativistic quantum theory a universal paramagnetic influence of spin fails to be true in general. Here we investigate the paramagnetism of spin in the framework of a classical theory. Applying previous results for the classical limit slash-h→O we obtain a classical expression corresponding to the quantum partition function of Hamiltonians with spin variables. For this classical partition function simple estimates lead to a paramagnetic inequality which demonstrates that indeed in the classical limit the spin shows a general paramagnetic behaviour. (author)

General treatment of quantum and classical spinning particles in external fields

Science.gov (United States)

Obukhov, Yuri N.; Silenko, Alexander J.; Teryaev, Oleg V.

2017-11-01

We develop the general theory of spinning particles with electric and magnetic dipole moments moving in arbitrary electromagnetic, inertial, and gravitational fields. Both the quantum-mechanical and classical dynamics is investigated. We start from the covariant Dirac equation extended to a spin-1/2 fermion with anomalous magnetic and electric dipole moments and then perform the relativistic Foldy-Wouthuysen transformation. This transformation allows us to obtain the quantum-mechanical equations of motion for the physical operators in the Schrödinger form and to establish the classical limit of relativistic quantum mechanics. The results obtained are then compared to the general classical description of the spinning particle interacting with electromagnetic, inertial and gravitational fields. The complete agreement between the quantum mechanics and the classical theory is proven in the general case. As an application of the results obtained, we consider the dynamics of a spinning particle in a gravitational wave and analyze the prospects of using the magnetic resonance setup to find possible manifestations of the gravitational wave on spin.

Quantum Models of Classical World

Directory of Open Access Journals (Sweden)

Petr Hájíček

2013-02-01

Full Text Available This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties, and the problem of quantum measurement. A considerable progress has been achieved, based on four distinct new ideas. First, objective properties are associated with states rather than with values of observables. Second, all classical properties are selected properties of certain high entropy quantum states of macroscopic systems. Third, registration of a quantum system is strongly disturbed by systems of the same type in the environment. Fourth, detectors must be distinguished from ancillas and the states of registered systems are partially dissipated and lost in the detectors. The paper has two aims: a clear explanation of all new results and a coherent and contradiction-free account of the whole quantum mechanics including all necessary changes of its current textbook version.

Classical fracture mechanics methods

International Nuclear Information System (INIS)

Schwalbe, K.H.; Heerens, J.; Landes, J.D.

2007-01-01

Comprehensive Structural Integrity is a reference work which covers all activities involved in the assurance of structural integrity. It provides engineers and scientists with an unparalleled depth of knowledge in the disciplines involved. The new online Volume 11 is dedicated to the mechanical characteristics of materials. This paper contains the chapter 11.02 of this volume and is structured as follows: Test techniques; Analysis; Fracture behavior; Fracture toughness tests for nonmetals

Stabilization of classic and quantum systems

International Nuclear Information System (INIS)

Buts, V.A.

2012-01-01

It is shown that the mechanism of quantum whirligig can be successfully used for stabilization of classical systems. In particular, the conditions for stabilization of charged particles and radiation fluxes in plasma are found.

Conjugate dynamical systems: classical analogue of the quantum energy translation

International Nuclear Information System (INIS)

Torres-Vega, Gabino

2012-01-01

An aspect of quantum mechanics that has not been fully understood is the energy shift generated by the time operator. In this study, we introduce the use of the eigensurfaces of dynamical variables and commutators in classical mechanics to study the classical analogue of the quantum translation of energy. We determine that there is a conjugate dynamical system that is conjugate to Hamilton's equations of motion, and then we generate the analogue of the time operator and use it in the translation of points along the energy direction, i.e. the classical analogue of the Pauli theorem. The theory is illustrated with a nonlinear oscillator model. (paper)

Two-slit experiment: quantum and classical probabilities

International Nuclear Information System (INIS)

Khrennikov, Andrei

2015-01-01

Inter-relation between quantum and classical probability models is one of the most fundamental problems of quantum foundations. Nowadays this problem also plays an important role in quantum technologies, in quantum cryptography and the theory of quantum random generators. In this letter, we compare the viewpoint of Richard Feynman that the behavior of quantum particles cannot be described by classical probability theory with the viewpoint that quantum–classical inter-relation is more complicated (cf, in particular, with the tomographic model of quantum mechanics developed in detail by Vladimir Man'ko). As a basic example, we consider the two-slit experiment, which played a crucial role in quantum foundational debates at the beginning of quantum mechanics (QM). In particular, its analysis led Niels Bohr to the formulation of the principle of complementarity. First, we demonstrate that in complete accordance with Feynman's viewpoint, the probabilities for the two-slit experiment have the non-Kolmogorovian structure, since they violate one of basic laws of classical probability theory, the law of total probability (the heart of the Bayesian analysis). However, then we show that these probabilities can be embedded in a natural way into the classical (Kolmogorov, 1933) probability model. To do this, one has to take into account the randomness of selection of different experimental contexts, the joint consideration of which led Feynman to a conclusion about the non-classicality of quantum probability. We compare this embedding of non-Kolmogorovian quantum probabilities into the Kolmogorov model with well-known embeddings of non-Euclidean geometries into Euclidean space (e.g., the Poincaré disk model for the Lobachvesky plane). (paper)

Mechanistic insights into Mg2+-independent prenylation by CloQ from classical molecular mechanics and hybrid quantum mechanics/molecular mechanics molecular dynamics simulations.

Science.gov (United States)

Bayse, Craig A; Merz, Kenneth M

2014-08-05

Understanding the mechanism of prenyltransferases is important to the design of engineered proteins capable of synthesizing derivatives of naturally occurring therapeutic agents. CloQ is a Mg(2+)-independent aromatic prenyltransferase (APTase) that transfers a dimethylallyl group to 4-hydroxyphenylpyruvate in the biosynthetic pathway for clorobiocin. APTases consist of a common ABBA fold that defines a β-barrel containing the reaction cavity. Positively charged basic residues line the inside of the β-barrel of CloQ to activate the pyrophosphate leaving group to replace the function of the Mg(2+) cofactor in other APTases. Classical molecular dynamics simulations of CloQ, its E281G and F68S mutants, and the related NovQ were used to explore the binding of the 4-hydroxyphenylpyruvate (4HPP) and dimethylallyl diphosphate substrates in the reactive cavity and the role of various conserved residues. Hybrid quantum mechanics/molecular mechanics potential of mean force (PMF) calculations show that the effect of the replacement of the Mg(2+) cofactor with basic residues yields a similar activation barrier for prenylation to Mg(2+)-dependent APTases like NphB. The topology of the binding pocket for 4HPP is important for selective prenylation at the ortho position of the ring. Methylation at this position alters the conformation of the substrate for O-prenylation at the phenol group. Further, a two-dimensional PMF scan shows that a "reverse" prenylation product may be a possible target for protein engineering.

Tensor algebra over Hilbert space: Field theory in classical phase space

International Nuclear Information System (INIS)

Matos Neto, A.; Vianna, J.D.M.

1984-01-01

It is shown using tensor algebras, namely Symmetric and Grassmann algebras over Hilbert Space that it is possible to introduce field operators, associated to the Liouville equation of classical statistical mechanics, which are characterized by commutation (for Symmetric) and anticommutation (for Grassmann) rules. The procedure here presented shows by construction that many-particle classical systems admit an algebraic structure similar to that of quantum field theory. It is considered explicitly the case of n-particle systems interacting with an external potential. A new derivation of Schoenberg's result about the equivalence between his field theory in classical phase space and the usual classical statistical mechanics is obtained as a consequence of the algebraic structure of the theory as introduced by our method. (Author) [pt

The nonlinear dynamics of the classical few body problem

International Nuclear Information System (INIS)

Tabor, M.

1981-01-01

The complicated behavior that small dynamical systems can display is reviewed and its relevance to such diverse fields as celestial mechanics, semi-classical mechanics and fluid dynamics is discussed. (orig.)

A derivation of the Derbenev-Kondratenko formula using semi-classical electrodynamics

International Nuclear Information System (INIS)

Mane, S.R.

1985-11-01

We present a detailed exposition of the mechanism for the build-up of polarization in electron storage rings. A semi-classical approach is used to derive the rate of growth and asymptotic degree of polarization in an electron storage ring (the Derbenev-Kondratenko formula). Statistical mechanical concepts used to obtain as classical an understanding as possible of this phenomenon. (orig.)

Non-classicality criteria: Glauber-Sudarshan P function and Mandel ? parameter

Science.gov (United States)

Alexanian, Moorad

2018-01-01

We calculate exactly the quantum mechanical, temporal Wigner quasiprobability density for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state. The Wigner function allows us to calculate the fluctuations in photon number and the quadrature variance. We contrast the difference between the non-classicality criteria, which is independent of the displacement parameter ?, based on the Glauber-Sudarshan quasiprobability distribution ? and the classical/non-classical behaviour of the Mandel ? parameter, which depends strongly on ?. We find a phase transition as a function of ? such that at the critical point ?, ?, as a function of ?, goes from strictly classical, for ?, to a mixed classical/non-classical behaviour, for ?.

Classical analog for electronic degrees of freedom in nonadiabatic collision processes

International Nuclear Information System (INIS)

Meyer, H.; Miller, W.H.

1979-01-01

It is shown how a formally exact classical analog can be defined for a finite dimensional (in Hilbert space) quantum mechanical system. This approach is then used to obtain a classical model for the electronic degrees of freedom in a molecular collision system, and the combination of this with the usual classical description of the heavy particle (i.e., nuclear) motion provides a completely classical model for the electronic and heavy particle degrees of freedom. The resulting equations of motion are shown to be equivalent to describing the electronic degrees of freedom by the time-dependent Schroedinger equation, the time dependence arising from the classical motion of the nuclei, the trajectory of which is determined by the quantum mechanical average (i.e., Ehrenfest) force on the nuclei. Quantizing the system via classical S-matrix theory is shown to provide a dynamically consistent description of nonadiabatic collision processes; i.e., different electronic transitions have different heavy particle trajectories and, for example, the total energy of the electronic and heavy particle degrees of freedom is conserved. Application of this classical model for the electronic degrees of freedom (plus classical S-matrix theory) to the two-state model problem shows that the approach provides a good description of the electronic dynamics

Beam structures classical and advanced theories

CERN Document Server

Carrera, Erasmo; Petrolo, Marco

2011-01-01

Beam theories are exploited worldwide to analyze civil, mechanical, automotive, and aerospace structures. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc.  Most of these models are problem dependent: they provide reliable results for a given problem, for instance a given section and cannot be applied to a different one. Beam Structures: Classical and Advanced Theories proposes a new original unified approach to beam theory that includes practically all classical and advanced models for be

Driven topological systems in the classical limit

Science.gov (United States)

Duncan, Callum W.; Öhberg, Patrik; Valiente, Manuel

2017-03-01

Periodically driven quantum systems can exhibit topologically nontrivial behavior, even when their quasienergy bands have zero Chern numbers. Much work has been conducted on noninteracting quantum-mechanical models where this kind of behavior is present. However, the inclusion of interactions in out-of-equilibrium quantum systems can prove to be quite challenging. On the other hand, the classical counterpart of hard-core interactions can be simulated efficiently via constrained random walks. The noninteracting model, proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013), 10.1103/PhysRevX.3.031005], has a special point for which the system is equivalent to a classical random walk. We consider the classical counterpart of this model, which is exact at a special point even when hard-core interactions are present, and show how these quantitatively affect the edge currents in a strip geometry. We find that the interacting classical system is well described by a mean-field theory. Using this we simulate the dynamics of the classical system, which show that the interactions play the role of Markovian, or time-dependent disorder. By comparing the evolution of classical and quantum edge currents in small lattices, we find regimes where the classical limit considered gives good insight into the quantum problem.

Breakdown of the classical description of a local system

DEFF Research Database (Denmark)

Eran, Kot; Grønbech-Jensen, Niels; Nielsen, Bo Melholt

2012-01-01

We provide a straightforward demonstration of a fundamental difference between classical and quantum mechanics for a single local system: namely, the absence of a joint probability distribution of the position x and momentum p. Elaborating on a recently reported criterion by Bednorz and Belzig...... of the breakdown of a classical description of the underlying state. Most importantly, the criterion used does not rely on quantum mechanics and can thus be used to demonstrate nonclassicality of systems not immediately apparent to exhibit quantum behavior. The criterion is directly applicable to any system...... [ Phys. Rev. A 83 052113 (2011)] we derive a simple criterion that must be fulfilled for any joint probability distribution in classical physics. We demonstrate the violation of this criterion using the homodyne measurement of a single photon state, thus proving a straightforward signature...

Bohmian measures and their classical limit

KAUST Repository

Markowich, Peter; Paul, Thierry; Sparber, Christof

2010-01-01

We consider a class of phase space measures, which naturally arise in the Bohmian interpretation of quantum mechanics. We study the classical limit of these so-called Bohmian measures, in dependence on the scale of oscillations and concentrations

Classical limit of the quantum inverse scattering problem

International Nuclear Information System (INIS)

Bogdanov, I.V.

1986-01-01

This paper studies the passage to the limit of classical mechanics which is realized in the formalism of Marchenko's method for a spherically symmetric inverse problem of quantum scattering for fixed angular momentum. The limit is considered for the general case of partial waves with arbitrary values of the orbital number 1>0 in the lowest order of perturbation theory. It is shown how in the limit h→0 in the quantum inverse problem the integral Able transformation characteristic of classical inverse problems arises. The classical inversion formula with delay time is derived from the Marchenko equation

Quantum vertex model for reversible classical computing.

Science.gov (United States)

Chamon, C; Mucciolo, E R; Ruckenstein, A E; Yang, Z-C

2017-05-12

Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex model and its complexity is reflected in the dynamics of the relaxation of the system to its ground state. We use thermal annealing with and without 'learning' to explore typical computational problems. We also construct a mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating an approach to reversible classical computation based on state-of-the-art implementations of quantum annealing.

First order mean field games - explicit solutions, perturbations and connection with classical mechanics

KAUST Repository

Gomes, Diogo A.

2016-01-06

We present recent developments in the theory of first-order mean-field games (MFGs). A standard assumption in MFGs is that the cost function of the agents is monotone in the density of the distribution. This assumption leads to a comprehensive existence theory and to the uniqueness of smooth solutions. Here, our goals are to understand the role of local monotonicity in the small perturbation regime and the properties of solutions for problems without monotonicity. Under a local monotonicity assumption, we show that small perturbations of MFGs have unique smooth solutions. In addition, we explore the connection between first-order MFGs and classical mechanics and KAM theory. Next, for non-monotone problems, we construct non-unique explicit solutions for a broad class of first-order mean-field games. We provide an alternative formulation of MFGs in terms of a new current variable. These examples illustrate two new phenomena: the non-uniqueness of solutions and the breakdown of regularity.

First order mean field games - explicit solutions, perturbations and connection with classical mechanics

KAUST Repository

Gomes, Diogo A.; Nurbekyan, Levon; Prazeres, Mariana

2016-01-01

We present recent developments in the theory of first-order mean-field games (MFGs). A standard assumption in MFGs is that the cost function of the agents is monotone in the density of the distribution. This assumption leads to a comprehensive existence theory and to the uniqueness of smooth solutions. Here, our goals are to understand the role of local monotonicity in the small perturbation regime and the properties of solutions for problems without monotonicity. Under a local monotonicity assumption, we show that small perturbations of MFGs have unique smooth solutions. In addition, we explore the connection between first-order MFGs and classical mechanics and KAM theory. Next, for non-monotone problems, we construct non-unique explicit solutions for a broad class of first-order mean-field games. We provide an alternative formulation of MFGs in terms of a new current variable. These examples illustrate two new phenomena: the non-uniqueness of solutions and the breakdown of regularity.

Is tapentadol different from classical opioids? A review of the evidence.

Science.gov (United States)

Langford, Richard M; Knaggs, Roger; Farquhar-Smith, Paul; Dickenson, Anthony H

2016-11-01

Tapentadol is a single molecule able to deliver analgesia by two distinct mechanisms, a feature which differentiates it from many other analgesics. Pre-clinical data demonstrate two mechanisms of action: mu-opioid receptor agonist activity and noradrenaline re-uptake inhibition. From these, one may predict that tapentadol would be applicable across a broad spectrum of pain from nociceptive to neuropathic. The evidence in animal models suggests that norepinephrine re-uptake inhibition (NRI) is a key mechanism and may even predominate over opioid actions in chronic (and especially neuropathic) pain states, reinforcing that tapentadol is different to classical opioids and may, therefore, be an a priori choice for the treatment of neuropathic and mixed pain. The clinical studies and subsequent practice experience and surveillance support the concept of opioid and non-opioid mechanisms of action. The reduced incidence of some of the typical opioid-induced side effects, compared to equianalgesic doses of classical opioids, supports the hypothesis that tapentadol analgesia is only partially mediated by opioid agonist mechanisms. Both the pre-clinical and clinical profiles appear to be differentiated from those of classical opioids.

On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type

Directory of Open Access Journals (Sweden)

Gülden Gün Polat

2014-01-01

Full Text Available In this study we apply partial Noether and λ-symmetry approaches to a second-order nonlinear autonomous equation of the form y′′+fyy′+g(y=0, called Liénard equation corresponding to some important problems in classical mechanics field with respect to f(y and g(y functions. As a first approach we utilize partial Lagrangians and partial Noether operators to obtain conserved forms of Liénard equation. Then, as a second approach, based on the λ-symmetry method, we analyze λ-symmetries for the case that λ-function is in the form of λ(x,y,y′=λ1(x,yy′+λ2(x,y. Finally, a classification problem for the conservation forms and invariant solutions are considered.

Nanotribology investigations with classical molecular dynamics

NARCIS (Netherlands)

Solhjoo, Soheil

2017-01-01

This thesis presents a number of nanotribological problems investigated by means of classical molecular dynamics (MD) simulations, within the context of the applicability of continuum mechanics contact theories at the atomic scale. Along these lines, three different themes can be recognized herein:

Classical and quantum dynamics from classical paths to path integrals

CERN Document Server

Dittrich, Walter

2016-01-01

Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name a few. Well-chosen and detailed examples illustrate the perturbation theory, canonical transformations, the action principle and demonstrate the usage of path integrals. This new edition has been revised and enlarged with chapters on quantum electrodynamics, high energy physics, Green’s functions and strong interaction.

Classical motion and coherent states for Poeschl-Teller potentials

International Nuclear Information System (INIS)

Cruz y Cruz, S.; Kuru, S.; Negro, J.

2008-01-01

The trigonometric and hyperbolic Poeschl-Teller potentials are dealt with from the point of view of classical and quantum mechanics. We show that there is a natural correspondence between the algebraic structure of these two approaches for both kind of potentials. Then, the coherent states are constructed and the appropriate classical variables are compared with the expected values of their corresponding quantum operators

Classical system boundaries cannot be determined within quantum Darwinism

Science.gov (United States)

Fields, Chris

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

Classical mechanics in non-commutative phase space

International Nuclear Information System (INIS)

Wei Gaofeng; Long Chaoyun; Long Zhengwen; Qin Shuijie

2008-01-01

In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. (authors)

Polarizable Force Field for DNA Based on the Classical Drude Oscillator: I. Refinement Using Quantum Mechanical Base Stacking and Conformational Energetics.

Science.gov (United States)

Lemkul, Justin A; MacKerell, Alexander D

2017-05-09

Empirical force fields seek to relate the configuration of a set of atoms to its energy, thus yielding the forces governing its dynamics, using classical physics rather than more expensive quantum mechanical calculations that are computationally intractable for large systems. Most force fields used to simulate biomolecular systems use fixed atomic partial charges, neglecting the influence of electronic polarization, instead making use of a mean-field approximation that may not be transferable across environments. Recent hardware and software developments make polarizable simulations feasible, and to this end, polarizable force fields represent the next generation of molecular dynamics simulation technology. In this work, we describe the refinement of a polarizable force field for DNA based on the classical Drude oscillator model by targeting quantum mechanical interaction energies and conformational energy profiles of model compounds necessary to build a complete DNA force field. The parametrization strategy employed in the present work seeks to correct weak base stacking in A- and B-DNA and the unwinding of Z-DNA observed in the previous version of the force field, called Drude-2013. Refinement of base nonbonded terms and reparametrization of dihedral terms in the glycosidic linkage, deoxyribofuranose rings, and important backbone torsions resulted in improved agreement with quantum mechanical potential energy surfaces. Notably, we expand on previous efforts by explicitly including Z-DNA conformational energetics in the refinement.

Classical and quantum investigations of four-dimensional maps with a mixed phase space

International Nuclear Information System (INIS)

Richter, Martin

2012-01-01

Systems with more than two degrees of freedom are of fundamental importance for the understanding of problems ranging from celestial mechanics to molecules. Due to the dimensionality the classical phase-space structure of such systems is more difficult to understand than for systems with two or fewer degrees of freedom. This thesis aims for a better insight into the classical as well as the quantum mechanics of 4D mappings representing driven systems with two degrees of freedom. In order to analyze such systems, we introduce 3D sections through the 4D phase space which reveal the regular and chaotic structures. We introduce these concepts by means of three example mappings of increasing complexity. After a classical analysis the systems are investigated quantum mechanically. We focus especially on two important aspects: First, we address quantum mechanical consequences of the classical Arnold web and demonstrate how quantum mechanics can resolve this web in the semiclassical limit. Second, we investigate the quantum mechanical tunneling couplings between regular and chaotic regions in phase space. We determine regular-to-chaotic tunneling rates numerically and extend the fictitious integrable system approach to higher dimensions for their prediction. Finally, we study resonance-assisted tunneling in 4D maps.

Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces

International Nuclear Information System (INIS)

Khrennikov, Andrei

2010-01-01

One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical random fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.

Classical and quantum chaotic scattering in a muffin tin potential

International Nuclear Information System (INIS)

Brandis, S.

1995-05-01

In this paper, we study the classical mechanics, the quantum mechanics and the semi-classical approximation of the 2-dimensional scattering from a muffin tin potential. The classical dynamical system for Coulombic muffin tins is proven to be chaotic by explicit construction of the exponentially increasing number of periodic orbits. These are all shown to be completely unstable (hyperbolic). By methods of the thermodynamic formalism we can determine the Hausdorff dimension, escape rate and Kolmogorov-Sinai-entropy of the system. An extended KKR-method is developed to determine the quantum mechanical S-matrix. We compare a few integrable scattering examples with the results of the muffin tin scattering. Characteristic features of the spectrum of eigenphases turn out to be the level repulsion and long range rigidity as compared to a completely random spectrum. In the semiclassical analysis we can rederive the regularized Gutzwiller trace formula directly from the exact KKR-determinant to prove that no further terms contribute in the case of the muffin tin potential. The periodic orbit sum allows to draw some qualitative conclusions about the effects of classical chaos on the quantum mechanics. In the context of scaling systems the theory of almost periodic functions is discussed as a possible mathematical foundation for the semiclassical periodic orbit sums. Some results that can be obtained from this analysis are developed in the context of autocorrelation functions and distribution functions for chaotic scattering systems. (orig.)

Comparison of Classical and Quantum Bremsstrahlung

International Nuclear Information System (INIS)

Pratt, R.H.; Uskov, D.B.; Korol, A.V.; Obolensky, O.I.

