The origin of cross section thresholds in H+H2: Why quantum dynamics appears to be more vibrationally adiabatic than classical dynamics

1983 ◽  
Vol 79 (11) ◽  
pp. 5386-5391 ◽  
Author(s):  
George C. Schatz
Keyword(s):  
Cross Section ◽  
Quantum Dynamics ◽  
Classical Dynamics

scholarly journals The stark effect of the fine-structure of hydrogen

1928 ◽  
Vol 119 (782) ◽  
pp. 313-334 ◽  
Keyword(s):  
Fine Structure ◽  
Hydrogen Atom ◽  
Electric Field ◽  
Quantum Dynamics ◽  
Stark Effect ◽  
Energy Levels ◽  
Structure Theory ◽  
Weak Electric Field ◽  
Classical Dynamics ◽  
Balmer Series

One of the earliest successes of classical quantum dynamics in a field where ordinary methods had proved inadequate was the solution, by Schwarzschild and Epstein, of the problem of the hydrogen atom in an electric field. It was shown by them that under the influence of the electric field each of the energy levels in which the unperturbed atom can exist on Bohr’s original theory breaks up into a number of equidistant levels whose separation is proportional to the strength of the field. Consequently, each of the Balmer lines splits into a number of components with separations which are integral multiples of the smallest separation. The substitution of the dynamics of special relativity for classical dynamics in the problem of the unperturbed hydrogen atom led Sommerfeld to his well-known theory of the fine-structure of the levels; thus, in the absence of external fields, the state n = 1 ( n = 2 in the old notation) is found to consist of two levels very close together, and n = 2 of three, so that the line H α of the Balmer series, which arises from a transition between these states, has six fine-structure components, of which three, however, are found to have zero intensity. The theory of the Stark effect given by Schwarzschild and Epstein is adequate provided that the electric separation is so much larger than the fine-structure separation of the unperturbed levels that the latter may be regarded as single; but in weak fields, when this is no longer so, a supplementary investigation becomes necessary. This was carried out by Kramers, who showed, on the basis of Sommerfeld’s original fine-structure theory, that the first effect of a weak electric field is to split each fine-structure level into several, the separation being in all cases proportional to the square of the field so long as this is small. When the field is so large that the fine-structure is negligible in comparison with the electric separation, the latter becomes proportional to the first power of the field, in agreement with Schwarzschild and Epstein. The behaviour of a line arising from a transition between two quantum states will be similar; each of the fine-structure components will first be split into several, with a separation proportional to the square of the field; as the field increases the separations increase, and the components begin to perturb each other in a way which leads ultimately to the ordinary Stark effect.

Primary state diffusion

1994 ◽  
Vol 447 (1929) ◽  
pp. 189-209 ◽  
Keyword(s):  
Quantum State ◽  
State Vector ◽  
Quantum Dynamics ◽  
Diffusion Theory ◽  
The State ◽  
Classical Dynamics ◽  
State Diffusion ◽  
Quantum State Diffusion ◽  
Spontaneous Localization ◽  
Ordinary Quantum

Primary quantum state diffusion (PSD) theory is an alternative quantum theory from which classical dynamics, quantum dynamics and localization dynamics are derived. It is based on four principles, that a system is represented by an operator, its state by a normalized state vector, the state vector satisfies a Langevin-Itô state diffusion equation, and the resultant density operator for an ensemble must satisfy an equation of elementary Lindblad form. There are three conditions. The ז 0 first determines the operator, to within an undetermined universal time constant ז 0 . The second and third conditions put opposing bounds on ז 0 . Dissipation of coherence is distinguished from destruction of coherence. The state diffusion destroys coherence and produces the localization or reduction that makes classical dynamics possible. PSD theory is a development of the environmental quantum state diffusion theory of Gisin and Percival and particularly resembles earlier proposals by Gisin and by Milburn. It is also related to the spontaneous localization theories of Ghirardi, Rimini and Weber, of Diósi and of Pearle. The non-relativistic PSD theory is of value only for systems which occupy small regions of space. Special relativity is needed for more extended systems even when they contain only slowly moving massive particles. Experiments on coherence lifetimes and matter interferometry are proposed which either measure ז 0 or put bounds on it, and which might distinguish between PSD and ordinary quantum mechanics.

