Characterization of the detrimental effects of type IV glandular trichomes on the aphid Macrosiphum euphorbiae in tomato (original) (raw)
Related papers
In sections of the literature it is assumed, following early comments by Dirac, that a desirable quantization operation should preserve the Possion bracket (rather than merely agree in the limit h → 0). A celebrated mathematical theorem establishes that this is impossible; hence a consistent quantization is often considered to be unattainable. Here we question whether the premise of exact correspondence is sensible from a physical viewpoint. In particular, we give an exact quantum mechanical version of classical dynamics in which the commutator of any two quantized operators is proportional to the Poisson bracket of the corresponding functions (in a manner which subtly evades the aforementioned theorem). We then relate this novel dynamical system to the standard quantum theory, and identify the bracket structure for the case of symmetric ordering. Our conclusion is that a consistent quantization should not be expected to preserve the Poisson bracket.
Quantum mechanics as a deformation of classical mechanics
Letters in Mathematical Physics, 1977
Mathematical properties of deformations of the Poisson Lie algebra and of the associative algebra of functions on a symplectic manifold are given. The suggestion to develop quantum mechanics in terms of these deformations is confronted with the mathematical structure of the latter. As examples, spectral properties of the harmonic oscillator and of the hydrogen atom are derived within the new formulation. Further mathematical generalizations and physical applications are proposed.
On the Classical-Quantum Relation of Constants of Motion
Frontiers in Physics, 2018
Groenewold-Van Hove theorem suggest that is not always possible to transform classical observables into quantum observables (a process known as quantization) in a way that, for all Hamiltonians, the constants of motion are preserved. The latter is a strong shortcoming for the ultimate goal of quantization, as one would expect that the notion of "constants of motion" is independent of the chosen physical scheme. It has been recently developed an approach to quantization that instead of mapping every classical observable into a quantum observable, it focuses on mapping the constants of motion themselves. In this article we will discuss the relations between classical and quantum theory under the light of this new form of quantization. In particular, we will examine the mapping of a class of operators that generalizes angular momentum where quantization satisfies the usual desirable properties.
Mixing quantum and classical mechanics
Physical Review A, 1997
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket is antisymmetric and satisfies the Jacobi identity, and, therefore, leads to a natural description of interaction between quantum and classical degrees of freedom. We apply the formalism to coupled quantum and classical oscillators and show how various approximations, such as the mean-field and the multiconfiguration mean-field approaches, can be obtained from the quantum-classical equation of motion.
Introduction to Quantum Mechanics and the Quantum-Classical transition
2007
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the action of the unitary group on the Hilbert space allows to relate both approaches. We also study Weyl-Wigner approach to Quantum Mechanics and discuss
From Classical Trajectories to Quantum Commutation Relations
Classical and Quantum Physics, 2019
In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian description because of the Noether theorem and because they are the starting point for the quantization. As a matter of fact many ambiguities arise in each step of such a reconstruction which must be solved by the ingenuity of the theoretician. In the present work we describe geometric structures emerging in Lagrangian, Hamiltonian and Quantum description of a dynamical system underlining how many of them are not really fixed only by the trajectories observed by the experimentalist. Contents 1 Introduction 2 Differential equations from experimental data 3 Dynamical systems and geometrical structures: Lagrangian picture 1
Classical and Quantum Systems: Alternative Hamiltonian Descriptions
Theoretical and Mathematical Physics, 2005
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson structures.
The Quantum-like Face of Classical Mechanics
arXiv (Cornell University), 2018
It is first shown that when the Schrödinger equation for a wave function is written in the polar form, complete information about the system's quantum-ness is separated out in a single term Q, the so called 'quantum potential'. An operator method for classical mechanics described by a 'classical Schrödinger equation' is then presented, and its similarities and differences with quantum mechanics are pointed out. It is shown how this operator method goes beyond standard classical mechanics in predicting coherent superpositions of classical states but no interference patterns, challenging deeply held notions of classical-ness, quantum-ness and macro realism. It is also shown that measurement of a quantum system with a classical measuring apparatus described by the operator method does not have the measurement problem that is unavoidable when the measuring apparatus is quantum mechanical. The type of decoherence that occurs in such a measurement is contrasted with the conventional decoherence mechanism. The method also provides a more convenient basis to delve deeper into the area of quantum-classical correspondence and information processing than exists at present.
Quantum Time: Time as a Dynamical Variable
2010
We will outline a formalism that treats time and space on equal footing as in special relativity. We will define an extended classical theory that treats time as a dynamical variable like the spacial coordinates. We will use canonical quantization to replace Poisson brackets with commutators and show how a generator of time translations can be defined using the commutation relationship in quantum mechanics. Using this new formalism, we will derive Schrtidinger's equation, Ehrenfest theorem, the propagator and expectation values of time for a simple harmonic oscillator potential.