2003-01-01

Classical features persist in bremsstrahlung at surprisingly high energies, while quantum features are present at low energies. For Coulomb bremsstrahlung this is related to the similar properties of Coulomb scattering. For bremsstrahlung in a screened potential, the low energy spectrum and angular distribution exhibit structures. In quantum mechanics these structures are associated with zeroes of particular angular-momentum transfer matrix elements at particular energies, a continuation of the Cooper minima in atomic photoeffect. They lead to transparency windows in free-free absorption. The trajectories of these zeroes in the plane of initial and final transition energies (bound and continuum) has been explored. Corresponding features have now been seen in classical bremsstrahlung, resulting from reduced contributions from particular impact parameters at particular energies. This has suggested the possibility of a more unified treatment of classical and quantum bremsstrahlung, based on the singularities of the scattering amplitude in angular momentum

Gauge fixings, evolution generators and world-line conditions in relativistic classical mechanics with constraints

International Nuclear Information System (INIS)

Lusanna, L.

1981-01-01

After a review of the main models for classical relativistic N-particle systems based upon Dirac's theory of constraints, a detailed study of their Hamiltonian formulation is made. The choice of the arbitrary functions and of the gauge-fixing constraints and the associated realizations of the reduced phase-space and of the observables by means of Dirac brackets are examined in detail. The restrictions on the gauge fixings to obtain compatibility between the evolution in the reduced phase space, generated by the total energy of the system, and the one in the constraint hypersurface, generated by the Dirac Hamiltonian, are found. It is also demonstrated that these restrictions are nothing else than the world-line conditions, i.e. gauge transformations are needed to ensure the objective existence of the world-lines and manifest covariance is broken. This is due to the property of the Dirac brackets of preserving the gauge fixings in every frame of reference. Predictive mechanics and the Currie-Hill world-line conditions are not in contradiction with the previous results: avoiding the Dirac-bracket mechanism, they save the manifest covariance but at the price of using accelerations which are complicated functions of the original potentials depending upon the whole history of the system. (author)

Construction of classical and non-classical coherent photon states

International Nuclear Information System (INIS)

Honegger, Reinhard; Rieckers, Alfred

2001-01-01

It is well known that the diagonal matrix elements of all-order coherent states for the quantized electromagnetic field have to constitute a Poisson distribution with respect to the photon number. The present work gives first the summary of a constructive scheme, developed previously, which determines in terms of an auxiliary Hilbert space all possible off-diagonal elements for the all-order coherent density operators in Fock space and which identifies all extremal coherent states. In terms of this formalism it is then demonstrated that each pure classical coherent state is a uniformly phase locked (quantum) coherent superposition of number states. In a mixed classical coherent state the exponential of the locked phase is shown to be replaced by a rather arbitrary unitary operator in the auxiliary Hilbert space. On the other hand classes for density operators--and for their normally ordered characteristic functions--of non-classical coherent states are obtained, especially by rather weak perturbations of classical coherent states. These illustrate various forms of breaking the classical uniform phase locking and exhibit rather peculiar properties, such as asymmetric fluctuations for the quadrature phase operators. Several criteria for non-classicality are put forward and applied to the elaborated non-classical coherent states, providing counterexamples against too simple arguments for classicality. It is concluded that classicality is only a stable concept for coherent states with macroscopic intensity

Classical, Semi-classical and Quantum Noise

CERN Document Server

Poor, H; Scully, Marlan

2012-01-01

David Middleton was a towering figure of 20th Century engineering and science and one of the founders of statistical communication theory. During the second World War, the young David Middleton, working with Van Fleck, devised the notion of the matched filter, which is the most basic method used for detecting signals in noise. Over the intervening six decades, the contributions of Middleton have become classics. This collection of essays by leading scientists, engineers and colleagues of David are in his honor and reflect the wide  influence that he has had on many fields. Also included is the introduction by Middleton to his forthcoming book, which gives a wonderful view of the field of communication, its history and his own views on the field that he developed over the past 60 years. Focusing on classical noise modeling and applications, Classical, Semi-Classical and Quantum Noise includes coverage of statistical communication theory, non-stationary noise, molecular footprints, noise suppression, Quantum e...

From classical physics to quantum physics. An historically-critical deductive derivation with application examples from solid-state physics

International Nuclear Information System (INIS)

Enders, P.

2006-01-01

This book goes a novel way from classical physics to quantum physics. After the description of Euler's and Helmholtz's representations of classical mechanics the Schroedinger equation is derivated without making any additional assumptions about the nature of quantum mechanical systems. Thereby not the differences between but the common properties of classical and quantum mechanics are accentuated and four fundamental problems of the quantization named by Schroedinger are solved. Extensively to the historical literature is related. This book applies not only to students and scientists but also to teachers and historians of natural sciences: It contains many details which enter no more into modern presentations of classical mechanics, but are important for the understanding of quantum mechanics [de

The Classic: On Rest and Pain: Lecture XIV.

Science.gov (United States)

Hilton, John

2009-09-01

This Classic article is a reprint of the original work by John Hilton, On Rest and Pain: Lecture XIV. An accompanying biographical sketch on John Hilton, MD, is available at DOI 10.1007/s11999-009-0927-2 . The Classic Article is reprinted with courtesy from Hilton J. On The Influence of Mechanical and Physiological Rest in the Treatment of Accidents and Surgical Diseases, and the Diagnostic Value of Pain. London, England: Bell and Daldy; 1863.

Axiomatic electrodynamics and microscopic mechanics

International Nuclear Information System (INIS)

Yussouff, M.

1981-04-01

A new approach to theoretical physics, along with the basic formulation of a new MICROSCOPIC MECHANICS for the motion of small charged particles is described in this set of lecture notes. Starting with the classical (Newtonian) mechanics and classical fields, the important but well known properties of Classical Electromagnetic field are discussed up to section 4. The next nection describes the usual radiation damping theory and its difficulties. It is argued that the usual treatment of radiation damping is not valid for small space and time intervals and the true description of motion requires a new type of mechanics - the MICROSCOPIC MECHANICS: Section 6 and 7 are devoted to showing that not only the new microscopic mechanics goes over to Newtonian mechanics in the proper limit, but also it is closely connected with Quantum Mechanics. All the known results of the Schroedinger theory can be reproduced by microscopic mechanics which also gives a clear physical picture. It removes Einstein's famous objections against Quantum Theory and provides a clear distinction between classical and Quantum behavior. Seven Axioms (three on Classical Mechanics, two for Maxwell's theory, one for Relativity and a new Axiom on Radiation damping) are shown to combine Classical Mechanics, Maxwellian Electrodynamics, Relativity and Schroedinger's Quantum Theory within a single theoretical framework under Microscopic Mechanics which awaits further development at the present time. (orig.)

Why quantum mechanics?

International Nuclear Information System (INIS)

Landsberg, P.T.

1988-01-01

It is suggested that an oversight occurred in classical mechanics when time-derivatives of observables were treated on the same footing as the undifferentiated observables. Removal of this oversight points in the direction of quantum mechanics. Additional light is thrown on uncertainty relations and on quantum mechanics, as a possible form of a subtle statistical mechanics, by the formulation of a classical uncertainty relation for a very simple model. The existence of universal motion, i.e., of zero-point energy, is lastly made plausible in terms of a gravitational constant which is time-dependent. By these three considerations an attempt is made to link classical and quantum mechanics together more firmly, thus giving a better understanding of the latter

Geometry-based approach to studying the semi-classical limit in quantum dynamics by the coherent states and quantum mechanics on the torus

International Nuclear Information System (INIS)

Faure, F.

1993-01-01

This thesis deals with problems linked to the study of the semi-classical limit in quantum dynamics. The first part presents a geometrical formulation which is tantamount to the time dependent variational principle. The classical dynamics is considered as an orthogonal projection of the quantum dynamics on the family of coherent states. The angle of projection provides an information on the validity of the approximation. This angle is studied in an illustrating example. In the second part, we study quantum mechanics on the torus as a phase space, and particularly degeneracies in the spectrum of Harper like models or kicked Harper like models which manifest chaotic dynamics. These models find direct applications in solid state physics, especially with the quantum Hall effect. In this study, we use the Chern index, which is a topological characterization of the localization of the eigenfunctions as some periodicity conditions are changed. The use of the Husimi distribution provides a phase space representation of the quantum states. We discuss the role played by separatrix-states, by the effects of quantum tunneling, and by a classically chaotic dynamics. (orig.)

Classical and sequential limit analysis revisited

Science.gov (United States)

Leblond, Jean-Baptiste; Kondo, Djimédo; Morin, Léo; Remmal, Almahdi

2018-04-01

Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic-plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity - in the absence of hardening and within a linearized geometrical framework -, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity - although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic-plastic coupling in the specific case considered.

Ensembles and Experiments in Classical and Quantum Physics

Science.gov (United States)

Neumaier, Arnold

A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the ''probability via expectation'' approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.

Evasive levels in quantisation through wavepacket coupling: a semi-classical investigation

International Nuclear Information System (INIS)

Amiot, P.; Giraud, B.

1984-01-01

A new method is presented to introduce classical mechanics elements into the problem of obtaining the spectrum of an operator H-circumflex(p-circumflex, q-circumflex). A finite-rank functional space is created by centering complex wavepackets on a discrete number of points on an equi-energy of the classical H(p,q) and by placing real wavepackets in the classically forbidden region. The latter span the active subspace, P, and the former the inactive subspace, Q, for an application of the method of Bloch-Horowitz. A semi-classical study of the Green function in the inactive subspace Q, classically allowed, gives a clear explanation of this phenomenon and sheds new light on the significance of this semi-classical approximation for the propagator. An extension to the problem of barrier penetration is proposed. (author)

Projective measurements in quantum and classical optical systems

CSIR Research Space (South Africa)

Roux, FS

2014-09-01

Full Text Available equally well to both classical and quantum optical systems. A projective measurement, in the context of quantum mechanics, is understood to be the process where a projection operator operates on some input state. Often this projection operator is composed...) Projective measurements in quantum and classical optical systems Filippus S. Roux* and Yingwen Zhang CSIR National Laser Centre, P.O. Box 395, Pretoria 0001, South Africa (Received 3 July 2014; published 22 September 2014) Experimental setups for the optical...

The significance of classical structures in quantum theories

International Nuclear Information System (INIS)

Lowe, M.J.

1978-09-01

The implications for the quantum theory of the presence of non-linear classical solutions of the equations of motion are investigated in various model systems under the headings: (1) Canonical quantisation of the soliton in lambdaphi 4 theory in two dimensions. (2) Bound for soliton masses in two dimensional field theories. (3) The canonical quantisation of a soliton like solution in the non-linear schrodinger equation. (4) The significance of the instanton classical solution in a quantum mechanical system. (U.K.)

Aspects of a representation of quantum theory in terms of classical probability theory by means of integration in Hilbert space

International Nuclear Information System (INIS)

Bach, A.

1981-01-01

A representation of quantum mechanics in terms of classical probability theory by means of integration in Hilbert space is discussed. This formal hidden-variables representation is analysed in the context of impossibility proofs concerning hidden-variables theories. The structural analogy of this formulation of quantum theory with classical statistical mechanics is used to elucidate the difference between classical mechanics and quantum mechanics. (author)

Classical probabilities for Majorana and Weyl spinors

International Nuclear Information System (INIS)

Wetterich, C.

2011-01-01

Highlights: → Map of classical statistical Ising model to fermionic quantum field theory. → Lattice-regularized real Grassmann functional integral for single Weyl spinor. → Emerging complex structure characteristic for quantum physics. → A classical statistical ensemble describes a quantum theory. - Abstract: We construct a map between the quantum field theory of free Weyl or Majorana fermions and the probability distribution of a classical statistical ensemble for Ising spins or discrete bits. More precisely, a Grassmann functional integral based on a real Grassmann algebra specifies the time evolution of the real wave function q τ (t) for the Ising states τ. The time dependent probability distribution of a generalized Ising model obtains as p τ (t)=q τ 2 (t). The functional integral employs a lattice regularization for single Weyl or Majorana spinors. We further introduce the complex structure characteristic for quantum mechanics. Probability distributions of the Ising model which correspond to one or many propagating fermions are discussed explicitly. Expectation values of observables can be computed equivalently in the classical statistical Ising model or in the quantum field theory for fermions.

Nonrelativistic Schroedinger equation in quasi-classical theory

International Nuclear Information System (INIS)

Wignall, J.W.G.

1987-01-01

The author has recently proposed a quasi-classical theory of particles and interactions in which particles are pictured as extended periodic disturbances in a universal field chi(x,t), interacting with each other via nonlinearity in the equation of motion for chi. The present paper explores the relationship of this theory to nonrelativistic quantum mechanics; as a first step, it is shown how it is possible to construct from chi a configuration-space wave function Psi(x 1 , X 2 , t), and that the theory requires that Psi satisfy the two-particle Schroedinger equation in the case where the two particles are well separated from each other. This suggests that the multiparticle Schroedinger equation can be obtained as a direct consequence of the quasi-classical theory without any use of the usual formalism (Hilbert space, quantization rules, etc.) of conventional quantum theory and in particular without using the classical canonical treatment of a system as a crutch theory which has subsequently to be quantized. The quasi-classical theory also suggests the existence of a preferred absolute gauge for the electromagnetic potentials

Gonadal function in male and female patients with classic galactosemia

NARCIS (Netherlands)

Rubio-Gozalbo, M. E.; Gubbels, C. S.; Bakker, J. A.; Menheere, P. P. C. A.; Wodzig, W. K. W. H.; Land, J. A.

2010-01-01

Hypergonadotropic hypoestrogenic infertility is the most burdensome complication for females suffering from classic galactosemia. In contrast, male gonadal function seems less affected. The underlying mechanism is not understood and several pathogenic mechanisms have been proposed. Timing of the

Classical molecular dynamics simulation of electronically non-adiabatic processes.

Science.gov (United States)

Miller, William H; Cotton, Stephen J

2016-12-22

Both classical and quantum mechanics (as well as hybrids thereof, i.e., semiclassical approaches) find widespread use in simulating dynamical processes in molecular systems. For large chemical systems, however, which involve potential energy surfaces (PES) of general/arbitrary form, it is usually the case that only classical molecular dynamics (MD) approaches are feasible, and their use is thus ubiquitous nowadays, at least for chemical processes involving dynamics on a single PES (i.e., within a single Born-Oppenheimer electronic state). This paper reviews recent developments in an approach which extends standard classical MD methods to the treatment of electronically non-adiabatic processes, i.e., those that involve transitions between different electronic states. The approach treats nuclear and electronic degrees of freedom (DOF) equivalently (i.e., by classical mechanics, thereby retaining the simplicity of standard MD), and provides "quantization" of the electronic states through a symmetrical quasi-classical (SQC) windowing model. The approach is seen to be capable of treating extreme regimes of strong and weak coupling between the electronic states, as well as accurately describing coherence effects in the electronic DOF (including the de-coherence of such effects caused by coupling to the nuclear DOF). A survey of recent applications is presented to illustrate the performance of the approach. Also described is a newly developed variation on the original SQC model (found universally superior to the original) and a general extension of the SQC model to obtain the full electronic density matrix (at no additional cost/complexity).

Semi-classical analysis of optical model ambiguities

International Nuclear Information System (INIS)

Cuer, M.

1979-01-01

The ambiguities in the inverse problem at fixed energy in quantum mechanics are analyzed in the framework of the JWKB method. When the classical turning point is unique for all values of the impact parameter (high energies region), the ambiguities proceed only from the quantization of the angular momentum. In the asymptotic region the difference between two particular equivalent potentials changes sign infinitely often. In addition, the set of equivalent potentials which have a given asymptotic form is bounded (except perhaps at the origin). When there are several turning points for small values of the impact parameter (low-energy region), new ambiguities arise from the fact that the parts of the potential that are located between turning points are not ''visible'' in the classical limit. The set of equivalent potentials wich have a given asymptotic form is then not bounded. Mumerical examples (of real and complex equivalent potentials) are given. The optical model ambiguities are studied. The potential depth ambiguities also appear in classical mechanics, but their discrete nature is a quantum property. The VR/sup p//sup( V/)=constant ambiguities can be explained by the quantum corrections to the spiral scattering phenomenon. An attempt to explain why ambiguities arise only with heavy particles scattering is also given

Young's moduli of carbon materials investigated by various classical molecular dynamics schemes

Science.gov (United States)

Gayk, Florian; Ehrens, Julian; Heitmann, Tjark; Vorndamme, Patrick; Mrugalla, Andreas; Schnack, Jürgen

2018-05-01

For many applications classical carbon potentials together with classical molecular dynamics are employed to calculate structures and physical properties of such carbon-based materials where quantum mechanical methods fail either due to the excessive size, irregular structure or long-time dynamics. Although such potentials, as for instance implemented in LAMMPS, yield reasonably accurate bond lengths and angles for several carbon materials such as graphene, it is not clear how accurate they are in terms of mechanical properties such as for instance Young's moduli. We performed large-scale classical molecular dynamics investigations of three carbon-based materials using the various potentials implemented in LAMMPS as well as the EDIP potential of Marks. We show how the Young's moduli vary with classical potentials and compare to experimental results. Since classical descriptions of carbon are bound to be approximations it is not astonishing that different realizations yield differing results. One should therefore carefully check for which observables a certain potential is suited. Our aim is to contribute to such a clarification.

A new approach to the semi-classical relativistic two-body problem for charged fermions

International Nuclear Information System (INIS)

Leiter, D.

1978-01-01

Generalizing from a recently developed hybrid formulation of classical electrodynamics with ''direct (charge-field) action'' structure an analogous semi-classical Dirac formulation of the theory is constructed, which is capable of describing the semi-classical quantum mechanics of two identical spin-1/2 particles. This semi-classical formulation is to be used as a heuristic aid in searching for the theoretical structure of a fully ''second quantized'' theory. The Pauli exclusion principle is incorporated by making the interaction fields (in the action principle) antisymmetric with respect to ''charge-field'' labeling. In this manner, ''position correlation'' effects associated with ''configuration interaction'' can also be accounted for. By studying the nature of the stationary-state solutions, the formalism is compared with the conventional quantum-mechanical one (to understand the similarities and the differences between this approach and the usual correlated Hartree-Fock approximation of ordinary relativistic quantum theory). The stationary-state solutions to the semi-classical formalism are shown to closely approximate the usual quantum-mechanical solutions when the wave functions are represented as a superposition of Slater determinants of Dirac-Coulombic-type wave functions with radial parts having a form which extremizes the total Breit energy. The manner in which this semi-classical theory might be extended to a fully ''second quantized'' formalism is sketched. (author)

Global aspects of classical integrable systems

CERN Document Server

Cushman, Richard H

2015-01-01

This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.

Quantum-Classical Correspondence: Dynamical Quantization and the Classical Limit

International Nuclear Information System (INIS)

Turner, L

2004-01-01

In only 150 pages, not counting appendices, references, or the index, this book is one author's perspective of the massive theoretical and philosophical hurdles in the no-man's-land separating the classical and quantum domains of physics. It ends with him emphasizing his own theoretical contribution to this area. In his own words, he has attempted to answer: 1. How can we obtain the quantum dynamics of open systems initially described by the equations of motion of classical physics (quantization process) 2. How can we retrieve classical dynamics from the quantum mechanical equations of motion by means of a classical limiting process (dequantization process). However, this monograph seems overly ambitious. Although the publisher's description refers to this book as an accessible entre, we find that this author scrambles too hastily over the peaks of information that are contained in his large collection of 272 references. Introductory motivating discussions are lacking. Profound ideas are glossed over superficially and shoddily. Equations morph. But no new convincing understanding of the physical world results. The author takes the viewpoint that physical systems are always in interaction with their environment and are thus not isolated and, therefore, not Hamiltonian. This impels him to produce a method of quantization of these stochastic systems without the need of a Hamiltonian. He also has interest in obtaining the classical limit of the quantized results. However, this reviewer does not understand why one needs to consider open systems to understand quantum-classical correspondence. The author demonstrates his method using various examples of the Smoluchowski form of the Fokker--Planck equation. He then renders these equations in a Wigner representation, uses what he terms an infinitesimality condition, and associates with a constant having the dimensions of an action. He thereby claims to develop master equations, such as the Caldeira-Leggett equation, without

A course in classical physics

CERN Document Server

Bettini, Alessandro

This first volume covers the mechanics of point particles, gravitation, extended systems (starting from the two-body system), the basic concepts of relativistic mechanics and the mechanics of rigid bodies and fluids. The four-volume textbook, which covers electromagnetism, mechanics, fluids and thermodynamics, and waves and light, is designed to reflect the typical syllabus during the first two years of a calculus-based university physics program. Throughout all four volumes, particular attention is paid to in-depth clarification of conceptual aspects, and to this end the historical roots of the principal concepts are traced. Writings by the founders of classical mechanics, G. Galilei and I. Newton, are reproduced, encouraging students to consult them. Emphasis is also consistently placed on the experimental basis of the concepts, highlighting the experimental nature of physics. Whenever feasible at the elementary level, concepts relevant to more advanced courses in modern physics are included. Each chapter b...

Semi-classical derivation of charge-quantization through charge-field self-interaction

International Nuclear Information System (INIS)

Kosok, M.; Madhyastha, V.L.

1990-01-01

A semi-classical synthesis of classical mechanics, wave mechanics, and special relativity yields a unique nonlinear energy-wave structure of relations (velocity triad uv = c 2 ) fundamental to modern physics. Through the above vehicle, using Maxwell's equations, charge quantization and the fine structure constant are derived. It is shown that the numerical value of the nonlinear charge-field self-interaction range for the electron is of the order of 10 -13 m, which is greater than the classical electron radius but less than the Compton wavelength of the electron. Finally, it is suggested that the structure of the electron-in-space is expressed by a self-extending nonlinear ''fractal geometry'' based on derived numerical values obtained from our model, thus opening this presentation of charge-field structure to experimental testing for possible verification

Unraveling Quantum Annealers using Classical Hardness

Science.gov (United States)

Martin-Mayor, Victor; Hen, Itay

2015-01-01

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as ‘D-Wave’ chips, promise to solve practical optimization problems potentially faster than conventional ‘classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize ‘temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip. PMID:26483257

Discrete allowed and forbidden states in the classical mechanical domain in the charged particle motion in a magnetic field

International Nuclear Information System (INIS)

Varma, R.K.; Punithavelu, A.M.; Banerjee, S.B.

1994-01-01

The properties of the motion of charged particles injected almost parallel to the magnetic field are studied by measuring the electron current as a function of the cathode voltage (electron energy), as electrons from the gun traverse a distance L to the detector. The plate current is found to exhibit oscillatory behaviour in contradistinction with the behaviour expected according to the standard classical mechanical paradigm, with the peaks fitting a relation obtained from a quantum like theory predicting such a behaviour. (author). 4 refs, 1 fig, 1 tab

Principles of discrete time mechanics

CERN Document Server

Jaroszkiewicz, George

2014-01-01

Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.

The semi classical laser theory and some applications of laser

International Nuclear Information System (INIS)

Abdalla, Abbaker Ali

1995-04-01

The semi classical laser theory is concerned with the interaction between light and matter in such a way that the matter is treated quantum-mechanically whereas light is treated in terms of the classical electromagnetic equations. In this work the Maxwell-Bloch equations are employed to describe the interaction between light and matter. Applications of the theory as well as different types of lasers are reviewed. (Author)

On the classical and quantum scattering cross-sections on the impenetrable sphere

International Nuclear Information System (INIS)

Afanasiev, G.N.; Dobromyslov, M.B.; Schpakov, V.P.