Observed quantum dynamics: classical dynamics and lack of Zeno effect

2020 ◽  
Vol 53 (37) ◽  
pp. 375306
Author(s):  
Julián López ◽  
Laura Ares ◽  
Alfredo Luis
Keyword(s):  
Quantum Dynamics ◽  
Classical Dynamics ◽  
Zeno Effect

scholarly journals A semiclassical reversibility paradox in simple chaotic systems

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150161 ◽  
Author(s):  
Steven Tomsovic
Keyword(s):  
Time Scale ◽  
Quantum Dynamics ◽  
Chaotic Systems ◽  
Classical Mechanics ◽  
Saddle Point Method ◽  
Classical Dynamics ◽  
Accurate Approximation ◽  
Overlap Integral ◽  
Semiclassical Methods ◽  
Ehrenfest Time

Using semiclassical methods, it is possible to construct very accurate approximations in the short-wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly chaotic, there is an exceedingly short logarithmic Ehrenfest time scale, beyond which the quantum and classical dynamics of a system necessarily diverge, and yet the semiclassical construction remains valid far beyond that time. This fact leads to a paradox if one ponders the reversibility and predictability properties of quantum and classical mechanics. They behave very differently relative to each other, with classical dynamics being essentially irreversible/unpredictable, whereas quantum dynamics is reversible/stable. This begs the question: ‘How can an accurate approximation to a reversible/stable dynamics be constructed from an irreversible/unpredictable one?’ The resolution of this incongruity depends on a couple of key ingredients: a well-known, inherent, one-way structural stability of chaotic systems; and an overlap integral not being amenable to the saddle point method.

scholarly journals QUANTUM DYNAMICS OF THE CUBIT SYSTEM IN EXTERNAL FIELDS

2021 ◽  
Vol 26 (4) ◽  
pp. 68-75
Author(s):  
A. V. Gorokhov ◽  
G. I. Eremenko
Keyword(s):  
Symmetry Group ◽  
Time Evolution ◽  
Coherent States ◽  
Quantum Dynamics ◽  
Dynamic Symmetry ◽  
Classical Dynamics ◽  
External Fields

A system of two dipole-dipole interacting two-level elements (qubits) in external fields is considered. It is shown that using the coherent states (CS) of the dynamic symmetry group of the SU(2)SU(2) system, the time evolution can be reduced to the "classical" dynamics of the complex parameters of the CS. The trajectories of the CS are constructed and the time dependences of the probability of finding qubits at the upper levels are calculated.

scholarly journals Classical dynamics as constrained quantum dynamics

2003 ◽  
Vol 36 (6) ◽  
pp. 1683-1704 ◽  
Author(s):  
Stephen D Bartlett ◽  
David J Rowe
Keyword(s):  
Quantum Dynamics ◽  
Classical Dynamics

scholarly journals Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 684
Author(s):  
Giovani Morales-Hernández ◽  
Juan Castellanos ◽  
José Romero ◽  
Andrei Klimov
Keyword(s):  
Classical Limit ◽  
Quantum Dynamics ◽  
Asymptotic Form ◽  
Star Product ◽  
Spin Systems ◽  
Classical Dynamics ◽  
Classical Dynamic ◽  
Variable Spin ◽  
Long Time ◽  
Dynamic Variables

We apply the semi-classical limit of the generalized SO(3) map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on T*S2. Using the asymptotic form of the star-product, we manage to “quantize” one of the classical dynamic variables and introduce a discretized version of the Truncated Wigner Approximation (TWA). Two emblematic examples of quantum dynamics (rotor in an external field and two coupled spins) are analyzed, and the results of exact, continuous, and discretized versions of TWA are compared.

scholarly journals A nanoscale experiment measuring gravity's role in breaking the unitarity of quantum dynamics

2011 ◽  
Vol 468 (2137) ◽  
pp. 35-56 ◽  
Author(s):  
Jasper van Wezel ◽  
Tjerk H. Oosterkamp
Keyword(s):  
Quantum Dynamics ◽  
Experimental Parameter ◽  
Theoretical Description ◽  
Classical Dynamics ◽  
Experimental Protocol ◽  
Usual Quantum ◽  
Alternative Scenarios ◽  
Set Up ◽  
Parameter Values ◽  
Theoretical Proposal

Modern, state-of-the-art nanomechanical devices are capable of creating spatial superpositions that are massive enough to begin to experimentally access the quantum to classical crossover, and thus force us to consider the possible ways in which the usual quantum dynamics may be affected. One recent theoretical proposal describes the crossover from unitary quantum mechanics to classical dynamics as a form of spontaneous symmetry breaking. Here, we propose a specific experimental set-up capable of identifying the source of unitarity breaking in such a mechanism. The experiment is aimed specifically at clarifying the role played by gravity, and distinguishes the resulting dynamics from that suggested by alternative scenarios for the quantum to classical crossover. We give both a theoretical description of the expected dynamics, and a discussion of the involved experimental parameter values and the proposed experimental protocol.

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