scholarly journals Hidden Nambu mechanics II: Quantum/semiclassical dynamics

2019 ◽  
Vol 2019 (12) ◽  
Author(s):  
Atsushi Horikoshi
Keyword(s):  
Time Evolution ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Hamiltonian Dynamics ◽  
Extended Phase ◽  
Nambu Mechanics ◽  
Mechanical Structure ◽  
Wave Packet Dynamics ◽  
Semiclassical Dynamics ◽  
Metastable Potential

Abstract Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. Theor. Exp. Phys. 2013, 073A01 (2013)] we revealed that the Nambu mechanical structure is hidden in Hamiltonian dynamics, that is, the classical time evolution of variables including redundant degrees of freedom can be formulated as Nambu mechanics. In the present paper we show that the Nambu mechanical structure is also hidden in some quantum or semiclassical dynamics, that is, in some cases the quantum or semiclassical time evolution of expectation values of quantum mechanical operators, including composite operators, can be formulated as Nambu mechanics. We present a procedure to find hidden Nambu structures in quantum/semiclassical systems of one degree of freedom, and give two examples: the exact quantum dynamics of a harmonic oscillator, and semiclassical wave packet dynamics. Our formalism can be extended to many-degrees-of-freedom systems; however, there is a serious difficulty in this case due to interactions between degrees of freedom. To illustrate our formalism we present two sets of numerical results on semiclassical dynamics: from a one-dimensional metastable potential model and a simplified Henon–Heiles model of two interacting oscillators.

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

scholarly journals Multiparticle quantum plasmonics

Nanophotonics ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. 1243-1269 ◽  
Author(s):  
Chenglong You ◽  
Apurv Chaitanya Nellikka ◽  
Israel De Leon ◽  
Omar S. Magaña-Loaiza
Keyword(s):  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Single Photon ◽  
Quantum Systems ◽  
Many Body ◽  
Statistical Fluctuations ◽  
Quantum Plasmonics ◽  
Control Of Quantum Systems ◽  
Multiparticle Systems ◽  
Quantum Photonics

AbstractA single photon can be coupled to collective charge oscillations at the interfaces between metals and dielectrics forming a single surface plasmon. The electromagnetic near-fields induced by single surface plasmons offer new degrees of freedom to perform an exquisite control of complex quantum dynamics. Remarkably, the control of quantum systems represents one of the most significant challenges in the field of quantum photonics. Recently, there has been an enormous interest in using plasmonic systems to control multiphoton dynamics in complex photonic circuits. In this review, we discuss recent advances that unveil novel routes to control multiparticle quantum systems composed of multiple photons and plasmons. We describe important properties that characterize optical multiparticle systems such as their statistical quantum fluctuations and correlations. In this regard, we discuss the role that photon-plasmon interactions play in the manipulation of these fundamental properties for multiparticle systems. We also review recent works that show novel platforms to manipulate many-body light-matter interactions. In this spirit, the foundations that will allow nonexperts to understand new perspectives in multiparticle quantum plasmonics are described. First, we discuss the quantum statistical fluctuations of the electromagnetic field as well as the fundamentals of plasmonics and its quantum properties. This discussion is followed by a brief treatment of the dynamics that characterize complex multiparticle interactions. We apply these ideas to describe quantum interactions in photonic-plasmonic multiparticle quantum systems. We summarize the state-of-the-art in quantum devices that rely on plasmonic interactions. The review is concluded with our perspective on the future applications and challenges in this burgeoning field.

Renormalization group approach to quantum Hamiltonian dynamics

2015 ◽  
Vol 30 (09) ◽  
pp. 1530023 ◽  
Author(s):  
Stanisław D. Głazek
Keyword(s):  
Renormalization Group ◽  
Quantum Dynamics ◽  
Broad Class ◽  
Hamiltonian Dynamics ◽  
Group Approach ◽  
Physical Problems ◽  
Minkowski Space Time ◽  
Renormalization Group Approach ◽  
Effective Theories ◽  
Dynamics Of Particles

Ken Wilson developed powerful renormalization group procedures for constructing effective theories and solving a broad class of difficult physical problems. His insights allowed him to later advance the Hamiltonian approach to quantum dynamics of particles and fields in the Minkowski space–time, motivated by QCD. The latter advances are described in this article, concluding with a remark on Ken's related interest in difficult systemic issues of society.

scholarly journals Spin-Orbit Entanglement in Time Evolution of Radial Wave Packets in Hydrogenic Systems

2004 ◽  
Vol 11 (04) ◽  
pp. 401-409
Author(s):  
Marcin Turek ◽  
Piotr Rozmej
Keyword(s):  
Wave Packet ◽  
Time Evolution ◽  
Time Scale ◽  
Degrees Of Freedom ◽  
Wave Packets ◽  
Characteristic Time Scale ◽  
Radial Wave ◽  
Mean Values ◽  
Breathing Motion ◽  
Wave Packet Revival