1980-01-01

The problem of the difference of particle scattering cross sections on the impenetrable sphere is considered in the frame of quantum mechanics and classical mechanics. Using plane waves for the incident particles and the solutions of the Schroedinger equation with the definite energy and momenta for the wave functions quantum and classical cross sections are compared. It is shown that these cross sections are the same if the incident flow is defined similarly in both cases and if the measuring apparatus is ideal

Unbiased estimators for spatial distribution functions of classical fluids

Science.gov (United States)

Adib, Artur B.; Jarzynski, Christopher

2005-01-01

We use a statistical-mechanical identity closely related to the familiar virial theorem, to derive unbiased estimators for spatial distribution functions of classical fluids. In particular, we obtain estimators for both the fluid density ρ(r) in the vicinity of a fixed solute and the pair correlation g(r) of a homogeneous classical fluid. We illustrate the utility of our estimators with numerical examples, which reveal advantages over traditional histogram-based methods of computing such distributions.

Transition from the mechanics of material points to the mechanics of structured particles

Science.gov (United States)

Somsikov, V. M.

2016-01-01

In this paper, necessity of creation of mechanics of structured particles is discussed. The way to create this mechanics within the laws of classical mechanics with the use of energy equation is shown. The occurrence of breaking of time symmetry within the mechanics of structured particles is shown, as well as the introduction of concept of entropy in the framework of classical mechanics. The way to create the mechanics of non-equilibrium systems in the thermodynamic approach is shown. It is also shown that the use of hypothesis of holonomic constraints while deriving the canonical Lagrange equation made it impossible to describe irreversible dynamics. The difference between the mechanics of structured particles and the mechanics of material points is discussed. It is also shown that the matter is infinitely divisible according to the laws of classical mechanics.

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

International Nuclear Information System (INIS)

Prants, S V

2017-01-01

This paper is a review article on some aspects of quantum–classical correspondence in chaotic dynamics of cold atoms interacting with a standing-wave laser field forming an optical lattice. The problem is treated from both (semi)classical and quantum points of view. In both approaches, the interaction of an atomic electic dipole with the laser field is treated quantum mechanically. Translational motion is described, at first, classically (atoms are considered to be point-like objects) and then quantum mechanically as a propagation of matter waves. Semiclassical equations of motion are shown to be chaotic in the sense of classical dynamical chaos. Point-like atoms in an absolutely deterministic and rigid optical lattice can move in a random-like manner demonstrating a chaotic walking with typical features of classical chaos. This behavior is explained by random-like ‘jumps’ of one of the atomic internal variable when atoms cross nodes of the standing wave and occurs in a specific range of the atom-field detuning. When treating atoms as matter waves, we show that they can make nonadiabatic transitions when crossing the standing-wave nodes. The point is that atomic wave packets split at each node in the same range of the atom-field detuning where the classical chaos occurs. The key point is that the squared amplitude of those semiclassical ‘jumps’ equal to the quantum Landau–Zener parameter which defines the probability of nonadiabatic transitions at the nodes. Nonadiabatic atomic wave packets are much more complicated compared to adiabatic ones and may be called chaotic in this sense. A few possible experiments to observe some manifestations of classical and quantum chaos with cold atoms in horizontal and vertical optical lattices are proposed and discussed. (paper)

Classical or equilibrium thermodynamics: basic conceptual aspects

Directory of Open Access Journals (Sweden)

Luiz Augusto Calvo Tiritan

2008-08-01

Full Text Available The Classical or Equilibrium Thermodynamics is one of the most consolidated fields of Physics. It is synthesized by a well-known and self coherent knowledge structure. The essence of the Classical Thermodynamics theoretical structure consists of a set of natural laws that rule the macroscopic physical systems behavior. These laws were formulated based on observations generalizations and are mostly independent of any hypotheses concerning the microscopic nature of the matter. In general, the approaches established for the Classical Thermodynamics follow one of the following alternatives: the historical approach that describes chronologically the evolution of ideas, concepts and facts, and the postulational approach in which postulates are formulated but are not demonstrated a priori but can be confirmed a posteriori. In this work, a brief review of the pre-classical historical approach conceptual evolution is elaborated, from the beginning of the seventeenth century to the middle of the nineteenth century. As for this, the following themes are dealt with in an evolutionary and phenomenological way: heat nature, thermometry, calorimetry, Carnot’s heat engine, heat mechanical equivalent and the first and second laws. The Zeroth law that was formulated afterwards is included in the discussion.

Characterization of particle states in relativistic classical quantum theory

International Nuclear Information System (INIS)

Horwitz, L.P.; Rabin, Y.

1977-02-01

Classical and quantum relativistic mechanics are studied. The notion of a ''particle'' is defined in the classical case and the interpretation of mechanics in space-time is clarified. These notions are carried over to the quantum theory, as much as possible. The relation between the results of Feyman's path integral approach and the theory of Horwitz and Piron is discussed. The ''particle'' interpretation is shown to imply an asymptotic condition for scattering. A general method of constructing the dynamical mass spectrum of composite ''particle'' states is discussed. An interference experiment is proposed to affirm the interpretation and applicability of Stueckelberg type wave functions for actual physical phenomena. Some discussion of the relation of this relativistic quantum theory to Feynman's approach to quantum field theory is also given

Hidden invariance of the free classical particle

International Nuclear Information System (INIS)

Garcia, S.

1994-01-01

A formalism describing the dynamics of classical and quantum systems from a group theoretical point of view is presented. We apply it to the simple example of the classical free particle. The Galileo group G is the symmetry group of the free equations of motion. Consideration of the free particle Lagrangian semi-invariance under G leads to a larger symmetry group, which is a central extension of the Galileo group by the real numbers. We study the dynamics associated with this group, and characterize quantities like Noether invariants and evolution equations in terms of group geometric objects. An extension of the Galileo group by U(1) leads to quantum mechanics

Classic-Ada(TM)

Science.gov (United States)

Valley, Lois

1989-01-01

The SPS product, Classic-Ada, is a software tool that supports object-oriented Ada programming with powerful inheritance and dynamic binding. Object Oriented Design (OOD) is an easy, natural development paradigm, but it is not supported by Ada. Following the DOD Ada mandate, SPS developed Classic-Ada to provide a tool which supports OOD and implements code in Ada. It consists of a design language, a code generator and a toolset. As a design language, Classic-Ada supports the object-oriented principles of information hiding, data abstraction, dynamic binding, and inheritance. It also supports natural reuse and incremental development through inheritance, code factoring, and Ada, Classic-Ada, dynamic binding and static binding in the same program. Only nine new constructs were added to Ada to provide object-oriented design capabilities. The Classic-Ada code generator translates user application code into fully compliant, ready-to-run, standard Ada. The Classic-Ada toolset is fully supported by SPS and consists of an object generator, a builder, a dictionary manager, and a reporter. Demonstrations of Classic-Ada and the Classic-Ada Browser were given at the workshop.

The ambiguity of simplicity in quantum and classical simulation

International Nuclear Information System (INIS)

Aghamohammadi, Cina; Mahoney, John R.; Crutchfield, James P.

2017-01-01

Highlights: • Simplicity depends on whether a system is represented classically or quantally. • We demonstrate that simplicity is unavoidably ambiguous. • Relative simplicity changes order moving between classical and quantum descriptions. • Ambiguity of simplicity bears directly on model selection. - Abstract: A system's perceived simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and express different properties and mechanisms. What is surprising is that, as we demonstrate, simplicity is ambiguous: the relative simplicity between two systems can change sign when moving between classical and quantum descriptions. Here, we associate simplicity with small model-memory. We see that the notions of absolute physical simplicity at best form a partial, not a total, order. This suggests that appeals to principles of physical simplicity, via Ockham's Razor or to the “elegance” of competing theories, may be fundamentally subjective. Recent rapid progress in quantum computation and quantum simulation suggest that the ambiguity of simplicity will strongly impact statistical inference and, in particular, model selection.

Classical mechanics Hamiltonian and Lagrangian formalism

CERN Document Server

Deriglazov, Alexei

2016-01-01

This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.

Complex classical paths and the one-dimensional sine-Gordon system

International Nuclear Information System (INIS)

Millard, P.A.

1985-01-01

The semiclassical limit of the Green function for a particle in the one-dimensional sine-Gordon potential is obtained by summing over complex classical paths. The results are the same as those obtained in the less physically intuitive WKB approach. In addition to being of practical utility for solving quantum mechanical problems involving tunnelling, the classical path method may show how to deal with dense configuration of instantons. (orig.)

Extending In Vitro Conditioning in "Aplysia" to Analyze Operant and Classical Processes in the Same Preparation

Science.gov (United States)

Brembs, Bjorn; Baxter, Douglas A.; Byrne, John H.

2004-01-01

Operant and classical conditioning are major processes shaping behavioral responses in all animals. Although the understanding of the mechanisms of classical conditioning has expanded significantly, the understanding of the mechanisms of operant conditioning is more limited. Recent developments in "Aplysia" are helping to narrow the gap in the…

Fundamental theories of waves and particles formulated without classical mass

Science.gov (United States)

Fry, J. L.; Musielak, Z. E.

2010-12-01

Quantum and classical mechanics are two conceptually and mathematically different theories of physics, and yet they do use the same concept of classical mass that was originally introduced by Newton in his formulation of the laws of dynamics. In this paper, physical consequences of using the classical mass by both theories are explored, and a novel approach that allows formulating fundamental (Galilean invariant) theories of waves and particles without formally introducing the classical mass is presented. In this new formulation, the theories depend only on one common parameter called 'wave mass', which is deduced from experiments for selected elementary particles and for the classical mass of one kilogram. It is shown that quantum theory with the wave mass is independent of the Planck constant and that higher accuracy of performing calculations can be attained by such theory. Natural units in connection with the presented approach are also discussed and justification beyond dimensional analysis is given for the particular choice of such units.

Loire Classics: Reviving Classicism in some Loire Poets

Directory of Open Access Journals (Sweden)

Wim Verbaal

2017-06-01

Full Text Available The term 'Loire poets' has come to refer to a rather undefinable group of poets that in the second half of the eleventh century distinguishes itself through its refined poetics. They are often characterized as medieval humanists thanks to their renewed interest in the classics. Sometimes their movement is labelled a 'classicist' one. But what does this 'classicism' mean? Is it even permitted to speak of medieval 'classicisms'? This contribution approaches the question of whether we can apply this modern label to pre-modern phenomena. Moreover, it explores the changes in attitude towards the classics that sets the Loire poets off from their predecessors and contemporaries. The article focuses on poems by Hildebert of Lavardin, Baudri of Bourgueil, Marbod of Rennes, and Geoffrey of Reims. They are compared with some contemporary poets, such as Reginald of Canterbury and Sigebert of Gembloux.

Classical system underlying a diffracting quantum billiard

Indian Academy of Sciences (India)

Manan Jain

2018-01-05

Jan 5, 2018 ... Wave equation; rays; quantum chaos. PACS Nos 03.65.Ge; 05.45.Mt; 42.25.Fx. 1. Introduction. Diffraction [1] is a complex wave phenomenon which manifests classically and quantum mechanically. Among a wide range of systems where diffraction becomes important, there is an interesting situation of.

Maxwell and the classical wave particle dualism.

Science.gov (United States)

Mendonça, J T

2008-05-28

Maxwell's equations are one of the greatest theoretical achievements in physics of all times. They have survived three successive theoretical revolutions, associated with the advent of relativity, quantum mechanics and modern quantum field theory. In particular, they provide the theoretical framework for the understanding of the classical wave particle dualism.

Noise-induced drift in systems with broken symmetry and classical routes to superconductivity

International Nuclear Information System (INIS)

Shapiro, V.E.

1994-01-01

We discuss concepts and mechanisms of particle motion in a variety of conditions of asymmetry towards spatial inversion that suggest an idea for the possibility of persistent currents within classical statistical considerations. We expose misapplications of Gibbs statistics and the Langevin approach and show that the idea does not contradict general principles. It gains support from the classical mechanism of capillary wave instability and keeps within the detailed balance and fluctuation-dissipation theorems. (author). 7 refs., 2 figs

Non-classical homogeneous precipitation mediated by compositional fluctuations in titanium alloys

International Nuclear Information System (INIS)

Nag, S.; Zheng, Y.; Williams, R.E.A.; Devaraj, A.; Boyne, A.; Wang, Y.; Collins, P.C.; Viswanathan, G.B.; Tiley, J.S.; Muddle, B.C.; Banerjee, R.

2012-01-01

This paper presents experimental evidence of homogeneous precipitation of the α-phase within the β matrix of a titanium alloy, and then accounts for this phase transformation by a new, non-classical mechanism involving compositional fluctuations, based on the pseudo-spinodal concept [1]. This mechanism involves local compositional fluctuations of small amplitude which, when of a certain magnitude, can favor thermodynamically certain regions of the β matrix to transform congruently to the α-phase but with compositions far from equilibrium. Subsequently, as measured experimentally using the tomographical atom probe, continuous diffusional partitioning between the parent β- and product α-phases during isothermal annealing drives their compositions towards equilibrium. For a given alloy composition, the decomposition mechanism is strongly temperature dependent, which would be expected for homogeneous precipitation via the compositional fluctuation-mediated mechanism but not necessarily for one based on classical nucleation theory. The applicability of this mechanism to phase transformations in general is noted.

EPRB Gedankenexperiment and Entanglement with Classical Light Waves

Science.gov (United States)

Rashkovskiy, Sergey A.

2018-06-01

In this article we show that results similar to those of the Einstein-Podolsky-Rosen-Bohm (EPRB) Gedankenexperiment and entanglement of photons can be obtained using weak classical light waves if we take into account the discrete (atomic) structure of the detectors and a specific nature of the light-atom interaction. We show that the CHSH (Clauser, Horne, Shimony, and Holt) criterion in the EPRB Gedankenexperiment with classical light waves can exceed not only the maximum value SHV=2 that is predicted by the local hidden-variable theories but also the maximum value S_{QM} = 2√2 predicted by quantum mechanics.

Quantum and classical dissipation of charged particles

Energy Technology Data Exchange (ETDEWEB)

Ibarra-Sierra, V.G. [Departamento de Física, Universidad Autónoma Metropolitana at Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Anzaldo-Meneses, A.; Cardoso, J.L.; Hernández-Saldaña, H. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana at Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana at Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Roa-Neri, J.A.E. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana at Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)

2013-08-15

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail. -- Highlights: •Hamiltonian of a damped charged particle in time dependent electromagnetic fields. •Exact Green’s function of a charged particle in time dependent electromagnetic fields. •Time evolution of a Gaussian wave packet of a damped charged particle. •Classical and quantum dynamics of a damped electric charge.

Quantum and classical dissipation of charged particles

International Nuclear Information System (INIS)

Ibarra-Sierra, V.G.; Anzaldo-Meneses, A.; Cardoso, J.L.; Hernández-Saldaña, H.; Kunold, A.; Roa-Neri, J.A.E.

2013-01-01

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases using canonical transformations applied to Hamiltonians for a particle with variable mass. Green’s function is constructed and, from it, the motion of a Gaussian wave packet is studied in detail. -- Highlights: •Hamiltonian of a damped charged particle in time dependent electromagnetic fields. •Exact Green’s function of a charged particle in time dependent electromagnetic fields. •Time evolution of a Gaussian wave packet of a damped charged particle. •Classical and quantum dynamics of a damped electric charge

Dielectric properties of classical and quantized ionic fluids.

Science.gov (United States)

Høye, Johan S

2010-06-01

We study time-dependent correlation functions of classical and quantum gases using methods of equilibrium statistical mechanics for systems of uniform as well as nonuniform densities. The basis for our approach is the path integral formalism of quantum mechanical systems. With this approach the statistical mechanics of a quantum mechanical system becomes the equivalent of a classical polymer problem in four dimensions where imaginary time is the fourth dimension. Several nontrivial results for quantum systems have been obtained earlier by this analogy. Here, we will focus upon the presence of a time-dependent electromagnetic pair interaction where the electromagnetic vector potential that depends upon currents, will be present. Thus both density and current correlations are needed to evaluate the influence of this interaction. Then we utilize that densities and currents can be expressed by polarizations by which the ionic fluid can be regarded as a dielectric one for which a nonlocal susceptibility is found. This nonlocality has as a consequence that we find no contribution from a possible transverse electric zero-frequency mode for the Casimir force between metallic plates. Further, we establish expressions for a leading correction to ab initio calculations for the energies of the quantized electrons of molecules where now retardation effects also are taken into account.

Classical and quantum position-dependent mass harmonic oscillators

International Nuclear Information System (INIS)

Cruz y Cruz, S.; Negro, J.; Nieto, L.M.

2007-01-01

The position-dependent mass oscillator is studied from both, classical and quantum mechanical points of view, in order to discuss the ambiguity on the operator ordering of the kinetic term in the quantum framework. The results are illustrated by some examples of specific mass functions

The ambiguity of simplicity in quantum and classical simulation

Energy Technology Data Exchange (ETDEWEB)

Aghamohammadi, Cina, E-mail: caghamohammadi@ucdavis.edu; Mahoney, John R., E-mail: jrmahoney@ucdavis.edu; Crutchfield, James P., E-mail: chaos@ucdavis.edu

2017-04-11

Highlights: • Simplicity depends on whether a system is represented classically or quantally. • We demonstrate that simplicity is unavoidably ambiguous. • Relative simplicity changes order moving between classical and quantum descriptions. • Ambiguity of simplicity bears directly on model selection. - Abstract: A system's perceived simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and express different properties and mechanisms. What is surprising is that, as we demonstrate, simplicity is ambiguous: the relative simplicity between two systems can change sign when moving between classical and quantum descriptions. Here, we associate simplicity with small model-memory. We see that the notions of absolute physical simplicity at best form a partial, not a total, order. This suggests that appeals to principles of physical simplicity, via Ockham's Razor or to the “elegance” of competing theories, may be fundamentally subjective. Recent rapid progress in quantum computation and quantum simulation suggest that the ambiguity of simplicity will strongly impact statistical inference and, in particular, model selection.

Scale covariant physics: a 'quantum deformation' of classical electrodynamics

International Nuclear Information System (INIS)

Knoll, Yehonatan; Yavneh, Irad

2010-01-01

We present a deformation of classical electrodynamics, continuously depending on a 'quantum parameter', featuring manifest gauge, Poincare and scale covariance. The theory, dubbed extended charge dynamics (ECD), associates a certain length scale with each charge which, due to scale covariance, is an attribute of a solution, not a parameter of the theory. When the EM field experienced by an ECD charge is slowly varying over that length scale, the dynamics of the charge reduces to classical dynamics, its emitted radiation reduces to the familiar Lienard-Wiechert potential and the above length scale is identified as the charge's Compton length. It is conjectured that quantum mechanics describes statistical aspects of ensembles of ECD solutions, much like classical thermodynamics describes statistical aspects of ensembles of classical solutions. A unique 'remote sensing' feature of ECD, supporting that conjecture, is presented, along with an explanation for the illusion of a photon within a classical treatment of the EM field. Finally, a novel conservation law associated with the scale covariance of ECD is derived, indicating that the scale of a solution may 'drift' with time at a constant rate, much like translation covariance implies a uniform drift of the (average) position.

Controlling the transport of an ion: classical and quantum mechanical solutions

International Nuclear Information System (INIS)

Fürst, H A; Poschinger, U G; Schmidt-Kaler, F; Singer, K; Goerz, M H; Koch, C P; Murphy, M; Montangero, S; Calarco, T

2014-01-01

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time. (paper)

The physical vulnerability of elements at risk: a methodology based on fluid and classical mechanics

Science.gov (United States)

Mazzorana, B.; Fuchs, S.; Levaggi, L.

2012-04-01

The impacts of the flood events occurred in autumn 2011 in the Italian regions Liguria and Tuscany revived the engagement of the public decision makers to enhance in synergy flood control and land use planning. In this context, the design of efficient flood risk mitigation strategies and their subsequent implementation critically relies on a careful vulnerability analysis of both, the immobile and mobile elements at risk potentially exposed to flood hazards. Based on fluid and classical mechanics notions we developed computation schemes enabling for a dynamic vulnerability and risk analysis facing a broad typological variety of elements at risk. The methodological skeleton consists of (1) hydrodynamic computation of the time-varying flood intensities resulting for each element at risk in a succession of loading configurations; (2) modelling the mechanical response of the impacted elements through static, elasto-static and dynamic analyses; (3) characterising the mechanical response through proper structural damage variables and (4) economic valuation of the expected losses as a function of the quantified damage variables. From a computational perspective we coupled the description of the hydrodynamic flow behaviour and the induced structural modifications of the elements at risk exposed. Valuation methods, suitable to support a correct mapping from the value domains of the physical damage variables to the economic loss values are discussed. In such a way we target to complement from a methodological perspective the existing, mainly empirical, vulnerability and risk assessment approaches to refine the conceptual framework of the cost-benefit analysis. Moreover, we aim to support the design of effective flood risk mitigation strategies by diminishing the main criticalities within the systems prone to flood risk.

Equilibrium statistical mechanics

CERN Document Server

Jackson, E Atlee

2000-01-01

Ideal as an elementary introduction to equilibrium statistical mechanics, this volume covers both classical and quantum methodology for open and closed systems. Introductory chapters familiarize readers with probability and microscopic models of systems, while additional chapters describe the general derivation of the fundamental statistical mechanics relationships. The final chapter contains 16 sections, each dealing with a different application, ordered according to complexity, from classical through degenerate quantum statistical mechanics. Key features include an elementary introduction t

Semi-classical estimation of ground state energies on a sphere

International Nuclear Information System (INIS)

Sollie, R.

1989-01-01

It is considered electrons confined to the surface of a sphere, and calculate the classical electrostatic energies for up to 32 electrons. It is introduced a magnetic field perpendicular to the surface of the sphere, by placing a magnetic monopole at the origin. The classical analysis can be extended by replacing the pair-potential by an effective potential, defined as the quantum mechanical energy of a pair of electrons at the appropriate distance. (A.C.A.S.) [pt

Quantum magnification of classical sub-Planck phase space features

International Nuclear Information System (INIS)

Hensinger, W.K.; Heckenberg, N.; Rubinsztein-Dunlop, H.; Delande, D.

2002-01-01

Full text: To understand the relationship between quantum mechanics and classical physics a crucial question to be answered is how distinct classical dynamical phase space features translate into the quantum picture. This problem becomes even more interesting if these phase space features occupy a much smaller volume than ℎ in a phase space spanned by two non-commuting variables such as position and momentum. The question whether phase space structures in quantum mechanics associated with sub-Planck scales have physical signatures has recently evoked a lot of discussion. Here we will show that sub-Planck classical dynamical phase space structures, for example regions of regular motion, can give rise to states whose phase space representation is of size ℎ or larger. This is illustrated using period-1 regions of regular motion (modes of oscillatory motion of a particle in a modulated well) whose volume is distinctly smaller than Planck's constant. They are magnified in the quantum picture and appear as states whose phase space representation is of size h or larger. Cold atoms provide an ideal test bed to probe such fundamental aspects of quantum and classical dynamics. In the experiment a Bose-Einstein condensate is loaded into a far detuned optical lattice. The lattice depth is modulated resulting in the emergence of regions of regular motion surrounded by chaotic motion in the phase space spanned by position and momentum of the atoms along the standing wave. Sub-Planck scaled phase space features in the classical phase space are magnified and appear as distinct broad peaks in the atomic momentum distribution. The corresponding quantum analysis shows states of size Ti which can be associated with much smaller classical dynamical phase space features. This effect may considered as the dynamical equivalent of the Goldstone and Jaffe theorem which predicts the existence of at least one bound state at a bend in a two or three dimensional spatial potential

Quantum tomography and classical propagator for quadratic quantum systems

International Nuclear Information System (INIS)

Man'ko, O.V.

1999-03-01

The classical propagator for tomographic probability (which describes the quantum state instead of wave function or density matrix) is presented for quadratic quantum systems and its relation to the quantum propagator is considered. The new formalism of quantum mechanics, based on the probability representation of the state, is applied to particular quadratic systems - the harmonic oscillator, particle's free motion, problems of an ion in a Paul trap and in asymmetric Penning trap, and to the process of stimulated Raman scattering. The classical propagator for these systems is written in an explicit form. (author)

Functional analysis of replication determinantsin classical swine fever virus

DEFF Research Database (Denmark)

Hadsbjerg, Johanne

and animal pathogens should facilitate finding new approaches for efficient disease control. The principal aim of this thesis is to characterise determinants involved in the replication of classical swine fever virus (CSFV). Classical swine fever is a highly contagious virus disease of domestic pigs and wild...... in cell culture. Knowledge of these sequence variations and putative long-range interactions will provide valuable insights into mechanisms underlying virustranslation and replication. In manuscript 3, a selection marker has been inserted into a CSFV-based replicon making it suitable for screening...

Generic emergence of classical features in quantum Darwinism

Science.gov (United States)

Brandão, Fernando G. S. L.; Piani, Marco; Horodecki, Paweł

2015-08-01

Quantum Darwinism posits that only specific information about a quantum system that is redundantly proliferated to many parts of its environment becomes accessible and objective, leading to the emergence of classical reality. However, it is not clear under what conditions this mechanism holds true. Here we prove that the emergence of classical features along the lines of quantum Darwinism is a general feature of any quantum dynamics: observers who acquire information indirectly through the environment have effective access at most to classical information about one and the same measurement of the quantum system. Our analysis does not rely on a strict conceptual splitting between a system-of-interest and its environment, and allows one to interpret any system as part of the environment of any other system. Finally, our approach leads to a full operational characterization of quantum discord in terms of local redistribution of correlations.

Integration of classical and quantum physics

International Nuclear Information System (INIS)

Tisza, L.

1989-01-01

The perennial aspect of the Newtonian foundation of mathematical physics is that the concept of ''motion,'' that is, ''kinematics,'' is to serve as the interface between mathematics and physics. Kinematics subdivides into the theory of orbital translation and that of undulation and spinning. Newtonian mechanics is based on giving to translational kinematics a priority over the other modes, since planetary revolution can be represented as translation modified by gravitation. The so-called breakdown of classical physics stems from giving the translational priority a canonical status and extending it to the constituents of matter. We claim that in this case the priority is to be reversed. The main content of this paper is to establish the algebraic model for an indivisible, undulating entity that we call a ''wave simplex.'' It is used as the point of departure for a non-Newtonian quantum dynamics in which physical and algebraic concepts are in close correspondence. The postulates of the classical phenomenological theories and those of the canonical theories based on translational priority are established as theorems under the proper limiting conditions, and forces are constructed rather than postulated. While the formal structure of two-level quantum mechanics is established as well, exception is taken to treating spin as a property of a point particle. It is considered self-evident that a spinning object is orientable, a property accounted for in terms of a unitary triplet. This is the point of departure for an intrinsic particle dynamics. A main result is the integration of classical and quantum physics, thus closing the gap created by the heuristic method of canonical quantization

Analytical mechanics for relativity and quantum mechanics

CERN Document Server

Johns, Oliver Davis

2011-01-01

Analytical Mechanics for Relativity and Quantum Mechanics is an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the introductory graduate level. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum...

A Synthetic Approach to the Transfer Matrix Method in Classical and Quantum Physics

Science.gov (United States)

Pujol, O.; Perez, J. P.

2007-01-01

The aim of this paper is to propose a synthetic approach to the transfer matrix method in classical and quantum physics. This method is an efficient tool to deal with complicated physical systems of practical importance in geometrical light or charged particle optics, classical electronics, mechanics, electromagnetics and quantum physics. Teaching…

Classical dynamics of triatomic system: energized harmonic molecules

International Nuclear Information System (INIS)

Parr, C.A.; Kuppermann, A.; Porter, R.N.

1976-01-01

The dynamical assumptions underlying the Slater and RRK classical-mechanical theories of unimolecular reaction rates are investigated. The predictions of these theories for several nonlinear, triatomic, harmonically-bonded molecular models are compared with the results obtained from the integration of the classical equations of motion. The accuracy of the small-vibration and weak-coupling assumptions are found to break down at energies above about one quarter of a bond dissociation energy. Nonetheless, the small-vibration approximation predicts reaction frequencies in good agreement with the exact results for the models. The effects of rotation on intramolecular energy exchange are examined and found to be significant

Classical model for nuclear collisions including the meson degree of freedom

International Nuclear Information System (INIS)

Babinet, R.; Kunz, J.; Mosel, U.; Wilets, L.

1980-01-01

Many different approaches have been taken to describe high energy heavy ion collisions. L. Wilets et al proposed a classical treatment of the problem. In his model non-relativistic nucleons move on classical trajectories. However, the Pauli-principle is simulated by a momentum dependent potential acting between the nucleons. This model is extended in two ways. The nucleons are coupled to a pionfield, which enables us to describe inelastic processes. Nucleons and pionfiled are treated completely relativistically, this also assures Lorentz invariance. We aim at a set of classical equations of motion describing the interacting system of nucleons and pionfield. These classical equations should have a quantum mechanical basis. Further, they should contain such fundamental properties of the pion-nucleon system as the Δ(3,3)-resonance, at least in a qualitative manner. (orig./FKS)

An analogue of the Heisenberg uncertainty relation in prequantum classical field theory

Energy Technology Data Exchange (ETDEWEB)

Khrennikov, Andrei, E-mail: Andrei.Khrennikov@vxu.s [International Center for Mathematical Modelling in Physics and Cognitive Sciences, University of Vaexjoe, Vaexjoe (Sweden) and Institute of Information Security, Russian State University for Humanities, Moscow (Russian Federation)

2010-02-01

Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility of representing averages of quantum observables, including correlations of observables on subsystems of a composite system, as averages with respect to fluctuations of classical random fields. PCSFT is a classical model of wave type. For example, 'electron' is described by electronic field. In contrast to quantum mechanics (QM), this field is a real physical field and not a field of probabilities. An important point is that the prequantum field of , for example, an electron contains the irreducible contribution of the background field vacuum fluctuations. In principle, the traditional QM-formalism can be considered as a special regularization procedure: subtraction of averages with respect to vacuum fluctuations. In this paper, we derive a classical analogue of the Heisenberg-Robertson inequality for dispersions of functionals of classical (prequantum) fields. The PCSFT Robertson-like inequality provides a restriction on the product of classical dispersions. However, this restriction is not so rigid as in QM.

An analogue of the Heisenberg uncertainty relation in prequantum classical field theory

International Nuclear Information System (INIS)

Khrennikov, Andrei

2010-01-01

Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility of representing averages of quantum observables, including correlations of observables on subsystems of a composite system, as averages with respect to fluctuations of classical random fields. PCSFT is a classical model of wave type. For example, 'electron' is described by electronic field. In contrast to quantum mechanics (QM), this field is a real physical field and not a field of probabilities. An important point is that the prequantum field of , for example, an electron contains the irreducible contribution of the background field vacuum fluctuations. In principle, the traditional QM-formalism can be considered as a special regularization procedure: subtraction of averages with respect to vacuum fluctuations. In this paper, we derive a classical analogue of the Heisenberg-Robertson inequality for dispersions of functionals of classical (prequantum) fields. The PCSFT Robertson-like inequality provides a restriction on the product of classical dispersions. However, this restriction is not so rigid as in QM.

Principles of maximally classical and maximally realistic quantum ...

Indian Academy of Sciences (India)

Principles of maximally classical and maximally realistic quantum mechanics. S M ROY. Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India. Abstract. Recently Auberson, Mahoux, Roy and Singh have proved a long standing conjecture of Roy and Singh: In 2N-dimensional phase space, ...

On the classical dynamics of charges in non-commutative QED

International Nuclear Information System (INIS)

Fatollahi, A.H.; Mohammadzadeh, H.

2004-01-01

Following Wong's approach to formulating the classical dynamics of charged particles in non-Abelian gauge theories, we derive the classical equations of motion of a charged particle in U(1) gauge theory on non-commutative space, the so-called non-commutative QED. In the present use of the procedure, it is observed that the definition of the mechanical momenta should be modified. The derived equations of motion manifest the previous statement about the dipole behavior of the charges in non-commutative space. (orig.)

Dynamics of electrically charged extended bodies: classical and quantum systems

International Nuclear Information System (INIS)

Aaberge, T.

1987-01-01

The author present generalizations of classical mechanics and quantum mechanics that make it possible to describe N charged extended bodies.In particular, we are able to write down a set of coupled equations for the system of N bodies plus field. The theory is based on a theory for the description of N charged chemical fluid components

Quantum mechanics

International Nuclear Information System (INIS)

Anon.

1990-01-01

The book is on quantum mechanics. The emphasis is on the basic concepts and the methodology. The chapters include: Breakdown of classical concepts; Quantum mechanical concepts; Basic postulates of quantum mechanics; solution of problems in quantum mechanics; Simple harmonic oscillator; and Angular Momentum

Why aortic elasticity differs among classical and non-classical mitral valve prolapsed?

Science.gov (United States)

Unlu, Murat; Demirkol, Sait; Aparci, Mustafa; Arslan, Zekeriya; Balta, Sevket; Dogan, Umuttan; Kilicarslan, Baris; Ozeke, Ozcan; Celik, Turgay; Iyisoy, Atila

2014-01-01

Mitral valve prolapse (MVP) is the most common valvular heart disease and characterized by the displacement of an abnormally thickened mitral valve leaflet into the left atrium during systole. There are two types of MVP, broadly classified as classic (thickness ≥5 mm) and non-classic (thickness elastic properties of the aorta in young male patients with classical and non-classical MVP. In the present study, 63 young adult males (mean age: 22.7 ± 4.2) were included. Patients were divided into classic MVP (n = 27) and non-classic MVP (n = 36) groups. Aortic strain, aortic distensibility and aortic stiffness index were calculated by using aortic diameters obtained by echocardiography and blood pressures measured by sphygmomanometer. There was no significant difference between the groups in terms of age, body mass index, left ventricular mass and ejection fraction. When comparing the MVP group it was found that aortic strain and aortic distensibility were increased (p = 0.0027, p = 0.016, respectively) whereas the aortic stiffness index was decreased (p = 0.06) in the classical MVP group. We concluded that the elastic properties of the aorta is increased in patients with classic MVP. Further large scale studies should be performed to understand of morphological and physiological properties of the aorta in patients with MVP.

Heat control in opto-mechanical system using quantum non-classicality

International Nuclear Information System (INIS)

Sharma, Sushamana; Senwar, Subash

2016-01-01

Cooling of matter to the quantum ground state is a primary directive of quantum control. In other words, to extract entropy from a quantum system, efficient indirect quantum measurements may be implemented. The main objective is the cooling of the oscillator either to its motional ground state or to non-classical states, such as low-number Fock states, squeezed states or entangled states. It is shown that the use of quantum control procedure is better choice for even experimental realizations because it leads to a squeezed steady state with less than one phonon on average. The steady state of system corresponds to cooling of the system.

Symmetries in discrete-time mechanics

International Nuclear Information System (INIS)

Khorrami, M.

1996-01-01

Based on a general formulation for discrete-time quantum mechanics, introduced by M. Khorrami (Annals Phys. 224 (1995), 101), symmetries in discrete-time quantum mechanics are investigated. It is shown that any classical continuous symmetry leads to a conserved quantity in classical mechanics, as well as quantum mechanics. The transformed wave function, however, has the correct evolution if and only if the symmetry is nonanomalous. Copyright copyright 1996 Academic Press, Inc

Classical Mechanics Experiments using Wiimotes

Science.gov (United States)

Lopez, Alexander; Ochoa, Romulo

2010-02-01

The Wii, a video game console, is a very popular device. Although computationally it is not a powerful machine by today's standards, to a physics educator the controllers are its most important components. The Wiimote (or remote) controller contains a three-axis accelerometer, an infrared detector, and Bluetooth connectivity at a relatively low price. Thanks to available open source code, such as GlovePie, any PC or Laptop with Bluetooth capability can detect the information sent out by the Wiimote. We present experiments that use two or three Wiimotes simultaneously to measure the variable accelerations in two mass systems interacting via springs. Normal modes are determined from the data obtained. Masses and spring constants are varied to analyze their impact on the accelerations of the systems. We present the results of our experiments and compare them with those predicted using Lagrangian mechanics. )

Dynamics of classical and quantum fields an introduction

CERN Document Server

Setlur, Girish S

2014-01-01

Dynamics of Classical and Quantum Fields: An Introduction focuses on dynamical fields in non-relativistic physics. Written by a physicist for physicists, the book is designed to help readers develop analytical skills related to classical and quantum fields at the non-relativistic level, and think about the concepts and theory through numerous problems. In-depth yet accessible, the book presents new and conventional topics in a self-contained manner that beginners would find useful. A partial list of topics covered includes: Geometrical meaning of Legendre transformation in classical mechanics Dynamical symmetries in the context of Noether's theorem The derivation of the stress energy tensor of the electromagnetic field, the expression for strain energy in elastic bodies, and the Navier Stokes equation Concepts of right and left movers in case of a Fermi gas explained Functional integration is interpreted as a limit of a sequence of ordinary integrations Path integrals for one and two quantum particles and for...

Some recent progress in classical general relativity

Science.gov (United States)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

2000-06-01

In this short survey paper, we shall discuss certain recent results in classical gravity. Our main attention will be restricted to two topics in which we have been involved; the positive mass conjecture and its extensions to the case with horizons, including the Penrose conjecture (Part I), and the interaction of gravity with other force fields and quantum-mechanical particles (Part II).

The ambiguity of simplicity in quantum and classical simulation

Science.gov (United States)

Aghamohammadi, Cina; Mahoney, John R.; Crutchfield, James P.

2017-04-01

A system's perceived simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and express different properties and mechanisms. What is surprising is that, as we demonstrate, simplicity is ambiguous: the relative simplicity between two systems can change sign when moving between classical and quantum descriptions. Here, we associate simplicity with small model-memory. We see that the notions of absolute physical simplicity at best form a partial, not a total, order. This suggests that appeals to principles of physical simplicity, via Ockham's Razor or to the ;elegance; of competing theories, may be fundamentally subjective. Recent rapid progress in quantum computation and quantum simulation suggest that the ambiguity of simplicity will strongly impact statistical inference and, in particular, model selection.

State-dependent classical potentials

International Nuclear Information System (INIS)

D'Amico, M.

2001-01-01

As alternative treatment to the potential operators of standard quantum mechanics is presented. The method is derived from Bohm's mechanics. The operator scalar (V) and vector (A) potential functions are replaced by a quantum potential. It is argued that the classical potential is a special limiting case of a more general quantum potential. The theory is illustrated by deriving an equivalent single-particle equation for the i-th particle of an n-body Bohmian system. The resulting effective state-dependent potential holds the interaction between the single-particle self-wave ψ s and the environment wave ψ e of the n - 1 remaining particles. The effective state-dependent potential is offered as a resolution to the Aharonov-Bohm effect where the phase difference is shown to result from the presence of ψ e . Finally, the interaction between ψ s and ψ e is illustrated graphically

Random electrodynamics: the theory of classical electrodynamics with classical electromagnetic zero-point radiation

International Nuclear Information System (INIS)

Boyer, T.H.

1975-01-01

The theory of classical electrodynamics with classical electromagnetic zero-point radiation is outlined here under the title random electrodynamics. The work represents a reanalysis of the bounds of validity of classical electron theory which should sharpen the understanding of the connections and distinctions between classical and quantum theories. The new theory of random electrodynamics is a classical electron theory involving Newton's equations for particle motion due to the Lorentz force, and Maxwell's equations for the electromagnetic fields with point particles as sources. However, the theory departs from the classical electron theory of Lorentz in that it adopts a new boundary condition on Maxwell's equations. It is assumed that the homogeneous boundary condition involves random classical electromagnetic radiation with a Lorentz-invariant spectrum, classical electromagnetic zero-point radiation. The implications of random electrodynamics for atomic structure, atomic spectra, and particle-interference effects are discussed on an order-of-magnitude or heuristic level. Some detailed mathematical connections and some merely heuristic connections are noted between random electrodynamics and quantum theory. (U.S.)

J. Genet. classic 101

Indian Academy of Sciences (India)

Journal of Genetics, Vol. 85, No. 2, August 2006. 101. Page 2. J. Genet. classic. 102. Journal of Genetics, Vol. 85, No. 2, August 2006. Page 3. J. Genet. classic. Journal of Genetics, Vol. 85, No. 2, August 2006. 103. Page 4. J. Genet. classic. 104. Journal of Genetics, Vol. 85, No. 2, August 2006. Page 5. J. Genet. classic.

J. Genet. classic 37

Indian Academy of Sciences (India)

Unknown

Journal of Genetics, Vol. 84, No. 1, April 2005. 37. Page 2. J. Genet. classic. Journal of Genetics, Vol. 84, No. 1, April 2005. 38. Page 3. J. Genet. classic. Journal of Genetics, Vol. 84, No. 1, April 2005. 39. Page 4. J. Genet. classic. Journal of Genetics, Vol. 84, No. 1, April 2005. 40. Page 5. J. Genet. classic. Journal of ...

Malaria parasite evasion of classical complement pathway attack

DEFF Research Database (Denmark)

Larsen, Mads Delbo; Ditlev, Sisse; Olmos, Rafael Bayarri

2017-01-01

of the protective antibodies that are gradually acquired in response to P. falciparum-IEs. Although this response is dominated by IgG1 and IgG3, complement-mediated attack following activation of the classical pathway does not appear to be a major effector mechanism. We hypothesized that this is related to the knob...... is that the knob-restricted expression of PfEMP1 on the IE surface may serve as a hitherto unappreciated immune evasion mechanism employed by P. falciparum parasites....

1000 Solved Problems in Classical Physics An Exercise Book

CERN Document Server

Kamal, Ahmad A

2011-01-01

This book basically caters to the needs of undergraduate and graduate physics students in classical physics, especially Classical Mechanics and Electricity and Electromagnetism. Lecturers/Tutors may use it as a resource book. The contents of the book are based on the syllabi currently used in the undergraduate courses in the USA, U.K., and other countries. The book consists of 15 chapters, each one beginning with a brief but adequate summary and necessary formulas and Line diagrams followed by a variety of typical problems useful for assignments and exams. Detailed solutions are provided at the end of each chapter.

Introduction to modern theoretical physics. Volume I. Classical physics and relativity

International Nuclear Information System (INIS)

Harris, E.G.

1975-01-01

The treatment covers vectors, tensors, and the structure of space, Newton's laws of motion and the law of gravitation, analytical mechanics, oscillatory motion, mechanics of a rigid body and of continuous media, classical fields, electromagnetic waves and radiation, the principle of relativity, relativistic electrodynamics and mechanics, general relativity theory and some of its consequences, and unified field theories and other modifications of the general theory of relativity

Classical trajectory in non-relativistic scattering

International Nuclear Information System (INIS)

Williams, A.C.

1978-01-01

With the statistical interpretation of quantum mechanics as a guide, the classical trajectory is incorporated into quantum scattering theory. The Feynman path integral formalism is used as a starting point, and classical transformation theory is applied to the phase of the wave function so derived. This approach is then used to derive an expression for the scattering amplitude for potential scattering. It is found that the amplitude can be expressed in an impact parameter representation similar to the Glauber formalism. Connections are then made to the Glauber approximation and to semiclassical approximations derived from the Feynman path integral formalism. In extending this analysis to projectile-nucleus scattering, an approximation scheme is given with the first term being the same as in Glauber's multiple scattering theory. Higher-order approximations, thus, are found to give corrections to the fixed scatterer form of the impulse approximation inherent in the Glauber theory

Classical trajectories and quantum field theory

International Nuclear Information System (INIS)

Vitiello, Giuseppe; Istituto Nazionale di Fisica Nucleare, Salerno

2005-01-01

The density matrix and the Wigner function formalism requires the doubling of the degrees of freedom in quantum mechanics (QM) and quantum field theory (QFT). The doubled degrees of freedom play the role of the thermal bath or environment degrees of freedom and are entangled with the system degrees of freedom. They also account for quantum noise in the fluctuating random forces in the system-environment coupling. The algebraic structure of QFT turns out to be the one of the deformed Hopf algebra. In such a frame, the trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations turn out to be classical trajectories and, under convenient conditions, they may exhibit properties typical of classical chaotic trajectories in nonlinear dynamics. The quantum Brownian motion and the two-slit experiment in QM are discussed in connection with the doubling of the degrees of freedom. (author)

Interferometric weak value deflections: Quantum and classical treatments

International Nuclear Information System (INIS)

Howell, John C.; Starling, David J.; Dixon, P. Ben; Vudyasetu, Praveen K.; Jordan, Andrew N.

2010-01-01

We derive the weak value deflection given in an article by Dixon et al.[P. B. Dixon et al. Phys. Rev. Lett. 102 173601 (2009)] both quantum mechanically and classically, including diffraction effects. This article is meant to cover some of the mathematical details omitted in that article owing to space constraints.

The sufficient condition for an extremum in the classical action integral as an eingenvalue problem

International Nuclear Information System (INIS)

Hussein, M.S.; Pereira, J.G.

The sufficient condition for an extremum in the classical action integral is studied using Morse's theory. Applications to the classical harmonic and anharmonic oscillators are made. The analogy of the calculations to the quantum mechanical problems in one dimension is stressed. (Author) [pt

Quantum theory of the classical: quantum jumps, Born's Rule and objective classical reality via quantum Darwinism.

Science.gov (United States)

Zurek, Wojciech Hubert

2018-07-13

The emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. In this paper, I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with the derivation of preferred sets of states that help to define what exists-our everyday classical reality. They emerge as a result of the breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification-of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and the emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection The pointer states obtained in this way determine what can happen-define events-without appealing to Born's Rule for probabilities. Therefore, p k =| ψ k | 2 can now be deduced from the entanglement-assisted invariance, or envariance -a symmetry of entangled quantum states. With probabilities at hand, one also gains new insights into the foundations of quantum statistical physics. Moreover, one can now analyse the information flows responsible for decoherence. These information flows explain how the perception of objective classical reality arises from the quantum substrate: the effective amplification that they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment-through quantum Darwinism This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Visualizing classical and quantum probability densities for momentum using variations on familiar one-dimensional potentials

International Nuclear Information System (INIS)

Robinett, R.W.

2002-01-01

After briefly reviewing the definitions of classical probability densities for position, P C L(x), and for momentum, P C L(p), we present several examples of classical mechanical potential systems, mostly variations on such familiar cases as the infinite well and the uniformly accelerated particle for which the classical distributions can be easily derived and visualized. We focus especially on a simple potential which interpolates between the symmetric linear potential, V(x)=F vertical bar x vertical bar, and the infinite well, which can illustrate, in a mathematically straightforward way, how the divergent δ-function classical probability density for momentum for the infinite well can be seen to arise. Such examples can help students understand the quantum mechanical momentum-space wavefunction (and its corresponding probability density) in much the same way that other semiclassical techniques, such as the WKB approximation, can be used to visualize position-space wavefunctions. (author)

Classical tachyons

International Nuclear Information System (INIS)

Recami, E.