Time evolution of radial wave packets built from the eigenstates of Dirac equation for a hydrogenic system is considered. Radial wave packets are constructed from the states of different n quantum numbers and the same lowest angular momentum. In general they exhibit a kind of breathing motion with dispersion and (partial) revivals. Calculations show that for some particular preparations of the wave packet one can observe interesting effects in spin motion, coming from inherent entanglement of spin and orbital degrees of freedom. These effects manifest themselves through some oscillations in the mean values of spin operators and through changes of spatial probability density carried by upper and lower components of the wave function. It is also shown that the characteristic time scale of predicted effects (called T ls ) is much smaller for radial wave packets than in other cases, reaching values comparable to (or even less than) the time scale for the wave packet revival.

scholarly journals Macroscopic Time Evolution and MaxEnt Inference for Closed Systems with Hamiltonian Dynamics

2011 ◽  
Vol 42 (2) ◽  
pp. 319-339 ◽  
Author(s):  
Domagoj Kuić ◽  
Paško Županović ◽  
Davor Juretić
Keyword(s):  
Time Evolution ◽  
Hamiltonian Dynamics ◽  
Closed Systems

scholarly journals Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 518 ◽  
Author(s):  
Alessandro Sergi ◽  
Gabriel Hanna ◽  
Roberto Grimaudo ◽  
Antonino Messina
Keyword(s):  
Constant Temperature ◽  
Degrees Of Freedom ◽  
Open Quantum Systems ◽  
Hamiltonian Dynamics ◽  
Quantum Systems ◽  
Classical Dynamics ◽  
Open Quantum ◽  
Time Translation ◽  
Translation Symmetry ◽  
Lie Brackets

Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein.

Design and Realization of a Flexible Claw of Rough Wall Climbing Robot

2011 ◽  
Vol 328-330 ◽  
pp. 388-392 ◽  
Author(s):  
Dong Liang Chen ◽  
Qun Zhang ◽  
Shao Zhi Liu
Keyword(s):  
Experimental Study ◽  
Degrees Of Freedom ◽  
Material Selection ◽  
Structure Design ◽  
Rough Wall ◽  
Flexible Structure ◽  
Climbing Robot ◽  
Mechanical Structure ◽  
Four Bar Linkage

Based on the research of foot characteristics of insecta, a climbing robot’s mechanical structure and kinematics are analyzed, and the main crawling institutions was designed by a kind of bionic four-bar linkage. Claws are made of sharp spines, claws are composed of a number of toes which are flexible structure with local degrees of freedom, they have a grate adaptivity to the rough wall. We have studied the characteristics of the rough wall climbing, and made analysis affection of reliability with the angle perched on. The experimental study indicates spine planning and structure design, material selection are reasonable.

scholarly journals Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Linyu Peng ◽  
Huafei Sun ◽  
Xiao Sun
Keyword(s):  
Hamiltonian System ◽  
Geometric Structure ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Hamiltonian Dynamics ◽  
Jacobi Field ◽  
Linear Hamiltonian System ◽  
Conformal Metric ◽  
Jacobi Equations ◽  
Special Case

We characterize the geometry of the Hamiltonian dynamics with a conformal metric. After investigating the Eisenhart metric, we study the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics. Furthermore, the equations for the conformal geodesics, for the Jacobi field along the geodesics, and the equations for a certain flow constrained in a family of conformal equivalent nondegenerate metrics are obtained. At last the conformal curvatures, the geodesic equations, the Jacobi equations, and the equations for the flow of the famous models, anNdegrees of freedom linear Hamiltonian system and the Hénon-Heiles model are given, and in a special case, numerical solutions of the conformal geodesics, the generalized momenta, and the Jacobi field along the geodesics of the Hénon-Heiles model are obtained. And the numerical results for the Hénon-Heiles model show us the instability of the associated geodesic spreads.

MBARS2: A New Design for a 3- Degrees of Freedom Parallel Structure for Joint Arthroplasty

2008 ◽  
Author(s):  
A. Wolf ◽  
S. Amir ◽  
A. B. Mor
Keyword(s):  
Coordinate System ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Joint Arthroplasty ◽  
Robotic System ◽  
Parallel Structure ◽  
Tracking Systems ◽  
Mechanical Structure ◽  
Workspace Analysis

In this report we present the second prototype of a 3-degrees-of-freedom active, miniature bone-attached, robotic system. The report focuses on the mechanical structure, workspace analysis and inverse kinematics solution. The robot is capable of preparing the bone cavity for an implant during joint arthroplasty procedures. This system, just as its predecessor is image-free and all planning is performed intraoperatively in the robot coordinate system, eliminating the need for external tracking systems in the OR. Experiments were conducted using the first robot prototype to evaluate its accuracy and the results supported the feasibility of the concept.

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