1984-01-01

A review of tachyons, with particular attention to their classical theory, is presented. The extension of Special Relativity to tachyons in two dimensional is first presented, an elegant model-theory which allows a better understanding also of ordinary physics. Then, the results are extended to the four-dimensional case (particular on tachyon mechanics) that can be derived without assuming the existence of Super-luminal reference-frames. Localizability and the unexpected apparent shape of tachyonic objects are discussed, and it is shown (on the basis of tachyon kinematics) how to solve the common causal paradoxes. In connection with General Relativity, particularly the problem of the apparent superluminal expansions in astrophysics is reviewed. The problem (still open) of the extension of relativitic theories to tachyons in four dimensions is tackled, and the electromagnetic theory of tachyons, a topic that can be relevant also for the experimental side, is reviewed. (Author) [pt

General classical and quantum-mechanical description of magnetic resonance: an application to electric-dipole-moment experiments

Energy Technology Data Exchange (ETDEWEB)

Silenko, Alexander J. [Belarusian State University, Research Institute for Nuclear Problems, Minsk (Belarus); Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna (Russian Federation)

2017-05-15

A general theoretical description of a magnetic resonance is presented. This description is necessary for a detailed analysis of spin dynamics in electric-dipole-moment experiments in storage rings. General formulas describing a behavior of all components of the polarization vector at the magnetic resonance are obtained for an arbitrary initial polarization. These formulas are exact on condition that the nonresonance rotating field is neglected. The spin dynamics is also calculated at frequencies far from resonance with allowance for both rotating fields. A general quantum-mechanical analysis of the spin evolution at the magnetic resonance is fulfilled and the full agreement between the classical and quantum-mechanical approaches is shown. Quasimagnetic resonances for particles and nuclei moving in noncontinuous perturbing fields of accelerators and storage rings are considered. Distinguishing features of quasimagnetic resonances in storage ring electric-dipole-moment experiments are investigated in detail. The exact formulas for the effect caused by the electric dipole moment are derived. The difference between the resonance effects conditioned by the rf electric-field flipper and the rf Wien filter is found and is calculated for the first time. The existence of this difference is crucial for the establishment of a consent between analytical derivations and computer simulations and for checking spin tracking programs. The main systematical errors are considered. (orig.)

Variational problems arising in classical mechanics and nonlinear elasticity

International Nuclear Information System (INIS)

Spencer, P.

1999-01-01

In this thesis we consider two different classes of variational problems. First, one-dimensional problems arising from classical mechanics where the problem is to determine whether there is a unique function η 0 (x) which minimises the energy functional of the form I(η) = ∫ a b L(x,η(x), η'(x)) dx. We will investigate uniqueness by making a change of dependent and independent variables and showing that for a class of integrands L with a particular kind of scaling invariance the resulting integrand is completely convex. The change of variables arises by applying results from Lie group theory as applied in the study of differential equations and this work is motivated by [60] and [68]. Second, the problem of minimising energy functionals of the form E(u) = ∫ A W(∇u(x)) dx in the case of a nonlinear elastic body occupying an annular region A contains R 2 with u : A-bar → A-bar. This work is motivated by [57] (in particular the example of paragraph 4). We will consider rotationally symmetric deformations satisfying prescribed boundary conditions. We will show the existence of minimisers for stored energy functions of the form W(F) = g-tilde(vertical bar-F-vertical bar, det(F)) in a class of general rotationally symmetric deformations of a compressible annulus and for stored energy functions of the form W(F) = g-bar(vertical bar-F-vertical bar) in a class of rotationally symmetric deformations of an incompressible annulus. We will also show that in each case the minimisers are solutions of the full equilibrium equations. A model problem will be considered where the energy functional is the Dirichlet integral and it will be shown that the rotationally symmetric solution obtained is a minimiser among admissible non-rotationally symmetric deformations. In the case of an incompressible annulus, we will consider the Dirichlet integral as the energy functional and show that the rotationally symmetric equilibrium solutions in this case are weak local minimisers in

Quantum mechanics with quantum time

International Nuclear Information System (INIS)

Kapuscik, E.

1984-01-01

Using a non-canonical Lie structure of classical mechanics a new algebra of quantum mechanical observables is constructed. The new algebra, in addition to the notion of classical time, makes it possible to introduce the notion of quantum time. A new type of uncertainty relation is derived. (author)

Classical impurity ion confinement in a toroidal magnetized fusion plasma.

Science.gov (United States)

Kumar, S T A; Den Hartog, D J; Caspary, K J; Magee, R M; Mirnov, V V; Chapman, B E; Craig, D; Fiksel, G; Sarff, J S

2012-03-23

High-resolution measurements of impurity ion dynamics provide first-time evidence of classical ion confinement in a toroidal, magnetically confined plasma. The density profile evolution of fully stripped carbon is measured in MST reversed-field pinch plasmas with reduced magnetic turbulence to assess Coulomb-collisional transport without the neoclassical enhancement from particle drift effects. The impurity density profile evolves to a hollow shape, consistent with the temperature screening mechanism of classical transport. Corroborating methane pellet injection experiments expose the sensitivity of the impurity particle confinement time to the residual magnetic fluctuation amplitude.

Quantum Computing's Classical Problem, Classical Computing's Quantum Problem

OpenAIRE

Van Meter, Rodney

2013-01-01

Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classica...

Scalability of a Low-Cost Multi-Teraflop Linux Cluster for High-End Classical Atomistic and Quantum Mechanical Simulations

Science.gov (United States)

Kikuchi, Hideaki; Kalia, Rajiv K.; Nakano, Aiichiro; Vashishta, Priya; Shimojo, Fuyuki; Saini, Subhash

2003-01-01

Scalability of a low-cost, Intel Xeon-based, multi-Teraflop Linux cluster is tested for two high-end scientific applications: Classical atomistic simulation based on the molecular dynamics method and quantum mechanical calculation based on the density functional theory. These scalable parallel applications use space-time multiresolution algorithms and feature computational-space decomposition, wavelet-based adaptive load balancing, and spacefilling-curve-based data compression for scalable I/O. Comparative performance tests are performed on a 1,024-processor Linux cluster and a conventional higher-end parallel supercomputer, 1,184-processor IBM SP4. The results show that the performance of the Linux cluster is comparable to that of the SP4. We also study various effects, such as the sharing of memory and L2 cache among processors, on the performance.

Generalization of the Activated Complex Theory of Reaction Rates. II. Classical Mechanical Treatment

Science.gov (United States)

Marcus, R. A.

1964-01-01

In its usual classical form activated complex theory assumes a particular expression for the kinetic energy of the reacting system -- one associated with a rectilinear motion along the reaction coordinate. The derivation of the rate expression given in the present paper is based on the general kinetic energy expression.

Foldy-Wouthuysen transformations for the classical relativistic electron. Non grassmannian description

International Nuclear Information System (INIS)

Pupasov-Maksimov, Andrey; Deriglazov, Alexei

2012-01-01

Full text: We consider a classical model of the relativistic electron proposed by A. Deriglazov in Phys. Lett. A 376 (2012) 309-313. Though this model contains only bosonic variables, its quantization leads to the Dirac equation and one-particle relativistic quantum mechanics of the electron. There are constraints and gauge symmetries, therefore 18 initial variables of the model {x μ , p μ , ω A , π A }, μ is an element of (0,4), A is an element of (0,5) do not correspond to the observable quantities. There are 10 physical degrees of freedom implying another set of 10 gauge invariant variables which will be interpreted as physically observable quantities. On the other hand, to have a consistent one-particle relativistic quantum mechanics one has to consider only even operators which do not mix quantum states with positive and negative energy states. Such separation can be obtained with the Foldy-Wouthuysen transformation and leads to the Foldy-Wouthuysen representation with new operators for coordinates and spin (so-called Newton-Wigner coordinates). In the present work we match these to pictures by comparing the choice of the gauge invariant classical variables and the transition to the even operators in the quantum mechanics. We study different canonical transformations of this classical model in order to separate the set of observable quantities from variables with ambiguous dynamics. The constraints of the model in the case of free particle can be chosen in such a way that the Dirac brackets coincide with the Poisson brackets. This choice significantly simplify calculations of transformed variables. Moreover, new variables are canonical variables by construction. It is shown that the following generator of an infinitesimal canonical transformation S=1/2J 5j p j A(p 2 ), can be associated with the Foldy-Wouthuysen transformation. Thus we obtain a classical analog of the Foldy- Wouthuysen transformation. Moreover, the gauge invariant variables in the

Exact, E = 0, classical and quantum solutions for general power-law oscillators

International Nuclear Information System (INIS)

Nieto, M.M.; Daboul, J.

1994-01-01

For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -γ/r ν , γ > 0 and -∞ 0 (t))] 1/μ , with μ = ν/2 - 1 ≠ 0. For ν > 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when ν > 2 the solutions are normalizable (bound), as in the classical case. Also, there are normalizable discrete, yet unbound, state which correspond to unbound classical particles which reach infinity in a finite time. These and other interesting comparisons to the classical system will be discussed

Semi-classical scalar propagators in curved backgrounds: formalism and ambiguities

Energy Technology Data Exchange (ETDEWEB)

Grain, J. [Laboratory for Subatomic Physics and Cosmology, Grenoble Universites, CNRS, IN2P3, 53, avenue de Martyrs, 38026 Grenoble cedex (France)]|[AstroParticle and Cosmology, Universite Paris 7, CNRS, IN2P3, 10, rue Alice Domon et Leonie Duquet, 75205 Paris cedex 13 (France); Barrau, A. [Laboratory for Subatomic Physics and Cosmology, Grenoble Universites, CNRS, IN2P3, 53, avenue de Martyrs, 38026 Grenoble cedex (France)

2007-05-15

The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing - often at the Gedanken experiment level - constraints on tentative theories of quantum gravity. Determining the dynamics of fields in curved backgrounds remains however a complicated task because of the highly intricate partial differential equations involved, especially when the space metric exhibits no symmetry. In this article, we provide - in a pedagogical way - a general formalism to determine this dynamics at the semi-classical order. To this purpose, a generic expression for the semi-classical propagator is computed and the equation of motion for the probability four-current is derived. Those results underline a direct analogy between the computation of the propagator in general relativistic quantum mechanics and the computation of the propagator for stationary systems in non-relativistic quantum mechanics. (authors)

Semi-classical scalar propagators in curved backgrounds: formalism and ambiguities

International Nuclear Information System (INIS)

Grain, J.; Barrau, A.

2007-05-01

The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing - often at the Gedanken experiment level - constraints on tentative theories of quantum gravity. Determining the dynamics of fields in curved backgrounds remains however a complicated task because of the highly intricate partial differential equations involved, especially when the space metric exhibits no symmetry. In this article, we provide - in a pedagogical way - a general formalism to determine this dynamics at the semi-classical order. To this purpose, a generic expression for the semi-classical propagator is computed and the equation of motion for the probability four-current is derived. Those results underline a direct analogy between the computation of the propagator in general relativistic quantum mechanics and the computation of the propagator for stationary systems in non-relativistic quantum mechanics. (authors)

Intrinsic resonance representation of quantum mechanics

DEFF Research Database (Denmark)

Carioli, M.; Heller, E.J.; Møller, Klaus Braagaard

1997-01-01

an optimal representation, based purely on classical mechanics. ''Hidden'' constants of the motion and good actions already known to the classical mechanics are thus incorporated into the basis, leaving the quantum effects to be isolated and included by small matrix diagonalizations. This simplifies...

A Simple Explanation of the Classic Hydrostatic Paradox

Science.gov (United States)

Kontomaris, Stylianos-Vasileios; Malamou, Anna

2016-01-01

An interesting problem in fluid mechanics, with significant educational importance, is the classic hydrostatic paradox. The hydrostatic paradox states the fact that in different shaped containers, with the same base area, which are filled with a liquid of the same height, the applied force by the liquid on the base of each container is exactly the…

Fermions from classical statistics

International Nuclear Information System (INIS)

Wetterich, C.

2010-01-01

We describe fermions in terms of a classical statistical ensemble. The states τ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities p τ amounts to a rotation of the wave function q τ (t)=±√(p τ (t)), we infer the unitary time evolution of a quantum system of fermions according to a Schroedinger equation. We establish how such classical statistical ensembles can be mapped to Grassmann functional integrals. Quantum field theories for fermions arise for a suitable time evolution of classical probabilities for generalized Ising models.

Classical limit for semirelativistic Hartree systems

KAUST Repository

Aki, Gonca L.

2008-01-01

We consider the three-dimensional semirelativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove by using Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive case. © 2008 American Institute of Physics.

The equation of motion of an electron: a debate in classical and quantum physics

International Nuclear Information System (INIS)

Kim, K.-J.

1999-01-01

The current status of understanding of the equation of motion of an electron is summarized. Classically, a consistent, linearized theory exists for an electron of finite extent, as long as the size of the electron is larger than the classical electron radius. Nonrelativistic quantum mechanics seems to offer a tine theory even in the point-particle limit

Foucault's contributions for understanding power relations in British classical political economy

Directory of Open Access Journals (Sweden)

Danielle Guizzo

2015-05-01

Full Text Available This paper analyzes the strategic role played by British classical political economy in constructing new technologies of power. Michel Foucault drew attention to a change that political economists promoted concerning the role of the state, which has been overlooked by historians of economic thought. This paper explores the main arguments provided by the most important British political economists of the 18th and 19th centuries on what concerns population management, State's role and economic dynamics in order to examine Foucault's considerations. Although British classical political economy consolidated the mechanism of markets and economic individuality, thus creating a system of truth that changed economic norms and practices, its discourse also established a political conduct that was responsible for creating mechanisms of control that disseminated new forms of power relations.

Qualitative insights on fundamental mechanics

OpenAIRE

Mardari, G. N.

2002-01-01

The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We show that the main parameters of any fundamental model must be theory-independent. They cannot be predicted, because they cannot have internal causes. However, it is possible to describe them in the language of classical mechanics. We invoke philosophical reas...

Isomorph invariance of the structure and dynamics of classical crystals

DEFF Research Database (Denmark)

Albrechtsen, Dan; Olsen, Andreas Elmerdahl; Pedersen, Ulf Rørbæk

2014-01-01

This paper shows by computer simulations that some crystalline systems have curves in their thermodynamic phase diagrams, so-called isomorphs, along which structure and dynamics in reduced units are invariant to a good approximation. The crystals are studied in a classical-mechanical framework...

Approach to measurement to quantum mechanics

International Nuclear Information System (INIS)

Sudarshan, E.C.G.; Sherry, T.N.; Gautam, S.R.

1977-10-01

An unconventional approach to the measurement problem in quantum mechanics is considered, the apparatus is treated as a classical system, belonging to the macro-world. In order to have a measurement the apparatus must interact with the quantum system. As a first step, the classical apparatus is embedded into a larger quantum mechanical structure, making use of superselection rules. Projection back to the classical system is possible. The apparatus and system are now coupled such that the apparatus remains classical (principle of integrity), and unambiguous information of the values of a quantum observable are transferred to the variables of the apparatus. Finally, projection back to the classical formulation is accomplished. Further measurement of the classical apparatus can be done, causing no problems of principle. Thus interactions causing pointers to move (which are not treat) can be added. The restrictions placed by the principle of integrity on the form of the interaction between classical and quantum systems are examined

Limiting processes in non-equilibrium classical statistical mechanics

International Nuclear Information System (INIS)

Jancel, R.

1983-01-01

After a recall of the basic principles of the statistical mechanics, the results of ergodic theory, the transient at the thermodynamic limit and his link with the transport theory near the equilibrium are analyzed. The fundamental problems put by the description of non-equilibrium macroscopic systems are investigated and the kinetic methods are stated. The problems of the non-equilibrium statistical mechanics are analyzed: irreversibility and coarse-graining, macroscopic variables and kinetic description, autonomous reduced descriptions, limit processes, BBGKY hierarchy, limit theorems [fr

Bidirectional Classical Stochastic Processes with Measurements and Feedback

Science.gov (United States)

Hahne, G. E.

2005-01-01

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

A classical model explaining the OPERA velocity paradox

CERN Document Server

Broda, Boguslaw

2011-01-01

In the context of the paradoxical results of the OPERA Collaboration, we have proposed a classical mechanics model yielding the statistically measured velocity of a beam higher than the velocity of the particles constituting the beam. Ingredients of our model necessary to obtain this curious result are a non-constant fraction function and the method of the maximum-likelihood estimation.

Experimental non-classicality of an indivisible quantum system.

Science.gov (United States)

Lapkiewicz, Radek; Li, Peizhe; Schaeff, Christoph; Langford, Nathan K; Ramelow, Sven; Wieśniak, Marcin; Zeilinger, Anton

2011-06-22

In contrast to classical physics, quantum theory demands that not all properties can be simultaneously well defined; the Heisenberg uncertainty principle is a manifestation of this fact. Alternatives have been explored--notably theories relying on joint probability distributions or non-contextual hidden-variable models, in which the properties of a system are defined independently of their own measurement and any other measurements that are made. Various deep theoretical results imply that such theories are in conflict with quantum mechanics. Simpler cases demonstrating this conflict have been found and tested experimentally with pairs of quantum bits (qubits). Recently, an inequality satisfied by non-contextual hidden-variable models and violated by quantum mechanics for all states of two qubits was introduced and tested experimentally. A single three-state system (a qutrit) is the simplest system in which such a contradiction is possible; moreover, the contradiction cannot result from entanglement between subsystems, because such a three-state system is indivisible. Here we report an experiment with single photonic qutrits which provides evidence that no joint probability distribution describing the outcomes of all possible measurements--and, therefore, no non-contextual theory--can exist. Specifically, we observe a violation of the Bell-type inequality found by Klyachko, Can, Binicioğlu and Shumovsky. Our results illustrate a deep incompatibility between quantum mechanics and classical physics that cannot in any way result from entanglement.

Wigner's dynamical transition state theory in phase space: classical and quantum

International Nuclear Information System (INIS)

Waalkens, Holger; Schubert, Roman; Wiggins, Stephen

2008-01-01

We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs the evolution from reactants to products in high dimensional systems. In the classical case this is the standard Poincaré–Birkhoff normal form. In the quantum case we develop a normal form based on the Weyl calculus and an explicit algorithm for computing this quantum normal form. The classical normal form allows us to discover and compute the phase space structures that govern classical reaction dynamics. From this knowledge we are able to provide a direct construction of an energy dependent dividing surface in phase space having the properties that trajectories do not locally 're-cross' the surface and the directional flux across the surface is minimal. Using this, we are able to give a formula for the directional flux through the dividing surface that goes beyond the harmonic approximation. We relate this construction to the flux–flux autocorrelation function which is a standard ingredient in the expression for the reaction rate in the chemistry community. We also give a classical mechanical interpretation of the activated complex as a normally hyperbolic invariant manifold (NHIM), and further describe the structure of the NHIM. The quantum normal form provides us with an efficient algorithm to compute quantum reaction rates and we relate this algorithm to the quantum version of the flux–flux autocorrelation function formalism. The significance of the classical phase space structures for the quantum mechanics of reactions is elucidated by studying the phase space distribution of scattering states. The quantum normal form also provides an efficient way of computing Gamov–Siegert resonances. We relate these resonances to the lifetimes of the quantum activated

Orbital classical solutions, non-perturbative phenomena and singularity at the zero coupling constant point

International Nuclear Information System (INIS)

Vourdas, A.

1982-01-01

We try to extend previous arguments on orbital classical solutions in non-relativistic quantum mechanics to the 1/4lambda vertical stroke phi vertical stroke 4 complex relativistic field theory. The single valuedness of the Green function in the semiclassical (Planksche Konstante → 0) limit leads to a Bohr-Sommerfeld quantization. A path integral formalism for the Green functions analogous to that in non-relativistic quantum mechanics is employed and a semiclassical approach which uses our classical solutions indicates non-perturbative effects. They reflect an esub(1/lambda) singularity at the zero coupling constant point. (orig.)

J. Genet. classic 235

Indian Academy of Sciences (India)

Unknown

Journal of Genetics, Vol. 83, No. 3, December 2004. 235. Page 2. J. Genet. classic. Journal of Genetics, Vol. 83, No. 3, December 2004. 236. Page 3. J. Genet. classic. Journal of Genetics, Vol. 83, No. 3, December 2004. 237. Page 4. J. Genet. classic. Journal of Genetics, Vol. 83, No. 3, December 2004. 238. Page 5 ...

Dynamics of unitarization by classicalization

International Nuclear Information System (INIS)

Dvali, Gia; Pirtskhalava, David

2011-01-01

We study dynamics of the classicalization phenomenon suggested in G. Dvali et al. , according to which a class of non-renormalizable theories self-unitarizes at very high-energies via creation of classical configurations (classicalons). We study this phenomenon in an explicit model of derivatively-self-coupled scalar that serves as a prototype for a Nambu-Goldstone-Stueckelberg field. We prepare the initial state in form of a collapsing wave-packet of a small occupation number but of very high energy, and observe that the classical configuration indeed develops. Our results confirm the previous estimates, showing that because of self-sourcing the wave-packet forms a classicalon configuration with radius that increases with center of mass energy. Thus, classicalization takes place before the waves get any chance of probing short-distances. The self-sourcing by energy is the crucial point, which makes classicalization phenomenon different from the ordinary dispersion of the wave-packets in other interacting theories. Thanks to this, unlike solitons or other non-perturbative objects, the production of classicalons is not only unsuppressed, but in fact dominates the high-energy scattering. In order to make the difference between classicalizing and non-classicalizing theories clear, we use a language in which the scattering cross section in a generic theory can be universally understood as a geometric cross section set by a classical radius down to which waves can propagate freely, before being scattered. We then show, that in non-classicalizing examples this radius shrinks with increasing energy and becomes microscopic, whereas in classicalizing theories expands and becomes macroscopic. We study analogous scattering in a Galileon system and discover that classicalization also takes place there, although somewhat differently. We thus observe, that classicalization is source-sensitive and that Goldstones pass the first test.

Inclination Mixing in the Classical Kuiper Belt

Science.gov (United States)

Volk, Kathryn; Malhotra, Renu

2011-07-01

We investigate the long-term evolution of the inclinations of the known classical and resonant Kuiper Belt objects (KBOs). This is partially motivated by the observed bimodal inclination distribution and by the putative physical differences between the low- and high-inclination populations. We find that some classical KBOs undergo large changes in inclination over gigayear timescales, which means that a current member of the low-inclination population may have been in the high-inclination population in the past, and vice versa. The dynamical mechanisms responsible for the time variability of inclinations are predominantly distant encounters with Neptune and chaotic diffusion near the boundaries of mean motion resonances. We reassess the correlations between inclination and physical properties including inclination time variability. We find that the size-inclination and color-inclination correlations are less statistically significant than previously reported (mostly due to the increased size of the data set since previous works with some contribution from inclination variability). The time variability of inclinations does not change the previous finding that binary classical KBOs have lower inclinations than non-binary objects. Our study of resonant objects in the classical Kuiper Belt region includes objects in the 3:2, 7:4, 2:1, and eight higher-order mean motion resonances. We find that these objects (some of which were previously classified as non-resonant) undergo larger changes in inclination compared to the non-resonant population, indicating that their current inclinations are not generally representative of their original inclinations. They are also less stable on gigayear timescales.

Classical and semi-classical solutions of the Yang--Mills theory

International Nuclear Information System (INIS)

Jackiw, R.; Nohl, C.; Rebbi, C.

1977-12-01

This review summarizes what is known at present about classical solutions to Yang-Mills theory both in Euclidean and Minkowski space. The quantal meaning of these solutions is also discussed. Solutions in Euclidean space expose multiple vacua and tunnelling of the quantum theory. Those in Minkowski space-time provide a semi-classical spectrum for a conformal generator

Classical confinement and outward convection of impurity ions in the MST RFP

Energy Technology Data Exchange (ETDEWEB)

Kumar, S. T. A.; Den Hartog, D. J.; Mirnov, V. V.; Eilerman, S.; Nornberg, M.; Reusch, J. A.; Sarff, J. S. [Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Caspary, K. J.; Chapman, B. E.; Parke, E. [Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Magee, R. M. [Department of Physics, West Virginia University, Morgantown, WV 26506 (United States); Brower, D. L.; Ding, W. X.; Lin, L. [Department of Physics and Astronomy, University of California, Los Angeles, California 90095 (United States); Craig, D. [Physics Department, Wheaton College, Wheaton, Illinois 60187 (United States); Fiksel, G. [Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Laboratory for Laser Energetics, University of Rochester, Rochester, New York (United States)

2012-05-15

Impurity ion dynamics measured with simultaneously high spatial and temporal resolution reveal classical ion transport in the reversed-field pinch. The boron, carbon, oxygen, and aluminum impurity ion density profiles are obtained in the Madison Symmetric Torus [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] using a fast, active charge-exchange-recombination-spectroscopy diagnostic. Measurements are made during improved-confinement plasmas obtained using inductive control of tearing instability to mitigate stochastic transport. At the onset of the transition to improved confinement, the impurity ion density profile becomes hollow, with a slow decay in the core region concurrent with an increase in the outer region, implying an outward convection of impurities. Impurity transport from Coulomb collisions in the reversed-field pinch is classical for all collisionality regimes, and analysis shows that the observed hollow profile and outward convection can be explained by the classical temperature screening mechanism. The profile agrees well with classical expectations. Experiments performed with impurity pellet injection provide further evidence for classical impurity ion confinement.

Prequantum classical statistical field theory: background field as a source of everything?

International Nuclear Information System (INIS)

Khrennikov, Andrei

2011-01-01

Prequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie's 'double solution' approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson's stochastic QM and its generalization by Davidson, 't Hooft's models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrodinger. There is no quantum particles at all, only waves. In particular, photons are simply wave-pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special 'prequantum fields': the electron field, the neutron field, and so on. PCSFT claims that (sooner or later) people will be able to measure components of these fields: components of the 'photonic field' (the classical electromagnetic field of low intensity), electronic field, neutronic field, and so on. At the moment we are able to produce quantum correlations as correlations of classical Gaussian random fields. In this paper we are interested in mathematical and physical reasons of usage of Gaussian fields. We consider prequantum signals (corresponding to quantum systems) as composed of a huge number of wave-pulses (on very fine prequantum time scale). We speculate that the prequantum background field (the field of 'vacuum fluctuations') might play the role of a source of such pulses, i.e., the source of everything.

Origin of Mass. Mass and Mass-Energy Equation from Classical-Mechanics Solution

OpenAIRE

Zheng-Johansson, J. X.; Johansson, P-I.

2005-01-01

We establish the classical wave equation for a particle formed of a massless oscillatory elementary charge generally also traveling, and the resulting electromagnetic waves, of a generally Doppler-effected angular frequency $\\w$, in the vacuum in three dimensions. We obtain from the solutions the total energy of the particle wave to be $\\eng=\\hbarc\\w$, $2\\pi \\hbarc$ being a function expressed in wave-medium parameters and identifiable as the Planck constant. In respect to the train of the wav...

An alternative phase-space distribution to sample initial conditions for classical dynamics simulations

International Nuclear Information System (INIS)

Garcia-Vela, A.

2002-01-01

A new quantum-type phase-space distribution is proposed in order to sample initial conditions for classical trajectory simulations. The phase-space distribution is obtained as the modulus of a quantum phase-space state of the system, defined as the direct product of the coordinate and momentum representations of the quantum initial state. The distribution is tested by sampling initial conditions which reproduce the initial state of the Ar-HCl cluster prepared by ultraviolet excitation, and by simulating the photodissociation dynamics by classical trajectories. The results are compared with those of a wave packet calculation, and with a classical simulation using an initial phase-space distribution recently suggested. A better agreement is found between the classical and the quantum predictions with the present phase-space distribution, as compared with the previous one. This improvement is attributed to the fact that the phase-space distribution propagated classically in this work resembles more closely the shape of the wave packet propagated quantum mechanically

From a quantum to a classical description of intense laser-atom physics with Bohmian trajectories

International Nuclear Information System (INIS)

Lai, X Y; Cai Qingyu; Zhan, M S

2009-01-01

In this paper, Bohmian mechanics is applied to intense laser-atom physics. The motion of an atomic electron in an intense laser field is obtained from the Bohm-Newton equation. We find that the quantum potential that dominates the quantum effect of a physical system becomes negligible as the electron is driven far from the parent ion by the intense laser field, i.e. the behavior of the electron smoothly tends towards classical soon after the electron is ionized. Our numerical calculations present direct positive evidence for semiclassical trajectory methods in intense laser-atom physics where the motion of the ionized electron is treated by classical mechanics, while quantum mechanics is needed before the ionization.

Classical plasma dynamics of Mie-oscillations in atomic clusters

Science.gov (United States)

Kull, H.-J.; El-Khawaldeh, A.

2018-04-01

Mie plasmons are of basic importance for the absorption of laser light by atomic clusters. In this work we first review the classical Rayleigh-theory of a dielectric sphere in an external electric field and Thomson’s plum-pudding model applied to atomic clusters. Both approaches allow for elementary discussions of Mie oscillations, however, they also indicate deficiencies in describing the damping mechanisms by electrons crossing the cluster surface. Nonlinear oscillator models have been widely studied to gain an understanding of damping and absorption by outer ionization of the cluster. In the present work, we attempt to address the issue of plasmon relaxation in atomic clusters in more detail based on classical particle simulations. In particular, we wish to study the role of thermal motion on plasmon relaxation, thereby extending nonlinear models of collective single-electron motion. Our simulations are particularly adopted to the regime of classical kinetics in weakly coupled plasmas and to cluster sizes extending the Debye-screening length. It will be illustrated how surface scattering leads to the relaxation of Mie oscillations in the presence of thermal motion and of electron spill-out at the cluster surface. This work is intended to give, from a classical perspective, further insight into recent work on plasmon relaxation in quantum plasmas [1].

Molecular dynamics simulations of classical sound absorption in a monatomic gas

Science.gov (United States)

Ayub, M.; Zander, A. C.; Huang, D. M.; Cazzolato, B. S.; Howard, C. Q.

2018-05-01

Sound wave propagation in argon gas is simulated using molecular dynamics (MD) in order to determine the attenuation of acoustic energy due to classical (viscous and thermal) losses at high frequencies. In addition, a method is described to estimate attenuation of acoustic energy using the thermodynamic concept of exergy. The results are compared against standing wave theory and the predictions of the theory of continuum mechanics. Acoustic energy losses are studied by evaluating various attenuation parameters and by comparing the changes in behavior at three different frequencies. This study demonstrates acoustic absorption effects in a gas simulated in a thermostatted molecular simulation and quantifies the classical losses in terms of the sound attenuation constant. The approach can be extended to further understanding of acoustic loss mechanisms in the presence of nanoscale porous materials in the simulation domain.

Quantum remnants in the classical limit

International Nuclear Information System (INIS)

Kowalski, A.M.; Plastino, A.

2016-01-01

We analyze here the common features of two dynamical regimes: a quantum and a classical one. We deal with a well known semi-classic system in its route towards the classical limit, together with its purely classic counterpart. We wish to ascertain i) whether some quantum remnants can be found in the classical limit and ii) the details of the quantum-classic transition. The so-called mutual information is the appropriate quantifier for this task. Additionally, we study the Bandt–Pompe's symbolic patterns that characterize dynamical time series (representative of the semi-classical system under scrutiny) in their evolution towards the classical limit. - Highlights: • We investigate the classical limit (CL) of a well known semi classical model. • The study is made by reference to the Bandt Pompe symbolic approach. • The number and type of associated symbols changes as one proceeds towards the CL. • We ascertain which symbols pertaining to the quantum zone remain in the CL.

Quantum remnants in the classical limit

Energy Technology Data Exchange (ETDEWEB)

Kowalski, A.M., E-mail: kowalski@fisica.unlp.edu.ar [Instituto de Física (IFLP-CCT-Conicet), Universidad Nacional de La Plata, C.C. 727, 1900 La Plata (Argentina); Comision de Investigaciones Científicas (CIC) (Argentina); Plastino, A., E-mail: plastino@fisica.unlp.edu.ar [Instituto de Física (IFLP-CCT-Conicet), Universidad Nacional de La Plata, C.C. 727, 1900 La Plata (Argentina); Argentina' s National Research Council (CONICET) (Argentina); SThAR, EPFL Innovation Park, Lausanne (Switzerland)

2016-09-16

We analyze here the common features of two dynamical regimes: a quantum and a classical one. We deal with a well known semi-classic system in its route towards the classical limit, together with its purely classic counterpart. We wish to ascertain i) whether some quantum remnants can be found in the classical limit and ii) the details of the quantum-classic transition. The so-called mutual information is the appropriate quantifier for this task. Additionally, we study the Bandt–Pompe's symbolic patterns that characterize dynamical time series (representative of the semi-classical system under scrutiny) in their evolution towards the classical limit. - Highlights: • We investigate the classical limit (CL) of a well known semi classical model. • The study is made by reference to the Bandt Pompe symbolic approach. • The number and type of associated symbols changes as one proceeds towards the CL. • We ascertain which symbols pertaining to the quantum zone remain in the CL.

Lie-admissible invariant treatment of irreversibility for matter and antimatter at the classical and operator levels

International Nuclear Information System (INIS)

Santilli, R.M.

2006-01-01

It was generally believed throughout the 20th century that irreversibility is a purely classical event without operator counterpart. however, a classical irreversible system cannot be consistently decomposed into a finite number of reversible quantum particles (and. vive versa), thus establishing that the origin of irreversibility is basically unknown at the dawn of the 21-st century. To resolve this problem. we adopt the historical analytical representation of irreversibility by Lagrange and Hamilton, that with external terms in their analytic equations; we show that, when properly written, the brackets of the time evolution characterize covering Lie-admissible algebras; we prove that the formalism has fully consistent operator counterpart given by the Lie-admissible branch of hadronic mechanics; we identify mathematical and physical inconsistencies when irreversible formulations are treated with the conventional mathematics used for reversible systems; we show that when the dynamical equations are treated with a novel irreversible mathematics, Lie-admissible formulations are fully consistent because invariant at both the classical and operator levels; and we complete our analysis with a number of explicit applications to irreversible processes in classical mechanics, particle physics and thermodynamics. The case of closed-isolated systems verifying conventional total conservation laws, yet possessing an irreversible structure, is treated via the simpler Lie-isotopic branch of hadronic mechanics. The analysis is conducted for both matter and antimatter at the classical and operator levels to prevent insidious inconsistencies occurring for the sole study of matter or, separately, antimatter

Comparison of classical and modern theories of longitudinal wave propagation in elastic rods

CSIR Research Space (South Africa)

Shatalov, M

2011-01-01

Full Text Available Conference on Computational and Applied Mechanics SACAM10 Pretoria, 10?13 January 2010 ? SACAM COMPARISON OF CLASSICAL AND MODERN THEORIES OF LONGITUDINAL WAVE PROPAGATION IN ELASTIC RODS M. Shatalov*,?,?? , I. Fedotov? 1 , HM. Tenkam? 2, J. Marais..., Pretoria, 0001 FIN-40014, South Africa 1fedotovi@tut.ac.za, 2djouosseutenkamhm@tut.ac.za ?? Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa Keywords: Elastic rod, wave propagation, classical...

Three-dimensional classical-ensemble modeling of non-sequential double ionization

International Nuclear Information System (INIS)

Haan, S.L.; Breen, L.; Tannor, D.; Panfili, R.; Ho, Phay J.; Eberly, J.H.

2005-01-01

Full text: We have been using 1d ensembles of classical two-electron atoms to simulate helium atoms that are exposed to pulses of intense laser radiation. In this talk we discuss the challenges in setting up a 3d classical ensemble that can mimic the quantum ground state of helium. We then report studies in which each one of 500,000 two-electron trajectories is followed in 3d through a ten-cycle (25 fs) 780 nm laser pulse. We examine double-ionization yield for various intensities, finding the familiar knee structure. We consider the momentum spread of outcoming electrons in directions both parallel and perpendicular to the direction of laser polarization, and find results that are consistent with experiment. We examine individual trajectories and recollision processes that lead to double ionization, considering the best phases of the laser cycle for recollision events and looking at the possible time delay between recollision and emergence. We consider also the number of recollision events, and find that multiple recollisions are common in the classical ensemble. We investigate which collisional processes lead to various final electron momenta. We conclude with comments regarding the ability of classical mechanics to describe non-sequential double ionization, and a quick summary of similarities and differences between 1d and 3d classical double ionization using energy-trajectory comparisons. Refs. 3 (author)

Mechanics and thermodynamics

CERN Document Server

Demtröder, Wolfgang

2017-01-01

This introduction to classical mechanics and thermodynamics provides an accessible and clear treatment of the fundamentals. Starting with particle mechanics and an early introduction to special relativity this textbooks enables the reader to understand the basics in mechanics. The text is written from the experimental physics point of view, giving numerous real life examples and applications of classical mechanics in technology. This highly motivating presentation deepens the knowledge in a very accessible way. The second part of the text gives a concise introduction to rotational motion, an expansion to rigid bodies, fluids and gases. Finally, an extensive chapter on thermodynamics and a short introduction to nonlinear dynamics with some instructive examples intensify the knowledge of more advanced topics. Numerous problems with detailed solutions are perfect for self study.

de Broglie Swapping Metadynamics for Quantum and Classical Sampling.

Science.gov (United States)

Nava, Marco; Quhe, Ruge; Palazzesi, Ferruccio; Tiwary, Pratyush; Parrinello, Michele

2015-11-10

This paper builds on our previous work on Path Integral Metadynamics [ Ruge et al. J. Chem. Theory Comput. 2015 , 11 , 1383 ] in which we have accelerated sampling in quantum systems described by Feynman's Path Integrals using Metadynamics. We extend the scope of Path Integral Metadynamics by combining it with a replica exchange scheme in which artificially enhanced quantum effects play the same role as temperature does in parallel tempering. Our scheme can be adapted so as to be used in an ancillary way to sample systems described by classical statistical mechanics. Contrary to Metadynamics and many other sampling methods no collective variables need to be defined. The method in its two variants, quantum and classical, is tested in a number of examples.

Remarks on the classical limit of quantum field theories

International Nuclear Information System (INIS)

Eckmann, J.P.

1977-01-01

Recently, there has been an increasing interest in computing quantum mechanical corrections to solutions of classical field equations. In this note, proceeding in the opposite way, theorems about the classical limit of relativistic quantum field models are summarized. These results are a byproduct of the so called 'constructive' approach to quantum field theory. Section 1 deals with generalities; in Section 2 the situation where no phase transitions occur is discussed in the limit h→0; and in Section 3 one result in the case where such a transition occurs is reformulated (Glimm et al). The validity of the loop expansion is discussed. It seems however that the tools to show the rigorous validity of soliton calculations are not yet prepared. (Auth.)

A generalization of Fermat's principle for classical and quantum systems

Science.gov (United States)

Elsayed, Tarek A.

2014-09-01

The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in many-dimensional spaces describing dynamical systems (i.e., the quantum Hilbert space and the classical phase and configuration space). We propose that if the notion of a metric distance is well defined in that space and the velocity of the representative point of the system is an invariant of motion, then a generalized version of Fermat's principle will hold. We substantiate this conjecture for time-independent quantum systems and for a classical system consisting of coupled harmonic oscillators. An exception to this principle is the configuration space of a charged particle in a constant magnetic field; in this case the principle is valid in a frame rotating by half the Larmor frequency, not the stationary lab frame.

Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

International Nuclear Information System (INIS)

Costa, Diogo Ricardo da; Dettmann, Carl P.; Oliveira, Juliano A. de; Leonel, Edson D.

2015-01-01

Some dynamical properties for an oval billiard with a scatterer in its interior are studied. The dynamics consists of a classical particle colliding between an inner circle and an external boundary given by an oval, elliptical, or circle shapes, exploring for the first time some natural generalizations. The billiard is indeed a generalization of the annular billiard, which is of strong interest for understanding marginally unstable periodic orbits and their role in the boundary between regular and chaotic regions in both classical and quantum (including experimental) systems. For the oval billiard, which has a mixed phase space, the presence of an obstacle is an interesting addition. We demonstrate, with details, how to obtain the equations of the mapping, and the changes in the phase space are discussed. We study the linear stability of some fixed points and show both analytically and numerically the occurrence of direct and inverse parabolic bifurcations. Lyapunov exponents and generalized bifurcation diagrams are obtained. Moreover, histograms of the number of successive iterations for orbits that stay in a cusp are studied. These histograms are shown to be scaling invariant when changing the radius of the scatterer, and they have a power law slope around −3. The results here can be generalized to other kinds of external boundaries

Classical and Quantum Models in Non-Equilibrium Statistical Mechanics: Moment Methods and Long-Time Approximations

Directory of Open Access Journals (Sweden)

Ramon F. Alvarez-Estrada

2012-02-01

Full Text Available We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb at thermal equilibrium at temperature T (either with ab initio dissipation or without it. Boltzmann’s classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomialsHn’s. The moments of non-equilibrium classical distributions, implied by the Hn’s, fulfill a hierarchy: for long times, the lowest moment dominates the evolution towards thermal equilibrium, either with dissipation or without it (but under certain approximation. We revisit that hierarchy, whose solution depends on operator continued fractions. We review our generalization of that moment method to classical closed many-particle interacting systems with neither a hb nor ab initio dissipation: with initial states describing thermal equilibrium at T at large distances but non-equilibrium at finite distances, the moment method yields, approximately, irreversible thermalization of the whole system at T, for long times. Generalizations to non-equilibrium quantum interacting systems meet additional difficulties. Three of them are: (i equilibrium distributions (represented through Wigner functions are neither Gaussian in momenta nor known in closed form; (ii they may depend on dissipation; and (iii the orthogonal polynomials in momenta generated by them depend also on positions. We generalize the moment method, dealing with (i, (ii and (iii, to some non-equilibrium one-particle quantum interacting systems. Open problems are discussed briefly.

Signaling pathways and immune evasion mechanisms in classical Hodgkin lymphoma.

Science.gov (United States)

Liu, W Robert; Shipp, Margaret A

2017-11-23

Classical Hodgkin lymphoma (cHL) is an unusual B-cell-derived malignancy in which rare malignant Hodgkin and Reed-Sternberg (HRS) cells are surrounded by an extensive but ineffective inflammatory/immune cell infiltrate. This striking feature suggests that malignant HRS cells escape immunosurveillance and interact with immune cells in the cancer microenvironment for survival and growth. We previously found that cHLs have a genetic basis for immune evasion: near-uniform copy number alterations of chromosome 9p24.1 and the associated PD-1 ligand loci, CD274/PD-L1 and PDCD1LG2/PD-L2, and copy number-dependent increased expression of these ligands. HRS cells expressing PD-1 ligands are thought to engage PD-1 receptor-positive immune effectors in the tumor microenvironment and induce PD-1 signaling and associated immune evasion. The genetic bases of enhanced PD-1 signaling in cHL make these tumors uniquely sensitive to PD-1 blockade. © 2017 by The American Society of Hematology.

Classical and quantum chaos in a circular billiard with a straight cut

International Nuclear Information System (INIS)

Ree, S.; Reichl, L.E.

1999-01-01

We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. Classically, this system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos as we vary the size of the cut. We plot Poincaracute e surfaces of section to study chaos. Quantum mechanically, we look at Husimi plots, and also use the quantum web, the technique primarily used in spin systems so far, to try to see differences in quantum manifestations of soft and hard chaos. copyright 1999 The American Physical Society

Semiclassical statistical mechanics

International Nuclear Information System (INIS)

Stratt, R.M.

1979-04-01

On the basis of an approach devised by Miller, a formalism is developed which allows the nonperturbative incorporation of quantum effects into equilibrium classical statistical mechanics. The resulting expressions bear a close similarity to classical phase space integrals and, therefore, are easily molded into forms suitable for examining a wide variety of problems. As a demonstration of this, three such problems are briefly considered: the simple harmonic oscillator, the vibrational state distribution of HCl, and the density-independent radial distribution function of He 4 . A more detailed study is then made of two more general applications involving the statistical mechanics of nonanalytic potentials and of fluids. The former, which is a particularly difficult problem for perturbative schemes, is treated with only limited success by restricting phase space and by adding an effective potential. The problem of fluids, however, is readily found to yield to a semiclassical pairwise interaction approximation, which in turn permits any classical many-body model to be expressed in a convenient form. The remainder of the discussion concentrates on some ramifications of having a phase space version of quantum mechanics. To test the breadth of the formulation, the task of constructing quantal ensemble averages of phase space functions is undertaken, and in the process several limitations of the formalism are revealed. A rather different approach is also pursued. The concept of quantum mechanical ergodicity is examined through the use of numerically evaluated eigenstates of the Barbanis potential, and the existence of this quantal ergodicity - normally associated with classical phase space - is verified. 21 figures, 4 tables

Random path formulation of nonrelativistic quantum mechanics

International Nuclear Information System (INIS)

Roncadelli, M.

1993-01-01

Quantum amplitudes satisfy (almost) the same calculus that probabilities obey in the theory of classical stochastic diffusion processes. As a consequence of this structural analogy, a new formulation of (nonrelativistic) quantum mechanics naturally arises as the quantum counterpart of the Langevin description of (classical) stochastic diffusion processes. Quantum fluctuations are simulated here by a Fresnel white noise (FWN), which is a (real) white noise with imaginary diffusion constant, whose functional (pseudo) measure yields the amplitude distribution for its configurations. Central to this approach is the idea that classical dynamical trajectories in configuration space are perturbed by the FWN. Hence, a single (arbitrary) classical dynamical path gets replaced by a family of quantum random paths (QRPs) - one for each FWN sample - all originating from the same space-time point (x', t'). The QRPs are the basic objects of the present formulation and are given by a Langevin equation with the FWN, whose drift is controlled by a (arbitrary) solution to the classical Hamilton-Jacobi equation. So, our approach is manifestly based on classical dynamics. Now, a transition amplitude is associated with each QRP: it gives the amplitude that a particle starting from (x', t') will reach (x'', t'') by travelling just along the considered QRP. The quantum mechanical propagator (x'', t'' modul x', t') then emerges as the FWN average of the transition amplitude along a QRP. Thus, quantum mechanics looks like classical mechanics as perturbed by the FWN. The general structure of this formulation is discussed in detail, along with some practical and conceptual implications. (author). 14 refs

On the suppression of chaos in quantum and classical physics

International Nuclear Information System (INIS)

Fried, H.M.; Gabellini, Y.

1997-01-01

A brief outline is presented of an example of potential-theory quantum chaos, which is suppressed by the full radiative corrections of quantum field theory. A similar mechanism may be devised and applied to classically chaotic systems, and provides an example in which an explicit diminution of the original chaos becomes apparent. (author)

A study of quantum mechanical probabilities in the classical Hodgkin-Huxley model.

Science.gov (United States)

Moradi, N; Scholkmann, F; Salari, V

2015-03-01

The Hodgkin-Huxley (HH) model is a powerful model to explain different aspects of spike generation in excitable cells. However, the HH model was proposed in 1952 when the real structure of the ion channel was unknown. It is now common knowledge that in many ion-channel proteins the flow of ions through the pore is governed by a gate, comprising a so-called "selectivity filter" inside the ion channel, which can be controlled by electrical interactions. The selectivity filter (SF) is believed to be responsible for the selection and fast conduction of particular ions across the membrane of an excitable cell. Other (generally larger) parts of the molecule such as the pore-domain gate control the access of ions to the channel protein. In fact, two types of gates are considered here for ion channels: the "external gate", which is the voltage sensitive gate, and the "internal gate" which is the selectivity filter gate (SFG). Some quantum effects are expected in the SFG due to its small dimensions, which may play an important role in the operation of an ion channel. Here, we examine parameters in a generalized model of HH to see whether any parameter affects the spike generation. Our results indicate that the previously suggested semi-quantum-classical equation proposed by Bernroider and Summhammer (BS) agrees strongly with the HH equation under different conditions and may even provide a better explanation in some cases. We conclude that the BS model can refine the classical HH model substantially.

Path integral approach to electron scattering in classical electromagnetic potential

International Nuclear Information System (INIS)

Xu Chuang; Feng Feng; Li Ying-Jun

2016-01-01

As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential. (paper)

Classical many-body theory with retarded interactions: Dynamical irreversibility and determinism without probabilities

Energy Technology Data Exchange (ETDEWEB)

Zakharov, A.Yu., E-mail: Anatoly.Zakharov@novsu.ru; Zakharov, M.A., E-mail: ma_zakharov@list.ru

2016-01-28

The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions is derived. It is shown that interactions retardation leads to irreversible behavior of many-body systems. - Highlights: • A new form of equation of motion of classical many-body system is proposed. • Interactions retardation as one of the mechanisms of many-body system irreversibility. • Irreversibility and determinism without probabilities. • The possible way to microscopic foundation of thermodynamics.

Classical statistical mechanics approach to multipartite entanglement

Energy Technology Data Exchange (ETDEWEB)

Facchi, P [Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy); Florio, G; Pascazio, S [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Marzolino, U [Dipartimento di Fisica, Universita di Trieste, and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34014 Trieste (Italy); Parisi, G [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, Centre for Statistical Mechanics and Complexity (SMC), CNR-INFM (Italy)

2010-06-04

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

Classical statistical mechanics approach to multipartite entanglement

Science.gov (United States)

Facchi, P.; Florio, G.; Marzolino, U.; Parisi, G.; Pascazio, S.

2010-06-01

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

Classical statistical mechanics approach to multipartite entanglement

International Nuclear Information System (INIS)

Facchi, P; Florio, G; Pascazio, S; Marzolino, U; Parisi, G

2010-01-01

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

On uncertainty relations in quantum mechanics

International Nuclear Information System (INIS)

Ignatovich, V.K.

2004-01-01

Uncertainty relations (UR) are shown to have nothing specific for quantum mechanics (QM), being the general property valid for the arbitrary function. A wave function of a particle simultaneously having a precisely defined position and momentum in QM is demonstrated. Interference on two slits in a screen is shown to exist in classical mechanics. A nonlinear classical system of equations replacing the QM Schroedinger equation is suggested. This approach is shown to have nothing in common with the Bohm mechanics

Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac's symbolic method

Science.gov (United States)

Fan, Hong-yi; Hu, Li-yun

2012-06-01

By virtue of the new technique of performing integration over Dirac's ket-bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel-Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac's assertion: "...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory".

Classical Trajectories and Quantum Spectra

Science.gov (United States)

Mielnik, Bogdan; Reyes, Marco A.

1996-01-01

A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but non-perturbative method of finding the eigenvalues, exploring the bifurcations of classical trajectories. The role of squeezing turns out decisive in the generation of the discrete spectra.

Classical mechanics

CERN Document Server

Corben, H C

1994-01-01

Applications not usually taught in physics courses include theory of space-charge limited currents, atmospheric drag, motion of meteoritic dust, variational principles in rocket motion, transfer functions, much more.

Phase space view of quantum mechanical systems and Fisher information

Energy Technology Data Exchange (ETDEWEB)

Nagy, Á., E-mail: anagy@madget.atomki.hu

2016-06-17

Highlights: • Phase-space Fisher information coming from the canonical distribution is derived for the ground state of quantum mechanical systems. • Quantum mechanical phase-space Fisher information contains an extra term due to the position dependence of the temperature. • A complete analogy to the classical case is demonstrated for the linear harmonic oscillator. - Abstract: Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini–Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.

Phase space view of quantum mechanical systems and Fisher information

International Nuclear Information System (INIS)

Nagy, Á.

2016-01-01

Highlights: • Phase-space Fisher information coming from the canonical distribution is derived for the ground state of quantum mechanical systems. • Quantum mechanical phase-space Fisher information contains an extra term due to the position dependence of the temperature. • A complete analogy to the classical case is demonstrated for the linear harmonic oscillator. - Abstract: Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini–Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.

New mechanism of spiral wave initiation in a reaction-diffusion-mechanics system.

Science.gov (United States)

Weise, Louis D; Panfilov, Alexander V

2011-01-01

Spiral wave initiation in the heart muscle is a mechanism for the onset of dangerous cardiac arrhythmias. A standard protocol for spiral wave initiation is the application of a stimulus in the refractory tail of a propagating excitation wave, a region that we call the "classical vulnerable zone." Previous studies of vulnerability to spiral wave initiation did not take the influence of deformation into account, which has been shown to have a substantial effect on the excitation process of cardiomyocytes via the mechano-electrical feedback phenomenon. In this work we study the effect of deformation on the vulnerability of excitable media in a discrete reaction-diffusion-mechanics (dRDM) model. The dRDM model combines FitzHugh-Nagumo type equations for cardiac excitation with a discrete mechanical description of a finite-elastic isotropic material (Seth material) to model cardiac excitation-contraction coupling and stretch activated depolarizing current. We show that deformation alters the "classical," and forms a new vulnerable zone at longer coupling intervals. This mechanically caused vulnerable zone results in a new mechanism of spiral wave initiation, where unidirectional conduction block and rotation directions of the consequently initiated spiral waves are opposite compared to the mechanism of spiral wave initiation due to the "classical vulnerable zone." We show that this new mechanism of spiral wave initiation can naturally occur in situations that involve wave fronts with curvature, and discuss its relation to supernormal excitability of cardiac tissue. The concept of mechanically induced vulnerability may lead to a better understanding about the onset of dangerous heart arrhythmias via mechano-electrical feedback.

The classic: Bone morphogenetic protein.

Science.gov (United States)

Urist, Marshall R; Strates, Basil S

2009-12-01

This Classic Article is a reprint of the original work by Marshall R. Urist and Basil S. Strates, Bone Morphogenetic Protein. An accompanying biographical sketch of Marshall R. Urist, MD is available at DOI 10.1007/s11999-009-1067-4; a second Classic Article is available at DOI 10.1007/s11999-009-1069-2; and a third Classic Article is available at DOI 10.1007/s11999-009-1070-9. The Classic Article is copyright 1971 by Sage Publications Inc. Journals and is reprinted with permission from Urist MR, Strates BS. Bone morphogenetic protein. J Dent Res. 1971;50:1392-1406.

Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions

Directory of Open Access Journals (Sweden)

Ryan eBabbush

2013-10-01

Full Text Available Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.

Dynamics in the quantum/classical limit based on selective use of the quantum potential

International Nuclear Information System (INIS)

Garashchuk, Sophya; Dell’Angelo, David; Rassolov, Vitaly A.

2014-01-01

A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the time-dependent Schrödinger equation. The quantum potential is a non-local quantity, defined in the trajectory-based form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantum-mechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed “quantum,” defines a hybrid quantum/classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or mean-field, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and double-well potentials, using conventional grid-based and approximate quantum-trajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction

Dynamics in the quantum/classical limit based on selective use of the quantum potential

Energy Technology Data Exchange (ETDEWEB)

Garashchuk, Sophya, E-mail: garashchuk@sc.edu; Dell’Angelo, David; Rassolov, Vitaly A. [Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208 (United States)

2014-12-21

A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the time-dependent Schrödinger equation. The quantum potential is a non-local quantity, defined in the trajectory-based form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantum-mechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed “quantum,” defines a hybrid quantum/classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or mean-field, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and double-well potentials, using conventional grid-based and approximate quantum-trajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction.

Wigner's dynamical transition state theory in phase space : classical and quantum

NARCIS (Netherlands)

Waalkens, Holger; Schubert, Roman; Wiggins, Stephen

We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs

Modelling Systems of Classical/Quantum Identical Particles by Focusing on Algorithms

Science.gov (United States)

Guastella, Ivan; Fazio, Claudio; Sperandeo-Mineo, Rosa Maria

2012-01-01

A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having…

Semiclassical asymptotic behavior and the rearrangement mechanisms for Coulomb particles

International Nuclear Information System (INIS)

Bogdanov, A.V.; Gevorkyan, A.S.; Dubrovskii, G.V.

1986-01-01

The semiclassical asymptotic behavior of the eikonal amplitude of the resonance rearrangement in a system of three Coulomb particles is studied. It is shown that the general formula for the amplitude correctly describes two classical mechanisms (pickup and knockout) and one nonclassical mechanism (stripping). The classical mechanisms predominate at high energies, while the stripping mechanism predominates at lower energies. In the region of medium energies the dominant mechanism is the pickup (or Thomas) mechanism, which is realized by nonclassical means. For such transitions the classical cross section diverges, and the amplitude must be computed on a complex trajectory. The physical reasons for introducing the approximate complex trajectories are discussed. The contributions of all the mechanisms to the rearrangement cross section are found in their analytic forms

Quantum and quasi-classical collisional dynamics of O2–Ar at high temperatures

International Nuclear Information System (INIS)

Ulusoy, Inga S.; Andrienko, Daniil A.; Boyd, Iain D.; Hernandez, Rigoberto

2016-01-01

A hypersonic vehicle traveling at a high speed disrupts the distribution of internal states in the ambient flow and introduces a nonequilibrium distribution in the post-shock conditions. We investigate the vibrational relaxation in diatom-atom collisions in the range of temperatures between 1000 and 10 000 K by comparing results of extensive fully quantum-mechanical and quasi-classical simulations with available experimental data. The present paper simulates the interaction of molecular oxygen with argon as the first step in developing the aerothermodynamics models based on first principles. We devise a routine to standardize such calculations also for other scattering systems. Our results demonstrate very good agreement of vibrational relaxation time, derived from quantum-mechanical calculations with the experimental measurements conducted in shock tube facilities. At the same time, the quasi-classical simulations fail to accurately predict rates of vibrationally inelastic transitions at temperatures lower than 3000 K. This observation and the computational cost of adopted methods suggest that the next generation of high fidelity thermochemical models should be a combination of quantum and quasi-classical approaches.

Variational principle in quantum mechanics

International Nuclear Information System (INIS)

Popiez, L.

1986-01-01

The variational principle in a standard, path integral formulation of quantum mechanics (as proposed by Dirac and Feynman) appears only in the context of a classical limit n to 0 and manifests itself through the method of abstract stationary phase. Symbolically it means that a probability amplitude averaged over trajectories denotes a classical evolution operator for points in a configuration space. There exists, however, the formulation of quantum dynamics in which variational priniple is one of basic postulates. It is explained that the translation between stochastic and quantum mechanics in this case can be understood as in Nelson's stochastic mechanics

Quantum classical correspondence in nonrelativistic electrodynamics

International Nuclear Information System (INIS)

Ritchie, B.; Weatherford, C.A.

1999-01-01

A form of classical electrodynamic field exists which gives exact agreement with the operator field of quantum electrodynamics (QED) for the Lamb shift of a harmonically bound point electron. Here it is pointed out that this form of classical theory, with its physically acceptable interpretation, is the result of an unconventional resolution of a mathematically ambiguous term in classical field theory. Finally, a quantum classical correspondence principle is shown to exist in the sense that the classical field and expectation value of the QED operator field are identical, if retardation is neglected in the latter

Introduction to Classical and Quantum Harmonic Oscillators

International Nuclear Information System (INIS)

Latal, H

1997-01-01

As the title aptly states, this book deals with harmonic oscillators of various kinds, from classical mechanical and electrical oscillations up to quantum oscillations. It is written in a lively language, and occasional interspersed anecdotes make the reading of an otherwise mathematically oriented text quite a pleasure. Although the author claims to have written an 'elementary introduction', it is certainly necessary to have a good deal of previous knowledge in physics (mechanics, electrodynamics, quantum theory), electrical engineering and, of course, mathematics in order to follow the general line of his arguments. The book begins with a thorough treatment of classical oscillators (free, damped, forced) that is followed by an elaboration on Fourier analysis. Lagrange and Hamilton formalisms are then introduced before the problem of coupled oscillations is attacked. A chapter on statistical perspectives leads over to the final discussion of quantum oscillations. With the book comes a diskette containing a number of worksheets (Microsoft Excel) that can be used by the reader for instant visualization to get a better qualitative and quantitative understanding of the material. To the reviewer it seems difficult to pinpoint exactly the range of prospective readership of the book. It can certainly not be intended as a textbook for students, but rather as a reference book for teachers of physics or researchers, who want to look up one or other aspect of harmonic oscillations, for which purpose the diskette represents a very valuable tool. (book review)

Theoretical physics 2 analytical mechanics

CERN Document Server

Nolting, Wolfgang

2016-01-01

This textbook offers a clear and comprehensive introduction to analytical mechanics, one of the core components of undergraduate physics courses.It follows on naturally from the previous volumes in this series, thus expanding the knowledge in classical mechanics. The book starts with a thorough introduction into Lagrangian mechanics, detailing the d’Alembert principle, Hamilton’s principle and conservation laws. It continues with an in-depth explanation of Hamiltonian mechanics, illustrated by canonical and Legendre transformation, the generalization to quantum mechanics through Poisson brackets and all relevant variational principles. Finally, the Hamilton-Jacobi theory and the transition to wave mechanics are presented in detail. Ideally suited to undergraduate students with some grounding in classical mechanics, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by ...

Fundamentals of continuum mechanics – classical approaches and new trends

Science.gov (United States)

Altenbach, H.

2018-04-01

Continuum mechanics is a branch of mechanics that deals with the analysis of the mechanical behavior of materials modeled as a continuous manifold. Continuum mechanics models begin mostly by introducing of three-dimensional Euclidean space. The points within this region are defined as material points with prescribed properties. Each material point is characterized by a position vector which is continuous in time. Thus, the body changes in a way which is realistic, globally invertible at all times and orientation-preserving, so that the body cannot intersect itself and as transformations which produce mirror reflections are not possible in nature. For the mathematical formulation of the model it is also assumed to be twice continuously differentiable, so that differential equations describing the motion may be formulated. Finally, the kinematical relations, the balance equations, the constitutive and evolution equations and the boundary and/or initial conditions should be defined. If the physical fields are non-smooth jump conditions must be taken into account. The basic equations of continuum mechanics are presented following a short introduction. Additionally, some examples of solid deformable continua will be discussed within the presentation. Finally, advanced models of continuum mechanics will be introduced. The paper is dedicated to Alexander Manzhirov’s 60th birthday.

Observational study of differences in head position for high notes in famous classical and non-classical male singers.

Science.gov (United States)

Amarante Andrade, Pedro; Švec, Jan G

2016-07-01

Differences in classical and non-classical singing are due primarily to aesthetic style requirements. The head position can affect the sound quality. This study aimed at comparing the head position for famous classical and non-classical male singers performing high notes. Images of 39 Western classical and 34 non-classical male singers during live performances were obtained from YouTube. Ten raters evaluated the frontal rotational head position (depression versus elevation) and transverse head position (retraction versus protraction) visually using a visual analogue scale. The results showed a significant difference for frontal rotational head position. Most non-classical singers in the sample elevated their heads for high notes while the classical singers were observed to keep it around the neutral position. This difference may be attributed to different singing techniques and phonatory system adjustments utilized by each group.

On the classical geometry of bosonic string dynamics

International Nuclear Information System (INIS)

Beig, R.

1989-01-01

We develop a treatment of bosonic strings on a general curved background in which the volume element and the coordinates of the worldsheet are related in a similar way as canonically conjugate quantities in mechanics. The resultant formalism is a particular variant of the multi-phase space approach to classical field theory put forward by Kijowski, Tulczyjew and others. We study conservation laws within this framework and find that all conserved quantities are related to point symmetries, i.e. isometries of the underlying spacetime. Thus the symmetries of relativistic mechanics coming from Killing-tensors have no analogue here. We furthermore deduce from the present scheme the covariant version of the usual phase space. 14 refs. (Author)

Resonance charge exchange mechanism at high and moderate energies

International Nuclear Information System (INIS)

Bogdanov, A.V.; Gevorkyan, A.S.

1984-01-01

Charge exchange mechanisms at high and medium energies are investigated, ta king the resonance charge exchange of a proton by an hydrogen atom as an example . It is established that there are two classical charge exchange mechanisms rel ated to direct proton knockout from the bound state and one quantum-mechanical mechanism corresponding to the electron tunnelling from one bound state to anoth er. The classical cross-section diverges for two of these mechanisms, and the quasiclassical scattering amplitude must be calculated on the base of a complex classical trajectory. Physical grounds for the choice of such trajectories are discussed and calculations of the Van Vleck determinant for these mechanisms a re presented. Contributions from different mechanisms to the total charge excha nge cross-section are analyzed. A comparison with experimental data and results of other authors is made

Massive open online courses: The new vector in classical university education

Directory of Open Access Journals (Sweden)

Mozhaeva Galina

2016-01-01

Full Text Available The influence of Massive Open Online Course (MOOC on classical university education is investigated. Opportunities and prospects of development of MOOC at classical universities, requirements to development and implementation of qualitative MOOC-projects, conditions and mechanisms of integration of MOOC into professional education are studied. Work is performed on the basis of the analysis of experience of the world MOOС-platforms and the Russian universities. The new vector in development of classical university under the influence of MOOC is considered on the example of National Research Tomsk State University (http://www.lektorium.tv/mooc. Questioning more than 5000 participants of MOOС-projects was carried out, motivators of learning are revealed, and marketing potential of MOOC and possibility of analytical work on an assessment of the contingent, quality of education and efficiency of the applied technologies are analyzed. The quantitative analysis of basic data is made; results of he analysis are described and presented in the graphic form

Markkinointiviestintäsuunnitelma : Classic Coffee Oy

OpenAIRE

Eerola, Laura

2015-01-01

Opinnäytetyön aiheena oli laatia markkinointiviestintäsuunnitelma kalenterivuodelle 2016 vuosikellon muodossa, toimintansa jo vakiinnuttaneelle Classic Coffee Oy:lle. Classic Coffee Oy on vuonna 2011 perustettu, Tampereella toimiva kahvila-alan yritys joka tarjoaa lounaskahvilatoiminnan lisäksi laadukkaita konditoria-palveluita, yritys- ja kokoustarjoiluja sekä tilavuokrausta. Classic Coffee Oy:llä on yksi kahvila, Classic Coffee Tampella. Kahvila sijaitsee Tampellassa, Tampereen keskustan vä...

Classical higher-order processes

DEFF Research Database (Denmark)

Montesi, Fabrizio

2017-01-01

Classical Processes (CP) is a calculus where the proof theory of classical linear logic types processes à la Π-calculus, building on a Curry-Howard correspondence between session types and linear propositions. We contribute to this research line by extending CP with process mobility, inspired by ...

Local quantum channels preserving classical correlations

International Nuclear Information System (INIS)

Guo Zhihua; Cao Huaixin

2013-01-01

The aim of this paper is to discuss local quantum channels that preserve classical correlations. First, we give two equivalent characterizations of classical correlated states. Then we obtain the relationships among classical correlation-preserving local quantum channels, commutativity-preserving local quantum channels and commutativity-preserving quantum channels on each subsystem. Furthermore, for a two-qubit system, we show the general form of classical correlation-preserving local quantum channels. (paper)

Classicalization of Gravitons and Goldstones

CERN Document Server

Dvali, Gia; Kehagias, Alex

2011-01-01

We establish a close parallel between classicalization of gravitons and derivatively-coupled Nambu-Goldstone-type scalars. We show, that black hole formation in high energy scattering process represents classicalization with the classicalization radius given by Schwarzschild radius of center of mass energy, and with the precursor of black hole entropy being given by number of soft quanta composing this classical configuration. Such an entropy-equivalent is defined for scalar classicalons also and is responsible for exponential suppression of their decay into small number of final particles. This parallel works in both ways. For optimists that are willing to hypothesize that gravity may indeed self-unitarize at high energies via black hole formation, it illustrates that the Goldstones may not be much different in this respect, and they classicalize essentially by similar dynamics as gravitons. In the other direction, it may serve as an useful de-mystifier of via-black-hole-unitarization process and of the role...

Classical dynamics a modern perspective

CERN Document Server

Sudarshan, Ennackal Chandy George

2016-01-01

Classical dynamics is traditionally treated as an early stage in the development of physics, a stage that has long been superseded by more ambitious theories. Here, in this book, classical dynamics is treated as a subject on its own as well as a research frontier. Incorporating insights gained over the past several decades, the essential principles of classical dynamics are presented, while demonstrating that a number of key results originally considered only in the context of quantum theory and particle physics, have their foundations in classical dynamics.Graduate students in physics and practicing physicists will welcome the present approach to classical dynamics that encompasses systems of particles, free and interacting fields, and coupled systems. Lie groups and Lie algebras are incorporated at a basic level and are used in describing space-time symmetry groups. There is an extensive discussion on constrained systems, Dirac brackets and their geometrical interpretation. The Lie-algebraic description of ...

Imaging learning and memory: classical conditioning.

Science.gov (United States)

Schreurs, B G; Alkon, D L

2001-12-15

The search for the biological basis of learning and memory has, until recently, been constrained by the limits of technology to classic anatomic and electrophysiologic studies. With the advent of functional imaging, we have begun to delve into what, for many, was a "black box." We review several different types of imaging experiments, including steady state animal experiments that image the functional labeling of fixed tissues, and dynamic human studies based on functional imaging of the intact brain during learning. The data suggest that learning and memory involve a surprising conservation of mechanisms and the integrated networking of a number of structures and processes. Copyright 2001 Wiley-Liss, Inc.

Classical orbits in power-law potentials

International Nuclear Information System (INIS)

Grant, A.K.; Rosner, J.L.

1994-01-01

The motion of bodies in power-law potentials of the form V(r)=λr α has been of interest ever since the time of Newton and Hooke. Aspects of the relation between powers α and bar α, where (α+2)(bar α+2)=4, are derived for classical motion and the relation to the quantum-mechanical problem is given. An improvement on a previous expression for the WKB quantization condition for nonzero orbital angular momenta is obtained. Relations with previous treatments, such as those of Newton, Bertrand, Bohlin, Faure, and Arnold, are noted, and a brief survey of the literature on the problem over more than three centuries is given

Classical spins in superconductors

Energy Technology Data Exchange (ETDEWEB)

Shiba, H [Tokyo Univ.; Maki, K

1968-08-01

It is shown that there exists a localized excited state in the energy gap in a superconductor with a classical spin. At finite concentration localized excited states around classical spins form an impurity band. The process of growth of the impurity band and its effects on observable quantities are investigated.

CLASSICS

Indian Academy of Sciences (India)

2013-11-11

Nov 11, 2013 ... Polanyi's classic paper, co-authored by Henry Eyring, reproduced in this ... spatial conf guration of the atoms in terms of the energy function of the diatomic .... The present communication deals with the construction of such .... These three contributions are complemented by a fourth term if one takes into.

Quantum mechanical models for the Fermi shuttle

Science.gov (United States)

Sternberg, James; Ovchinnikov, S. Yu.; Macek, J. H.

2009-05-01

Although the Fermi shuttle was originally proposed as an explanation for highly energetic cosmic rays, it is also a mechanism for the production of high energy electrons in atomic collisions [1]. The Fermi shuttle is usually thought of as a classical effect and most models of this process rely on classical or semi-classical approximations. In this work we explore several quantum mechanical models for ion-atom collisions and examine the evidence for the Fermi shuttle in these models. [4pt] [1] B. Sulik, Cs. Koncz, K. Tok'esi, A. Orb'an, and D. Ber'enyi, Phys Rev. Lett. 88 073201 (2002)

New mechanism of spiral wave initiation in a reaction-diffusion-mechanics system.

Directory of Open Access Journals (Sweden)

Louis D Weise

Full Text Available Spiral wave initiation in the heart muscle is a mechanism for the onset of dangerous cardiac arrhythmias. A standard protocol for spiral wave initiation is the application of a stimulus in the refractory tail of a propagating excitation wave, a region that we call the "classical vulnerable zone." Previous studies of vulnerability to spiral wave initiation did not take the influence of deformation into account, which has been shown to have a substantial effect on the excitation process of cardiomyocytes via the mechano-electrical feedback phenomenon. In this work we study the effect of deformation on the vulnerability of excitable media in a discrete reaction-diffusion-mechanics (dRDM model. The dRDM model combines FitzHugh-Nagumo type equations for cardiac excitation with a discrete mechanical description of a finite-elastic isotropic material (Seth material to model cardiac excitation-contraction coupling and stretch activated depolarizing current. We show that deformation alters the "classical," and forms a new vulnerable zone at longer coupling intervals. This mechanically caused vulnerable zone results in a new mechanism of spiral wave initiation, where unidirectional conduction block and rotation directions of the consequently initiated spiral waves are opposite compared to the mechanism of spiral wave initiation due to the "classical vulnerable zone." We show that this new mechanism of spiral wave initiation can naturally occur in situations that involve wave fronts with curvature, and discuss its relation to supernormal excitability of cardiac tissue. The concept of mechanically induced vulnerability may lead to a better understanding about the onset of dangerous heart arrhythmias via mechano-electrical feedback.

Advanced mechanics from Euler's determinism to Arnold's chaos

CERN Document Server

Rajeev, S G

2013-01-01

Classical Mechanics is the oldest and best understood part of physics. This does not mean that it is cast in marble yet, a museum piece to be admired from a distance. Instead, mechanics continues to be an active area of research by physicists and mathematicians. Every few years, we need to re-evaluate the purpose of learning mechanics and look at old material in the light of modern developments. Once you have learned basic mechanics (Newton's laws, the solution of the Kepler problem) and quantum mechanics (the Schrodinger equation, hydrogen atom) it is time to go back and relearn classical mechanics in greater depth. It is the intent of this book to take you through the ancient (the original meaning of "classical") parts of the subject quickly: the ideas started by Euler and ending roughly with Poincare. We then take up the developments of twentieth century physics that have largely to do with chaos and discrete time evolution (the basis of numerical solutions).

Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Kalnins, E G [Department of Mathematics and Statistics, University of Waikato, Hamilton (New Zealand); Miller, W Jr; Post, S [School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (United States)], E-mail: miller@ima.umn.edu

2010-01-22

We review the fundamentals of coupling constant metamorphosis (CCM) and the Staeckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the momenta to polynomials in the momenta. We study specializations of these actions which preserve polynomials and also the structure of the symmetry algebras in both the classical and quantum cases. We give several examples of non-constant curvature third- and fourth-order superintegrable systems in two space dimensions obtained via CCM, with some details on the structure of the symmetry algebras preserved by the transform action.

Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics

International Nuclear Information System (INIS)

Kalnins, E G; Miller, W Jr; Post, S

2010-01-01

We review the fundamentals of coupling constant metamorphosis (CCM) and the Staeckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the momenta to polynomials in the momenta. We study specializations of these actions which preserve polynomials and also the structure of the symmetry algebras in both the classical and quantum cases. We give several examples of non-constant curvature third- and fourth-order superintegrable systems in two space dimensions obtained via CCM, with some details on the structure of the symmetry algebras preserved by the transform action.

The essentials of quantum mechanics

International Nuclear Information System (INIS)

Omnes, R.

2006-09-01

This book is an introduction to quantum mechanics, the author explains the foundation, interpretation and today limits of this science. The consequences of quantum concepts are reviewed through the lens of recent experimental data. In that way, issues like wave-particle duality, uncertainty principle, decoherence, relationship with classical mechanics or the unicity of reality, issues that were difficult to grasp before, appear now clearer. The book has been divided into 8 chapters: 1) possibility and chance, 2) quantum formalism, 3) fundamental quantum concepts, 4) how to deal with quantum mechanics, 5) decoherence theory, 6) the quantum logic system, 7) the emergence of classical physics, and 8) quantum measurements. (A.C.)

A comparison of wood density between classical Cremonese and modern violins.

Directory of Open Access Journals (Sweden)

Berend C Stoel

Full Text Available Classical violins created by Cremonese masters, such as Antonio Stradivari and Giuseppe Guarneri Del Gesu, have become the benchmark to which the sound of all violins are compared in terms of their abilities of expressiveness and projection. By general consensus, no luthier since that time has been able to replicate the sound quality of these classical instruments. The vibration and sound radiation characteristics of a violin are determined by an instrument's geometry and the material properties of the wood. New test methods allow the non-destructive examination of one of the key material properties, the wood density, at the growth ring level of detail. The densities of five classical and eight modern violins were compared, using computed tomography and specially developed image-processing software. No significant differences were found between the median densities of the modern and the antique violins, however the density difference between wood grains of early and late growth was significantly smaller in the classical Cremonese violins compared with modern violins, in both the top (Spruce and back (Maple plates (p = 0.028 and 0.008, respectively. The mean density differential (SE of the top plates of the modern and classical violins was 274 (26.6 and 183 (11.7 gram/liter. For the back plates, the values were 128 (2.6 and 115 (2.0 gram/liter. These differences in density differentials may reflect similar changes in stiffness distributions, which could directly impact vibrational efficacy or indirectly modify sound radiation via altered damping characteristics. Either of these mechanisms may help explain the acoustical differences between the classical and modern violins.

Three-space from quantum mechanics

International Nuclear Information System (INIS)

Chew, G.F.; Stapp, H.P.

1988-01-01

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

Discrete mechanics

International Nuclear Information System (INIS)

Lee, T.D.

1985-01-01

This paper reviews the role of time throughout all phases of mechanics: classical mechanics, non-relativistic quantum mechanics, and relativistic quantum theory. As an example of the relativistic quantum field theory, the case of a massless scalar field interacting with an arbitrary external current is discussed. The comparison between the new discrete theory and the usual continuum formalism is presented. An example is given of a two-dimensional random lattice and its duel. The author notes that there is no evidence that the discrete mechanics is more appropriate than the usual continuum mechanics

Phase space bottlenecks: A comparison of quantum and classical intramolecular dynamics for collinear OCS

International Nuclear Information System (INIS)

Gibson, L.L.; Schatz, G.C.; Ratner, M.A.; Davis, M.J.

1987-01-01

We compare quantum and classical mechanics for a collinear model of OCS at an energy (20 000 cm -1 ) where Davis [J. Chem. Phys. 83, 1016 (1985)] had previously found that phase space bottlenecks associated with golden mean tori inhibit classical flow between different chaotic regions in phase space. Accurate quantum eigenfunctions for this two mode system are found by diagonalizing a large basis of complex Gaussian functions, and these are then used to study the evolution of wave packets which have 20 000 cm -1 average energies. By examining phase space (Husimi) distributions associated with the wave functions, we conclude that these golden mean tori do indeed act as bottlenecks which constrain the wave packets to evolve within one (or a combination of) regions. The golden mean tori do not completely determine the boundaries between regions, however. Bottlenecks associated with resonance trapping and with separatrix formation are also involved. The analysis of the Husimi distributions also indicates that each exact eigenstate is nearly always associated with just one region, and because of this, superpositions of eigenstates that are localized within a region remain localized in that region at all times. This last result differs from the classical picture at this energy where flow across the bottlenecks occurs with a 2--4 ps lifetime. Since the classical phase space area through which flux must pass to cross the bottlenecks is small compared to h for OCS, the observed difference between quantum and classical dynamics is not surprising. Examination of the time development of normal mode energies indicates little or no energy flow quantum mechanically for wave packet initial conditions

Classical Conditioning Fails to Elicit Allodynia in an Experimental Study with Healthy Humans

NARCIS (Netherlands)

Madden, Victoria J; Russek, Leslie N; Harvie, Daniel S; Vlaeyen, Johan W S; Moseley, G Lorimer

2016-01-01

OBJECTIVE : Associative learning has been proposed as a mechanism behind the persistence of pain after tissue healing. The simultaneous occurrence of nociceptive and non-nociceptive input during acute injury mimics the pairings thought to drive classical conditioning effects. However, empirical

Semi-classical approximation and the problem of boundary conditions in the theory of relativistic particle radiation

International Nuclear Information System (INIS)

Akhiezer, A.I.; Shul'ga, N.F.

1991-01-01

The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is in expressing the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation. We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation. The method we used to deal with the problem is similar to the method employed by Fock to analyze the problem of a canonical transformation in classical and quantum mechanics. (author)

Twisted classical Poincare algebras

International Nuclear Information System (INIS)

Lukierski, J.; Ruegg, H.; Tolstoy, V.N.; Nowicki, A.

1993-11-01

We consider the twisting of Hopf structure for classical enveloping algebra U(g), where g is the inhomogeneous rotations algebra, with explicite formulae given for D=4 Poincare algebra (g=P 4 ). The comultiplications of twisted U F (P 4 ) are obtained by conjugating primitive classical coproducts by F element of U(c)xU(c), where c denotes any Abelian subalgebra of P 4 , and the universal R-matrices for U F (P 4 ) are triangular. As an example we show that the quantum deformation of Poincare algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincare algebra. The interpretation of twisted Poincare algebra as describing relativistic symmetries with clustered 2-particle states is proposed. (orig.)

The Relation between Classical and Quantum Electrodynamics

Directory of Open Access Journals (Sweden)

Mario Bacelar Valente

2011-01-01

Full Text Available Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as an more fundamental theory, but as an upgrade of classical electrodynamics, which permits an extension of classical theory to the description of phenomena that, while being related to the conceptual framework of the classical theory, cannot be addressed from the classical theory.

Quantum and quasi-classical collisional dynamics of O{sub 2}–Ar at high temperatures

Energy Technology Data Exchange (ETDEWEB)

Ulusoy, Inga S. [IHP, Im Technologiepark 25, 15236 Frankfurt (Oder) (Germany); Center for Computational and Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 (United States); Andrienko, Daniil A.; Boyd, Iain D. [Nonequilibrium Gas and Plasma Dynamics Laboratory, Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109-2140 (United States); Hernandez, Rigoberto, E-mail: hernandez@gatech.edu [Center for Computational and Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 (United States)

2016-06-21

A hypersonic vehicle traveling at a high speed disrupts the distribution of internal states in the ambient flow and introduces a nonequilibrium distribution in the post-shock conditions. We investigate the vibrational relaxation in diatom-atom collisions in the range of temperatures between 1000 and 10 000 K by comparing results of extensive fully quantum-mechanical and quasi-classical simulations with available experimental data. The present paper simulates the interaction of molecular oxygen with argon as the first step in developing the aerothermodynamics models based on first principles. We devise a routine to standardize such calculations also for other scattering systems. Our results demonstrate very good agreement of vibrational relaxation time, derived from quantum-mechanical calculations with the experimental measurements conducted in shock tube facilities. At the same time, the quasi-classical simulations fail to accurately predict rates of vibrationally inelastic transitions at temperatures lower than 3000 K. This observation and the computational cost of adopted methods suggest that the next generation of high fidelity thermochemical models should be a combination of quantum and quasi-classical approaches.

Quantum symmetries of classical spaces

OpenAIRE

Bhowmick, Jyotishman; Goswami, Debashish; Roy, Subrata Shyam

2009-01-01

We give a general scheme for constructing faithful actions of genuine (noncommutative as $C^*$ algebra) compact quantum groups on classical topological spaces. Using this, we show that: (i) a compact connected classical space can have a faithful action by a genuine compact quantum group, and (ii) there exists a spectral triple on a classical connected compact space for which the quantum group of orientation and volume preserving isometries (in the sense of \\cite{qorient}) is a genuine quantum...

Doing classical theology in context

Directory of Open Access Journals (Sweden)

Gerrit Neven

2007-05-01

Full Text Available This article is about doing classical theology in context. The weight of my argument is that classical text of Karl Barth’s theology is great intellectual text means: being addressed by this text in the context in which one lives. The basic keywords that constitute a rule for reading those texts are “equality”, “event” and “re-contextualisation”. The article contains two sections: The first section elaborates statements about the challenge of the event and the project of rereading classics by way of recontextualisation. The word “event” refers to true and innovating moments in history which one can share, or which one can betray. Classical texts always share in those liberative moments. The question then is in what sense do they present a challenge to the contemporary reader. The second section elaborates the position of man as central and all decisive for doing theology in context now. In this section, the author appeals for a renewal of the classical anthropology as an anthropology of hope. This anthropology contradicts postmodern concepts of otherness.

Classical approach in atomic physics

International Nuclear Information System (INIS)

Solov'ev, E.A.

2011-01-01

The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a semiclassical spectrum of a hydrogen atom in crossed electric and magnetic fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's approach to Stark problem, long-lived excited states of a helium atom discovered with the help of Poincare section, inelastic transitions in slow and fast electron-atom and ion-atom collisions - is reviewed. Further, a classical representation in quantum theory is discussed. In this representation the quantum states are treated as an ensemble of classical states. This approach opens the way to an accurate description of the initial and final states in classical trajectory Monte Carlo (CTMC) method and a purely classical explanation of tunneling phenomenon. The general aspects of the structure of the semiclassical series such as renormalization group symmetry, criterion of accuracy and so on are reviewed as well. (author)

Modeling classical and quantum radiation from laser-plasma accelerators

Directory of Open Access Journals (Sweden)

M. Chen

2013-03-01

Full Text Available The development of models and the “Virtual Detector for Synchrotron Radiation” (vdsr code that accurately describe the production of synchrotron radiation are described. These models and code are valid in the classical and linear (single-scattering quantum regimes and are capable of describing radiation produced from laser-plasma accelerators (LPAs through a variety of mechanisms including betatron radiation, undulator radiation, and Thomson/Compton scattering. Previous models of classical synchrotron radiation, such as those typically used for undulator radiation, are inadequate in describing the radiation spectra from electrons undergoing small numbers of oscillations. This is due to an improper treatment of a mathematical evaluation at the end points of an integration that leads to an unphysical plateau in the radiation spectrum at high frequencies, the magnitude of which increases as the number of oscillation periods decreases. This is important for betatron radiation from LPAs, in which the betatron strength parameter is large but the number of betatron periods is small. The code vdsr allows the radiation to be calculated in this regime by full integration over each electron trajectory, including end-point effects, and this code is used to calculate betatron radiation for cases of experimental interest. Radiation from Thomson scattering and Compton scattering is also studied with vdsr. For Thomson scattering, radiation reaction is included by using the Sokolov method for the calculation of the electron dynamics. For Compton scattering, quantum recoil effects are considered in vdsr by using Monte Carlo methods. The quantum calculation has been benchmarked with the classical calculation in a classical regime.

Statistical mechanics and applications in condensed matter

CERN Document Server

Di Castro, Carlo

2015-01-01

This innovative and modular textbook combines classical topics in thermodynamics, statistical mechanics and many-body theory with the latest developments in condensed matter physics research. Written by internationally renowned experts and logically structured to cater for undergraduate and postgraduate students and researchers, it covers the underlying theoretical principles and includes numerous problems and worked examples to put this knowledge into practice. Three main streams provide a framework for the book; beginning with thermodynamics and classical statistical mechanics, including mean field approximation, fluctuations and the renormalization group approach to critical phenomena. The authors then examine quantum statistical mechanics, covering key topics such as normal Fermi and Luttinger liquids, superfluidity and superconductivity. Finally, they explore classical and quantum kinetics, Anderson localization and quantum interference, and disordered Fermi liquids. Unique in providing a bridge between ...

Classical Electrodynamics Coupled to Quantum Mechanics for Calculation of Molecular Optical Properties: a RT-TDDFT/FDTD Approach

Energy Technology Data Exchange (ETDEWEB)

Chen, Hanning; McMahon, J. M.; Ratner, Mark A.; Schatz, George C.

2010-09-02

A new multiscale computational methodology was developed to effectively incorporate the scattered electric field of a plasmonic nanoparticle into a quantum mechanical (QM) optical property calculation for a nearby dye molecule. For a given location of the dye molecule with respect to the nanoparticle, a frequency-dependent scattering response function was first determined by the classical electrodynamics (ED) finite-difference time-domain (FDTD) approach. Subsequently, the time-dependent scattered electric field at the dye molecule was calculated using the FDTD scattering response function through a multidimensional Fourier transform to reflect the effect of polarization of the nanoparticle on the local field at the molecule. Finally, a real-time time-dependent density function theory (RT-TDDFT) approach was employed to obtain a desired optical property (such as absorption cross section) of the dye molecule in the presence of the nanoparticle’s scattered electric field. Our hybrid QM/ED methodology was demonstrated by investigating the absorption spectrum of the N3 dye molecule and the Raman spectrum of pyridine, both of which were shown to be significantly enhanced by a 20 nm diameter silver sphere. In contrast to traditional quantum mechanical optical calculations in which the field at the molecule is entirely determined by intensity and polarization direction of the incident light, in this work we show that the light propagation direction as well as polarization and intensity are important to nanoparticle-bound dye molecule response. At no additional computation cost compared to conventional ED and QM calculations, this method provides a reliable way to couple the response of the dye molecule’s individual electrons to the collective dielectric response of the nanoparticle.

Locking classical correlations in quantum States.

Science.gov (United States)

DiVincenzo, David P; Horodecki, Michał; Leung, Debbie W; Smolin, John A; Terhal, Barbara M

2004-02-13

We show that there exist bipartite quantum states which contain a large locked classical correlation that is unlocked by a disproportionately small amount of classical communication. In particular, there are (2n+1)-qubit states for which a one-bit message doubles the optimal classical mutual information between measurement results on the subsystems, from n/2 bits to n bits. This phenomenon is impossible classically. However, states exhibiting this behavior need not be entangled. We study the range of states exhibiting this phenomenon and bound its magnitude.

Symmetrical Windowing for Quantum States in Quasi-Classical Trajectory Simulations

Science.gov (United States)

Cotton, Stephen Joshua

An approach has been developed for extracting approximate quantum state-to-state information from classical trajectory simulations which "quantizes" symmetrically both the initial and final classical actions associated with the degrees of freedom of interest using quantum number bins (or "window functions") which are significantly narrower than unit-width. This approach thus imposes a more stringent quantization condition on classical trajectory simulations than has been traditionally employed, while doing so in a manner that is time-symmetric and microscopically reversible. To demonstrate this "symmetric quasi-classical" (SQC) approach for a simple real system, collinear H + H2 reactive scattering calculations were performed [S.J. Cotton and W.H. Miller, J. Phys. Chem. A 117, 7190 (2013)] with SQC-quantization applied to the H 2 vibrational degree of freedom (DOF). It was seen that the use of window functions of approximately 1/2-unit width led to calculated reaction probabilities in very good agreement with quantum mechanical results over the threshold energy region, representing a significant improvement over what is obtained using the traditional quasi-classical procedure. The SQC approach was then applied [S.J. Cotton and W.H. Miller, J. Chem. Phys. 139, 234112 (2013)] to the much more interesting and challenging problem of incorporating non-adiabatic effects into what would otherwise be standard classical trajectory simulations. To do this, the classical Meyer-Miller (MM) Hamiltonian was used to model the electronic DOFs, with SQC-quantization applied to the classical "electronic" actions of the MM model---representing the occupations of the electronic states---in order to extract the electronic state population dynamics. It was demonstrated that if one ties the zero-point energy (ZPE) of the electronic DOFs to the SQC windowing function's width parameter this very simple SQC/MM approach is capable of quantitatively reproducing quantum mechanical results for

Citation Classics from Industrial Marketing Management

DEFF Research Database (Denmark)

Lindgreen, Adam; Di Benedetto, C. Anthony

2017-01-01

, system sellers and systems integrator, third-party logistics providers, and value). Finally, each of the 30 citation classics is introduced, and the classics' theoretical implications to business-to-business marketing management and fields related to (e.g., supply chain management, strategic management......This article proposes a categorization of what constitutes a citation classic. General observations reveal, with regard to the top 30 citation classics from Industrial Marketing Management, the number of authors per article, country of origin of the lead author, and type of article (literature...... review, qualitative methodology, or quantitative methodology). In addition, these citation classics can be classified by topic (firm performance, goods-dominant and service-dominant logics, Internet and high-technology markets, product innovation, relationships and business networks, supply chains...

Gauge-fields and integrated quantum-classical theory

International Nuclear Information System (INIS)

Stapp, H.P.

1986-01-01

Physical situations in which quantum systems communicate continuously to their classically described environment are not covered by contemporary quantum theory, which requires a temporary separation of quantum degrees of freedom from classical ones. A generalization would be needed to cover these situations. An incomplete proposal is advanced for combining the quantum and classical degrees of freedom into a unified objective description. It is based on the use of certain quantum-classical structures of light that arise from gauge invariance to coordinate the quantum and classical degrees of freedom. Also discussed is the question of where experimenters should look to find phenomena pertaining to the quantum-classical connection. 17 refs

Quantum mechanics and stochastic mechanics for compatible observables at different times

International Nuclear Information System (INIS)

Correggi, M.; Morchio, G.

2002-01-01

Bohm mechanics and Nelson stochastic mechanics are confronted with quantum mechanics in the presence of noninteracting subsystems. In both cases, it is shown that correlations at different times of compatible position observables on stationary states agree with quantum mechanics only in the case of product wave functions. By appropriate Bell-like inequalities it is shown that no classical theory, in particular no stochastic process, can reproduce the quantum mechanical correlations of position variables of noninteracting systems at different times

Nonmonotonic quantum-to-classical transition in multiparticle interference

DEFF Research Database (Denmark)

Ra, Young-Sik; Tichy, Malte; Lim, Hyang-Tag

2013-01-01

Quantum-mechanical wave–particle duality implies that probability distributions for granular detection events exhibit wave-like interference. On the single-particle level, this leads to self-interference—e.g., on transit across a double slit—for photons as well as for large, massive particles...... that interference fades away monotonically with increasing distinguishability—in accord with available experimental evidence on the single- and on the many-particle level. Here, we demonstrate experimentally and theoretically that such monotonicity of the quantum-to-classical transition is the exception rather than...

On the Hamiltonian and Lagrangian formulation of classical dynamics for particles with spin

NARCIS (Netherlands)

Ruijgrok, Th.W.; Vlist, H. van der

The classical mechanics of nonrelativistic particles is generalized by also considering the spin components as canonical variables. Poisson-brackets and canonical transformations are discussed. The Lagrangian equations of motion are given and it is shown how rotational invariance leads to well known

Role of classical conditioning in learning gastrointestinal symptoms.